BACKGROUND DOCUMENT
GROUND WATER SCREENING PROCEDURE
OFFICE OF SOLID WASTE
U.S. ENVIRONMENTAL PROTECTION AGENCY
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TABLE OF CONTENTS
Background Document
1. Ground Water Screening Procedure
Appendix A - Development of Three-Dimensional Analytical Solution
For Contaminant Transport
Appendix B - Tables of Dimensionless Concentration CQ versus XD
Appendix C - Development of Land Disposal Banning Decisions Under
Uncertainty
Appendix D - Analysis of Engineered Controls of Subtitle C
Facilities for Land Disposal Restrictions Determi-
nations
Appendix E - Analysis of Engineered Controls of Subtitle C
Facilities for Land Disposal Restrictions Determi-
nations Revised Distribution of Leaching Rates
Appendix F - Analysis of the "Infinite Source" Assumption Used
in the Groundwater Model for Land Disposal Banning
Evaluation
Appendix G - Fortran Listing Ground Water Screening Procedure
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1 INTRODUCTION
The Resource Conservation and Recovery Act (RCRA) as ammended
in 1984 requires EPA to promulgate regulations which restrict land
disposal of hazardous wastes unless it is determined by EPA that a
prohibition is not required to protect human health and the
environment The restrictions apply for as long as the waste remains
hazardous.
In promulgating such regulations. Congress has directed EPA
to consider:
A. The long-term uncertainties associated with land disposal;
B. The goal of managing hazardous wastes in an appropriate
manner; and
C. The persistence, toxicity, mobility, and propensity of
hazardous wastes and their constituents to bioaccumulate.
EPA*s Office of Solid Waste (OSW) reviewed a number of
approaches which could serve to evaluate the need to ban or further
restrict hazardous wastes from land disposal. The general approaches
examined included decision criteria schemes, numerical schemes,
modeling schemes, and combinations of all three. The approach
presented in this paper, developed by OSW represents one option
considered by EPA. It combines a mathematical model for solute
transport with health based concentration limits and a leach test.
EPA's approach provides a systematic, consistent, and non-
capricious method for determining the need to restrict hazardous
wastes from land disposal. EPA's approach is designed to establish
acceptable concentrations for specific chemical constituents in
waste extracts by working backward from a point of potential human
exposure (through air, groundwater, and surface water) to the land
disposal unit. Health assessment levels for each constituent will
be appropriately partitioned into the three media.
This paper presents the groundwater screening component of EPA's
approach. It is important note that in this approach decisions on
restricting land disposal of hazardous wastes will be made on a
national basis. The RCRA reauthorization legislation establishes
a petition process for consideration of site specific factors.
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The groundwater screening procedure presented in this paper
involves application of an analytic solute transport equation in
conjunction with values for hydrogeoiogic parameters, such as
groundwater velocity, soil porosity, net infiltration, etc., that
are applied in a Monte Carlo routine to derrive a distribution
of outputs.
The EPA approach is based on the following general assumptions:
(1) Decisions to restrict the land disposal of hazardous
wastes will be made on a national basis.
(2) Restrictions decisions will be linked to health assessment
levels, i.e., the reference dose.
(3) The procedure developed by EPA to restrict the land
disposal of hazardous wastes are to accomodate the
variations in environmental settings, and the uncertainties
in specific chemical properties.
The scenario to be applied in conjunction with the ground water
screening procedure is a land disposal unit with a fixed point of
measurement established at distance x^ down gradient. Figure 1
illustrates a cross section and a plan view of this system.
The groundwater screening procedure can be described
qualitatively as follows.
(1) A waste will be determined accepatble for land disposal
if specific chemical constituents are projected to migrate
to the fixed measurement point at concentrations equal
to or less than the reference dose for those chemicals.
(2) If constituents in hazardous wastes migrate to the fixed
measurement point at concentrations above the reference
dose, then the waste will be restricted from land disposal.
(4) Land disposal will be permitted, however, if it is possible
to pretreat the waste such that the constituent concen-
tration in the groundwater at the measurement point no
longer exceeds the reference dose.
In order to apply the groundwater screening procedure, one must
be able to measure, estimate, or predict:
(1) leachate concentrations of specific chemical constituents
from a waste; and
(2) the migration of the chemical constituents in the leachate
to the measurement point.
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2 MATHEMATICAL MODEL
A mathematical model is used to provide an instrument for
computing concentration distributions in the generic groundwater
system (depicted in Figure 1). The model is explained below in
general terms, and sample calculations are provided. A detailed
explanation of the mathematical techniques employed in the model is
presented in Appendix A at the end of the paper. The mathematical
techniques employed in the model are, however, based upon analytical
solution procedures well established in the scientific literature.
The ground water back-calculation model properly accounts for
most of the major physical and chemical processes known to influence
movement and transformations of chemicals in simple, homogeneous
and isotropic porous media under steady flow conditions (constant
velocity). The important mechanisms considered include advection,
hydrodynamic dispersion in the longitudinal, lateral and vertical
dimensions, adsorption, and chemical degradation. The model assumes
first-order chemical reactions, and linear equilibrium sorption
isotherms.
The three-dimensional solute transport equation upon which the
ground water screening model is based is presented below as
Equation (1), written in the form (Bear, 1979):
c + Ic (1)
Rf
where :
x,y,z = spatial coordinates in the longitudinal, lateral
and vertical directions, respectively, (m)
c = dissolved concentration of chemical, (g/ml)
Dxx, Dyy, = retarded dispersion coefficients in the x, y and z
Dzz directions, respectively, (m2/yr)
V » groundwater seepage velocity, assumed to be in the
x-direction, (m/yr)
Rf = retardation factor, (dimensionless)
t = elapsed time, (yr)
= effective first-order decay constant, (yr~l)
9 = volumetric water content of the porous medium,
I = rate of ground water recharge from precipitation
(yr-1)
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The retardation factor, R, and the effective decay constant,^ ,
are defined as follows:
Rf - 1
e (2)
and, > = - (3)
9 +
where :
Pk = bulk density of the porous medium, (g/cm3)
K < y <«<>), and finite in the z-direction (0 £ z _<_ B).
Initially, the aquifer is assumed to be free of contamination
The solution treats the source concentration (i.e., the
contaminant concentration in the leachate directly below the land
disposal unit) as a Gaussian distribution in the lateral direction
(along the y-axis corresponding to the leading, down gradient edge of
the unit), and a uniform distribution over the vertical mixing or
penetration depth, H. The maximum dissolved concentration of the
contaminant, co, occurs at the center of the Gaussian distribution
(i.e., at y = 0; under the midpoint of the disposal unit). The
Gaussian distribution of the contaminant concentration is then defined
by its standard deviation, 0", as illustrated in Figure 2. The
standard deviation of the distribution,
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-2 PLANE
PERSPECTIVE PLOT
FIGURE: 2 Schematic Description of Thr««-Dlm«n»lon«l N»0ien for
Th« Analytletl Solution.
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Based on the stated assumptions, the initial and boundary
conditions employed may be written as follows:
c (x, y, z, 0 ) = 0 (4)
c(0, y, z, t) = cQe-y2/2fl-2 (5)
c (x,oo, z, t) =0 (6)
c(x, -<*>, z, t) = 0 (7)
c(*», y, z, t) =0 (8)
dc
•— (x, y, 0, t) = 0 (9)
<9z
dc
(x, y, B, t) = 0 (10)
Oz
where B is the aquifer thickness.
The solution of equation (1) subjected to equations (4)-(10)
is derived in Appendix A. This three-dimensional analytical solution
can be written in a simple functional form as follows:
H
Cp(x,y, z, t) = — Cf(x, y, t) +Acp(x, y, z, t) (11)
B
where H/B is the penetration ratio and Cf (x, y, t) and
Acp (x, y, z, t) are functions defined in Appendix A.
Note that the function Cf (x, y, t) turns out to be identical
to the two-dimensional analytical solution of a corresponding case
where full penetration of the source (or complete vertical mixing)
over the entire aquifer thickness is assumed. According to equation
(11), the solution for the general partial penetration case,
Cp (x, y, z, t), consists of two terras. The first term is the
product of the penetration ratio and the solution of the corresponding
full-penetration case. It may be interpreted as the concentration
that would be predicted if vertical spreading of the contaminant plume
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is not allowed. The second term, cp(x, y, z, t), is a correction
term necessary to allow for the partial penetration effect which
leads to vertical spreading or vertical dispersion. Vertical
dispersion will cause the contaminant plume to grow in the vertical
direction with increasing longitudinal distance from the source.
The vertical extent of the plume is, however, limited by the
available aquifer thickness.
3 GENERAL DIMENSIONLESS RELATIONSHIPS
To allow simple use of the analytical model, dimensionless
relationships are introduced. First, equation (11) is rewritten as
H
» — ~ CfD + AcpD (12)
B
where cpD, Cfp, and AcpD are dimensionless functions obtained by
normalizing cp, Cf and Acp with respect to the maximum source
concentration, co .
Second, another dimensionless function, referred to as a
dilution factor for partial penetration, ^, is introduced as
cfD cf
Thus it follows that is given by
H
4 • --- CfD + CpD (14)
B
The dilution factor will be used as a vehicle for evaluating
concentration values for the partial penetration case using
concentration values for the corresponding fully-penetration case.
The normalized concentrations, CPD and Cfp, and the dilution
factor jf, can be expressed as functions of several dimensionless
variables as shown in Appendix A. For convenience, the important
dimensionless variables are categorized as follows:
8
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(1) Dimenaionlesa coordinates: xD, yD and zD, defined as
(is.)
Vsy y
yD = ZTH = I£f (15b)
V z
„._.._.
where the retarded dispersion coefficients/ Dxx, Dyy and Dzz are
computed from:
°*LVg, Dyy -'Vs, and Dzz - °
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(5) Penetration ratio of contaminant source: H/B.
(6) Aquifer thickness to vertical dispersivity ratio: B/tXz.
In general, the relative concentration for the partial penetration
case can be expressed as
H B
CPD = /cfD = CPD(XD, yD, ZD, tD, AD'<3"D' - ' - ) (19)
B ^z
where Cfp and (24)
B «
10
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It is seen that c*f$ is a .function of three dimensionless variables,
whereas f* is a function of five dimensionless variables. Physical
considerations suggest, however, some of the variables in equation
(24) may not have significant influences on the value of the dilution
factorj*« Via sentivity analysis, it is concluded in Appendix A that
an approximate functional expression forT* may be written as
x B H
/* = /* ( , , ) (25)
B <*z B
A comparison of equations (24) and (25) shows that the dimensionless
decay and standard deviation parameters would have secondary effects
on the value of 3f* for specified values of x/B, B/»z and H/B.
5 EVALUATION OF STEADY-STATE MAXIMUM CONCENTRATION VALUES
The steady-state, three-dimensional analytical solution developed
in Appendix A has been implemented into a FORTRAN computer code,
EPASMOD-P. This code can be used to evaluate concentration values
at any specified location and time. It can also be used to obtain
dimensionless type curves (or tables of values) of the dimensionless
concentration and the dilution factor. Once they have been produced,
the type curves can be used as an alternative tool for providing a
quick estimate or prediction of concentration values at measurement
points. The case where the contaminant concentration will be
maximum corresponds to the situation in which the point of measurement
depicted in Figure 1 is located on the x-axis along the top of the
aquifer. The maximum concentration values attainable at this
point corresponds to the steady-state concentration values at the
distance x from the source.
According to the analysis given in the previous section, steady-
state concentration distributions along the x-axis can be represented
by equation (22), which expresses c*pp for the partially-penetrating
case as the product of the steady-state dilution factor,j*, and the
steady-state dimensionless concentration for the corresponding fully-
penetrating case, c*fo* To provide a simple means for evaluating
concentration values at the point of measurement, the functions c*fD
and 3"* are evaluated for realistic ranges of physical parameters.
Figure 3 shows two graphs of dimensionless concentration function
c*fD* Each graph is prepared for a specified value of O*D, and
contains one family of type curves of c*fQ versus XD, for specified
values of AD* The effect of AD and CTJ) on values of c*fD may be
noted.
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1.0
0.0
100
1000
DIMENSIONLESS DISTANCE, x
0.0
100
DIMENSIONLESS DISTANCE, X
1000
Figure 3. Type curves of dimensionless concentration, c2D versus
dimensionless distance, XD.
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As expected,AD has a significant influence on the type curves
whereas O*D has only a slight influence. The effect of CTD is almost
negligible for values of XD _< 10.
Figure 4 shows two graphs of dilution factor J**. The first graph
is prepared for a specified value of penetration ratio, H/B = 0.25,
and contains type curves corresponding to eight selected values of
B/°
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0.3
3.3
3.2
1.3
3.0 4.0
X/B - VflLUE
5.0
2.3
3.3 4.0
X/B - VflLUE
5.0
6.0
7.0
8.a
6.0
7.0 3.3
Figure 4. Type curves of dilution factor 5* versus ratio of distance
to aquifer thickness, x/B. (XQ = 0, OD = 4.2).
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6 EXAMPLE CALCULATIONS: DOWN GRADIENT CONCENTRATION
For the sake of convenience in the computation of actual
concentration, tabulated values of c*fQ versus x^ and %* versus
x/B are given for fairly wide and realistic ranges of the relevant
dimensionless variables. The tables of c*fo and ?* values are given
in Appendix B. (Note that the tables should be used in preference
to the graphs since the graphs may not provide sufficient accuracy
in the interpolation of functional values.)
The values of steady-state concentration along the x-axis can
be readily computed using either the type curves or the tables of
c*fo and i** values. To show the utility of the type curves and the
tables, the following sample calculations are provided.
Example 1. Consider the migration of Chemical A from a land disposal
unit. Let the average groundwater velocity in the flow region, V,
be taken as 30 m/yr. The saturated water content and the bulk
density of the aquifer material are taken as 0.35 and 1.70 g/ml,
respectively. The longitudinal, transverse and vertical dispersivi-
ties, **L» '^ and °*2 are taken as 15.4 m, 1.54 and 1.54 m, respectively.
The standard deviation of the Gaussian source, , is taken as 97.3 m.
The chemcial properties of Chemical A are:
Solubility, S - 3.8 x 10~3 mg/i
Distribution coefficient, Kd = 5.5 x 10"3 ml/g
Effective decay constant, A = 3.65 x 10~7 yr'1
We wish to calculate the concentration, c, at a measurement point
located at x - 308 m from the landfill. We will assume that the
initial source concentration, co, equals the solubility, S. The
penetration thickness of the contaminant source and the aquifer
thickness are assumed to be 10 and 40 m, respectively.
The calculation procedure consists of three steps. The first and
second steps involve the determination of values of c*fo and 1** from
the type curves using the given values of various physical parameters
to compute values of the relevant dimensionless variables. The third
step involves the determination of the required concentration value
from known values of c*fp, f* and co .
15
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Step 1: Determination of c*fD-value
To use the type curves, we need to compute the values of the
dimensionless parameters, Xp, D* an(^ D* Using the given data, one
obtains:
308
2(15.4)
= 10
D =
97.3
2(«L°
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1.0
0.0
100
DIMENSIONLESS DISTANCE, x_
1000
Figure 5. Determination of cln-value using type curves of cJL versus
fD
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We then use the computed value of B/'Xj to select the most appropriate
curve, and enter the value x/B to determine the corresponding value of
/* as illustrated in Figure 6. From the graph, it is seen that 5* =
0.28.
Step 3: Determination of concentration value at the measurement point
The required value of maximum attainable or steady-state
concentration c*p at x = 308 m is obtained as follows:
c*p = c*pD c0
• 2**c*fD • °'28 x 0-863 = 0.242
Hence c*p = 0.242 x 3.8 x 10~3
0.92 x 10-3 mg/1
Example 2. In this example, we consider the migration of Chemical B
from a land disposal unit. The chemical properties of Chemical B are
Solubility, S 0.18 mg/1
Distribution coefficient, Kd 96 ml/g
Effective decay constant, 7.3 x 10~3 yr"1
Suppose we wish to know the steady-state concentration at
x = 154 m, given that the groundwater velocity at the site is now
300 m/yr (ten times the velocity used in Example 1). The remaining
transport parameters and aquifer and contaminant source characteristics
are the same as before.
Step 1: Determination of c*fD-value
From the given data, we obtain:
CTD = 10 (as in Example 1)
x x
D
vs v/(i + Kd/g/e)
18
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0.0
1.0
2.0
3.0 4.0
X/B - VRLUE
6.0
7.0
= 0.28
8.0
Figure 6. Determination of c*-value using type curves of c* versus x/B.
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7.3 x lO'Syr'1 x 154m
300m/yr /(I + 96ml/g x 1.76g/ml/0.35)
1.75
We then use the determined value of CT^ and^D to locate the
appropriate table in Appendix B. In this case, the most appropriate
table to use is Table 7. Thus, the values ofAD and XD are
entered into this table. The next step is to determine c*fo via
linear interpolation shown below.
Given D = 1.75, and using the given value of XD = 5, one obtains
from Table 7 in Appendix C: c*fp = 0.241 for D = 1.6 and c*fD=
0.207 for D = 1.8. The desired value of c*fD is that which
corresponds to Q = 1.75, and is given by
0.241-0.207
c*fD = 1.75 = 0.241 - ( ) (1.6 - 1.75)
1.6 - 1.8
= 0.216
Step 2: Determination of value of dilution factorf*
From the given data, we obtain:
x 154
B 40
B 40
= = 25.97
2 1.54
We use the value of H/B to locate the appropriate table in
Appendix C. In this case, the most appropriate table to use is
Table 3. The values of B/°*z and X/B are then entered into this
table to determine the corresponding value of the dilution factor
J*. It follows that * = 0.36.
Step 3: Determination of concentration value at the measurement point
The required value of steady-state concentration c*p at x = 154 m
is obtained as follows:
c*p - c*pD c0
G*pD * ^*c*fD = 0.36 x 0.216 = 0.0778
20
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Hence
c*p = 0.0778 x 0.18
= 0.014 mg/1
7 BACK-CALCULATION OF MAXIMUM LEACHATE CONCENTRATION
It has been shown that for any combination of parameter values,
the steady-state, down-gradient concentration, c = Cp, at the fixed
point x can be readily determined using the type curves or tables of
function values. One can also determine the maximum concentration
at the source, (co) that corresponds to a prescribed or set value
of the downstream concentration, c. (We call this the back-
calculation process.) Thus, if c is assumed to be a concentration
value sufficient to meet a health assessment level such as the
reference dose for a specific chemical, then the computed co will
be the leachate quality required to yield the reference dose at the
fixed distance. This "back calculated" leachate concentration can
then be compared to expected values from a leach test or by a
comparison to a maximum solubility value.
The above examples illustrate the calculation of steady-
state concentration distributions along the x-axis for a given
set of input parameters using the steady-state solution.
However, rather than specify one "reasonable worst case" land
disposal scenario, EPA has developed a procedure that accommodates
the possible variation in environmental settings, uncertainties
in chemical specific properties, and uncertainties in the range
of impact of engineered system releases from land disposal units.
This procedure termed Monte Carlo simulation is most suitable for
investigating the land disposal restrictions process.
8 LOGIC FLOW CHART FOR LAND DISPOSAL SCREENING
A logic flow chart for the screening procedure is presented
in Figure 7. The flow chart combines the steps EPA must take in
developing and implementing the procedure with the steps generators
and owner/operators.must take in determining whether or not their
waste can be land disposed.
Using the information available at each critical step in the
flow chart (diamond shaped boxes), generators and owner/operators
must answer the following questions:
21
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1 Determine ADI
J Ce«c«r.tr3iion, C
Determine Distance
to Hazardous Waste
Measurement Point. X,
Obtain list of
Leeehote Concentrations,
C, for all Chemicals
Obtain Information
from Generator
I Compute
I
type curves or tables
-
Waste Not
Hazardous Bcsed
on this Chemical
Develop List of
Crtticol Values. C0.
for oil Chemicals
Set Reduced Value
for C,
Wcste is Banned
from Land Disposal
Based on this Chemical
FIGURE 7
SCREENING PROCEDURE FLOW CHART
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1. Does the leachate quality for each constituent in the
hazardous waste indicate that it is acceptable for land
disposal?
2. If the leachate quality indicates that the hazardous waste
is not acceptable for land disposal, can it be pretreated or
treated such that the leachate quality indicates that the
hazardous waste is acceptable for land disposal?
The answers to these questions lead to yes or no decisions and
dictate the action to be taken. Further, question two provides a
point where treatment of wastes can be taken into account prior to
making a final decision. A detailed, step-by-step description of
the screening procedure is given below. The parentheses indicate
who is responsible for each step, EPA or the generator/owner/operator
(Gen;0/0).
PART A: Restriction of Hazardous Waste From Land Disposal
Step 1 (EPA).. Determine "Reference Dose Concentration
For each individual constituent in the waste, there must be an
appropriate toxicologically based limit expressed in concentration
units. This value, once determined, is set to be the steady-state
down gradient concentration, c, at the fixed measurement point (x).
The steady-state value downgradient, c, will be pre-determined
by the levels evaluated in a risk assessment of each constituent in
the waste. The maximum concentration of each constituent at the
point of measurement cannot exceed either reference dose for non-
carcinogens or the a dose at a 10"^ risk level for carcinogens.
Step 2 (EPA): Determine Distance to Measurement Point
The lateral, downgradient distance from the land disposal
facility to the measurement point, x, must be specified. At this
point, the presence of a constituent at concentrations exceeding
a health assessment level will result in a waste being banned from
land disposal. In this approach, we are setting x equal to 500ft.
23
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Step 3 (EPA).. Compute co
This step can be achieved using the type curves or tables of
dimensionless functions, c*fD and *.
For the determination of c*fD~value, input values of the
dimensionless parameters XD,/^D, and CT^ are required. By
definition, these dimensionless parameters depend on the distance,
x, the longitudinal and transverse dispersivities, ®«L an
the standard deviation of the Gaussian distribution at the
source, CT, the chemical decay constant,/} , and the transit time
T (T = x/vs).
For the determination of Cf*-value, input values of x/B, H/B,
and B/**z are required. By definition, these dimensionless parameters
depend on the distance, x, the aquifer thickness, B, the penetration
thickness of the source, H, and the vertical dispersivity, °*z.
Values of the longitudinal, the transverse, and the vertical
dispersivities can be determined from published data. In the field,
the longitudinal dispersivity may vary from 5 to 100 m. The
transverse dispersivity value is usually taken to be the same as the
vertical dispersivity. The value of lateral dispersivity is a
fraction of the value of longitudinal dispersivity. The ratio of
*L to ^T may vary from 2 to 20.
The standard deviation has a similar range of variation to **L
and^rp. For a conservative prediction of downstream concentration,
the value of should be selected to be at least the same or twice the
longitudinal dispersivity. The effective decay constant,/^ , is
chemical specific. Assuming simple hydrolysis,/} , can be determined
using the procedures described in detail in Section 9.
Step 4 (EPA): Develop and Promulgate List of Screening
levels/ co, for Land Disposal Restrictions
Determinations for All Chemicals
Through the use of the computer model, EPASMOD, EPA will
develop a list of co values for all chemical constituents. The c0
values can also be computed using the dimensionless functions and
tabulated values. The co values can be viewed as maximum acceptable
extract concentrations for each waste constituent if the waste is
to be considered acceptable for land disposal.
Step 5 (Gen;0/0).. Determine The Leachate Concentration, CL
The concentration in the leachate CL will be determined by a
test similar to the EPA extraction procedure (EP), developed
specifically to address organic as well as inorganic constituents.
(This test, is termed the Toxicity Characteristic Leaching
Procedure.) CL must be determined for each chemical constituent
24
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in the waste for which the Agency ha's established values for c0.
This step is the responsibility of the waste generator.
Step 6 (Gen;0/0).. Is CL > co ?
Once a generator determines the actual leachate concentration,
CL, of each chemical constituent in a wasce, a simple comparison is
made with the list of maximum acceptable leach concentrations, co,
developed by EPA in Step 4. If, for each chemical constituent in
the waste, the leachate concentration, CL» is not greater than the
listed maximum acceptable concentration, co, for that constituent,
then the waste can be land disposed. If, the leachate concentration,
CL, for any constituent in the waste exceeds the listed maximum
acceptable concentration, co, for that constituent, the waste
is banned from land disposal.
Step 7 (Gen; 0/0): Can CL be Reduced?
If it is possible for the generator to reduce the leachate
concentration via pretreatment or treatment such that the resulting
leachate concentration, CL» for each chemical constituent in the
waste is no longer greater than the listed maximum acceptable
concentration, co, then the waste (following pretreatment or
treatment) can be land disposed as a hazardous waste. If the
leachate concentration, CL« /for any chemical constituent in the
waste can not be reduced via pretreatment or treatment to a level
equal to or less than it's listed maximum acceptable concentration,
CQ, the waste is banned from land disposal.
9 CALCULATION OF EFFECTIVE DECAY CONSTANT
The effective decay constant, A , is chemical specific. Assuming
simple hydrolysis, , can be determined from
0
(27)
e + Kd 'b
where " = lumped first-order degradation rate constant, yr~l
/\± = first-order hydrolysis rate constant for the dissolved
constituent, yr~l
^2 = first-order hydrolysis rate constant for the sorbed
constituent, yr~l
= distribution coefficient, cm3g~1
= volumetric water content of soil,
= soil bulk density, g/orr
25
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. fi»
and Rf = 1 +
9
From process theory (Mill et al., 1981) we know that for
hydrolysis, the decay constant for the i phase can be determined from:
Ai = Ka[H+] + Kn + Kb[OH-], i = 1,2 (28)
where Ka = second order rate constant for acid catalyzed hydrolysis,
M-1 yr-1
Kn = neutral hydrolysis rate constant, yr"^
Rfc = second order rate constant for base catalyzed hydrolysis,
M"1 yr'1
[H4"] = hydrogen ion concentration, M
[OH~] = hydroxyl ion concentration, M
Because both the sorbed and dissolved states exist we must
develop expressions for /\i and /\2 The dissolved case is simply as
depicted above. The pH of the groundwater must be known. For the
sorbed case, an "effective" pH of the sorbent must be known, i.e.,
what is the >JH of the adsorbing surface? This can vary depending
upon the soil type but a conservative estimate is one pH unit less
than the bulk fluid. Evidence also exists to suggest alkaline
hydrolysis does not operate for the sorbed state (Wolfe, 1984).
Using this approximation we have:
^2 = 10Ka [H+] + Kn (29)
We can now write
. (Ka[H+] + Kn + Kb[OH~1])e -I- (10Ka[H+] + Kn) Kd ^
A = ( (30)
e + Kd tb
From this analysis it is clear that two things are required to compute
A. First the second-order rate constants must be known, measured,
or estimated and the pH of the groundwater must be known.
p
Other parameter values required are: the bulk density, 'b,
saturated moisture content, 9, the solute velocity, Vs, and the
distribution coefficient, K
-------
The problem remains to estimate the distribution coefficient, Kd,
needed for both the overall rate expression and the retardation
coefficient, Rf. In general, this term is dependent upon both the
chemical properties and the sorbent properties. For organic,
hydrophobic chemicals Kd is commonly correlated to the organic carbon
fraction of the sorbent (Karickhoff, 1979; Lyman, 1982). Thus, if one
knows the normalized distribution coefficient for organic carbon, Koc,
for a specific chemical and the fraction organic carbon, foc for the
soil then,
(31)
Values for Koc are often available for chemicals and in many cases can
be estimated from Kow (octanol-water partition coefficient)
(Karickhoff, 1979). KQW values can be either measured or calculated
from well-known and usually reliable relationships (Lyman et al . ,
1982; Mill et al., 1984). The problem remains to specify the organic
carbon content, foe' °f tne saturated zone. This value is expected to
be quite low and can be determined from surveys, published data, or
from engineering judgement. Caution must be exercised in assigning a
very low value for fOc* At such values (e.g., fpc <.001 - .005) other
sorbent characteristics contribute more to sorption. The soil mineral
content, for example, will influence sorption. In any case, our
assumptions are conservative in that estimated Kg values will be
smaller than if other mechanisms were included. Sample calculations
of and R are given below.
Example Calculations for A and Rf
Given: groundwater pH at 6.5
0 = 0.35
0.00
1.20 gm on~J
chemical is X
chemical properties
water solubility, 700 mg/1
K_ - 5.04 * 10"4 M'1 hr'1
1C =2.5 * 10"3 hr'1
Kb = 1638 M'1 hr'1
Log Kow =2.55
Find A! = Ka[H+] + Kn -I- Kb[OH]
>2 = 10 Ka[H+] + Kn
at pH =6.5 [H+] =3.16 * lO"7 M
[OH-] =3.16 * 10~8 M
27
foc = 0.001
-------
Converting Ka, Y^, Kb to units of yr"1 we have
K. = 5.04*10~4M~1hr~1 * 8.76 hr yr'1 * 103 = 4.415 M'1 yr'1
Kl = 2.5*10'3 hr'1 * 8.760 hr yr"1 * 103 =21,9 yr'1
K? = 1638M'1 * 8.76*103 hr yr'1 = 14.35*10° M'1 yr"1
Now
for A, = 4.415 * 3.16*1CT7 -I- 21.9 + 14.35*106 * 3.16*10~8
>, = 1.4*10~6 + 21.9 + .453
22.4 yr'1
* 10 x 4.415CKT7] -»• 21.9
= 21.9 yr'1
Find: Kd
From Karickhoff (1979) we have
1°9 Koc = 1»00 log Kow - 0.21
so log Koc = 1.00 * 2.55 - 0.21
and Koc = 219
* foc * Koc = *001 * 219 ° 0.219
(22.4 * 0.35 + 21.9 * 0.219 * 1.2)
Finally,
0.35 -I- 0.219 * 1.2
22.19 yr'1
.219 * 1.2
and R = (1 + ) = 1.75
0.35
10 SUMMARY AND OBSERVATIONS
The proposed approach is conservative but not unrealistic/ since
it accommodates the opportunity for degradation (due to hydrolysis),
retardation, and dispersion in the longitudinal, lateral and vertical
directions. The proposed procedure does not require considerable
effort to execute. A careful analysis of the data required to
run the model is presented in the following section on Monte Carlo
simulation techniques.
28
-------
REFERENCES
Carslaw, H.S., and J.C. Jaeger, Conduction of Heat in Solids, 510 pp,
1959.
Churchill, R.V., Operational Mathematics, McGraw-Hill, 481 pp, 1972.
Dominico, P.A., and V.V. Palciaukus, 1985, Alternative methods for the
prediction of leachate plume migration, Ground Water Monitoring
Review, 5(2), pp 46-59.
Gureghian, A.B., D.S. Ward, and R.W. Cleary, 1980, A finite element
model for the migration of leachate from a sanitary landfill in
Long Island, New York—Part I: Theory, Water Resources Bulletin,
16(5), pp 900-096.
Gureghian, A.B., D.S. Ward, and R.W. Cleary, 1981, A finite element
model for the migration of leachate from a sanitary landfill in
Long Island, New York—Part II: Application, Water Resources
Bulletin, 17(1), pp 62-66.
Kent, D.C., N.A. Pettyjohn, and T.A. Prickett, 1985, Analytical
methods for the prediction of leachate plume migration, Ground Water
Monitoring Review, 5(2), pp 46-59.
Prakash, A., 1984, Ground-water contamination due to transient sources
of pollution, Amer. Soc. Civ. Engrs., J. Hydraulics Div., IIO(HYII),
pp 1642-1658.
Sagar, B., 1982, Dispersion in three dimensions: Approximate analytic
solutions, Amer. Soc. Civ. Engrs., J. Hydraulics Div., 108(HYI),
pp 47-62.
Shen, H.T., 1976, Transient dispersion in uniform porous media flow,
Araer. Soc. Civ. Engrs., J. Hydraulics Div., 102(HY6), pp 707-718.
Wilson, J.L., and P.J. Miller, 1978, Two-dimensional plume in uniform
9round water flow, Amer. Soc. Civ. Engrs., J. Hydraulics Div.,
104(HY4), pp 503-514.
29
-------
APPENDIX A
DEVELOPMENT OF THREE-DIMENSIONAL
ANALYTICAL SOLUTIONS FOR CONTAMINANT TRANSPORT
-------
INTRODUCTION
The model described in the main body of this report is based on
three-dimensional, transient and steady-state, analytical solutions for
solute transport from a distributed source in a homogeneous and isotropic
aquifer through which there is uniform groundwater flow. These solutions
are derived herein.
GOVERNING EQUATIONS
Consider the region with the distributed source shown in Figure 1.1.
The advective-dispersive equation for the transport of a nonconservative
contaminant in an adsorbing homogeneous and isotropic porous medium with
fully-saturated uniform flow can be written as
Ve H - Dy "~c - DY _
5 3x "3X7 ly7 * IT7 u 3t (1)
0 f X £ « — £ y ^ . 0
-------
where c is the peak concentration at the source, o is the standard
deviation of the Gaussian distribution centered at x = y = 0, and U(z) is
the unit step function defined as
U(z) • 1 , HX < z < H2
U(z) =0 , z > HX or z > H2.
DERIVATION OF TRANSIENT ANALYTICAL SOLUTION
To derive the transient analytical solution for a Gaussian distributed
source in y with the concentration at any point y for x = 0 being uniform
between z = H^ and z = H«, we will first derive a fundamental solution for
an infinitely thin Gaussian source located at depth z = z1. We will then
integrate this solution with respect to z1 between the depth limits H^ and
Hp.
The fundamental solution must satisfy equation (1) and the initial and
boundary conditions (2a)-(2f), as well as the following source boundary
condition:
c (0, y, z, t) = (H? - H,) c- exp ("y2) 6 (z-z1) (2h)
where c and a are the peak concentration and the standard deviation of the
Gaussian distribution, respectively, and 6(z-z') is the Dirac delta
function.
We introduce the following exponential Fourier transform in the
y-space:
c (x, o, z, t) - I c (x, y, z, t) exp (-i a y) dy
Fe [ c (x, y, z, t)] (3)
-------
Applying the above transform to, equation (1) and making use of
boundary conditions (2c) and (2d), one obtains:
II + Vs § -Dx $ +Dy .«c- -D, * xc *lc
By means of the exponential transform, the remaining initial and
boundary conditions (2a), (2b), (2e), (2f), and (2h) can be converted to
c (x, a, z, o) =0 (5a); c («, a, z, t) =0 (5b)
3C (x, a, B, t) « 0 (5c); 3c (x, a, o, t) = 0 (5d)
3z 3z
c (o, a, z, t) = (2ir) * mo exp (=S^L) 6(z-z') (5e)
where, for the sake of convenience, we let m = (H2"Hi^co' Note that
equation (5e) was obtained using the relation:
I exp (- £ )U 2 («)Jexp (-c
Fe I exp ( - fc )I • 2 (we)* exp (-c a«) (6)
Next, we introduce the finite Fourier cosine transform in the z-space:
(7)
c (x, a, n, t) =/ c (x, a, z, t) cosf^Ii^dz
0 \ B /
Using this transform, equation (4), with (5c) and (5d), and the remaining
initial and boundary conditions (5a), (5b), and (5e) can be converted to
and c («, a, z, t) « 0 (9a)
c (x, a, n, o) = 0 (9b)
c (o, o, n, t) • (2ir)* moexp f - a2a2 ] cos ( mrz' ) (9c)
V ~~T I \ ~B/
Finally, we introduce the Laplace transform in the time domain:
OB
! (x, o, n, p) = / exp (-pt) ! (x, o, n, t) dt (10)
o
-------
Using the Laplace transform, equation (8) with (9a), and the remaining
boundary conditions (9b) and (9c) can be converted to
and
+ V D-
s dx x
(«, a, n, p) = 0
D a2! - -— o,e + xe + ic = o
y B2 z
(11)
(12a)
(2i)* /-O2a2x ,mrz'
£ (o, a, n, p) = mo exp ( ] cos
P v 2
Equation (11) can rearranged to yield:
(12b)
_- li :: - _ (P + x +1
dx2 Dx dx Dx
e = o
B2
The general solution to the second-order, ordinary, homogeneous
differential equation (13) is given by
expy
where
^ +
V
V
4 (p + X + I + D
4 (p + x + I+Do2 + nD )
^ y
1/2
1/2
and
(13)
(14)
Because the solution must be bounded as x •*• 0 according to (12a), the
constant of integration A • 0. Boundary condition gives:
B = (2Tt)1/2m o exp
P
cos
(15)
Substitution of A = 0 and B given by (15) into (14) gives, after
slight algebra:
(2»)1/2m a exp(-
(16)
-------
. 1 exp
P
-
p +X+I+ V2/4D +c
K s x
x*Dy + nDz
Dx
1/2
x
the subsidiary solution (15) must now be inverted. We will apply the
inverse Laplace transform first. Although the function
H -* !•! 1/2<]
is easily inverted using tabulated results (see Carslaw and Jaeger, 1959,
p. 495), the resulting function is complicated and will therefore make
application of the inverse Exponential Fourier transform difficult.
Therefore, we will make use of the following relations:
and
f (T) di
(17a)
(17b)
where the shift theorem was made use of in the first inverse. Using the
results, the inverse Laplace transform of (16) is
c (x, a, n, t) - max
V x
exp (- afaf) cos (mrz1) exp ( s )
(2DX)
•
1/2
/
^~
1 exp
77Z
-vl' +
. w«
T
a 20
T - X
(18)
dr
Although the above integral can be evaluated analytically, the resulting
expression will make inversion with respect to o extremely difficult.
Thus, the time Integral will be retained.
The inverse Exponential Fourier transform will be applied next. To
facilitate inversion, (18) can be written in the form:
/V.x\
c (x, a, n, t)
max
<»„)
cos
(19)
exp
(v
X2
dr
-------
We need the following inverse Exponential Fourier transform
(Churchill, 1979, p. 472)
exp
< V *
exp
T+02
Using (20) the inverse of (19) with respect to a is:
E (x, y, n, t) = mgx .1, exp (!& cos (Sp-)
2(2»DJ1/Z ZDx
/2)1
/ 1
0 T3/2 (D T + £-)
•
n D,+ X + I)T j di
(21)
Finally, our fundamental solution will be completed after making use
of the following inversion formula for the Finite Fourier Cosine transform:
c(x.y. 2. t) -c (x> ^n
2
n = i c (x, y, n, t) cos
(22)
Substitution of (21) into (22) gives
c (x, y, z, t) = mox m exp U§*-)
2B(2irDw)i/^ ^Ux
V
dT + 2
x2
m^m
X' 4(0.
n = 1
V!T
cos
(23)
B2
Having obtained the fundamental solution, the remaining step is to use
it to obtain the final solution by converting the infinitely thin Gaussian
source to the finite Gaussian source of equal strength and extending
from z = H. to z » Hg. This is achieved by integrating (23) with respect
to z1 between the limits H, and H» and dividing by the source thickness,
H-H. The result is given by
-------
c ax
c (x, y, z, t) = .1;? exp
V x
H2'H1
J
1
a t3«(Dt +
(24)
-
4(0 T + fl)
mrH,
sin
- sin (
dT
nirH,
«
aM/2
"V
exp
X+I)T
dt
Equation (24) may be expressed in a simple form as
cp(x, y, z, t) . • J cf(x, y, t) + Acp(x, y, z, t) (25)
where we have assumed that H^ = 0 and Hg = H (i.e., the source extends from
the top of the aquifer through the thickness H), c (x, y, z, t) now
replaces c(x, y, z, t) and cf(x, y, t) and AC (x, y, z, t) are defined as
Cf(x, y, t) - 5 /
T o
40
exp
x1 4Dyr
Ac (x, y, z, t) = I cos
n = 1
sin
(26)
(27)
o
in which
* «yt)>'z '
c ax
* 8T)dT
T 4D T+ ?-' n
V.x
(28)
Vs2
n - ^- + x+I
(29)
-------
8n = n + -p-*- (30)
It should be noted that c^(x, y, t) is identical to the two-dimensional
analytical solution for the case where the Gaussian source fully
penetrates the entire aquifer thickness.
According to equation (25), the analytical solution for the case
of a partially-penetrating Gaussian source consists of two terms. The
first term is the product of penetration ratio H/B, and the solution
for the corresponding fully-penetrating case, c^. The second term is
Ac , which may be interpreted as a correction term that accounts for
the effect of partial penetration.
STEADY-STATE ANALYTICAL SOLUTION
A steady-state condition may be approached by letting t approach
infinity. Under this condition, the analytical solution given in (25)
may be expressed as
cj(x, y, z) = §cf(x, y) + AcJ(x, y, z) (31)
where the asterisk superscript is used to denote the steady-state
condition, and cjf(x, y) and Ac*(x, y, z) are obtained from (26) and
(27) with the upper limit of the time integral set to infinity.
An alternative steady-state analytical solution can also be
obtained by direct solution of the steady-state advective-dispersive
transport equation (equation (1) without the time-derivative term),
subjected to the boundary conditions given by (2b)-(2g). This
solution can be expressed in a concise form using equation (31) but
with the function c£(x, y) and Ac*(x, y» z) defined as
2 2
c*(x. y) = c- f «*P(-y' /2° > pp
f J jx2 + (y'-y)2 Dx/Dy J *
nx + n(y'-y)2 1 *
y \/ I
A y j
dy'
(32)
8
-------
V' y> Z)
K
1.,
J1
exp(-y'/2g2)
i- (y'-y)2 D/I
dy'
(33)
x y
in which y1 is a dummy variable of integration, C1 is a constant defined as
xco /~^n Vsx
v y x
n and B are given by equations (29) and (30), and K^(') is the modified
Bessel function of the second kind and of first order.
In a special case where one is interested in obtaining a steady-state
concentration distribution along the x-ax1s, equation (31) becomes
cj(x, 0, 0) - J cf(x. 0) + AcJ(x, 0, 0)
where ci(x, 0) and Ac£(x, 0, 0) are obtained by reducing equations (32) and
(33) to the following:
(34)
(35)
cf(x,0)
(36)
AcJ(x.O.O) - f .
• 5* 1 exp
with C* defined as o
C* 2c a
' 0
= — — exp
/2 IT
V x
s
x
-
(37)
(38)
-------
Figure 1.1.
Schematic picture of the solution region with a contaminant
source having concentration distribution that is Gaussian in
the lateral direction and uniform between H. _< z _< H£ in the
vertical direction.
10
-------
APPENDIX B
TABLES OF DIMENSIONLESS CONCENTRATION c*Q VERSUS XQ
-------
TABLE 1: XD VERSUS CD FOR S16D • 0.500E 01
LAND* O.OOOE 00
XD-VALUE CD-VALUE
LAND* 0.40UE-01
CO-VALUE
LAUD* 0.100E 00 LA.1D* 0.200E 00 LAND* 0.300E 00
CD-VALUE CD-VALUE CD-VALUE
0.100E
0.1SUE
0.200E
0.300e
U.400E
U.SUUE
0.4UOE
0.703E
3.SOOE
0.900E
U.100E
U.150E
0.200E
0.250E
J.JOJt
3.403E
3.50JE
0.600E
3.70JE
3.30UE
3.90JE
J.100E
3.1 JOE
U.200E
J.300E
3.400E
J.5U3c
J.600E
U.70UE
3.303E
•J.90JE
3.103k
01
01
01
01
01
01
01
01
01
01
02
01
01
01
02
02
02
02
02
02
02
03
03
03
01
03
03
03
03
OS
03
04
0.9311
0.972E
0.963E
0.946E
O.V30E
O.V15E
0.90UE
0.886E
0.873E
0.860E
0.848E
0.793E
0.748E
O.MOE
0.677E
0.622E
U.S7VE
O.S44E
O.SUE
0.489E
0.467E
0.449E
0.379E
0.334E
U.^78E
0.243E
U.118E
O.^OUE
0.186E
0.174E
0.164E
0.150E
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
0.944E
0.935E
0.916E
0.9101
0.894E
0.879E
0.865E
0.85ZE
0.839E
0.827E
0.81JE
0.763E
0.719E
0.6B2E
0.6SOE
O.JV8E
0.5S7E
O.S23E
0.494E
0.470E
0.449E
0.4116
0.364E
0.321E
0.267E
0.233E
0.210E
0.192c
0.1 79E
0.167E
O.liSe
O.liOt
00
00
00
00
00
00
00
00
00
UO
00
UO
UO
00
00
00
00
UO
UO
00
00
00
UO
UO
00
UO
UO
UO
UO
00
UO
UO
U.893E
0.634E
0.87SE
0.859E
0.844E
0.830E
O.B16E
0.803E
0.791E
0.780E
0.768E
0.719E
0.678E
0.643E
0.61JE
O.S64E
O.S25E
0.493E
0.466E
0.443E
U.423E
0.4U6E
0.343E
U.301E
0.2S1E
U.220E
0.198E
U.1B1E
U.168E
U.1SBE
0.149E
U.141E
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
Oil
00
ou
00
00
00
0.31VE
o.aodE
0.798E
0.781E
0.767E
0.7S4E
0.741E
0.730E
0.718E
0.707E
0.697E
0.652E
0.614E
0.583E
0.55SE
0.51 U
0.47SE
0.446E
0.422C
0.401E
0.383E
0^367E
0.31UE
0.273E
0.227E
0.1 99E.
0.179E
0.164E
0.15
-------
TABLE 2: XD VERSUS CD FOR SIGD • 0.500E 01
LAID* 0.400E 00
XD-VALUE CO-VALUE
LAMD« 0.600E 00
CD-VALUE
LAID- O.SOOE 00 LAHD« 0.100E 01 LAUD* 0.120E 01
CD-VALUE CD-VALUE CD-VALUE
3.
0.
3.
0.
U.
0.
3.
J.
0.
U.
0.
U.
0.
U.
U.
U.
a.
0.
3.
J.
J.
J.
3.
J.
0.
3.
U.
3.
U.
U.
U.
0.
100E
150E
203E
30UE
400E
SOOE
»OJE
70'JE
80UE
»OOE
100E
1SUE
200E
2SOE
300E
40UE
SOUE
60UE
700E
SOOE
90UE
100E
1SOE
20JE
300E
403E
50 Je
»OOE
70JE
SOOE
70UE
100E
01
01
01
01
01
01
01
01
01
01
02
02
02
02
02
02
02
02
02
02
02
01
01
01
01
01
01
01
01
03
03
04
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
. 0.
0.
.0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
70UE
6B3E
671E
653E
63BE
626E
614E
604E
J94E
SS4E
576E
S37E
506E
479E
4S6E
419E
39UE
364E
346E
32VE
3UE
301E
2S4E
224E
186E
163E
U6E
134E
12SE
117E
110E
105E
00
OU
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
OU
00
00
00
00
00
00
00
00
00
00
OU
00
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
6U9E
5H6E
S7U
SSOE
S3SE
523E
SIZE
SU2E
4V3E
485E
477E
443*
417E
394E
37SE
345E
320E
3UOE
294E
270E
258E
247E
2U8E
104E
1S3E
133E
120E
110E
1U2E
00
00
00
00
00
00
UO
UO
UO
UO
UO
UO
00
UO
00
UO
00
UO
UO
uu
UO
UO
00
UO
00
00
00
UO
UO
956E-01
903t-Jl
858E-U1
U.S15E 00
O.S08E 00
U.491E 00
0.468E 00
0.4S1E 00
0.439E 00
U.42BE 00
U.419E 00
U.411E 00
0.403E 00
0.3V6E 00
0.367E 00
U.344E 00
0.32SE 00
0.309E 00
U.2B4E 00
0.263E 00
0.247E 00
0.233E 00
0.222E OU
0.211E 00
U.2U3E 00
0.171E 00
U.1S1E OU
0.12SE 00
U.109E 00
U.983E-01
U.90UE-01
0.836E-01
U.783E-01
U.740E-01
U.702E-01
0.476E 00
0.445E UO
0.425E 00
0.400E UO
0.3B3E UO
0.37UE UO
0.36UE UO
0.3S1E 00
0.3446 UO
0.337E 00
0.33UE UO
0.304E UO
0.28SE 00
0.26VE 00
0.2SSE 00
0.233E 00
0.217E 00
0.203E 00
0.192E 00
0.182E 00
0.174E 00
0.166E 00
0.14UE UO
0.123E 00
0.102E 00
0.895E-01
0.80SE-U1
0.737E-U1
O.S84E-01
0.641E-U1
0.606E-U1
0.575E-U1
U.4ZSE 00
0.392E 00
U.371E 00
U.344E 00
U.3Z7E 00
U.314E 00
U.3O4E 00
U.29AE 00
U.286E 00
U.«!32E 00
U.276E 00
0.2S3E 00
U.236E 00
U.222E 00
U.211E 00
U.192E 00
U.170E 00
0.167E 00
U.1S7E 00
U.1SOE 00
U.143E 00
U.137E 00
U.115E 00
U.101E 00
0. 94OE-01
0.733E-01
U. 6S9E-01
U.604E-01
U. 561 E-01
U.525E-01
U.496E-01
0.471 E-01
-------
TABLE 3: XO VERSUS CO FOR SIGO • 0.500E 01
LAID- O.UOE 01
XD-VALUE CD-VALUE
LAND* 0.16UE 01 LAHD« 0.180E 01 LAMD- O.ZOOE 01 LAND* 0.250E 01
CD-VALUE CD-VALUE CD-VALUE
U.100E 01
O.UOE 01
O.ZOOE 01
0.300E 01
J.400E 01
O.JOOE 01
J.600E 01
U.700E 01
o.sooe 01
J.903E 01
U.100E 02
J.150E 02
J.200E 02
0.25JE 02
J.30JE 02
0.403E 02
U.JOJE 02
3.600E 02
0.70UE 02
0.30JE U2
0.900E 02
J.10UE U5
0.150E 05
J.200E 05
J.300E 05
J.4QUE 05
O.SOUc 05
0.60UE 05
U.700E 05
J.SOUE 05
0.900E 05
U.100E 0*
0.3B3E 00
O.J48E 00
O.J25E 00
0.i»BE 00
0.280E 00
0.268E 00
0.258E 00
0.250E 00
0.243E 00
0.237E 00
0.232E 00
0.211E 00
0.196E 00
0.184E 00
0.17*6 00
0.159E 00
O.U7E 00
0.137E 00
O.UOE 00
0.123E 00
0.1 UE 00
0.112E 00
O.V44E-01
0.830E-01
0.688E-01
0.601E-01
0.495E-01
0.459E-01
U.430E-01
0.406E-01
U.586E-01
0.347E 00
0.310E 00
0.287E UO
0.2S9E 00
0.24.U 00
0.229E UO
0.219E 00
0.212£ 00
0.205E 00
0.2UOE 00
0.1951 UO
0.1 76E 00
0.163E UO
0.155E 00
0.144E UO
0.151E 00
0.121E 00
0.113E 00
0.107E 00
0.1U1E 00
0.964E-U1
0.774E-01
0.681E-U1
0.564E-U1
0.493E-U1
0.445E-U1
0.405E-J1
0.376e-U1
0.5i3E-Ul
0.3531-U1
0.516E-U1
0.31SE 00
0.278E 00
0.2S4E 00
0.226E 00
0.208E 00
0.196E 00
U.187E 00
U.I SUE 00
0.174E 00
0.169E 00
0.164E 00
0.147E 00
U.136E 00
U.127E 00
U.119E UO
U.108E 00
U.999E-01
U.932E-01
U.878E-01
0.832E-01
0.792E-01
U.758E-01
U.636E-01
0.558E-01
0.465E-01
0.404E-01
U.365E-01
U.352E-0!
U.308E-01
U.289E-01 .
0.273E-01
U.259E-01
0.288E UO
0.250t 00
0.226E 00
0.198E 00
0.1 81E 00
0.16VE 00
0.140E UO
0.1S3E 00
0.140E 00
0.143E 00
0.139E 00
0.123E 00
0.115E 00
0.10SE 00
0.991E-01
0.996E-01
O.S25E-01
0.769E-01
0.723E-U1
0.685E-01
0.652E-01
0.624E-01
O.S22E-U1
0.458E-01
0.379E-01
0.331E-U1
0.2V7E-01
0.272E-01
0.2S3E-01
0.237E-U1
0.223E-01
0.212E-01
CD-VALUE
U.233E 00
U.19SE 00
U.172E 00
0.14SE 00
U.129E 00
0.118E 00
U.110E 00
U.104E 00
U.994E-01
U.V54E-01
O.V19E-01
U.799E-01
U.667E-01
U.624E-01
0.560E-01
U.513E-01
0.476E-01
U.446E-01
0.422E-01
0.401E-01
0.i83E-01
U.319E-01
U.280E-01
O.231E-01
U.201E-01
U.181E-01
U.165E-01
0.153E-01
U.144E-01
U.136E-01
U.129E-01
-------
TABLE 4: XD VERSUS CO FOR SIGD • 0.500E 01
LAID" O.SOOE 01
XO-VALUE CD-VALUE
LAND* 0.400E 01
CO-VALUE
LAND* 0.400E 01
CD-VALUE
LAND' O.SOOE 01
CD-VALUE
LAMD» 0.100E 02
CD-VALUE
0.100E 01
0.150E 01
0.20UE 01
3.30UE 01
0.40UE 01
0.30UE 01
U.60UE 01
3.700E 01
U.SOJE 01
J.90JE 01
U.10JE 02
0.15'JE 01
J.20UE 02
U.25JE 02
U.SOOe 02
J.40JE 02
U.SO'Je 02
J.60UE 02
J.700E 02
J.SOUE 02
0.90UE 02
U.1UOE 03
U.150E 05
0.20'JE 0)
U.30JE 01
0.40'JE 03
J.50JE 03
J.60JE 03
U.^O'JE 03
U.90JE 03
J.90'JE 03
U.109E 04
0.191E 00
0.155E 00
0.133E 00
0.108E 00
O.V33E-01
0.8J8E-01
0.771E-01
0./20E-01
0.6791-01
0.645E-01
0.617E-01
0.i23E-01
0.466E-01
0.426E-01
0.396E-01
U.3S1E-01
0.320E-U1
0.296E-01
0.277E-01
0.^61E-01
U.247E-01
U.436E-01
U.196E-01
0.171E-01
0.141E-01
0.123E-01
0.11UE-U1
U.101E-01
O.V33E-02
O.B74E-02
U.024E-02
0./82E-02
0.134E 00
0.1026 UO
O.B29E-U1
0.624E-U1
O.S12E-01
0.44U-U1
0.3V3E-U1
0.357E-U1
0.329E-U1
0.3J7E-01
0.289E-01
0.231E-U1
0.198E-U1
0.177E-U1
0.162E-U1
O.U1E-01
0.126E-01
0.115E-U1
0.107E-U1
0.100E-01
0.9I.8E-02
0.9UOE-U2
0.739E-02
0.6
-------
M9LE S: XO VERSUS CD FOR S1GO > O.tOOE 02
LA10« O.OOOE 00
XD-VALUE CO-VALUE
LAHO* 0.40UE-01
CO-VALUE
LAMO" 0.100E 00 LA«0« 0.200E 00 LAND- O.300E 00
CO-VALUE CO-VALUE CO-VALUE
3.100E
0.150E
U.ZO'Jt
0. 500E
0.400E
0.500E
0.6006
0.700c
J.900E
0.70UE
J.IOUc
J.liOE
U.200E
U.2SUE
o.3uoe
U.400E
U.JOOE
U.ftOOc
U.70UE
U.80UE
J.900E
U.10JE
U.15UE
U.20UE
0. JOJt
O.IOOE
0.50JE
0.40UE
•J.700E
J.3UUE
J. »OJE
J.10JE
01
01
01
01
01
01
01
01
01
01
02
U2
02
02
02
02
02
02
02
02
02
03
03
03
03
OS
03
03
03
03
U3
04
.0.99JE
0.993E
0.990E
0.98JE
0.981E
0.976E
0.971E
0.967E
0.962E
O.V5BE
U.V54E
U.V33E
O.V13E
0.09SE
0.878E
O.B46E
O.SUE
0. /91E
0./68E
0./46E
0.726E
O.^OBE
0.633E
O.S78E
U.500E
0.44/E
0.408E
U.378E
0.3S4E
0.333E
0.316E
O.JOIE
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
0.957E
0.954E
0.952t
0.947E
0.94.3E
0.9381:
0.934t
0.929E
0.92SE
0.921E
0.9m
0.8V7t
0.878E
0.860e
0.343E
0.613E
0.7dSE
0.760E
0.73Be
0.717t
0.698t
0.680E
0.608E
O.SSSE
0.481E
0.4JOE
0.3V2E
0.363E
0.340E
0.3
-------
TA9LS 6: XO VERSUS CO FOA SIGO » 0.1006 02
LA10» 0.400E 00
HO-VALUE CO-VALUE
U.100E 01
U.1JUE 01
J.ZOJE 01
U.300E 01
J.400E 01
0.50UE 01
U.600E 01
0.700E 01
3.900E 01
J.900E 01
U.100E 02
J.150E 02
U.200E 02
J.250E 02
0.30UE 02
J.40UE 02
J.iOUE 02
0.500E 02
J.7UUE 02
3.S03E 02
J.900E 02
J.IOUE OS
'J.IJOe 03
J.203E 03
50Jt 03
J.4UOE 03
J.iOJE 03
J.iOCJc 03
J.703E 03
'J.300E 03
J.'OJE 03
0.1OOE 04
0
0.708E 00
0.69SE 00
0.687E 00
0.677E 00
0.671E 00
0.66SE 00
U.661E 00
0.656E 00
0.612E 00
0.64VE 00
0.6*Se 00
0.630E 00
O.S16E 00
0.603E 00
O.S91E 00.
O.S69E 00
O.J4VE 00
O.S32E 00
O.iUE 00
U.S01E 00
0.488E 00
0.47SE 00
0.42SE 00
0.388E 00
0.336E 00
0.300E 00
0.274E 00
0.2S4E 00
0.237E 00
0.224E 00
0.212E 00
0.202E OU
L*f1D« 0.600E 00
CO-VALUE
0.61SE 00
O.S96E JO
0.584fc 00
O.S70E UO
O.S61E UO
0.555E UO
0.549E UO
0.545E UO
0.541E UO
O.S37E UO
0.5J4t UO
0.519E UO
0.507E 00
0.496E UO
0.486E UO
0.467E 00
0.45U 00
0.436E 00
0.«23E UO
0.411E UO
0.400E UO
0.3?0fc UO
0.348E UO
0.318E 00
0.27SE 00
0.2= 0.120E 01
CO-VALUE CO-VALUE CO-VALUE
0.540E 00
O.S16E 00
U.501E UO
0.4B3E OU
0.473E 00
U.4A5E 00
0.459E 00
U.454E 00
O.450E 00
O.446E 00
0.4*3E 00
0.429E 00
0.418E OO
U.408£ 00
U.400E 00
0.364E
0.370E
U.358E
0.347E 00
0.337E 00
0.328E 00
0.320E 00
0.28SE 00
0.260E OU
0.225E 00
U.2U1E 00
0.194E 00
U.17UE 00
0.15VE 00
0.150E OU
0.142E 00
0.136E 00
00
00
00
00
UO
0.480E 00
0.451E 00
0.434E 00
0.413E
0.401E
0.392E UO
0.3B5E 00
0.38UE 00
0.376E 00
0.372E 00
0.369E UO
0.355E 00
0.345E UO
0.337E UO
0.329E UO
0.316E UO
0.30SE UO
0.29«E UU
0.285E UO
0.277E UO
0.260E 00
0.262E UO
0.234E UO
0.213E UU
0.185E UO
0.1&5E UO
0.1S1E UO
00
0.139E
0.130E UO
0.123E 00
0.116E 00
0.111E OU
0.429E 00
U.397E 00
U.378E OU
0.35SE 00
0.141E 00
U.332E 00
U.32SE 00
U.J20E 00
0.315E 00
U.311E OO
U.308E OO
U.29JE 00
0.296E 00
U.278E OO
0.272E 00
U.460E OO
U.2S1E 00
U.142E OO
U.234E 00
U.227E OO
U.221E OO
U.21SE OO
U.192E OO
U.17SE OO
U.1S1E OO
U.13SE OO
U.123E OO
U.114E OO
U.107E 00
U.101E 00
U.V54E-01
U.V10E-01
-------
TABLE 7: XD VERSUS CD FOR SIGO * 0.100E 02
LAID' O.UOE 01
ID-VALUE CD-VALUE
LAND* O.UOE 01
CD-VALUE
LA.10» 0.1 80E 01
CD-VALUE
LAHD» 0.20UE 01
CD-VALUE
LAMO- 0.2SOE U1
CD-VALUE
U.100E 01
U.15UE 01
•J.ZOOE 01
0.300E 01
U.40UE 01
U.500E 01
D.600E 01
U.703E 01
U.30UE 01
I).900e 01
i).10UE 02
0.1JOE 02
U.20JE U2
J.250E 02
U.50JE 02
0.400E 02
J.JOOt 02
0.40UE 02
i).70'JE 02
U.SOlIE 02
3.90JE 02
J.10UE 0)
J.1SOE 03
U.200E 03
0.30UE 03
0.400E 03
U.SU'JE 03
J.609E 03
J.FOiJE 03
U.SOUe J3
J.9UJc 03
O.IOUt 04
0.3866 00
0.352E 00
0.331E 00
O.J07E 00
0.292E 00
0.282E 00
0.275E 00
0.270E 00
0.26JE 00
0.
-------
r»9LE 8: XD VERSUS CO FOR SI6D » 0.100E 02
LAID* 0.300E 01
XD-VALUE CD-VALUE
LAND* 0.400E 01 LAMD« 0.600E 01 LAND* 0.80UE 01 LAMD* 0.100E 03
CD-VALJE CD-VALUE CD-VALUE CO-VALUE
U.100E 01
0.150E 01
J.203E 01
J.50CJE 01
0.4006 01
3.500E 01
U.60UE 01
J.700E 01
J.303E 01
0.9006 01
0.103E 02
U.15UE 02
U.20UE 02
0.25Ue 02
J.50UE 02
U.400e 02
0.30JE 02
J.40JE 02
J.703E 02
U.BUOE 02
U.900E 02
O.lOOe 05
U.150E 05
(I. lOUt 05
U.500E 05
U.400E 03
U.SOUc 03
0.600E 03
U.70UE 05
J.SOOE 03
J.90UE 03
O.IOOt U4
0.193E 00
0.1S6E 00
0.13JE 00
0.110E 00
U.V66E-U1.
0.878E-01
0.816E-01
0./70E-U1
0.681E-01
0.603E-01
O.S59E-01
0.529E-01
0.506E-01
0.42/E-01
0.*10E-01
0.395E-01
0.382E-01
0.371E-01
0.526E-01
0.396E-01
0.41E-02
0.21.TE-02
0.134E-02
0.101E-02
0.921E-03
0. 70 '• .- -03
0.438E-03
0.435E-05
0.397E-03
0.3676-03
0.5«4E-03
0.32SE-03
0.2646-03
0.22VE-U5
0.18SE-03
0.164E-05
0.1W£-03
0.134E-U3
0.125E-03
0.11/6-03
0.11UE-03
O.IObE-03
0.278E-01
0.153E-01
U. V69E-02
0.493J-02
U.301E-02
0.150E-02
0.115E-02
0.923E-03
0./62E-03
0.544E-OJ
0.349E-05
U.236E-03
0.179E-O3
U.146E-03
U.108E-03
U.S81E-04
U.7S6E-O4
U.66VE-O4
0.606E-04
0.557E-04
0.518E-04
U.400E-04
U.338E-04
U.270E-O4
0.232E-0*
U.206E-04
0.138E-04
0.173E-04
U. 1626-04
U.152E-04
0.14SE-04
-------
TABLE 9: XD VERSUS CD FOR SIGD * 0.1SOE 02
LAND* O.OOOE 00
XO-VALUE CO-VALUE
LAND* U.40UE-01 LA«D« 0.100E 00 LAND* 0.200E OU LAID* 0.300E (JO
CO-VALUE CD-VALUE CO-VALUE CD-VALUE
0.100E
U.150E
U.200E
0.300E
U.400E
0.500E
3.500e
0.7006
3.SOOE
J.'OOC
U.IOOe
0.15UE
3.200E
J.25UE
U.300E
J.400E
O.JOOE
J.40JE
3.700c
J.SOUE
U.900E
U.103E
O.ISOt
J.20JE
0.500E
J.40JE
U.50JE
J.40JE
U.700E
0.90JE
U.900e
J.10JE
01
01
01
01
01
Of
01 .
01
01
01
02
02
01
02
02
02
02
02
02
02
02
03
03
03
03
03
03
03
03
03
03
04
0.998E
0.997E
0.996E
0.993E
0.991E
0.989E
0.987E
O.V85E
0.983E
O.V81E
0.979E
0.968E
O.V5BE
0.949E
O.V39E
0.922E
0.90JE
0.089E
O.B74E
O.HS9E
O.S4JE
0.832E
o.rrsE
0./28E
0.655E
0.60UE
U.SS7E
O.S22E
0.493E
0.469E
U.447E
0.429E
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
OU
00
0.959E
0.9S8E
0.95fE
0.955E
0.953E
0.951E
0.9I.8E
0.9«6e
0.94.4E
0.9<,2E
0.940E
. 0.930E
0.9elE
0.912E
0.9U3E
0.806k
0.869E
0.854E
0.8i9fc
0.826E
0.812E
o.auot
0.745E
0.699E
0.629E
0.577fc
0.$3SE
O.S02E
0.474E
0.4SOE
0.4JOE
0.412t
00
UO
UO
00
00
00
00 .
00
UO
00
00
00
UO
00
UO
00
00
00
UO
00
00
00
UO
00
00
00
00
UO
UO
UO
00
00
0.907E
0.9USE
0.9U3E
0.901E
0.898E
" 0.896E
U.894E
0.892E
0.390E
0.88BE
0.886E
0.877E
0.8&BE
0.85VE
U.850E
0.814E
0.819E
0.8U4E
0.791E
0.77BE
0.76SE
0.7S3E
0.701E
0.6S9E
O.S93E
O.S43E
O.SU4E
0.4ME
0.446E
0.424E
U.405E
0.388E
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
0.331E
0.826E
0.823E
0.8196
0.816E
0.813E
O.B11E
O.B09E
0.807E
0.905E
0.803E
0.794E
0.766E
0.77BE
0.77UE
0.755E
0.7»1E
0.72BE
0.716E
0.704E
0.6V3E
0.682E
0.635E
O.S76E
0.536E
0.492E
0.456E
0.429E
0.404E
0.384E
0.366E
0.331E
00
00
00
00
00
00
UO
00
00
UO
UO
00
00
00
UO
00
00
00
00
00
00
OU
00
00
00
00
00
00
00
00
00
00
0. 766E
0. 75 BE
U.7S3E
0.746E
U.743E
0.739E
0.737E
0.735E
0.732E
U.730E
0.729E
U.720E
U.712E
0.70SE
0.697E
0.684E
U.671E
0.659E
0.648E
U.637E
0.627E
U.617E
U.J74E
0.540E
0.48SE
U.44SE
U.413E
0.387E
0.366E
O.J47E
0.331E
0.318E
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
-------
M9LE 10: XO VERSUS CD FOR SIGD * 0.150E 02
LAND' 0.400E 00
XD-VALUE CD-VALUE
LAND* 0.600E 00
CD-VALUE
LAND* 0.000E 00 LAID* 0.100E 01 LAND* 0.120E 01
CD-VALUE CD-VALUE CD-VALUE
3.100E
J.150E
9.20JE
'J.300E
3.40UE
J.SOJE
'J.SOOE
0.7001
O.SOUE
J.'OJE
0.100E
J.15UE
U.2UUE
U.25UE
0.3005
J.40JE
(J.SOOc
J.500E
j.73jc
J.SOUE
J.'OOE
J.10UE
J.ISJe
J.200E
J.300E
0.4QUE
0.500E
J.60JE
1.7 OUt
J.9JJE
U.90UE
J.IOJc
01
01
01
01
01
01
01
01
01
01
02
01
02
02
02
Of
02
02
02
02
02
OS
03
03
03
03
03
03
03
03
03
04
0.709E
0.696E
0.691E
0.682E
0.677E
0.673E
0.670E
0.666E
U.666E
0.663E
0.662E
U.653E
U.645E
U.63VE
0.632E
U.61VE
0.600E
O.S97E
U.J87E
U.»77E
O.S68E
O.J59E
O.J20E
0.48UE
0.43VE
0.403E
0.374E
0.350E
0.331E
0.3UE
0.30UE
0.tB7t
00
00
00
00
00 .
00
00
0(1
00
00
00
00
00
00
00
OJ
00
OJ
00
00
00
00
00
00
00
00
00
00
00
00
00
00
0.616E
0.54SE
O.S87E
o.sm
0.566E
0.56U
0.557E
0.554E
0.55U
0.549E
O.S47E
0.538E
0.531E
O.S2SE
0.5196
0.509E
0.499E
0.490E
0.481E
0.473E
0.465E
0.4J8E
0.426E
0.4UOE
0.360E
0.330E
0.306E
0.2B7E
0.271E
0.257E
0.246E
0.235E
00
00
00
00
UO
UO
00
UO
00
UO
UO
UO
UO
UO
00
UO
UO
UO
UO
UO
UO
UO
00
UO
00
00
00
00
UO
00
UO
UO
0.541E
O.J18E
U.SU3E
0.437E
0.477E
U.47UE
U.466E
U.462E
U.4S9E
U.4S6E
0.4S4E
U.44SE
U.438E
0.432E
0.427E
0.418E
U.41UE
U.4U2E
0.39SE
U.3S8E
U.3S2E
0.376E
U.349E
U.329E
U.29SE
U.27UE
U.2S1E
U.23SE
U.222E
U.211E
U.201E
U.193E
00
00
00
00
00
00
00
00
00
OU
00
00
OU
00
OU
00
UO
00
00
00
OU
00
00
00
00
00
00
00
00
00
00
UO
0.46UE
0.4SIE
O.*35t
0.416E
0.404E
0.3V6E
0.3VU
0.386E
0.333E
0.3JUE
0.377E
0.369E
0.362E
0.3S7E
0.3S2E
0.304E
0.337E
0.33UE
0.324E
0.31»E
0.313E
0.303E
0.286E
0.26VE
0.2o«!E
0.221E
0.20$E
0.1V2€
0.182E
0.173E
0.165E
0.158E
UO
00
00
00
UO
UO
UO
UO
UO
UO
00
00
OU
UO
00
00
UO
UO
00
OU
00
UO
00
UO
UO
00
00
UO
00
UO
UO
UO
U.OOE
U.39BE
U.379E
U.357E
U.344E
U.336E
U.329E
U.32SE
U.321E
U.J1BE
U.315E
U.306E
U.i»99E
U.294E
O.«!90E
U.
-------
TABLE 11: XO VERSUS CD FOR SIGD « 0.150E 02
LAND« O.UOE 01
XD-VALUE CO-VALUE
L*HO« 0.160E 01
CD-VALUE
LAMD«'0.180E 01
CD-VALUE
LA*D« 0.200E 01
CD-VALUE
LAND* 0.2SOE 01
CO-VALUE
0.109E
U.ISdE
0.20UE
U.309E
0.40UE
0.500E
0.600E
J.TOOi
O.SUUE
3.900E
O.IOOc
U.15UE
J.200E
U.250E
U.SOOe
l).4i)Ue
0.5U3E
J.4UJE
J.70UE
U.900E
3.90'JE
J.IOOc
U.150E
J.200E
0.300E
J.400E
U.SOUE
•J.40UE
0.703E
J.SOOE
0.90UE
U.10UE
01
01
01
01
01
01
01
01
01
01
02
02
02
02
02
02
02
02
02
02
02
03
03
33
03
03
03
03
03
03
03
04
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
u.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
387E
353E
332E
JOSE
295E
2S5E
2m
274E
27UE
266E
264E
IS4E
24BE
24JE
24UE
233E
228E
223E
219€
USE
211E
208E
193E
181E
162E
149E
138E
129E
122E
115E
11UE
1U6E
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
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00
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00
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00
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0.
0.
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0.
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0.
0.
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0.
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350E
31 4 e
2V3E
268E
253E
244E
237E
2321
218E
224E
221E
212E
2U6E
2U2E
198E
192E
188E
1S4E
1BOE
177E
mE
171k
158E
USE
133E
I22t
113E
106E
00
00
00
00
00
00
UO
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UO
00
00
00
00
UO
UO
UO
UO
UO
00
UO
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UO
UO
UO
UO
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999E-01
9*8E-U1
905E-01
867E-U1
0.31BE 00
0.281E 00
0.2S9E 00
0.234E 00
0.219E 00
U.209E OU
U.202E 00
U.197E 00
0.192E 00
0.1 89E 00
U.186E 00
0.177E 00
U.171E 00
U.167E OU
U.164E 00
U.159E 00
0.1 55E 00
0.151E OU
0.14BE 00
U.145E OU
0.143E 00
0.14UE 00
0.130E 00
U.122E 00
0.109E 00
0.998E-01
U.92SE-01
U.867E-01
O.B1BE-01
0.777E-01
0.741E-01
0.710E-01
0.29UE 00
0.2S3E 00
0.231E 00
0.2USE 00
0.190E 00
0.1BOE 00
0.173E 00
0.167E UO
O.U3E 00
0.160E 00
0.1S7E UO
0.14BE 00
O.UJE 00
0.139E 00
0.136E UO
0.131E 00
0.129E 00
0.125E 00
0.122E UU
0.12UE 00
0.117E 00
0.115E UO
0.107E 00
0.997E-01
O.S94E-01
O.B1SE-01
0.7SBE-U1
0.71UE-01
0.67UE-01
0.636E-U1
0.607E-01
0.5B2e-U1
U.
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234E 00
197E OO
me oo
149E 00
135E 00
123E 00
11CE 00
113E 00
110E OO
106E 00
104E 00
955E-01
908E-01
877E-01
853E-01
918E-01
792E-01
770E-01
752E-01
735E-01
721E-01
707E-01
4S1E-01
609E-01
544E-01
498E-01
461E-01
432E-01
407E-01
J87E-01
369E-01
353E-01
-------
M3LE 12: XD VERSUS CD FOft SIGD « 0.150E 02
LAUD" 0.300E 01
XD-VALUE CD-VALUE
LAND* 0.40UE 01
CD-VALUE
LAID* 0.600E 01
CD-VALUE
LAUD" O.BOOE 01
CO-VALUE
LAND* U.100E UZ
CD-VALUE
J.100E
U.1SUE
u.zooi
U.30UE
0.40JE
J.500E
U.60UE
0.70UE
3.80UE
J. VOOE
U.IOUE
J.15UE
U.20UE
0.25JE
J.300E
U.40'JE
J.JOJc
3.400E
J.70UE
•J.80UE
0.»OOE
U.100E
0.1JOE
3.200E
0.300E
•J.40JE
3.500E
J.600E
J.7UUE
J.40JE
J.VOOE
O.IOUe
01
01
01
01
01
01
01
01
01
01
02
02
02
02
02
02
02
02
02
02
02
03
03
03
03
03
03
03
03
03
03
04
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
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193E 00
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13JE 00
11 IE 00
973E-01
HB6E-01
B25E-01
780E-01
746E-01
718E-01
695E-01
623E-01
564E-01
558E-01
53VE-01
512E-01
493E-01
478E-01
46SE-U1
454E-01
444E-01
435E-01
39VE-01
372E-01
33iE-01
J03E-01
2B1E-01
263E-01
24BE-01
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224E-01
215E-U1
0.
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103E UO
942E-01
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532E-01
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418E-01
385E-U1
3S9E-U1
339E-01
323E-01
273E-01
247E-01
231E-U1
219E-U1
204E-01
193E-J1
186E-31
179E-U1
174E-01
170E-U1
166E-J1
150S-01
139S-01
124C-01
112E-U1
1U4E-01
972E-U2
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244E-01
182E-01
146E-01
123E-01
107E-01
946E-02
356E-OZ
785E-02
S81E-02
483E-02
426E-02
389E-02
342E-02
312E-02
292E-02
277E-02
2ASE-02
255E-02
247E-02
217E-02
198E-02
173E-02
156E-UZ
44E-02
34E-02
26E-02
1VE-02
13E-02
108E-02
0
0
0
0
0
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440E-01
267E-01
1831-01
105E-01
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410E-02
336E-02
2B3E-02
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216E-02
13SE-02
104E-02
86U-03
7*7e-03
612£-03
535E-03
484E-03
447E-03
420E-03
39BE-03 '
33UE-03
3226-03
2B7E-03
2*6E-03
21VE-03
20UE-OS
18&E-U3
174E-03
1642-03
156E-03
UV£-U3
0.278E-01
U.1S3E-01
U.V71E-02
U.495E-02
U.302E-02
U.206E-02
U.1S1E-02
0.116E-02
U.»3*E-03
U. t? if. -03
U.634E-03
U.338E-03
U.24SE-03
U.1S8E-03
U.154E-03
U.117E-03
U. 964E-04
U.E39E-04
0. 753E-04
0.691 E-04
0.6*£E-04
0. 60 fc E-04
0.417E-04
U. 424E-04
0.353E-04
U.310E-04
O.«f!1 E-04
0.259E-04
o.^*eE-o«
0.«T27E-04
0.216E-04
U.
-------
TABLE 13: XD VERSUS CD FOR S1GO » 0.200E 02
LAND" O.OOOE 00
XD-tfALUE CO-VALUE
LAND* 0.40UE-01
CD-VALUE
LAHD- 0.100E 00 LAHD" 0.20UE 00 LAUD" 0.3UOE UO
CD-VALUE CO-VALUE CD-VALUE
J.IOJt
J.ISOe
J.20JE
0.30UE
J.40JE
U.JOOE
(J.60JE
0.700E
0.90UE
0.700E
J.10UE
O.ISOe
J.200E
J.250c
3.300E
0.400E
o.jout
U.603E
J.700E
O.BOOc
J.900E
0.10UE
J.liJE
0.20UE
J.30JE
0.400E
J.SOJt
0.60JE
U.70JE
U.30UE
J.VOOE
0.10JE
01
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01
01
01
01
01
01
01
01
02
02
02
02
02
02
02
02
02
02
02
03
03
03
03
03
03
03
03
03
03
04
O.V9VE
O.V9BE
0.y98E
O.V96E
O.V95E
0.994E
O.V93E
O.V9U
O.V90E
o.va9E
O.VBdE
O.VB2E
. O.V76E
O.V7UE
O.V65E
O.yStE
O.V43E
O.V33E
O.V23E
O.V13E
O.VO*E
0.895E
O.flSiE
0.d17E
0./56e
0./07E
0.067E
0.633E
O.OOJE
O.S77E
U.b5iE
O.SJ5E
00
00
00
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00
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0.960E
0.960E
0.9S9t
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0.9S6E
0.9SSE
O.V5*t
0.953t
0.9J1E
0.950E
0.9*9t
0.943E
O.V38E
0.932E
0.927E
0.916E
0.9061
0.8V6E
O.BB7E
0.877t
O.B63c
0.660E
0.820E
0.7B5E
0.726E
O.oHOE
0.6*1E
0.608E
0.5BOE
0.5i5E
O.S33E
O.S14E
UO
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00
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0.9UBE
0.906E
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0.903E
0.902E
0.900E
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0.897E
0.895E
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0.889E
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0.878E
0.873E
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0.844E
0.8J5E
0.826E
0.818E
0.810E
0.772E
0.739E
0.634E
0.64UE
0.603E
U.S72E
U.5*6E
O.S23E
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00
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O.S32E
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0.824E
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0.81VE
0.817E
0.81SE
0.814E
O.B13E
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O.B1UE
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0.79SE
0.7VUE
0.781E
0.772E
0.764E
0.7S6t
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0.7*0e
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0.69VE
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0.619E
0.579E
0.546E
0.518E
0.494E
0.473E
0.4S4E
0.43dE
UO
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0.743E
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U.73BE
U.736E
U.73SE
U.730E
U.72SE
U.720E
U.MoE
U.707E
U.699E
0.692E
0.084E
0.677E
U.670E
U.063E
U.632E
0.005E
U.>6UE
0.524E
U.49«.E
U.469E
U.447E
U.426E
U.411E
U.396E
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
ou
00
00
-------
TABLE U: XO VERSUS CD FOR SIGD • 0.200E 02
LA1D» 0.400E 00
XD-VALUE CD-VALUE
LAND" 0.600E 00
CD-VALUE
LAID- 0.800E 00
CD-VALUE
LAND- 0.10UE 01
CD-VALUE
LAND" 0.120E 01
CD-VALUE
0.103E
0.1JOE
J.20l)e
O.JOJE
0.400E
O.SOJE
U.60UE
U.70UE
O.SOOE
3.900E
J.10UE
0.1SUE
J.20UE
D.25'JE
'J.3UOE
0.40UE
O.SOJE
0.600E
3.703E
'J.SOUE
•J.70JE
3.100E
J.1SOE
U.20UE
0.509E
3.400E
3.500E
0.400E
0.70UE
a.SOJE
J.»OJE
J.100E
01
01
01
01
01
01
01
01
01
01
02
0?
02
02
02
02
02
02
02
02
02
0)
01
03
05
03
03
03
03
03
03
04
O.MUE
0.09BE
0.692E
0.6B4E
0.480E
0.076E
0.67*8
0.672E
0.670E
0.669E
0.668E
0.662E
0.657E
0.6J3E
0.649E
U.641E
0.633E
0.626E
0.619E
0.613E
0.607E
0.60UE
O.S72E
O.S4BE
O.S07E
0.474E
0.447E
0.424E
0.404E
0.3B7E
0.372E
U.3$8E
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
ou
00
00
00
00
00
00
00
00
00
00
00
00
00
00
uo
00
0.616E
O.S98£
O.S88E
o.srsE
0.56BE
0.564E
0.560E
0.558E
0.555E
0.553E
O.SS2E
0.54JE
O.J41E
O.S37E
O.J33c
O.S^6E
O.S20E
O.S14E
0.5U8E
O.S02E
0.497E
0.492E
0.469E
0.4*9t
0.41SE
0.388E
0.366E
0.347E
0.331E
0.317E
U.3U5t
0.294E
UO
00
00
00
00
00
UO
00
00
UO
00
UO
UO
00
UO
00
UO
00
UO
UO
00
UO
UO
00
UO
00
UO
00
UO
UO
UO
UO
O.S42E
O.S1BE
O.S04E
0.4B8E
0.479E
U.472E
0.46BE
0.46SE
0.462E
0.460E
0.458E
0.4S1E
0.446E
0.442E
0.43BE
0.434E
0.427E
0.422E
0.417E
0.412E
0.40BE
0.404E
0.384E
0.36BE
0.340E
0.318E
0.300E
0.28SE
0.271E
0.260E
0.249E
0.240E
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
ou
00.
00
00
00
00
00
00
00
00
ou
00
00
00
0.481E
0.4S3E
0.436E
0.416E
0.405E
0.39BE
0.393E
0.369E
0.386E
0.383E
0.381E
0.373E
0.36dt
0.364E
0.361E
0.3S5E
0.3S1E
0.346e
0.342c
0.33BE
0.335E
0.331E
0.31SE
0.301E
0.27VE
0.261E
0.246E
0.233E
0.221E
0.213E
0.204E
0.197E
00
UO
00
00
00
00
00
00
00
00
00
UO
00
00
00
00
UO
00
00
00
UO
00
00
00
00
00
00
00
03
00
00
00
U.430E
U. 399E
U. 380E
0.358E
U.J4SE
0.337E
U.331E
U.327E
0.323E
U.320E
U.31BE
U.310E
U.30SE
U. 301E
U.i?3E
U.293E
U. 236E
U.285E
U. 291E
U.27BE
U.17SE
U.272E
U. 258E
U.247E
U.22BE
0.214E
U.201E
U.191E
U.182E
U.174E
U.167E
U.161E
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
ou
00
00
ou
00
00
00
00
00
00
00
00
00
-------
'ABLE 13: XO VERSUS CO TOR S1GO .
0.200E 02
J.100E 01
U.150E 01
0.200E 01
O.JOJE 01
3.403E 01
U.30UE 01
0.600E 01
O./OOE 01
0.30UE 01
3.900E 01
U.100E 02
0.1 SUE 02
J.20JE 02
0.25JE J2
0.30'JE 02
0.40UE 02
3.500E 02
U.SOdc 02
3.703E 02
•J.JOOE 02
3.900E 02
J.150E OJ
0.20UE OJ
U.JOOE OJ
U.40UE OJ
U.SOUE OJ
3.60UE OJ
'J.70JE OJ
U.SOUE OJ
U.90UE OJ
E Ot
L*'10" °'UOE 01
CD-VALUE
O.J87E 00
O.J5JE 00
O.JJJE 00
O.J09E 00
0.293E 00
0.2B7E 00
0.280E 00
0.275E 00
0.272E 00
0.268E 00
0.266E 00
0.*S7£ 00
0.23/E 00
0.249E 00
0.<«6E 00
0.241E 00
0.237E 00
0.234E 00
0.131E 00
0.228E 00
0.226E 00
0.22JE 00
0.212E 00
0.20JE 00
0.187E 00
0.17SE 00
0.16SE 00
0.156E 00
0.149E 00
O.UJE 00
0.1J7E 00
0.1J2E 00
LAND* 0.160E 01 LAUD" 0.100E 01 LAND* 0.200E 01 LAHD" 0.2SOE U1
CP-VALUE CD-VALUE CD-VALUE CD-VALUE
0.3SOE UO
0.31SE 00
0.2VJ£ 00
0.269t 00
0.2i*t UO
0.24SE oo
0.2J8E UO
0.2J3E UO
0.229E UO
0.226E UO
0.223E 00
0.21SE 00
0.209E 00
0.206E OU
0.2U3E 00
0.199E 00
0.19SE UO
0.193C UO
0.190E 00
0.188E UO
0.1«5t UO
0.18JE UO
0.174E UO
0.166E 00
0.15JC UO
0.13SE UO
0.128E 00
0.122E UO
0.117E UO
0.112E UO
0.108E UO
0.31 BE 00
0.282E 00
(I.2&UE 00
0.2S4E 00
0.219E UO
U.210E 00
0*20JE OU
0.1 98E 00
0.1906 00
U.1B8E 00
0.1 ?9£ 00
0.1 7lf 00
U.171E 00
0.168E OU
0.164E 00
0.161E 00
0.139E 00
0.156E 00
U.15*E 00
U.132E 00
0.1 51E 00
O.UJE 00
0.136E 00
U.126E 00
0.118E 00
0.11 IE 00
0.105E 00
0.100E 00
U.919E-OJ
0.886E-01
0.29UE 00
0.2S3E UO
0.231E UO
0.205E 00
0.19UE 00
0.18UE 00
0.1/JE UO
0.168E 00
0.16*E 00
0.161E UO
0.130E 00
O.ISOt 00
O.U5E 00
0.1»«TE 00
0.1J9E 00
0.1J6E 00
O.UJE oo
0.1J1E 00
0.1296 UO
0.12FE 00
0.12SE 00
0.124E 00
0.11 re oo
0.112E 00
0.10JE 00
0.94J6-01
0.9Q7E-U1
O.B60E-U1
0.81VE-01
o.rg«E-oi
0.75JE-U1
0.725E-01
00
0.197E 00
U.175E 00
U.U9E 00
U.13SE 00
0.125E 00
U.119E 00
U.1UE 00
0.110E OU
U.107E 00
U.103E 00
U.V67E-01
U.y2JE-01
0.895E-01
0.574E-01
0.345E-01
0.824E-01
U.807E-01
0.79JE-01
0. 780E-01
0. 769E-01
U. 759E-01
U./16E-01
U.682E-01
0.628E-01
0. SB6E-01
0.552E-01
0.523E-01
U.fc98E-01
0.457E-01
0.441E-01
-------
TABLE 16: XD VERSUS CD FOR S1GD « 0.200E 02
LAND* 0.300E 01
AD-VALUE CO-VALUE
LAHO = 0.400E 01
CO-VALUE
LAMD« 0.6006 01
CD-VALUE
LAND* 0.800E 01
CO-VALUE
LAND* 0.100E 02
CO-VALUE
U.100E
U.15JE
3.203E
0.30UE
0.4006
3.SOJ6
0.60JE
0.700E
O.SOOe
3.90UE
D.100E
0.1SOE
0.200E
a.2SUe
3.30'JE
J.tOUe
J.500E
3.60JE
U.70JE
'J.SOJJE
J.700E
U.IO'JE
0.150E
0.20UE
U.3UOE
J.400E
J.50UE
J.400E
0.700E
U.SO'JE
U.900t
J.10UE
01
01
01
01
01
01
01
01
01
01
02
02
02
02
02
02
02
02
U2
02
02
05
03
03
03
03
03
03
03
03
03
04
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
u.
0.
0.
0.
0.
0.
0.
u.
0.
0.
0.
0.
0.
0.
0.
u.
0.
u.
0.
0.
193E 00
156E 00
135E 00
111 E 00
975E-01
S8V6-01
029E-01
7S4E-01
7506-01
7236-01
7001-01
631E-01
S93E-01
S69E-01
5526-01
S29E-01
5136-01
500E-U1
490E-01
481E-U1
474E-01
467E-Q1
439E-01
*17E-01
383E-01
357E-U1
336E-01
318E-01
303E-01
289E-01
278E-01
^48E-U1
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
u.
USE UO
103e 00
S*3E-U1
642E-01
533fc-01
46«E~U1
420E-01
387E-U1
361E-01
3«1E-ai
325E-01
276E-U1
2iU-Ul
235E-01
22SE-01
210E-U1
2U1E-01
1V4E-01
189E-U1
185t-Ul
181E-01
178t-Ul
16SE-U1
1S6E-U1
1*3E-01
132E-U1
124E-U1
118E-01
112E-U1
107E-U1
1U3E-U1
988E-U2
0.
0.
U.
0.
0.
U.
U.
0.
0.
0.
0.
U.
0.
0.
U.
U.
U.
0.
U.
0.
U.
0.
U.
0.
0.
0.
0.
0.
u.
u.
u.
u.
738C-01
498E-01
372E-01
245E-01
183E-01
147E-01
123E-01
107E-01
951E-02
361E-02
7906-02
587E-02
*90E-02
*3«,E-02
3986-02
3526-02
32*6-02
3066-02
2»26-02
2816-02
2726-02
2646-02
2396-02
222E-02
2UU6-U2
1846-02
17^6-02
16^6-02
1546-02
1476-02
1416-02
1356-02
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
4406-01
2676-01
1836-01
106E-U1
7116-02
5256-02
4116-02
3376-02
285E-02
246E-02
217E-02
139E-02
106E-02
577E-03
763E-03
630E-03
555E-03
505E-03
47UE-03
*44t-03
423E-03
407E-03
353E-03
322E-03
Z33E-U3
258E-03
23VE-03
225E-03
212E-U3
202E-03
193E-03
186E-U3
U.
U.
0.
U.
U.
U.
U.
0.
U.
U.
U.
U.
0.
U.
U.
U.
0.
U.
U.
U.
U.
0.
u.
u.
u.
u.
u.
u.
u.
u.
u.
u.
278E-01
153E-01
V72E-02
495E-02
303E-02
206E-02
151E-02
117E-02
V38E-03
776E-03
657E-03
342E-03
448E-03
19H-03
157E-03
120E-03
V99E-04
876E-04
791E-04
730E-04
633E-04
646E-04
534E-04
474E-04
406E-04
365E-04
336E-04
313E-0*
495E-04
2BUE-04
267E-04
250E-04
-------
TABLE 17: XO VERSUS CD FOR SIGD * O.Z50E 02
LAID* O.OOOE 00
XD-VALUE CD-VALUE
LAUD* 0.400E-01
CD-VALUE
LAND* 0.100E 00 LAND* 0.200E 00 LA«D* 0.300E UO
CD-VALUE CD-VALUE CO-VALUE
0.100E
U.1SJE
0.20'JE
O.JOJe
U.400E
J.503E
U.iOOE
J.700E
U.800E
U.900E
U.10UE
J.15JE
0.20UE
0.2506
3.300E
J.tOJc
J.500E
J.40JE
O.OOOE
3.800E
O.VOOe
0.100E
0.15UE
3.200e
3.300E
J.400E
0.503E
J.60UE
0.700E
J.900E
J.900e
J.100E
01
01
01
01
01
01
01
01
01
01
02
02
02
02
02
02
02
02
02
02
02
03
03
03
03
03
03
03
03
03
03
04
0.999E
0.999E
0.99BE
0.998E
O.V97E
0.996E
O.V9SE
U.994E
O.V94E
0.993E
U.9»2E
O.V88E
O.V846
0.981E
0.977E
O.V69E
O.V62E
0.95SE
0.948E
O.V42E
0.93SE
U.V29E
0.898E
0.870E
0.822E
0./81E
O.'tSE
0.714E
0.687E
U.042E
0.64UE
0.020E
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
0.961E
0.960E
0.960E
0.959E
0.958E
0.957E
0.9J6E
0.9S6E
0.955E
0.7S4E
0.9J3E
0.9iOE
0.9«6E
0.942E
0.939E
0.932E
0.92SE
0.918E
0.911E
0.9USE
0.898E
0.392E
0.863E
0.836E
0.790t
0.7SOE
0.716E
0.686t
0.660E
0.636E
0.615E
O.S96E
00
00
00
UO
00
00
00
00
UO
00
00
00
00
00
00
00
00
UO
00
00
00
UO
00
00
00
00
00
00
00
UO
00
UO
U.908E
0.907E
0.906E
0.904E
0.933E
0.902E
0.901E
U.901E
0.900E
U.899E
0.89BE
0.89SE
O.B91E
0.888E
U.894E
0.377E
U.871E
U.864E
0.8S8E
0.852E
U.8
-------
TABLE IS: XD VERSUS CD FOR SIGD > 0.250E 02
LAID* 0.400E 00
XD-VALUE CO-VALUE
LAUD" 0.600E 00
CD-VALUE
LAND* 0.800E 00 LAHD» 0.10UE 01 LA«0= 0.120E 01
CD-VALUE CD-VALUE CD-VALUE
0.100E
0.15'JE
0.200E
9.300E
0.403E
3.SOJE
0.60JE
0.70UE
U.500E
J.9Q3E
J.100E
U.150E
0.200?
0.25UE
U.30UE
U.400E
3.50UE
J.&OUE
0.700e
U.SOOE
3.900E
J.IOOe
J.150E
J.200E
0.300E
0.400e
O.SOJE
U.600E
0.700e
0.800E
0.9QOE
3.100E
01
01
01
01
01
01
01
01
01
01
02
02
02
02
02
U2
02
02
02
02
02
03
03
03
03
03
03
03
03
03
03
01
O.MOE
0.699E
0.«92E
0.685E
0.681E
0.678E
0.676E
0.674E
0.673E
0.671E
0.670E
0.646E
0.6631
0.660E
0.6S7E
0.6S1E
0.646E
0.641E
0.637E
U.632E
0.627E
0.623E
0.602E
O.iSoE
0.551E
0.*24E
O.iOOE
0.479E
0.461E
U.***E
0.429E
0.416E
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
0.616E
0.598E
0.588E
0.576E
O.S69E
0.565E
0.562E
0.559E
O.SS7t
O.SSSt
0.554E
O.S49E
0.545E
0.342E
O.S40E
O.S3SE
O.S30E
O.J26E
O.S22E
0.518E
O.SUE
0.511E
0.494E
0.478E
0.4S2E
0.429E
0.409E
0.3V2E
0.377E
0.364E
0.3S2E
0.3<.1£
00
00
00
00
00
UO
UO
UO
UO
00
00
00
00
UO
00
00
00
00
00
00
00
UO
UO
UO
00
00
00
00
00
00
00
UO
O.S42E
O.S1BE
O.S04E
0.488E
0.479E
0.473E
0.469E
0.466E
0.463E
0.461E
0.459E
U.4S3E
0.449E
0.446E
0.444E
0.439E
0.43SE
U.432E
U.428E
0.42SE
0.422E
U.419E
0.4051
0.391E
0.370E
U.3S1E
0.33SE
U.321E
0.309E
0.298E
0.238E
0.279E
00
00
00
00
00
00
00
00
00
00
00
00
00
00
ou
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
0.481E
0.4S3E
0.436E
0.417E
0.406E
0.39VE
0.394E
0.390E
0.387E
0.3d4E
0.381E
0.375E
0.371E
0.3ABE
0.365E
0.361E
0.358E
0.355E
0.3S2E
0.349E
0.346E
0.344E
0.332E
0.321E
0.303E
0.288E
0.27SE
0.263E
0.2S3E
0.244E
0.236E
0.228E
00
00
00
00
00
00
UO
00
00
UO
00
UO
00
00
UO
uu
UO
UO
00
UO
00
UO
00
UO
00
UO
UO
UO
UO
00
00
UO
0.430E
U.399E
U.3BOE
U.358E
0.346E
U.338E
U.332E
U.327E
0.324E
U.321E
0.319E
U.311E
U.307E
U.304E
U.301E
0.297E
0.29«E
U.291E
U.289E
U.486E
U.2S4E
U.232E
U.272E
U.263E
0.248E
U.236E
0.22JE
U.216E
U.207E
0.200E
U.193E
U.187E
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
oo
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
-------
TABLE 19: XD VERSUS CD FOR SIGD » 0.250E 02
LAID* O.UOE 01
XD-VALUE CD-VALUE
LAND- 0.160E 01
CD-VALUE
LAUD* 0.1SOE 01 LAND* 0.200E 01 LAND* O.Z50E 01
CD-VALUE CD-VALUE CD-VALUE
0.100E
J.150E
0.203E
J.30JE
U.4UOE
U.500E
3.400E
0.700E
U.900E
0.9UUE
0.100E
J.1JOE
U.200E
U.250E
J.300E
3.400E
J.50UE
0.60UE
i.TOJi
O.SOOE
3.900E
J.100E
3.150E
0.200E
J.SOJE
J.*OOE
0.500E
J.603E
U.70UE
U.803E
J.900E
0.10JE
01
01
01
01
01
01
01
01
01
01
02
02
02
02
02
02
02
02
02
02
02
03
03
03
03
03
03
03
03
03
03
04
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
397E
353E
333E
309E
29«E
2B7E
281E
276E
272E
26VE
267E
2S9E
2J4E
251E
2*9E
2*SE
2*2E
-------
1A9LE 20: XD VERSUS CO FOR SIGD * 0.250E 02
LAID* 0.300C 01
XD-VALUE CD-VALUE
LAND* 0.400E 01
CO-VALUE
LAND* 0.600E 01 LAND* 0.800E 01 LAND* 0.100E 02
CD-VALUE CD-VALUE CD-VALUE
J.100E 01
J.150E 01
J.200E 01
0.30UE 01
J.40JE 01
J.500E 01
9.60JE 01
0.700E 01
3.80QE 01
0.90UE 01
J.10JE 02
0.150E 02
J.203E 02
0.250c 02
J.50JE 02
U.40UE 02
3.500E 02
0.6006 02
J./OOE 02
J.503E 02
J.900E 02
3.100E 03
J.15UE 03
J.200E 03
O.JOOE 03
0.400E 03
J.SOUE 03
O.iOJE 03
0.7006 03
U.303t 03
J.70UE 03
J.IOJc 04
0.193E 00
0.157E 00
0.1 351 00
0.111E 00
0.976E-01
0.890E-01
0.850E-01
0.786E-01
0.752E-01
0.725E-01
0. 7O3E-01
0.634E-01
0.59bE-01
0.57SE-01
0.55VE-01
O.J37E-01
0.523E-01
O.S12E-01
O.S03E-01
0.496E-01
0.49OE-01
0.484E-01
0.461E-01
0.444E-01
0.416E-01
0.394E-01
0.37SE-01
0.359E-01
0.345E-01
0.33^E-01
0.321E-01
0.31OE-01
0.135E 00
0.103E UO
0.8436-01
0.642E-01
0.534E-U1
0.467E-01
0.421E-U1
0.3876-01
0.3626-01
0.3426-01
0.3266-01
0.2786-01
0.2536-01
0.2386-01
0.2276-01
0.2146-01
0.2056-01
0. 1996-01
0.1946-01
0. 190E-U1
0.1876-01
0.1846-01
0.174E-01
0. 1666-01
0.1J5C-01
0. U6E-01
0.139E-U1
0.1336-01
0.1276-01
0.123E-U1
0.118E-01
0.115E-U1
0.738E-01
0.498E-01
0.372E-01
0.245E-01
0.133E-01
U.147E-01
0.123E-01
0.107E-01
0.953E-02
U.843E-02
0.792E-02
0.5906-02
U.494E-02
0.438£-02
O.«02£-02
0.357E-02
0.3316-02
U.312E-02
0.2996-02
0.289E-02
0.231E-02
0.274E-02
0.251E-02
0.236E-02
0.217E-02
0.2036-02
0.192E-02
0.183E-02
0.175E-02
0.168E-02
0.162E-02
U.157E-02
0.440E-01
3.2676-01
0.133E-01
0.100E-01
0.7116-02
0.525E-02
0.412E-02
0.337E-02
0.2H5E-02
0.247E-02
0.218E-02
O.UOE-02
0.107E-02
0.834E-03
0.771E-03
0.6JVE-03
. 0.565E-03
0.516E-03
0.482E-03
0.457E-03
0.437E-03
0.421E-03
0.371E-03
3.34<£-03
0.307E-03
0.2846-03
0.2676-03
0.253E-U3
0.242E-03
0.232E-03
0.223E-03
0.215E-03
0.278E-01
U.153E-01
0.972E-02
U.49SE-02
U.303E-02
0.207E-02
U.152E-02
U.117E-02
O.V40E-03
U.777E-03
U.659E-03
U.363E-03
0.250E-03
0.192E-03
0.159E-03
0.122E-03
0.102E-03
O.S94E-04
0.311E-04
0.751E-04
U.705E-04
U.669E-04
0.561E-04
0.»04E-04
0.441E-04
0.402E-04
0.375E-04
U.333E-04
0.336E-04
0.321E-04
0.30SE-04
0.297E-04
-------
fABLE 21: XO VERSUS CO FOR SI6D » 0.300E 02
LAHO» O.OOOE 00
KD-VALUE CO-VALUE
LAHO« 0.403E-01
CO-VALUE
LAHO« 0.100E 00 LAND* 0.200E 00 LAID* 0.300E 00
CO-VALUE CO-VALUE CO-VALUE
U.iOOE
0.153E
J.20JE
J.30UE
J.403E
O.SOOE
3.60JE
o.7ooc
0.9006
U.90UE
J.10JE
O.ISOc
a.20u£
0.2SJ6
J.JOUc
J.40Jc
J.SOUe
0.50'JE
0.7036
U.BOOt
0.90UE
U.IOOE
O.MUe
3.203E
J. 50'JE
J.4UUE
U.SOUE
0.600E
0.7QOE
0.900E
U.90UE
U.IOOE
01
01
01
01
01
01
01
01
01
01
02
02
02
02
02
02
02
02
02
02
02
03
03
03
03
03
03
03
03
03
03
04
0.999E
0.9996
0.999E
O.V98E
0.99dE
0.997E
0.99ft
0.996E
0.996E
0.99JE
0.994E
O.V92E
0.989E
O.V86E
O.V8*e
0.979E
0.7/3E
0.968E
0.963E
O.V5«E
0.9S3E
O.V49E
.0.926E
0.90SE
0.864E
0.032E
0.902E
0./75E
O.ISOE
0.72BE
0.797E
0.6886
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
uo
00
00
00
00
00
00
0.961E
0.9616
0.960E
0.9S9C
0.9S9E
0.958E
0.9)86
0.957E
0.9576
0.9S6E
0.956E
0.9S3E
0.9)06
0.948E
0.9«S6
0.940E
0.9356
0.930c
0.9266
0.9216
0.916c
0.912E
0.8906
0.8696
O.B32E
O.BUOc
0.7 rot
0.74«£
0.7216
0.6V9E
0.679fc
O.661E
00
00
UO
UO
00
00
UO
00
00
UO
00
UO
UO
00
UO
UO
UO
00
UO
00
UO
00
00
UO
00
UO
UO
00
UO
00
UO
UO
U.909E
0.907E
U.906E
0.905E
U.901E
0.903E
0.903E
U.902E
U.901E
0.901E
U.9UOE
0.898E
0.89SE
U.393E
U.99QE
0.886E
0.381E
0.876E
U.S72E
0.867E
O.B63E
0.859E
0.938E
0.819E
0.734E
0.7536
0.726E
0.701E
0.679E
0.6S8E
0.6406
0.623E
00
00
00
00
00
00
00
00
UO
00
00
00
00
00
00
00
UO
00
00 '
00
ou
00
ou
00
00
uu
00
00
00
00
ou
00
0.831E
0.8206
0.82$E
0.823E
0.321E
0.82UE
0.8196
0.818E
0,8176
0.817E
0.516E
0.313E
0.811E
0.8086
0.8U6E
0.8U2E
0.797E
0.793E
0.7896
0.78SE
0.781E
0.777E
0.7S8E
0.74U
0.7U9E
0.681E
0.6S7E
0.634E
0.61*6
0.5966
0.579E
0.56*6
00
00
00
00
00
00
00
00
UO
00
00
UO
UO
UO
00
00
00
UO
00
UO
00
uu
00
00
00
uu
00
00
UO
UO
00
00
U.767E
0.7S9E
0.7556
U.7SOE
0.7*76
U.745E
U.744E
0.7436
U.742E
0.7416
0.7406
U.737E
0.7J46
U.732E
0.730E
0.726E
U.722E
0.71 BE
U.714E
U.710E
U.707E
0.7036
U.696E
0.670E
U.642E
0.6176
U.594E
0.574E
U.556E
U.539E
U.524E
U.510E
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
-------
TABLE 22: XO VERSUS CD FOR SIGD * 0.300E 02
LAMO- 0.400E 00
XO-VALUE CD-VALUE
LAND* 0.600E 00
CD-VALUE
LAND" 0.800E 00 LAMD« 0.10UE 01 LAND- 0.120E 01
CD-VALUE CD-VALUE CD-VALUE
J.100E
J.1SOC
U.20JE
•J.30UE
U.40JE
J.500E
U.ftOOE
J.70UE
U.90UE
U.90UE
0.10UE
J.15UE
O.ZOUE
0.253E
3.3006
3.400E
0.500E
0.400E
0.7U3E
U.SOOE
U.'OUE
0.100E
U.1SOE
U.20UE
U.300E
J.4UUE
U.50UE
U.40UE
U.70'JE
0.300E
J.»OUt
J.10UE
01
01
01
01
01
01
U1
01
01
01
01
01
01
02
02
02
02
02
02
02
02
OS
03
03
03
03
03
U3
03
03
03
04
O.MOE
0.699E
0.693E
0.635E
0.681E
0.679E
0.677E
0.67SE
0.674E
0.673E
0.672E
0.668E
0.666E
0.663E
0.661E
0.6S7E
0.654E
0.650E
0.647E
0.643E
0.640E
0.6S7E
0.621E
0.607E
O.S91E
O.iSBE
O.J3B6
0.519E
U.503E
0.49HE
0.*/*E
0.4i61E
00
OU
00
00
00
00
00
00
00
OU
00
OU
OU
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
OU
0.617E
0.599E
0.588E
0.5ME
O.S70E
0.565E
O.S62E
0.560E
0.558t
O.SS7E
0.555E
0.5S1E
0.51.86
0.5*56
0.5*36
0.5406
0.536E
0.5336
0.530c
0.5276
0.524E
0.522E
O.S09E
0.497c
0.4766
0.4576
0.440E
0.42SE
0.4126
0.400c
0. 3d8E
0.378c
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
U.S42E
U.S18E
O.SOSE
U.489E
0.480E
0.474E
0.470E
U.467E
U.464E
0.462E
0.460E
0.45SE
0.4S1E
U.449E
0.447E
0.443E
0.440E
0.438E
U.435E
0.432E
0.430E
0.428c
0.417E
0.407E
0.390E
0.374E
0.361E
0.348E
U.337E
U.327E
0.318E
U.309E
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
o.*au
0.453E
0.436E
0.417E
0.406E
0.399E
0.394E
0.39UE
0.387E
0.38SE
0.383E
0.377E
0.373E
0.37UE
0.3686
0.365E
0.362E
0.35VE
0.3S7E
0.355E
0.3S3E
0.351t
0.342E
0.334E
0.319E
0.307E
0.29SE
0.28SE
0.276E
0.26Bt
0.26UE
0.2536
00
UO
UO
00
00
00
UO
00
UO
UO
UO
UO
UO
UO
00
00
00
UO
uu
UO
00
00
UO
UO
UO
00
UO
UO
UO
UO
UO
uu
0.430H
U.399E
U.380E
0.356E
U.346E
U.338E
U.332E
U.328E
U.325E
U.322E
U.320E
U.312E
U.30dE
U.306E
O.J03E
U.300E
U.298E
0.295E
U.293E
U.291E
U.290E
U.28HE
U.2BOE
0.274E
U.262E
0.251E
U.242E
U.234E
0.126E
0.219E
U.cUE
-O.^OBE
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
OU
00
00
00
00
00
00
00
00
00
00
00
00
-------
CABLE 23: XO VERSUS CO FOR SIGO > 0.300E 02
LANO« O.UOe 01
XO-VALUE CO-VALUE
LA«0« 0.16UE 01
CO-VALUE
LAMO" 0.180E 01 LAUD- 0.20UE 01 LAPD» 0.250E 01
CO-VALUE CO-VALUE CD-VALUE
J.100E
0.153E
U.203E
J.JOJE
0.4Ul)t
0.50JE
J.60Je
J.70Jt
O.JOJc
J.90Jt
J.IOOe
J.1SOE
0.20Ue
J.2SOE
0.300c
J.400c
J.50UE
U.SOOe
U.700E
J.8JUE
J.90UE
U.IOJt
3.15Jc
J.20JE
0. JOUc
J.40JE
J.SOJc
J.600E
J.70JE
J.5U3E
O.'OUc
0.100E
01
01
01
01
01
01
01
01
01
01
02
02
02
02
02
92
02
02
02
02
02
03
0)
05
03
03
03
03
03
03
OJ
04
0.387E
0.3S3E
0.3J3E
0.310E
0.29o£
J.i87E
Ui281£
O.tJtl
0.273E
O.V70E
0.2«aE
0.260E
0.2S6E
O.^SJE
0.2SJE
0.247E
0.24JE
U.2«3E
0.^*16
0.239E
0.230E
0.23oE
0.230E
0.22HE
0.2UE
0.206E
0.19HE
0.1 VIE
0.13JE
0.180E
o.im
O.UOE
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
0.3SOE
0.315E
0.294£
0.2«9E
0.2i5E
0.2*5e
0.239E
0.234E
0.230E
0.227E
0.22«e
0.216E
0.212e
0.209E
0.207e
0.20*6
0.202E
0.2JOE
O.IVSe
0.1V7t
0.1VSE
o.me
0.189E
0.184E
0.176E
0.169E
0.1o2E
0.1S7E
0.1S2E
O.U7C
O.U3e
0.139E
00
00
00
JO
00
00
UO
00
00
00
00
00
00
UO
UO
UO
JO
JO
UO
UO
UO
UO
00
JO
JO
00
00
00
UO
JO
UO
UO
0.318E
U.282E
J.26UE
0.23tE
0.22UE
0.210E
U.203E
0.198E
U.19SE
0.191E
0.189E
0.181E
U.176E
0.173E
U.171E
0.168E
0.166E
U.161E
0.163E
U.162E
U.161E
D.1S9E
0.1556
0.151E
0.144E
0.13BE
0.133E
0.128E
0.124E
0.121E
0.117E
0.1UE
00
00
OU
00
00
00
00
00
00
00
00
00
00
00
00
OU
00
00
00
OU
00
00
00
00
00
00
00
00
00
OU
00
00
0.29UE
0.253E
0.231E
0.205E
0.190E
0.181E
0.174E
0.169E
0.16SE
0.162E
0.1S9E
0.1S1E
0.147E
0.144E
0.142E
0.139E
0.137E
0.13SE
0.134E
0.133E
0.132E
0.131E
0.127E
0.124E
0.118C
0.113E
0.109E
0.10SE
0.102E
00
00
00
UO
00
do
UO
UO
UO
00
UO
UO
UO
UO
UO
UO
UO
UO
UO
UO
UO
UO
00
00
00
00
00
UO
UO
0.9K8E-U1
0.9eUE-U1
0.934E-01
u.
u.
u.
u.
u.
u.
u.
u.
u.
u.
u.
u.
u.
0.
u.
u.
u.
u.
0.
u.
u.
u.
u.
u.
u.
u.
0.
u.
u.
u.
0.
u.
23SE 00
197E 00
17SE 00
150E 00
135E 00
126E 00
119E 00
114E 00
11 IE 00
108E 00
10SE 00
97JE-01
934E-01
V08E-01
U90E-01
866E-01
849E-01
B57E-01
U27E-01
U18E-01
dllE-01
80 * E -01
777E-01
75SE-01
719E-01
689E-01
663E-01
640E-01
619E--01
oOOE-01
583E-01
567E-01
-------
APPENDIX C
TABLES OF DILUTION FACTOR 5* VERSUS x/B
-------
TABLE 1« Dilution Factor(ZETA) versus X/B for Penetration Ratio(H/B> = D.5DGE-D1
X/B-Value
0.1DDDOE QD
0.15QODE 00
D.2DDDDE 00
0.30000E 00
Q.4DDDDE 00
0.50000E 00
0.6000DE 00
0.70000E 00
0.8DDODE 00
D.70DODE 00
D.I DO DDE 01
0.15DODE 01
D.2DDDDE 01
D.25DDDE 01
0.3000DE 01
0.40000E 01
D.5DDDDE 01
0.60000E 01
0.70000E 01
D.8DDDDE 01
0.70000E 01
D.1DDDDE 02
0.15000E 02
D.2DDDOE 02
0.30QOOE 02
0.4DDDDE 02
0.50000E 02
0.60000E 02
0.70000E 02
D.8DDDDE 02
0.70000E 02
0.1DOOOE 03
B/ALFAz
= 0.500E 01
Zeta-Va 1 ue
0.35731E 00
0.26821E 00
0.21738E 00
0.1626QE 00
0.1333DE 00
0.11487E 00
0.10212E 00
0.72725E-01
0.85516E-01
0.77812E-01
0.75200E-01
0.61483E-01
0.5540BE-01
0.52562E-01
0.51213E-01
0.50271E-01
0.50060E-01
0.50013E-01
0.50003E-01
0.50001E-01
0.50000E-01
0.50000E-01
0.5000DE-01
D.50000E-01
D.5000DE-01
0.50000E-01
0.5000DE-01
0.50000E-01
0.50000E-01
O-SOOOOE-Ol
0.-5000DE-01
0.50DOOE-01
B/ALFAz
= 0.100E 02
Zeta-Va I ue
0.47177E 00
0.362&6E 00
0.29757E 00
0.22462E 00
0.18469E 00
0.15927E 00
0.14152E 00
0.12832E 00
D.118D8E DO
0.1098AE 00
a.l030(7E 00
0.81532E-01
0.&9%5E-01
0.62
-------
TABLE 2» Dilution Factor(ZETA) versus X/B for Penetration Ratio(H/B) = 0.500E-01
X/B-Value
D.1DODDE 00
0.150DOE 00
0.20000E 00
0.300DOE 00
0.400QQE 00
0.5000QE 00
O.&OOODE 00
Q.70000E 00
0.6QOOOE 00
0.90000E 00
0.10DOQE 01
0.15000E 01
0.20DDDE 01
0.25000E 01
0.300QOE 01
0.40000E 01
D.5DDDOE 01
0.6000DE 01
D.70DODE 01
0.80QOOE 01
0.7000DE 01
Q.1QOOOE 02
D.150DDE 02
D.20DODE 02
0.30000E 02
Q.4QOODE 02
Q.50000E 02
0.60000E 02
0.70000E 02
0.80DDDE 02
0.9000DE 02
0.10000E 03
B/ALFAz
= 0.350E 02
Zeta-Va 1 ue
0.69468E 00
0.58286E 00
D.5Q102E 00
0.39475E 00
0.33043E 00
D.28755E 00
0.25&65E 00
0.23367E 00
D.21548E 00
0.20077E 00
0.18B57E 00
0.14899E 00
0.12669E 00
Q.112DOE 00
0.10142E 00
0.86975E-01
0.77452E-01
0.70704E-01
0.&5738E-01
0.&Z011E-01
0.59184E-01
0.57029E-01
0.51851E-01
0.50487E-01
0.50034E-01
0.50002E-01
0.5DOOOE-01
0.50000E-01
0.50DOOE-01
0.50000E-01
0.5QOODE-01
0.50000E-01
B/ALFAz
= 0.50DE 02
Zeta-Va 1 ue
0.75Z53E 00
0.64986E 00
0.56926E 00
0.45777E 00
0.38&90E 00
D.33845E 00
0.3D326E 00
0.2764&E 00
0.25530E 00
0.23B11E 00
D.22382E 00
0.17721E 00
0.150B2E 00
0.13340E 00
Q.12063E 00
0.10357E 00
0.92091E-01
0.83761E-01
0.77416E-01
0.72430E-01
0.68434E-01
0.65190E-01
0.55856E-01
0.52268E-01
0.50340E-01
0.50051E-01
0.50008E-01
0.50001E-01
0.5000DE-01
0.5000DE-01
0.50000E-01
0.50000E-01
B/ALFAz
» 0.750E 02
Zeta-Va 1 ue
0.81109E 00
0.72285E 00
0.64776E 00
0.53563E 00
0.45720E 00
0.40475E 00
D.3MME 00
0.33352E 00
0.30870E 00
0.28837E 00
0.27143E 00
Q.21564E 00
Q.1B38QE 00
0.1A271E 00
0.14746E 00
0.12&47E 00
0.1124&E 00
0.10225E 00
D.?43«7DE-01
0.88113E-01
0.82%4E-01
0.78655E-01
0.64756E-01
0.57751E-01
0.52152E-01
0.50598E-01
0.50166E-01
0.50046E-01
0.50D13E-01
0.50004E-01
0.50001E-01
0..5000DE-01
B/ALFAz
= 0.10DE 03
Zeta-Va lue
0.84725E 00
0.77076E DO
0.70235E 00
0.59338E DO
0.51498E DO
0.45747E DO
Q.41386E DO
0.37971E DO
0.35223E DO
0.3296DE DO
D.31D6DE 00
D.24758E DO
0.21134E 00
0.18723E OD
0.1&977E DO
D.14572E OD
0.12961E DD
0.11786E DO
0.10881E DD
0.1D157E DD
D.95599E-D1
0.9D578E-01
0.73862E-01
D.M538E-D1
D.55509E-D1
0.52094E-01
0.5D796E-01
D.5D3D3E-D1
D.50115E-01
D.5D044E-D1
D.5DD17E-D1
D.5DD06E-D1
-------
TABLE 3* Dilution Factor(ZETA) versus X/B for Penetration Ratio(H/B) = D.1DOE DO
X/B-Value
0.1 DO DOE DO
0.15DOOE 00
0.20DODE 00
0.30000E 00
0.40000E 00
0.50000E 00
Q.60000E 00
0.70000E 00
O.BOOOOE 00
0.9QOOOE 00
0.10000E 01
Q.15000E 01
Q.20000E 01
Q.25000E 01
0.3000QE 01
0.40000E 01
0.500QOE 01
0.60000E 01
0.70000E 01
0.60000E 01
0.9000DE 01
0.1000QE 02
0.15000E 02
0.2000QE 02
0.3000DE 02
0.40000E 02
O.BOOOOE 02
O.BOOOOE 02
0.70000E 02
O.BOOOOE 02
0.90000E 02
0.10000E 03
B/ALFAz
« 0.500E 01
Zeta-Va 1 ue
D.fe0207E 00
0.48521E 00
0.40771E 00
0.31447E 00
0.261 DEE 00
0.22637E 00
0.20197E DO
0.18383E 00
0.16981E 00
0.15668E 00
0.14%5E 00
0.12267E 00
0.11068E 00
0.10506E 00
0.1Q24QE 00
0.10054E 00
0.10012E 00
0.1D003E 00
0.10001E 00
0.10000E DO
0.1DOOOE 00
Q.100QOE 00
0.10000E 00
0.10000E 00
0.100QOE 00
0.10000E 00
0.100QOE 00
0.1 00 ODE 00
0.10000E 00
0.100QOE 00
0.1000DE 00
0.1QOOOE DO
B/ALFAz
= 0.100E 02
Zeta-Va 1 ue
D.72057E 00
0.61228E 00
0.53067E 00
0.42193E 00
0.35478E 00
0.30753E 00
0.27693E 00
0.25223E 00
0.232B1E 00
0.21708E 00
D.2D405E 00
0.1621 IE 00
0.13937E 00
0.12557E 00
0.11675E 00
0.10725E 00
Q.10314E 00
0.10136E 00
0.10059E 00
0.10025E 00
0.1001 IE 00
0.10005E 00
0.10000E 00
0.10000E 00
0.10000E 00
0.1000DE 00
D.10000E 00
0.10000E 00
D.10000E 00
0.10000E 00
D.10000E 00
D.10000E 00
B/ALFAz
= 0.150E 02
Zeta-Va 1 ue
0.78246E 00
0.&8&4QE 00
0.&0808E 00
0.47555E 00
0.42173E 00
0.3703BE 00
0.33268E 00
0.30378E 00
0.2BOB5E 00
0.2&216E 00
0.24659E 00
0.19568E 00
0.16701E 00
0.14648E 00
0.13564E 00
0.1196EE 00
0.11093E 00
Q.1Q607E 00
0.10339E 00
0.10189E 00
0.10105E 00
0.10059E 00
0.10003E 00
0.10000E 00
0.10000E 00
0.1QOOOE 00
0.10000E 00
0.10000E 00
0.10000E 00
0.10000E 00
0.10000E OD
0.10000E 00
B/ALFAz
= 0.25DE 02
Zeta-Va lue
0.84875E 00
0.77272E 00
0.70459E 00
0.595B5E 00
0.5174BE 00
0.45971E 00
0.4 162 IE 00
0.38196E 00
0.35438E 00
0.33166E 00
0.31257E 00
0.24921E 00
0.21275E 00
0.18854E 00
0.171 IDE 00
0.14752E 00
0.1324BE 00
0.1224DE 00
0.11551E 00
0.11075E 00
0.10745E 00
0.10517E 00
0.100B3E 00
0.10013E 00
0.10000E 00
0.1000DE 00
0.10000E OD
D.1DODDE DD
0.1DDDDE DD
D.1DDDDE DD
0.1DODOE DD
D.1DDDDE DD
-------
TABLE 4' Dilution Factor(ZETA) versus X/B for Penetration Ratio(H/B) = Q.1DOE DD
X/B-Value
0.10DDDE DD
0.15DDDE 00
0.2DDDDE 00
D.300DDE 00
D.4DODDE 00
0.500QOE 00
O.&OOODE 00
D.700DDE 00
O.BOOOOE 00
0.90000E 00
0.10000E 01
D.15DDOE 01
0.20000E 01
0.25000E 01
0.30000E 01
0.40QQOE 01
D.5DDODE 01
0.60000E 01
0.70000E 01
Q.800QOE 01
0.90000E 01
0.10000E 02
D.15DDOE 02
0.20000E 02
D.3DDDDE 02
0.40000E 02
0.50000E 02 .
O.iOOODE 02
0.70000E 02
O.BOOOOE 02
0.90000E 02
0.10QDDE 03
B/ALFAz
= 0.35DE 02
Zeta-Va 1 ue
D.B6461E 00
0.82261E 00
0.7&389E 00
0.66333E 00
0.58555E 00
0.52576E 00
0.47901E 00
0.44165E 00
0.41113E 00
0.38573E 00
0.36423E 00
0.29192E 00
0.24976E 00
0.2215SE 00
O.Z01Q6E 00
D.1728AE 00
0.15416E 00
0.14087E 00
D.131D8E 00
0.12372E 00
0.1 181 4E 00
0.11388E 00
D.1D366E 00
Q.10096E 00
D.10007E 00
Q.IOOODE 00
D.10DDDE 00
D.10DQDE 00
Q.1QOOOE 00
Q.ioaaaE oo
D.10DDDE 00
Q.10000E 00
B/ALFAz
= 0.500E 02
Zeta-Va 1 ue
Q.91587E DO
0.86804E 00
D.B203SE 00
Q.732&5E 00
D.65925E 00
0.59961E 00
0.55116E 00
Q.51137E 00
0.47825E 00
D.45027E 00
0.42633E 00
0.34430E 00
0.295S8E 00
0.26269E 00
D.23665E 00
0.20532E 00
0.162B9E 00
Q.1&657E 00
D. 154 IDE 00
0.14428E 00
D.13MDE 00
D.13DDDE 00
0.11157E 00
0.10446E 00
D.1DD67E 00
D. IODIDE 00
0.10002E 00
0.1000DE 00
0.1QOOOE 00
0.100DOE 00
D.1DDDDE 00
D.1000DE 00
B/ALFAz
= 0.75DE 02
Zeta-Va 1 ue
0.9435BE 00
D.90987E 00
O.B7463E OD
0.80472E 00
0.74DBOE OD
0.6B509E DO
0.63743E 00
0.57676E 00
0.56172E 00
0.531B4E DD
0.50566E 00
0.41325E 00
0.35671E DD
0.3179^ OD
0.26946E 00
0.247&OE 00
0.22258E DD
0.2D275E DO
0.1B741E DO
0.17512E OD
0.1650 IE DD
0.15654E OD
D.12915E DD
0.11531E DD
D.1D425E DD
0.1011BE DO
0.1D033E DO
0.10007E DO
0.1DD03E 00
0.1DD01E DO
0.10DOOE DD
D.10DDDE DO
B/ALFAz
= D.1DDE 03
Zeta-Va 1 ue
0.95872E DD
D.93338E DD
D.9D611E DD
0.84945E DD
0.7944DE DD
0.7439DE DO
0.69BBBE DD
0.65922E OD
D.62438E DD
0.59371E DD
D.5666DE DO
0.4£618E DD
0.40£>24E DD
0.36321E OD
0.33125E DD
D.2Bf>29E DD
0.255&3E OD
D.23304E DD
0.21552E DD
0.2D143E DD
D.18979E DO
D.17996E OD
0.1471 IE DO
D.12871E DD
D.11088E DO
0.1D414E DD
D.10157E DD
D. IODIDE DO
0.1DD23E DD
D.1DDD9E DO
D.1DDD3E DD
D.1DDD1E DD
-------
TABLE 5: Dilution Factor(ZETA) versus X/B for Penetration Ratio(H/B) = D.15DE 00
X/B-Value
D.1DQDDE 00
0.15000E 00 .
0.200QOE 00
0.30000E 00
0.40000E 00
0.500DDE 00
0.60000E 00
0.70000E 00
D.8DDDDE 00
0.90000E 00
0.10000E 01
04 i™ rtrtnt* tt4
. 1500QE 01
0.20000E 01
0.2SODDE 01
D.300DDE 01
D.40DDDE 01
D.5DDDOE 01
O.&OOOOE 01
0.7000DE 01
D.800QQE 01
0.90000E 01
0.10DOOE 02
0.15000E 02
D.20000E 02
0.3000QE 02
0.40QQOE 02
D.5DDQQE 02
O.&OOOOE 02
0.700DOE 02
0.80DOOE 02
0.90000E 02
0.1DODOE 03
B/ALFAz
- 0.500E 01
Zeta-Va 1 ue
0.74390E 00
0.&3744E 00
0.55858E 00
0.44818E 00
0.37872E 00
0.33155E 00
0.27751E 00
0.27181E 00
0.25175E 00
0.23570E 00
0.22262E 00
04 ^y*9*w~ JIM
.1B327E 00
Q.1U5&1E 00
0.15743E 00
0.15352E 00
0.15079E 00
0.1501BE 00
0.1S004E 00
0.150D1E 00
0.15QDDE 00
0.150DDE 00
0.15000E 00
0.15000E 00
0.15000E 00
D.150DDE 00
0.15000E 00
D.150DDE 00
0.15DOOE 00
D.15DODE 00
0.15000E 00
0.15000E 00
D.15DDDE 00
B/ALFAz
= 0.10DE 02
Zeta-Va 1 ue
0.83871E 00
0.75900E 00
0.68868E 00
0.57857E 00
D.50062E 00
0.44397E 00
0.40125E 00
0.36794E 00
0.34122E 00
0.31728E 00
0.30D72E 00
0.24081E 00
0.20776E 00
0.18754E 00
Q.174&OE 00
0.160&5E 00
0.15461E 00
0.15199E 00
0.15D86E 00
0.15037E 00
0.15016E 00
0.15007E 00
0.1500DE 00
0.15000E 00
0.15000E 00
D.1500DE 00
0.15000E 00
0.15QOOE 00
0.15000E 00
0 . 15000E 00
D.15DDDE 00
0.1500DE 00
B/ALFAz
- 0.150E 02
Zeta-Va 1 ue
0.882&3E 00
0.81767E 00
0.76023E 00
0.65875E 00
0.58104E 00
0.52135E 00
0.47479E 00
0.43762E 00
0.40730E 00
Q.38208E 00
0.3&075E 00
0.28923E 00
0.2479SPE 00
D.22106E 00
0.20230E 00
0.17886E 00
D.1^06E 00
0.15895E 00
0.1549'9E 00
0.15278E 00
0.15155E 00
0.15086E 00
0.15005E 00
0.150DDE 00
0.15000E 00
0.15QOOE 00
0.15000E 00
0.15000E 00
0.15000E 00
0.15000E 00
0.15000E 00
0.15000E 00
B/ALFAz
= 0.25DE 02
Zeta-Va 1 ue
0.9255
-------
TABLE 6! Dilution Factor(ZETA) versus X/B for Penetration Ratio(HXB) = D.15DE 00
X/B-Value
0.1DDDOE 00
D.150DDE 00
0.20DDDE 00
0.30000E 00
0.40000E 00
0.50000E 00
O.&OOOOE 00
0.70000E 00
O.BOODDE 00
0.90000E 00
0.1QOOOE 01
D.150DOE 01
0.2DDDDE 01
0.25DODE 01
0.3DDDDE 01
0.40000E 01
0.50000E 01
O.&OOOOE 01
0.70000E 01
0.80DDDE 01
0.90000E 01
0.10QOOE 02
0.150DDE 02
D.2000DE 02
0.30000E 02
0.4QQODE 02
D.50DDDE 02
O.&OOOOE 02
0.70000E 02
0.80000E 02
0.90000E 02
0.10000E 03
B/ALFAz
= 0.350E 02
Zeta-Va 1 ue
O.^A^SE 00
0.91499E 00
0.88137E 00
0.814D3E 00
0.75171E 00
0.&9686E 00
0.64956E 00
Q.&Q898E 00
0.57404E 00
0.54378E 00
0.51736E 00
0.423&3E 00
0.3&599E 00
0.32641E 00
O.Z9724E 00
0.2S&&OE 00
O.Z2940E 00
O.Z0998E 00
0.19563E 00
0.16464E 00
0.17665E 00
Q.17040E 00
0.15537E 00
Q.15141E 00
0.15010E 00
0.15QD1E 00
D.150QOE 00
0.150DOE 00
0.150DOE 00
D.I 50 DDE 00
0.15000E 00
0.15000E 00
B/ALFAz
= 0.500E 02
Zeta-Value
0.96427E 00
0.94208E 00
0.91793E 00
Q.8&A80E oo
0.81587E 00
0.7&812E 00
D.72475E 00
0.68598E 00
0.6S152E 00
Q.62090E 00
0.593&2E 00
0.49320E 00
0.42906E 00
0.3841 BE 00
0.35070E 00
0.30344E 00
0.27118E 00
0.24751E 00
0.22934E 00
0.21478E 00
0.20344E 00
0.19405E 00
0.1&699E 00
0.15658E 00
0.15099E 00
0.15015E 00
0.15D02E 00
0.15DDOE 00
0.15000E 00
0.15000E 00
0.1500DE 00
0.15000E 00
B/ALFAz
= 0.750E 02
Zeta-Value
0.97B41E 00
0.764A1E 00
D.?4«71AE 00
0.91465E 00
0.87762E 00
0.84034E 00
0.60434E DO
0.77044E 00
0.73897E 00
0.71000E 00
0.68344E 00
0.58005E 00
0.51004E 00
0.45756E 00
0.42122E 00
0.3&624E 00
0.32B15E 00
0.29984E 00
0.27776E 00
0.25977E 00
0.24527E 00
0.23292E 00
0.17281E 00
0.17247E 00
0.15&25E 00
0.15173E 00
0.15048E 00
0.15013E 00
0.15004E 00
D.15001E 00
0.15000E 00
Q.150DOE 00
B/ALFAz
= 0.100E 03
Zeta-Value
0.98548E 00
0.97&07E 00
0.96534E 00
0.94062E 00
0.91283E 00
0.88352E 00
O.B5394E 00
0.82498E 00
0.7971SE 00
0.77085E 00
0.7461DE 00
0.&44S7E 00
0.57258E 00
0.51894E 00
0.47749E 00
0.41713E 00
0.37479E 00
0.34306E 00
0.31817E 00
0.29800E 00
0.2812ZE 00
0.2670 IE 00
0.21914E 00
0.19217E 00
0.16599E 00
0.15608E 00
0.15231E 00
0.15088E 00
0.15033E 00
0.15013E 00
0.15005E 00
0.15002E 00
-------
TABLE 7: Dilution Factor(ZETA) versus X/B for Penetration Ratio(H/B> = D.250E DO
*..,
X/B-Value
D.10QDDE 00
D.150DDE 00
D.2DODDE 00
0.30000E 00
0.40DDDE 00
0.50DOOE 00
0.60DDDE 00
D.7000DE 00
D.80DDOE DO
0.90000E 00
a.lDOODE 01
0.15000E 01
O.ZOODDE 01
0.25000E 01
0.30DDDE 01
0.40000E 01
O.SOODOE 01
0.60000E 01
0.70000E 01
0.80DODE 01
0.90000E 01
0.100DDE 02
0.15000E 02
0.20000E 02
0.3DDODE 02
0.40000E 02
0.50DODE 02
0.6000DE 02
D.70000E 02
D.8DDDOE 02
0.9DOODE 02
D.1DDODE 03
B/ALFAz
= 0.5QDE 01
Zeta-Va 1 ue
0;8796&E 00
0.61504E 00
0.75437E 00
0.65200E 00
0.57416E 00
0.51514E 00
0.46956E 00
D.43362E 00
0.40473E 00
0.38114E 00
0.36162E 00
0.301&5E 00
0.27441E 00
0.26156E DO
0.25548E 00
0.25123E 00
0.25027E 00
0.250D6E 00
0.25DD1E 00
Q.25000E 00
D.250DDE 00
0.2500DE 00
D.250DDE DO
O.Z500DE 00
0.25000E 00
0.2500DE 00
0.2500DE 00
0.2SODDE DO
O.ZSOOOE DD
O.Z500DE 00
O.ZSOOOE 00
0.250DDE OD
B/ALFAz
= 0.100E 02
Zeta-Va 1 ue
0.93491E 00
0.89635E 00
O.B5656E 00
0.77971E 00
0.71168E 00
0.65400E 00
0.60567E 00
0.56511E 00
0.53080E 00
0.50150E 00
0.4762SE 00
0.38939E 00
0.33943E 00
D.30B33E DD
D.28828E 00
0.2665BE 00
0.25718E DD
0.25311E DO
D.25134E DD
0.25058E DO
D.25D25E OD
0.2501 IE DO
0.2500DE DO
0.2500DE OD
0.25000E OD
0.250DOE DO
D.25DDDE DO
0.25000E DO
D.25DDOE DD
D.25DDDE OD
D.250DDE DD
D.25DDDE DO
B/ALFAz
= D.150E 02
Zeta-Va 1 ue
D.75723E DD
0.9308BE DD
0.70257E 00
0.8440 IE DO
D.78754E DO
0.73612E DD
D.69056E DD
0.&5063E 00
D.61570E DD
0.585D6E 00
0.55804E DO
0.4A070E DO
0.4DD47E DO
D.35988E DO
0.33115E DD
D.294?1E DD
D.27501E OD
0.2&374E DO
0.25777E DO
0.25433E OD
0.2524 IE DO
D.25134E 00
D.25DD7E DD
0.25000E 00
D.25DDDE OD
0.250DOE OD
D.250DOE 00
0.25000E 00
0.25000E 00
0.25DDOE 00
D.25DDDE DO
0.25000E DD
B/ALFAz
= D.25DE 02
Zeta-Va 1 ue
0.97666E DD
D.?617AE OD
0.9451 IE OD
D.9D815E 00
D.86867E OD
0.8298DE DD
D.79242E DO
D.75751E OD
0.72535E OD
0.67593E DD
D.6fe?07E DD
0.56567E DD
0.4%47E DD
0.447D2E DD
0.4D987E DD
D.35796E DD
D. 3241 IE OD
0.3D121E DD
D.28547E DD
0.27459E OD
D.267D5E OD
D.26183E DO
0.251B9E OD
0.25D3DE DO
D.25DD1E DD
0.25DDOE DO
0.25DDOE DD
D.25000E DO
D.250DOE 00
0.25000E DD
D.250DOE 00
0.25000E DO
-------
TABLE 8» Dilution Factor(ZETA) versus X/B for Penetration Ratio(H/B> = D.25DE DO
X/B-Value
0.10DDOE 00
0.15000E 00
0.20000E 00
0.30000E 00
0.40000E 00
0.50000E 00
0.60000E 00
0.70000E 00
0.60000E 00
0.70000E 00
0.10000E 01
0.15000E 01
0.20000E 01
D.250DOE 01
0.30000E 01
0.4000QE 01
0.50QODE 01
0.60000E 01
0.70QDOE 01
0.60000E 01
0.90000E 01
0.10000E 02
0.15000E 02
0.20000E 02
0.300DOE 02
0.40000E 02
0.50000E 02
0.60000E 02
0.70000E 02
0.80000E 02
0.70000E 02
0.10000E 03
B/ALFAz
- 0.350E 02
Zeta-Va 1 ue
D.9851GE 00
0.97555E 00
0.76457E 00
0.93930E 00
0.71093E 00
0.88107E 00
O.B5105E 00
Q.82171E 00
0.79362E 00
0.76705E 00
0.74213E 00
0.&4054E 00
0.56B30E 00
D.51482E 00
0.47360E 00
0.41378E 00
0:37270E 00
D.34313E 00
0.32076E 00
0.30422E 00
0.27149E 00
0.2817AE 00
0.25837E 00
0.25220E 00
0.25015E 00
0.25001E 00
0.250QDE 00
Q.25000E 00
0.25000E 00
0.25000E 00
0.25000E 00
0.25000E 00
B/ALFAz
= 0.500E 02
Zeta-Va 1 ue
0.99134E 00
0.98564E 00
0.97903E 00
0.%329E 00
0.94474E 00
0.9241&E 00
0.90234E 00
0.87998E 00
0.85762E 00
0.835&4E 00
0.81431E 00
0.7207DE 00
0.&4871E 00
0.59314E 00
0.54B8BE 00
0.48275E 00
0.43591E 00
0.40047E 00
0.37287E 00
0.35087E 00
D.33306E 00
0.31853E 00
0.27646E 00
Q.26025E 00
0.25154E 00
0.25023E 00
0.25003E 00
0.25001E 00
0.250QOE 00
0.25000E 00
0.25000E 00
0.25000E 00
B/ALFAz
= 0.750E 02
Zeta-Va 1 ue
0.97568E 00
0.77279E 00
0.98940E 00
0.7810SE 00
0.77081E 00
0.75681E 00
0.?4539E 00
D.73088E 00
0.71564E 00
0;89775E 00
0.88408E 00
0.80745E 00
0.74135E 00
Q.68654E 00
0.&4110E 00
0.570A2E 00
0.51848E 00
0.47815E 00
0.44588E 00
0.41940E 00
0.37724E 00
0.37845E 00
0.31661E 00
0.28503E 00
0.25773E 00
0.25270E 00
0.25075E 00
0.25021E 00
0.25006E 00
0.250Q2E 00
0.25000E 00
0.25000E 00
B/ALFAz
= 0.100E 03
Zeta-Va 1 ue
0.79752E 00
0.79586E 00
0.79388E 00
0.78895E 00
0.78270E 00
0.97515E 00
0.%642E 00
0.95667E 00
0.74606E 00
0.93478E 00
0.72301E 00
O.a&l&SE 00
0.80352E 00
0.75232E 00
0.7D812E 00
0.63693E 00
0.58252E 00
0.53957E 00
0.50468E 00
0.47568E 00
0.45113E 00
0.43004E 00
0.35734E 00
0.315&3E 00
0.27490E 00
0.25947E 00
0.25360E 00
O.Z5137E 00
0.25052E 00
0.25020E 00
0.250D8E 00
0.25003E 00
-------
TABLE 9« Dilution Factor(ZETA) versus X/B for Penetration Ratio(HXB) = D.375E DO
X/B-Value
D.1DDDOE 00
D.150DDE 00
0.200DDE 00
0.3000DE 00
D.40DDOE 00
0.50000E 00
0.60000E 00
0.70000E DO
0.80000E 00
0.90000E 00
D.10DDDE 01
0.1SOOOE 01
0.20000E 01
0.25000E 01
0.30000E 01
0.40000E 01
Q.500DOE 01
0.60000E 01
0.70000E 01
0.60QOOE 01
0.7QQOOE 01
0.10DOOE 02
0.15000E 02
0.20000E 02
Q.30000E 02
0.40000E 02
0.50000E 02
O.&OOOOE 02
0.70000E 02
0.800DOE 02
0.90000E 02
0.1 DO DDE 03
B/ALFAz
= 0.500E 01
Zeta-Va 1 ue
0.94506E 00
0.91164E 00
0.8765QE 00
0.60670E 00
0.74306E 00
O.A8801E 00
0.64139E 00
0.60214E 00
0.5691QE 00
0.54119E 00
0.51753E 00
0.44209E 00
0.40685E 00
0.39012E 00
0.3B217E 00
0.376&QE 00
0.37536E 00
0.37508E 00
0.37502E 00
0.37500E 00
0.37500E 00
0.3750DE 00
0.37500E 00
0.37500E 00
0.37500E 00
0.37500E 00
0.37500E 00
0.37500E OD
0.3750DE 00
0.3750DE 00
0.37500E 00
0.3750DE 00
B/ALFAz
= 0.100E 02
Zeta-Va 1 ue
0.97443E 00
0.95806E 00
0.939B3E 00
0.899&6E 00
0.85756E 00
0.81623E 00
0.77725E 00
0.74132E 00
0.7Q860E 00
0.&79DDE 00
0.65228E 00
0.55258E 00
Q.47Q64E 00
0.45087E 00
0.42493E DO
0.39&65E 00
0.38438E 00
0.37906E 00
0.37&75E 00
0.37576E 00
0.37533E 00
0.37514E 00
0.3750DE 00
0.3750DE 00
0.3750DE 00
0.37500E 00
0.3750DE 00
0.37500E 00
0.3750DE 00
0.37500E 00
0.375DDE 00
0.375DDE 00
B/ALFAz
= 0.150E 02
Zeta-Va 1 ue
0.98494E 00
0.9751 IE 00
0.96390E 00
0.93804E 00
0.90906E 00
D.67663E 00
0.84810E 00
0.81836E 00
D.78997E 00
0.76320E 00
0.73816E 00
0.63705E 00
0.56679E 00
0.51674E 00
0.46033E 00
0.43357E 00
0.40766E 00
0.39321E 00
0.3B515E 00
0.3S065E 00
0.37B15E 00
0.37&75E 00
0.37509E 00
D.37500E 00
0.37500E 00
0.37500E 00
0.37500E 00
0.37500E 00
0.3750DE 00
0.37500E 00
0.3750DE 00
0.37500E OD
B/ALFAz
= 0.25DE D2
Zeta- Value
D.99306E DO
0.98645E DO
0.98307E DO
0.9701 IE OD
0.95455E DO
0.93696E DD
0.91797E DO
0.89816E DD
D.878D3E 00
0.85796E DO
0.83823E DD
0.74929E DO
0.67862E OD
D.62315E OD
0.579D9E DD
0.51473E DD
0.47145E DD
0.4418DE DO
0.42131E DD
D.40712E DD
D.39728E DD
0.39D45E DD
D.37747E OD
D.3754DE DO
D.37501E DD
D.375DDE DD
D.3750DE DD
D.375DDE DO
D.375DDE DD
0.375DDE DO
D.375DDE DD
D.3750DE DD
-------
TABLE IDs Dilution Factor(ZETA) versus X/B for Penetration Ratio(H/B) = D.375E DO
X/B-Value
D.1QDODE 00
0.15000E 00
D.20DQDE 00
D.3000DE 00
0.40000E 00
0.50DODE 00
0.60000E 00
D.70QODE 00
0.8QOOOE 00
0.9000DE 00
D.1DDODE 01
0.15000E 01
O.ZOOOOE 01
0.2500QE 01
0.30000E 01
0.4000QE 01
D.50DOOE 01
O.&OOQOE 01
0.70000E 01
0.80000E 01
0.90000E 01
0.10000E 02
0.1500DE 02
0.20DODE 02
0.3DDDDE 02
0.40000E 02
0.50000E 02
0.6000DE 02
0.70000E 02
0.80000E 02
0.900DOE 02
0.10DOOE 03
B/ALFAz
= 0.350E 02
Zeta-Va 1 ue
0.99615E 00
0.99357E 00
0.99053E 00
0.98302E 00
0.97368E 00
0.96269E 00
0.95029E 00
0.93679E 00
0.92251E DO
0.90771E 00
0.89263E 00
0.81879E oo
0.75396E 00
0.69971E 00
0.65452E 00
0.58459E 00
0.53379E 00
0.49598E 00
0.46744E 00
0.44573E 00
0.42916E 00
0.41M8E 00
0.38593E 00
0.3778BE 00
0.37520E 00
0.37501E 00
0.37500E 00
0.37500E 00
0.37500E 00
0.37500E 00
0.37500E 00
0.37500E 00
B/ALFAz
= 0.500E 02
Zeta-Va 1 ue
0.99810E 00
0.99682E 00
0.99529E 00
0.99145E 00
0.(76£>52E 00
0.98049E 00
0.97342E 00
D.96540E 00
D.95655E 00
0.94701E 00
0.93672E 00
0.88243E 00
0.62852E 00
0.77%2E 00
0.73fc58E 00
O.^b^DZE 00
0.61149E 00
Q.56646E 00
D.53400E 00
Q.50&02E 00
Q.4B314E 00
D.4M35E 00
0.40757E 00
0.38839E 00
Q.37701E 00
Q.37530E 00
D.37504E 00
0.37501E 00
D.37500E 00
0.37500E 00
Q.3750DE 00
0.37500E 00
B/ALFAz
= 0.750E 02
Zeta-Va 1 ue
0.97725E 00
0.97873E 00
0.99812E DO
0.9%S5E 00
D.99446E 00
0.99183E 00
0.986&2E 00
0.98483E 00
0.7B046E 00
0.97555E 00
0.97013E 00
0.93726E 00
0.89939E 00
0.861QBE 00
0.82459E 00
0 . 75990E 00
0.7Q&14E 00
0.6&143E DO
0.62389E 00
0.59203E 00
0.56474E 00
0.54120E 00
0.46186E 00
0.42075E 00
0.38771E 00
0.37853E 00
0.37598E 00
0.37527E DO
0.37508E DO
0.37502E OD
0.37501E DO
0.3750DE DD
B/ALFAz
= 0.10DE 03
Zeta-Value
0.99964E 00
0.99940E DD
0.9991 IE 00
0.99835E OD
D.99733E DD
D.99601E DO
0.99437E OD
0.99238E OD
D.99DD2E DO
0.9873DE DD
D.98421E DO
D.93B5E DD
0.93755E DD
0.9D846E DD
D.87882E DD
0.82245E DD
D.77253E OD
D.72922E DD
0.69171E DD
D.A59D5E 00
0.&3043E 00
D.60519E DD
D.51446E DO
0.460&3E OD
D.40753E DD
D.38737E DD
D.3797DE DO
0.37679E DD
D.37568E DD
D.37526E OD
D.3751DE DD
D.375D4E DD
-------
TABLE 11» Dilution Factor(ZETA) versus X/B for Penetration Ratio(HXB) = D.50DE DO
X/B-Value
D.1DDDDE 00
0.150DDE 00
D.20QDOE 00
0.3QOOOE 00
0.400DOE 00
0.50000E 00
0.60000E 00
0.7DDOOE 00
O.BOOOOE 00
0.90000E 00 .
0.10000E 01
G.15000E 01
O.ZQOQOE 01
0.25000E 01
0.3DDODE 01
0.4QOOOE 01
0.5000QE 01
0.60000E 01
0.70000E 01
0.800DDE 01
0.90000E 01
0.1QOOOE 02
0.15000E 02
0.20000E 02
0.30DDDE 02
0.400DOE 02
0.50000E 02
0.60000E 02
0.7000DE 02
D.8DDDOE 02
0.900DOE 02
0.1 ODD DE 03
B/ALFAz
= 0.500E 01
Zeta-Va 1 ue
0.9723ZE 00
0.95455E 00
0.9348DE 00
Q.89178E 00
0.84760E 00
0.80526E DO
0.7&636E 00
0.73150E 00
0.70071E 00
0.67374E 00
0.65025E 00
0.57213E 00
0.53441E 00
Q.51&36E 00 :
0.50775E 00
0.50173E 00
0.50D39E 00
0.50009E 00
0.50002E 00
D.5000DE 00
0.5QQDOE 00
0.50000E 00
0.5000DE 00
0.50000E 00
0.50000E 00
D.5000DE 00
O.BOOOOE 00
0.5000DE 00
0.50000E 00
0.5000DE 00
0.50000E 00
0.5000DE 00
B/ALFAz
= 0.100E 02
Zeta-Va 1 ue
0.9B872E 00
0.9B12AE 00
0.972&4E 00
0.95237E 00
0.92699E 00
0.90374E 00
0.87772E 00
0.85181E 00
O.B2661E oo
0.80250E 00
0.77970E 00
0.^a^>7E 00
0.^23ME 00
0.58171E 00
0.55373E 00
0.52343E 00
0.51015E 00
0.50439E 00
0.50170E 00
0.50082E 00
Q.50035E 00
Q.50015E 00
0.5000DE 00
0.50QOOE 00
0.50000E 00
0.50QOOE 00
0.50000E 00
0.50000E 00
0.5000DE 00
0.5000DE 00
O.BOOOOE 00
0.500DQE 00
B/ALFAz
= 0.150E 02
Zeta-Va 1 ue
0.79400E 00
0.78979E 00
0.78528E 00
0.97385E 00
O.TST'raE 00
0.94412E 00
0.72681E 00
0.70859E 00
0.86770E 00
O.B7114E 00
0.85258E 00
0.76824E 00
0.70167E 00
0.^5114E 00
0.&1313E 00
0.56326E 00
0.53533E 00
0.51971E 00
0.51078E 00
0.50&12E 00
0.50341E 00
0.50170E 00
0.500 IDE 00
0.50001E 00
O.BOOOOE 00
0.50000E 00
O.BOOOOE 00
0.50000E 00
0.500QOE 00
O.BOOOOE 00
0.50000E 00
O.BOOOOE OD
B/ALFAz
= 0.25DE 02
Zeta-Value
0.99765E 00
0.99606E 00
0.99417E 00
0.98944E 00
0.9B340E 00
0.97608E 00
0.96759E DO
0.95807E 00
0.94769E 00
0.93664E 00
0.92508E 00
0.864ME 00
0.80741E 00
0.75741E 00
0.71499E OD
0.64956E OD
0.60392E OD
0.57216E DO
D.55DD9E 00
0.53476E DD
D. 5241 IE DO
0.51&72E OD
D.50268E 00
0.50D43E OD
O.B0001E OD
0.5DODOE OD
D.5DDDDE DD
0.50DDOE 00
D.5DDODE DD
O.SDDDDE OD
D.5DDDDE DD
D.5DDDDE DO
-------
TABLE 12« Dilution Factor(ZETA) versus X/B for Penetration Ratio(H/B) = D.500E DO
X/B-Value.
0.1000DE DO
D.15DDDE DO
0.2DDDOE DO
D.3DDDDE DO
D.400DDE 00
D.5DDDDE DO
O.&OOOQE 00
0.700DDE 00
O.BOOOOE 00
0.70DOOE 00
0.10DDDE 01
0.15000E 01
0.20DDOE 01
O.Z5000E 01
0.30DDOE 01
0.4DDDDE 01
0.50000E 01
0.60000E 01
0.70000E 01
O.BOOOOE 01
0.9000DE 01
0.10000E 02
0.15000E 02
0.20000E 02
0.300QOE 02
0.40000E 02
0.50000E 02
0.6000DE 02
0.70000E 02
0.80QOOE 02
0.90000E 02
0.1 ODD OE 03
B/ALFAz
= 0.350E 02
Zeta-Va 1 ue
a.9988&E 00
0.99808E DO
0.99715E DD
0.99478E OD
0.99168E 00
0.987B1E 00
0.983UE 00
0.97776E DO
0.97165E 00
0.96490E OD
0.95759E 00
0.91548E 00
0.8702BE 00
0.8269&E 00
0.7B74AE OD
0.72107E OD
Q.667ME 00
0.&3009E 00
0.59973E 00
0.57644E OD
0.55857E OD
0.54488E 00
0.51183E DO
0.5031 IE OD
0.50022E 00
0.50001E 00
0.50DOOE 00
0.5DOOOE DO
0.5DDOOE DD
0.50000E 00
0.50000E 00
0.5DOOOE DO
B/ALFAz
= 0.50DE D2
Zeta-Va 1 ue
Q.99952E OD
0.99920E 00
0.99BBOE 00
0.99779E 00
0.99643E DD
0.79469E 00
Q.99253E DO
0.78994E 00
0.78690E 00
0.78343E DO
0.77953E DO
0.954A4E DO
O.^SB'JE OD
0.891 IDE DO
0.85B&5E OD
0.77895E OD
0.74BD3E 00
D.70547E 00
D.67012E DO
0.64DB2E 00
0.61655E 00
0.59646E 00
D.53741E DD
D.51450E 00
0.50217E 00
0.50033E 00
0.5DD05E 00
0.5000 IE DO
0.5QOOOE 00
0.50000E 00
0.5000DE DO
0.50000E DO
B/ALFAz
= 0.75DE 02
Zeta-Va 1 ue
0.99785E DO
0.79975E 00
0.997A2E DO
0.9*792<7IE 00
0.99884E OD
D.99825E 00
0.99750E DO
0.79657E 00
0.99545E 00
0.9941 IE 00
0.99255E OD
D.98139E 00
0.9&517E 00
0.94536E 00
0.92354E OD
D.87837E DO
0.83517E OD
0.79581E 00
0.7606AE 00
0.72953E 00
0.70205E 00
0.^7784E 00
0.59386E 00
0.54950E 00
D.5137&E 00
0.503B2E DO
0.50106E 00
D.5D029E OD
0.50D08E 00
D.50D02E 00
0.5000 IE 00
0.50000E 00
B/ALFAz
= 0.1DDE D3
Zeta-Va lue
D.99974E 00
0.9999DE 00
0.99985E 00
0.99972E 00
0.99954E 00
0.99930E 00
0.99899E DO
0.99860E 00
0.99811E 00
0.99752E 00
0.99682E 00
0.9914DE 00
0.98255E DO
0.97058E 00
D.95621E 00
0.92337E 00
0.8888 IE 00
0.85512E 00
0.82344E 00
0.79415E 00
0.76732E 00
0.74283E 00
0.&4994E 00
0.59252E 00
0.5352DE 00
0.51339E 00
0.50509E 00
D.50193E 00
0.50073E OD
0.50028E 00
0.5001 IE OD
0.50004E 00
-------
TABLE 13'- Dilution Factor(ZETA) versus X/B for Penetration Ratio(H/B) = 0.60DE DO
X/B-Value
Q.1DDQDE 00
0.15000E 00
0.2000DE 00
0.30QOOE 00
0.40000E 00
0.5000QE 00
a.6aOOOE 00
Q.7000DE 00
0.6QOOOE 00
0.90000E 00
D.1QDDOE 01
0.15000E 01
0.20000E 01
0.25000E 01
0.30000E 01
Q.40000E 01
0.50000E 01
0.6000QE 01
0.70000E 01
0.8QOOOE 01
0.90000E 01
0.10000E 02
0.15QOOE 02
0.2DDDOE 02
0.3000DE 02
0.40000E 02
0.50000E 02
0.60000E 02
0.70000E 02
0.60000E 02
0.90000E 02
0.10QOQE 03
B/ALFAz
= 0.500E 01
Zeta-Value
0.9B345E 00
D.972S6E 00
0.76015E 00
0.93186E 00
0.90089E 00
O.B6938E 00
O.B3B6BE 00
O.B1035E 00
0.78428E 00
0.7A082E 00
0.73996E 00
0.&6823E 00
0.&326BE 00
0.&1555E 00
0.&0737E 00
0.&Q1&5E 00
0.&0037E 00
0.&0008E 00
0.60002E 00
0.6000QE 00
0.60000E 00
O.&OOOOE 00
Q.&OaOQE 00
0.6000DE 00
O.feOODDE 00
O.&OOODE 00
O.&OODOE 00
0.60000E 00
O.feOOOOE 00
O.&OOOOE 00
O.&OQOOE 00
D.^OQODE 00
B/ALFAz
= 0.100E 02
Zeta-Va 1 ue
Q.99387E 00
0.78776E 00
Q.98493E 00
0.97321E 00
D.95703E 00
D.94290E 00
D.92542E 00
0.9071&E 00
D.86861E 00
Q.B7016E 00
O.B5217E 00
Q.77347E 00
Q.71644E 00
0.67737E 00
0.65120E 00
0.62228E 00
0.6Q766E 00
0.60418E 00
0.&01B1E 00
a.60078E 00
0.6D034E 00
Q.6QQ14E 00
D.6DDDDE 00
0.60000E 00
D.60DDDE 00
0.60000E 00
0.60000E 00
0.60000E 00
D.6DDDDE 00
D.60DDDE 00
D.feDDODE 00
D.6DDOOE 00
B/ALFAz
= 0.150E 02
Zeta-Value
0.79&9BE 00
0.99494E 00
0.99252E 00
0.9B&48E 00
0.978B7E 00
0.9&977E 00
D.95937E 00
0.94792E 00
0.93565E 00
0.92281E 00
0.90963E 00
0.64427E 00
0.7B746E 00
0.74203E 00
0.70692E 00
0.^>006E 00
0.63356E 00
0.&1874E 00
D.61D44E 00
0.60582E 00
0.6D324E 00
0.&0180E 00
D.60D1DE 00
D. 6000 IE 00
0.60000E 00
0.60000E 00
O.&OOOOE 00
0.6QOOQE 00
0.60000E 00
Q.&OOOOE 00
D.60DOOE 00
0.600DOE 00
B/ALFAz
= 0.250E 02
Zeta-Va 1 ue
0.99896E 00
0.99825E 00
0.99739E 00
0.99522E 00
0.99236E 00
0.98877E 00
0.98445E 00
0.9794 IE 00
0.97369E 00
0.96735E 00
0.96046E 00
0.92054E 00
0.87756E 00
0.836&8E 00
0.80005E 00
0.74096E 00
0.&9B46E 00
0.6^853E 00
0.64761E DO
0.63305E 00
0.62293E 00
0.&159QE 00
0.60255E 00
0.6004 IE 00
0.6000 IE 00
0.60000E 00
0.60000E DO
0.60000E 00
0.60000E 00
0.60000E 00
0.60000E DO
D.6DODDE DO
-------
TABLE 14: Dilution Factor(ZETA) versus X/B for Penetration Ratio(H/B) = D.6QOE DO
X/B-Va 1 ue
D.1DDDDE 00
D4 fnnrv fin
. 1 DODGE DO
O.ZODOOE 00
D.30DOOE 00
0.40000E 00
0.500QOE 00
0.60000E 00
0.70DDOE 00
D.60DDDE 00
0.9000DE 00
0.1DDDDE 01
0.1500DE 01
0.20DDDE Gl
0.250QOE 01
0.3DDDDE 01
0.40000E 01
D.5DDODE 01
0.60000E 01
0.70000E 01
D.8DOODE 01
0.90DOOE 01
D.10DDDE 02
0.15000E O2
D.20DDOE 02
D.3DDOOE 02
0.40000E O2
0.50000E 02
0.60000E 02
0.70000E 02
D.8QOODE O2
0.90000E 02
0.1000DE 03
B/ALFAz
= 0.350E 02
Zeta-Va 1 ue
0.99954E 00
OC^Dcy^^ff* nn
.Trr/2ot 00
0.99885E 00
0.99787E 00
0.99657E 00
0.99489E 00
0.99280E 00
0.99029E 00
0.98735E 00
0.98397E 00
0.98018E 00
0.95569E 00
0.92585E 00
0.89389E 00
D.86250E 00
0.80592E 00
0.75963E 00
Q.723D6E 00
0.69457E 00
0.67259E 00
0.&5567E 00
0.642&7E 00
0.61125E 00
D.^0296E 00
0.60020E 00
0.60001E 00
O.^OOOOE 00
0.60000E 00
D.6DDODE 00
0.6QOOOE 00
D.6QDODE 00
0.6DDQOE 00
B/ALFAz
= 0.500E 02
Zeta-Va 1 ue
0.979B3E 00
Q.99772E 00
0^ j^ji j^itjfT nn
. ViT/ujat uu
0.99721E 00
0.99871E 00
0.99806E 00
0.99723E DO
0.99620E 00
0.99495E 00
0.99348E 00
0.99177E 00
0.979&5E 00
0.96229E 00
0.74140E 00
0.91872E 00
0.87267E 00
0.82996E 00
0.79242E 00
0.76027E 00
0.73317E 00
0.71047E 00
0.&9155E 00
Q.&3556E 00
D.61377E 00
0.6Q207E 00
0.&0031E 00
0.6Q005E 00
D.600D1E 00
O.^ODDOE 00
0.&aOQOE 00
0.60DOOE 00
D.60DDDE 00
B/ALFAr
= 0.750E 02
Zeta-Va 1 ue
0.97996E 00
0.99992E 00
0.99989E 00
0.99977E 00
0.97965E 00
0.97947E 00
0.99723E 00
0.97893E 00
0.99856E 00
0.99810E 00
0.99755E 00
0.99322E 00
0.78572E 00
0.97575E 00
0.96325E 00
0.73386E 00
0.90216E 00
0.87088E 00
O.B4136E 00
0.81422E 00
0.78963E 00
0.7&756E 00
0.68912E 00
0.64707E 00
0.61308E 00
0.603A3E 00
0.601 DIE 00
0.60028E 00
0.&OOD8E 00
Q.&OQ02E 00
0.6000 IE 00
0.60000E 00
B/ALFAz
= 0.100E 03
Zeta-Va 1 ue
0.99997E 00
0.79997E 00
0.99796E 00
0.77993E 00
0.77988E 00
0.97782E 00
0.97974E 00
0.97963E 00
0.99949E 00
0.79932E 00
0.99911E 00
0.99736E 00
0.97406E 00
0.98896E 00
0.98207E DO
0.9^383E OD
D.94168E 00
0.91777E 00
0.89355E 00
0.86992E 00
0.84737E 00
0.82617E 00
0.74184E 00
0.68787E 00
D.fc3348E 00
0.61273E 00
0.60484E 00
0.&0184E 00
0.60070E 00
0.60027E 00
0.60010E 00
0.60004E 00
-------
TABLE 15= Dilution Factor(ZETA) versus X/B for Penetration Ratio(H/B) = D.BDQE DD
X/B-Value
0.1DDDOE 00
0.150DOE 00
0.20000E 00
0.30000E 00
0.40DQDE DO
0.50000E 00
O.&OOOOE 00
0.700DOE 00
O.BOOOOE 00
0.90000E 00
0.100DOE 01
0.1500DE 01
D.2DDODE 01
D.2500DE 01
0.3QOOOE 01 .
0.4QOOOE 01
0.50000E 01
0.60000E 01
0.700QOE 01
O.BOOOOE 01
0.90000E 01
0.100QOE 02
0.150QOE 02
0.20000E 02
0.30QOQE 02
Q.400QOE 02
0.50000E 02
0.6000DE 02
D.7DODOE 02
0.8QDDDE 02
0.900QOE 02
0.1DDDDE 03
B/ALFAz
» 0.500E 01
Zeta-Va 1 ue
0.99440E 00
0.990&3E 00
0.98621E 00
0.97562E 00
0.9&31&E 00
0.94951E 00
0.93537E 00
0.92135E 00
0.9078BE 00
0.89528E 00
0.8B371E 00
O.B41BOE 00
O.B2015E 00
O.B0961E 00
O.B0456E 00
O.B0102E 00
O.B0023E 00
0.8QDD5E 00
D. 6000 IE 00
O.BOOOOE 00
O.BOOOOE 00
O.BOOQOE 00
O.BOOOOE 00
O.BOODOE 00
O.BOOQOE 00
O.BOOOOE 00
D.80000E 00
0.800 DOE 00
O.BOOOOE 00
O.BOOODE 00
0.80000E 00
0.80000E 00
B/ALFAz
= 0.100E 02
Zeta-Va lue
0.99BZ2E 00
Q.99701E 00
0.99556E 00
0.99191E 00
0.98726E 00
0.98164E 00
0.97515E 00
0.9&795E 00
0.96020E 00
0.952QBE 00
0.94375E DO
0.90336E 00
O.B7DB4E 00
O.B4751E 00
O.B3155E 00
0.8137AE 00
D.80597E 00
D.B025BE 00
0.80112E 00
0.80046E 00
O.B0021E DO
O.BQOD7E 00
O.BOQOOE 00
0.80DDOE 00
D.BODDOE 00
0.8QODOE 00
D.8QDDDE 00
0.8QDOOE 00
0.8DOOOE 00
O.BODDOE 00
D.BOOOOE 00
0.8DODDE 00
B/ALFAz
-= 0.150E 02
Zeta-Va lue
0.99923E 00
0.99B7DE 00
0.99807E 00
0.79644E 00
0.99427E 00
0.99159E 00
0.9BB34E 00
0.98453E 00
0.9B022E 00
0.9754&E 00
0.97031E 00
0.94115E 00
0.91170E 00
O.BB609E 00
0.86541E 00
0.83702E 00
O.B2074E 00
0.81158E 00
0.80645E 00
0.803AOE 00
0.80200E 00
O.B0111E 00
0.80006E 00
O.BOOOOE 00
O.BOOQOE 00
Q.800QOE 00
0.80000E OQ
0.80000E QQ
Q.BQOQQE 00
Q.BQQQQE 00
0.80000E 00
0.80000E 00
B/ALFAz
= Q.250E Q2
Zeta-Va lue
D.99979E 00
0.99964E 00
0.99946E 00
Q.99B99E QQ
0.99836E OQ
0.99754E QQ
Q.99650E 00
0.99522E 00
0.99370E QQ
Q.99193E 00
Q.989B9E 00
0.9762QE OQ
Q.95B25E 00
0.938&4E QQ
0.9193BE 00
Q.BB53&E 00
O.B6Q49E QQ
Q.B4225E OQ
Q.B2939E OQ
0.82042E 00
Q.81417E OQ
Q.8Q983E QQ
Q.80157E 00
0.8QQ25E QQ
Q.8QQQ1E DO
0.80QQOE 00
Q.80QQQE DO
Q.800QOE 00
D.8DDDDE 00
D.8DDDDE 00
D.8DDDDE 00
Q.8QQQQE 00
-------
TABLE
Dilution Factor(ZETA) versus X/B for Penetration Ratio(H/B) = D.BDDE DD
X/B-Value
0.10DDDE 00
0.15DODE 00
0.2DDDDE 00
0.3QQDDE 00
D.40DDDE 00
0.50DDOE 00
0.6000QE 00
D"*| mm lf^|'Hf' " nO
. 70DQQE 00
O.BODDOE 00
0.90DQOE 00
D.1DDDOE 01
0.15ODOE 01
0.20DDDE 01
Q.25OODE 01
Q.30DDDE 01
0.40DDOE 01
0.50DQOE 01
0.600QOE 01
D.7DDQDE 01
o.aoaooE 01
D.90DDDE 01
Q.10DODE 02
0.150DOE 02
D.20DODE 02
0.3DDOOE 02
0.40DOOE 02
0.50DOOE 02
D.6DDDDE 02
0.70DDOE 02
0.80DQOE 02
0.90000E 02
0.10DDOE 03
B/ALFAz
= 0.350E 02
Zeta-Va 1 ue
0.99992E 00
0.99987E 00
0.99980E 00
0.999&3E 00
0.99939E 00
0.9990BE 00
0.99867E 00
DijMaQ4 / f* nn
.99816E 00
0.99754E 00
0.99679E 00
0.99590E 00
0.98929E 00
0.97915E 00
0.96636E 00
0.9521DE 00
0.92305E 00
O.B9698E 00
0.87539E 00
O.B5B20E 00
0.84476E 00
0.83437E 00
0.82636E 00
O.B0696E 00
Q.B01B3E 00
O.B0013E 00
O.B0001E 00
O.BQOOOE 00
O.BOOOOE 00
D.8DDDDE 00
0.80DODE 00
D.BDDDDE 00
D.80DODE 00
B/ALFAz
= D.50DE 02
Zeta-Va 1 ue
0.99998E 00
0.9?9?6E 00
0.97994E 00
0.99789E 00
0.99982E 00
0.99773E 00
0.99961E 00
0.99945E 00
0.79925E 00
0.9?900E 00
0.99870E 00
0.«739E 00
0.91577E 00
0.87757E 00
0.88155E 00
0.86789E 00
0.85637E 00
0.82178E 00
D.8D852E 00
0.80128E 00
0.8Q019E 00
Q.80003E 00
0.8DOQOE 00
D.BDDDDE 00
O.BOOOOE 00
D.BDODDE 00
O.BQOOOE 00
B/ALFAz
* 0.750E 02
Zeta-Va 1 ue
0.10000E 01
0.99979E 00
O.TTTTTE 00
0.99998E 00
O.TTTTTE 00
0.77975E 00
0.99792E 00
0.99989E 00
0.79785E 00
0.99980E 00
0.99773E 00
0.99715E 00
0.99794E 00
0.79587E 00
0.97280E 00
0.98372E 00
0.97151E 00
0.75747E 00
0.94283E 00
0.92840E 00
0.91469E 00
0.90200E 00
0.85493E 00
0.82908E 00
0.80807E 00
0.80225E 00
0.800&2E 00
0.80017E 00
0.80005E 00
0.80001E 00
0.80000E 00
0.80000E OD
B/ALFAz
= 0.100E 03
Zeta-Value
0.1DDDDE 01
0.10000E 01
D.1DDDDE 01
Q.10000E 01
0.99999E 00
0.99999E 00
0.99998E 00
0.99997E 00
0.99976E 00
0.79795E 00
0.97993E 00
0.79976E 00
O.^T^SBE 00
0.99865E 00
0.99745E 00
0.99334E 00
D.98683E 00
0.97827E 00
0.96826E 00
0.75740E 00
0.94622E 00
0.93510E 00
0.88689E 00
0.85418E 00
0.82069E 00
O.BD787E 00
O.B0299E 00
0.80114E 00
O.B0043E 00
D.8DD16E 00
O.BOD06E 00
0.80002E OD
-------
Development of Land Disposal Banning Decisions
Under Uncertainty
Environmental Research Laboratory
U.S. Environmental Protection Agency
Athens/ Georgia
APPENDIX C
-------
-1-
Developnent of Land Disposal Banning Decisions Under Uncertainty
1.0 Introduction
1.1 Background and Relevant History
Increasingly, the Agency is required to regulate the use or disposal
of toxic chemicals including hazardous wastes before such materials
become part of a specific, permitted system for use or disposal. The
regulatory approach developed in response to such legislative mandates is
necessarily generic in nature and must be largely based upon inherent
chemical properties. In general, however, the behavior of specific
chemicals in the environment and the subsequent health risks posed to
populations are highly dependent on both the environmental setting and the
chemical properties.
An obvious dilemma arises fron the requirement to regulate (based on
risks posed to human health) on a national basis when the exposure is
determined by a combination of site- and chemical-specific factors. The
errors and uncertainties inherent in site-specific analyses are further
complicated by uncertainty about how to properly specify a national environ-
ment. The land disposal restrictions requirements of the RCRA amendments
pose just such a dilemma. Specifically, how can the Agency determine the
national acceptability (or specify required treatment levels) of the land
disposal of hazardous wastes based on an evaluation of risk to human
health?
As initially conceived by the OSW, "screening levels were to be
developed to specify maximum acceptable contaminant concentrations in
waste extracts. Concentration-based fate and transport models for
groundwater, air, and surface waters were to be developed for
-------
-2-
a "worst case" or "reasonable worst case" land disposal scenario to
allow back calculation of acceptable leachate contaminations commencing
from a reference dose (or a ql* concentration for carcinogens) at a
point of potential human exposure at a specified distance directly
down gradient (e.g. water supply well, surface water intake, or
downwind exposure point). As this approach was further developed two
major issues emerged: (1) how can the reasonable worst case be defined
to avoid unrealistic situations and permit some site-specificity and;
(2) how can the considerable uncertainties inherent in any analysis of
this nature be factored into the process.
1.2 Objectives
The objectives of the material presented in the following sections
are to develop and demonstrate a procedure for applying the initially-
developed concept that accommodates the possible variation in environmental
settings, the uncertainties in specific chemical properties, and the range
of impact of engineered system releases from disposal facilities. The
developed approach is intended to present decision-makers, for each chemical,
the level of treatment (or restriction) required to achieve any desired level
of "protection" expressed as the percentage of all possible land disposal
scenarios that are more protective than the level chosen. In this manner
the scenario selected can be evaluated for its probability of occurence.
At one level one may say, for example, that 90% of all possible sites are
more protective than the health based threshold while 10% of all possible
sites are less protective. In this case the decision-maker can be assured
that the level of treatment selected will ensure that downgradient
concentrations will not exceed the specified target concentration in more
than 10% of all possible environmental settings.
-------
-3-
Meeting this overall objective requires that the following subobjectives
be met:
o Identify and characterize the environnental and chemical properties
contributing to variation in the release, fate, and transport of chemicals.
o Identify and characterize the errors in estimating or measuring relevant
chemical properties.
o Develop a technique to synthesize input data for use in investigating
model variations and uncertainties.
2.0 The Concept of Uncertainty
2.1 Definitions
Uncertainty is generally defined as the absence of information about
the subject under consideration. In this context the absence or lack of
information usually refers to information about past, present, or future
events, values, or conditions. Howe (1977) describes two basic types of
uncertainty: (1) descriptive uncertainty and (2) measurement uncertainty.
Descriptive uncertainty is a measure of the lack of information about the
identity of variables that define the system under study. Measurement
uncertainty is a measure of the lack of information about how to quantify
those variables. Uncertainty analyses are typically completed for measure-
ment uncertainty with the .assistance of a system model that transforms
inputs to output* via some mathematical description of the "real world"
system of interest. The objective is to quantify the model output uncer-
tainties given a knowledge of the input uncertainties. Several formal
methods exist to conduct such analyses as summarized by Cox and Baybutt
(1981). Usually, such analyses do not address descriptive uncertainty.
That is, the model itself is assumed to adequately describe the "real
-------
-4-
world" system being simulated. Uncertainty (descriptive) about the
system irodel will almost always exist and in some cases this uncertainty
is acknowledged but ignored because of policy objectives. In other
cases, descriptive uncertainty is unknown (and unknowable) and is simply
ignored.
2.2 Application to the land Disposal Banning Process
The application of uncertainty analyses to the procedures developed
for setting limits on land disposal is highly desirable. Indeed, the
HCRA amendments directed that such regulations be developed with proper
accounting for the long-term uncertainties of land disposal technologies.
It follows that any provisions granted for continued use of land disposal
should properly account tor the uncertainties in the technical basis for
such provisions. Following the previous discussion of uncertainty, two
problems must be addressed: descriptive uncertainty and measurement
uncertainty.
The choice of the models used in the procedure and the conceptualiza-
tion of the physical system acknowledges the descriptive uncertainty in the
process. In this sense, assumptions made about land disposal performance,
location of fixed, downgradient exposure points, and the use of unit
risk numbers (e.g., Reference Dose Values) are ways to include descriptive
uncertainty. For example, it is generally conceded that landfills have
and could in the future be designed such that their lower boundary is
near or actually in the saturated zone. The uncertainty about this
descriptive variable is simply handled by assuming all facilities are
located such that any leakage will be directly to the saturated zone.
Additional, specific assumptions and decisions imbedded in the procedure
that fall into the descriptive uncertainty category are:
-------
-5-
(1) all engineered systems fail given sufficient tine
(2) the adjective-dispersion equation with reaction and sorption
is an accurate description of chemical fate and transport in
groundvBter, surface water, and air
(3) all processes that can degrade organics in groundwater other
than hydrolysis are Ignored
(4) for metals and organics, equilibrium, reversible spedation and
sorption are appropriate
(5) the leach test (EP III) is an accurate measure of the leachate
concentration resulting when failure of the facility occurs
(6) the contaminant source is sufficiently large in mass to enable
an assumption of an infinite source, i.e., down gradient
contamination once reached will be maintained
(7) transient behavior is unimportant and the overall response can
be represented by steady-state estimates
Most of the assumptions listed above eliminate consideration of
possible effects or variables that can conceivably lead to differences
between the real and modeled systems. These expected differences
resulting fron emission of such effects represent uncertainty that is
quantified only in one sense—their exclusion will result in a more
conservative analysis. Conservative in this case simply means that a
more restrictive outcome for land disposal is generated. Tb the extent
that this is desired, the assumptions per se represent an acconnDdation
of descriptive uncertainty. The modeling approach and its assumptions
with their descriptive uncertainty in land-related hazardous waste manage-
ment are consistent with the strong legislative presumption against land
disposal.
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-6-
The problem remains to evaluate measurement uncertainty. In this
case, measurement is taken to mean assignment of specific re lues to each
of the model variables and parameters. Cftce a model is chosen to represent
the conceptualized system, specific \elues must be chosen to further
describe the behavior of the modeled system. The groundwater model
relies on two general types of data:
- data on the physical, chemical, and toxicological properties of
the hazardous constituents (e.g., K^, Kg^, acid, neutral, and
base-catalyzed hydrolysis rates, and Reference Dose)
- data on the environmental properties of land disposal settings
that impact the release, fate, and transport of each hazardous
constituent (e.g., groundwater velocity, thickness of the saturated
zone, bulk density, groundvater temperature and pH, dispersivities)
Measurement uncertainty applied to the first data type is taken to
mean the errors resulting from laboratory or theoretical analyses used to
estimate their numerical values. In addition to experimental precision
and accuracy, errors may arise in extrapolation fron measurement conditions
to environmental conditions (e.g., hydrolysis experiments conducted at
elevated temperatures extrapolated to groundveter temperatures). Fbr
some parameters, most notably partition coefficients, semi-empirical methods
are used to estimate values and in such cases the errors in the empiricisms
contribute to uncertainty.
Measurement uncertainty applied to the second data type, characteriza-
tion of the relevant environmental properties, is taken to mean the
variation expected to occur across possible land disposal settings. In
the strictest sense analyses of known variation are more properly referred
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-7-
to as sensitivity analyses. Within the ooritext of defining the range of
possible regulatory outcomes, however, we elect to describe the characteri-
zation of variation as representing uncertainty. An important distinction
is made here between variation (and measurement errors in characterizing
that variation) at a given site and variation from site to site, \feriation
within a site is an important phenomenon in site-specific issues like
permit evaluations, designs, and remedial action alternatives. The
uncertainty in the performance of a given system will in large part
reflect the uncertainty about the characterization of the given site.
For example, the location of dawn-gradient monitoring wells to detect
future leaks is chosen based on measurements that define the direction
of groundwater flow. If uncertainty exists in the determination of the
flow direction, then the performance of the detection system is also made
uncertain, this "within-site" variation is not the most important source
of uncertainty, however, for the land disposal banning process because we
are concerned with a presumed national (generic) site. The major concern
for this case is uncertainty in specifying the range of possible sites.
The generic nature of the present regulatory process leads to a
major uncertainty in characterization of the presumed national site.
Assuming it is possible to accurately measure site properties (e.g.,
groundwater velocities and pH) the problem reduces to one of properly
specifying the many possible combinations of conditions that can exist in
possible sites for land disposal, uncertainty in this sense, is simply
an explicit representation of the variation in site conditions that can
exist. From such information the levels chosen for regulating land
disposal restrictions can be easily referenced to the full range of
possible outcomes or restrictions.
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-8-
3.0 Technical Approach
3.1 Monte Carlo Analyses
The recent review by Cox and Baybutt (198L) noted five different
methods for conducting uncertainty analyses. The choice of any one method
is largely determined by the structure of the system model and the objective
of the analyses. In some cases the methods are quite limited because of
the requirements imposed for their use. For example, analytic techniques
require a mathematically tractable system model that permits direct
calculation of output uncertainties given the input distributions. In
sane cases, knowledge about the source of the output uncertainty given a
multitude of possible input uncertainties is needed in order to minimize
or reduce uncertainty; for these cases, techniques that randomly combine
individual inputs to produce a single output are unacceptable because it
is not possible to know the source of the uncertainty. However, the
monte carlo method remains the most widely-used procedure and is suitable
for investigating the land disposal restrictions process.
Before further elaboration on the monte carlo method it is useful to
review the needs foe the land disposal restrictions process:
(1) portray in a concise manner the field of information describing
an estimate of all possible exposures
(2) demonstrate that all reasonable steps were taken to reflect
the wide range of possible site conditions for land disposal
systems
(3) investigate the range and distribution of possible restrictions
needed to insure specified levels of protection
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-9-
(4) properly reflect the uncertainty introduced by laboratory-
measured itodel parameters for hydrolysis and sorption
The emphasis here is on the output of the modeling process. The exact
cause of output variation is less important at this stage of developing the
restrictions. For these reasons, the monte carlo approach is appropriate,
relatively easy to implement, and oonputationly efficient for the system
model used.
Figure 1 illustrates the monte carlo procedure used in this analysis.
If G(X) represents the desired output distribution for a given variable,
i.e., CL, the acceptable leachate concentration, then the process Is
represented by:
G(X) = f(Fi, F2, ...Fn) (1)
where f ( ) = the system node!
FI, F2 ... Fn = input distributions for
parameters or variables.
G(X) is defined from the distribution produced from a large number of
simulations, i.e., 5000 -10,000.
Note frcra Figure 1 that two kinds of inputs are defined - parameters
and forcing function values. Model parameters are representations of
physical or chemical properties (e.g. soil bulk density, hydrolysis rate
constants). Forcing function values correspond to variables or constants
that specify conditions or states of the system. In some groundwater
transport models such inputs are internally estimated rather than externally
derived as shown here.
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-10-
parameters
forcing function
values
>
>
. . V
M
0
D
E
L
OUTPUT STATE VARIABLE
f(Flf F2,
G(X)
G(X)
INPUT
VALUES
OUTPUT
VALUES
INPUT
VALUES
INPUT
VALUES
INPUT
VALUES
INPUT DISTRIBUTIONS
OUTPUT DISTRIBUTION
Figure 1. The Monte Carlo Process for Developing Distributional
(Cumulative Frequencies) Results fron Models
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-11-
The monte carlo process proceeds as follows:
o values frcm each irput distribution are selected at randan.
o a value for the desired output variable, G, is computed for each
rardonly selected set of irput s
o the input selection and computation steps are repeated a large
number of times, e.g., 5,000
o the output values are analyzed for presentation as a distribution.
An important point to remember in completing the monte carlo process is
the notion that the derived output distribution, G(X), is greatly influenced
by the input distributions, F^,F2...Fn. This is true even if the system
model is known to be a perfectly correct representation of the physical
system (i.e., no descriptive uncertainty).
3.2 Modecc, Eerameters and Input Eata
The groundvater model parameters and input data requirements are given
in detail in the mathematical description of the model. The major question
for their use in raonte carlo analyses is their relationship one to the
other. In the siinplist case where all input values are independent, the
monte carlo process is straightforward. Chce each input distribution
is developed the process is executed as described. Where inputs are
correlated, and therefore dependent, the proper specification of each
distribution becomes much more difficult. For example, if ?2 is dependent
upon FI then FI and F2 have a joint distribution. That is, any value
of F2 is the probability of F2 given a corresponding value of F^
(and vice versa). For other situations vhere dependence exists among
more than two variables the problem is further compounded with requirements
for joint probability functions. Before developing input data distributions,
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-12-
it is first necessary to determine the existence of any dependence anong
the data.
Table 1 illustrates the expected dependence among the groundwater
model's parameters and input data. This table was constructed from a
conbination of documented observations and engineering judgement. In
sane cases very weak dependence may exist but an assumption of independence
is acceptable in light of the model's sensitivity to the assumption. The
data pairs denoted by D are thought to be sufficiently dependent to
require generation of correlated input sequences. All pairs denoted by I
are considered independent. The downgradient distance, X will be fixed
and thus it can be deleted because it will take on a single, known value.
3.3 Data and Information Sources
The single values or distributions of values for the various input
parameters and variables must be developed fron data, theoretical
constructs, expert judgement or policy considerations. A number of
different sources can be used in developing this information including
the following:
o the scientific and engineering literature
o laboratory experiments and measurements for specific chemical reactions
o EPA directed surveys
o chendcal structure-property correlations and structure-activity
relationships
o mathematical modeling
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-13-
Tfcble 1. Staaary of Relationships Jtoong Model Parameters and Input
Values
av X o H B foc PH T kft kjj kb JcD
p
«L
UT
av
o
i
oc
PH
T
*.
kn
*b
*D
Z
Z
Z
z
z
z
z
z
z
z
z
z
z
I
z
z
z
z
z
z
z
z
z
z
z
z
z
z
z
z
z
z
z
z
I
z
z
z
z
z
z
z
In n
u u
Z Z Z Z
z z z z
z z z z
z z z z
z z z z
z z z z
z z z z
Z Z Z Z Z D
Z Z 0 Z D D
Z Z D D D Z
ZOO Z Z Z
Z Z D Z Z Z
Z D D Z I Z
0 D Z Z Z Z
D denotes dependence
*
Z denotes weak or no dependence
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-14-
The required data can be further characterized according to type.
That is, data that describe pollutant transport, data that characterize
the environment, and data that characterize the individual chemicals. The
major data influencing transport are flow velocity, V, and dispersivities
<*!/ **T' and °
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-15-
judgement can determine for many chemicals "if hydrolysis will degrade the
chemical. The assignment of a zero rate constant for non-hydrolyzable
chemicals allows the analysis to proceed without the need for experimental
data. In other cases structure—activity relationships can be used to
estimate needed parameters, for example, the octanol-viater partition
coefficient can be reliably estimated from knowledge of molecular structure.
The proper interpretation of data generated from the above methods. This
can be addressed by convening expert panels to review reported data,
specify limits of uncertainty, and delineate appropriate ranges of applica-
tion.
3.4 Data Generation Procedures
The input data and parameters listed in Table 1 must be generated
before monte carlo analyses can proceed. It is convenient to separate
this activity into two tasks: generating independent data sets; and
generating correlated or dependent data sets. Independent data sets can
be developed as empirical distributions of observed data, as theoretical
distributions from a "best-fit" analyses of observed data, or as assumed
distributions. Dependent data sets can be developed as empirical, joint,
or multivariate distributions, theoretical distributions, or from functional
dependencies among the variables and parameters.
3.4.1 Independent Ebrameters and Variables
The summary shown in Table 1 suggests that none of the variables or
parameters is totally independent from all other variables or parameters.
In some cases, however, an independent "seed" distribution can be generated
to which other variables are correlated. For example, the temperature
(T) will influence the hydrolysis rate constants (kg, 1^, kj-,) but the
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-16-
reverse is not true nor tor the system studied does anything else influence
temperature. Thus temperature distributions can be developed as an
independent variable. Following this rationale, the parameters and
variables to be generated independently are as follows:
B - the thickness of the saturated zone
foe - the fractional organic carbon content of the soils
pH - the groundwater hydrogen ion activity
T - the groundwater temperature
H - the leachate penetration depth into the saturated zone
The thickness of the saturated zone, B, influences the opportunity
for vertical dispersive mixing as the plume moves down gradient. Literature
values taken from measurements and surveys were used to derive a distribution
for this parameter.
The fractional organic carbon content, foe, is used to determine the
distribution coefficient, KQ. Recall from the groundwater model description
that
KD = foe Hoc (2)
where Koc = distribution coefficient normalized to organic carbon. It is
clear from this relationship that the variation in foe leads directly to
variation in the KQ and hence retardation of the solute in grcundwater.
Unfortunately, few if any comprehensive subsurface characterizations of
organic carbon content exist. In general the values are known to be very
low, typically less than .01. In the absence of evidence to the contrary
the approach taken was to assume a low range of foe. A distribution
shape for this range was determined by the distribution of measured
dissolved organic carbon recorded as entries to STORET. The assumption
is that dissolved organic carbon reflects the existence (and hence distrj-
-------
-17-
bution) of organic carbon in the subsurface environment being considered.
The node! assumes that the grcundwater is sufficiently buffered to
insure that the pH is not influenced by input of contaminants or changes
in temperature. This permits a pH distribution to be derived independently.
STORET data were analyzed, a distribution developed and summary statistics
generated for pH.
Assumptions about the independence of grcundwater temperature are
essentially the same as for pH. Temperature influences hydrolysis reactions
but the reverse is ignored. Actually, temperature can also influence
sorption but such effects are ignored in this analysis.
The depth, H, to which the leachate flow penetrates the saturated
zone is probably related to the relative differences in the leachate
velocity and the groundwater velocity. Because disposal of free liquids
is not permitted, density gradients or stratification of "floaters" or
"sinkers" are not likely to occur. Lacking any meaningful data, a simple,
independent, uniform distribution ranging from a fixed minimum to a fixed
maximum was used.
A summary of the procedures used to generate the independent input
data sets is given in Table 2. The fitted distribution (FD) method refers
to the development of a mathematically-defined frequency distribution
function by "fitting" various possible distributions (e.g., normal, log
normal, exponential) or mixtures of distributions to the "observed" data
and selecting the "best fit" distribution for use in the nonte carlo
process. The distributions selected for each variable or parameter are
given in section 4.0 of this report. Inall cases we recognize the possi-
bility that the data in STORE! may represent a biased sample. However,
lacking a better alternative the data were accepted as representative of
grcundwater and subsurface conditions.
-------
-18-
Table 2. Summary of Procedures Used to Generate Independent
Input Data Sets
Input Data
B
FOG
pH
T
H
*fitted distribution
Method of
Generation
FD*
FD
FD
FD
AD**
to anoirical data
Source of
Data and/or Reference
Various literature
STCRET, assumptions
STORET
STORE7T
—
'
**assuned distribution
3.4.2 Dependent Parameters and Variables
The remaining input parameters and variables are dependent and cannot
be generated without properly "matching" each value with other related
values. Recall that our objective is to provide a consistent set of data
that when viewed as descriptions of site-specific scenarios will produce
situations that occur in nature. The main purpose of building in
dependencies is to avoid unrealistic or impossible sets of data. For
example, a uniform soil having high porosity because of high clay content
will rarely if ever have high groundwater velocities because of the low
hydraulic conductivities. Failure to exclude such possibilities however
by assuming that porosity and velocity are independent will lead to
unrealistic if not incorrect modeling results.
The "consistency" criterion intended here needs further elaboration.
In general, precise functional relationships among all the dependent
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-19-
variables or parameters do not exist. Similarly, observed data for all
values taken in sets do not exist or are inadequate in number to permit a
statistical representation of the dependencies. Fortunately, however,
equations do exist in the engineering and scientific literature to permit
generation of sets of "possible" combinations of input data. Generation
of consistent sets of irput data is much easier to accomplish than the
more rigorous but related task of predicting a precise, site-specific set
of values given only one or two measurements at that site. The parameters
and variables to be generated as dependent values are as follows:
<*L'Qir'*'V s dispersivities in the longitudinal, lateral, and
vertical directions assumed to be largely dependent on
distance, x
e = porosity of the soil or porous media is assumed to be
largely dependent on soil properties including particle
sizes textural classes, bulk densities, and parent material
P - bulk density of the soil or porous media is assumed to
be largely dependent on soil properties including
porosity
V = groundwater flow velocity is assumed to be largely
dependent on soil properties including hydraulic con-
ductivities, porosity, bulk density and on hydraulic
gradient (groundwater slope)
(T a the standard deviation of the gaussian distribution
representation of the source concentration is related
via mass balance principles to leachate volumes, ground-
water velocity, porosity, and depth of Leachate penetra-
tion into the saturated zone
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-20-
ka,kn,kfc = hydrolysis rate constants are assumed to be largely
dependent on groundwater pH and temperature and on
specific chemical properties
KD = effective distribution coefficient for each specific
chemical is assumed to be largely dependent on the organic
carbon content of the soil or porous media and in some
cases on the pH as well as on specific chemical properties
of the pollutant
3.4.2.1 QLspersivity
The "spreading" of solutes transported by groundwater is usually
described as a combination of molecular diffusion and mechanical mixing.
The relative magnitudes of each are such that molecular diffusion can be
ignored. The property of the soil or porous medium that is commonly used
to define the magnitude and direction of dispersion is included in the
dispersivity parameters. A generalized theory to describe dispersivity
has not yet been developed but recent work has noted a strong dependence
on scale (Sudicky et al., 1983; Anderson, 1979; Pickens and Grisak, 198L;
Pickens and Grisak, 19SL; Molz et al., 1983; Gelhar et al., 1985). Seme
investigators (Pickens and Grisak, 1981) have reported simple, linear
dependencies for longitudinal dispersivity,
-------
-21-
Many experimental data suggest that equation 3 is a reasonable approximation
for&^L given our limited objective of "consistency" in the input data set.
Transverse dispersivity, «
-------
-22-
where x is the downgradient exposure point distance selected for
implementation of the decision rule.
3.4.2.2 Porosity
The porosity, 9, of a uniform porous media is largely a function of
particle size. For small particle sizes like clay, porosity increases to
a maximum of around 50%. Porosities of coarser media like gravel decrease
to a minimum of around 30%. These measured ranges of porosities suggest
a strong correlation with mean particle diameter, d. Data reported by
Davis (1969) were used to develop a regression equation relating porosity
to d as follows
6 = 0.261 - 0.0385 Ind (9)
Because porosities are generally known for a wide range of soils and
porous media another approach to generating input values is to determine
a distribution for 9 from observed data. It will be shown later, however,
that 9 is linked to velocity, V, through the mean particle size, d. Thus,
to preserve this relationship, the distribution far 9 is generated from
a "seed" distribution for d via equation 9. The mean plarticle diameter
as the single correlated property to porosity ignores the influence of
particle sorting within porous media and hence may not be the most accurate
approach in developing the dependence. Unfortunately, at the present time
the distribution of sorting and mean particle size in materials in the
saturated zones is not well enough known to be used in the methodology.
The distribution of particle sizes selected for this study should
reflect the distribution of subsurface characteristics in all areas
subject to potential use for land disposal. While specific case studies
exist, apparently no general characterization is areilable. Cne approach
is to assume a distribution bounded by reported ranges. In the absence
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-23-
of data both a uniform and a log-miform distribution were investigated.
As will be shown later, the log-uniform distribution was selected because
it more heavily weights the influence of smaller particle sizes and
because the related, derived velocity distribution is more consistent
with observed data.
3.4.2.3 Bulk Density
The soil's bulk density, p, is defined as the mass of dry soil
divided by its total (or bulk) volume. Bulk density directly influences the
retardation of solutes and is related to soil structure. In general, as
soils became itore compact their bulk density increases. This relationship
produces a dependency between porosity, 9, and p. Freeze and Cherry (1979)
note that
9 = 1 - p (10)
ft
where ft, « particle density, g/cm3
By assuming ft, = 2.65, equation 10 can be rearranged to yield an expression
for estimating p given 9 as follows
= 2.65 (1-9) (11)
The particle density of soil materials varies over a very narrow range
and can be fixed at a value of 2.65 gm/on3. Equation 11 can be used to
derive a frequency distribution for given the previously generated
distribution for 9.
3.4.2.4 Velocity
The velocity of groundwater is a major determinant of the transport
of solutes in subsurface systems. In uniform porous media it is the
-------
-24-
doninant factor and must be properly specified in the nonte carlo process.
Dependencies among the input data (9 and n) must be preserved while
generating realistic values of velocity.
Groundwater flow velocities vary widely. Mackay et al. (1985) report
that velocities typically range between 1-100 m/yr. These ranges apply to
typical "natural gradient" conditions and higher velocities can exist inder
both man-induced (e.g., well-field drawdown) and extreme natural situations.
For example, velocities in excess of 9000 m/yr have been reported (Guven et
al., 1984) for a glacial outwash material. Such data sources could be used
to develop an empirical frequency distribution for velocity but the require-
ment to maintain dependencies with soil properties is not easily net using
this approach. The EPA survey of tert B permit applications for velocity
could be used to generate empirical distribution, but in addition to the
dependency problem just described, this limited sample is likely to be
biased.
Velocities are related to soil properties and other site-specific
factors through Darcy's law. Using Carey's law and assumptions of steady
flow in uniform, saturated media yields the following expression for
average pore velocity, V
Kg S
(12)
e
where Kg =» saturated hydraulic conductivity, cm/sec
S = hydraulic gradient
Because an expression for porosity, e, has already been developed, equation
12 properly relates V and 9. The saturated hydraulic conductivity, Kg,
reflects the "ease" with which water is transported through porous media
-------
-25-
and for any given fluid Kg is a function of porous medium properties such as
particle size, grain shape, connectivity, and tortuosity. To the extent
that Kg is related to such properties if functional relationships exist
for Kg then dependencies among V, Kg and 9 can also be represented.
Individual, site-specific measurements for Kg are usually difficult
to make and the spatial variability of "point" measurements is the subject
of much current research. Also, site-specific variations in Kg values
introduce considerable uncertainty in modeling groundwater flew vtoen point
estimates or averaged point values are used as model inputs. Recall that
the objective here is to insure consistency in results vftile representing
the wide variations expected from site to site. Given this objective (that
is much less demanding than an attenpt to predict an accurate Kg far any
given site), it is reasonable to use an approximate functional relationship.
The most notable among these is the Karmen-Cozeny equation (Bear, 1979),
93 o
K =478[ d2] (13)
3 (1-9)2
where 9 = porosity
d = mean particle diameter
Note that equation 13 relates Kg to 9 and d. Furthermore, 9 is derived
from d that is generated from a "seed" distribution.
The remaining factor in equation 12 for velocity is the gradient, S.
In general the gradient is a function of the local topography, groundveter
recharge volumes and locations, and the influence of withdrawals (e.g.,
well fields). It is also likely to be indirectly related to porous media
properties. Rarely are large gradients associated with very high conducti-
vities. No functional relationships exist, however, to express this
-------
-26-
association. Thus, another independent "seed" distribution is required.
The potential problem with the independence assumption is in "extrarie"
values. Eata sets having large values for both Kg and S will also have
very large values for velocities resulting in unrealistic conditions.
Such condition can be prevented by bounding the velocities such that a
fixed maximum is not exceeded. The observed value of 9250 m/yr was
selected for this purpose.
The distribution for the gradient can be assumed or derived from
observations. Gradient data were included in the EPA survey of tert B
permit applications and were analyzed to develop a frequency distribution.
Results are given in later sections of this report.
3.4.2.5 Standard Deviation of the Gaussian Distrubtion for the Source
Concentration
The parameter defines the nature of the leachate after it has mixed
with the underlying saturated zone. Because sigma reflects the nature
and extent of the leachate interaction with the groundwater beneath the
facility, it and hence also reflects the failure of the engineered controls
on the facility (e.g., liners, caps). Fran ness balance principles is
related to the environmental setting by
o" -qAwcyv2/n veHc-, (14)
where q » unit area! flux of leachate through the land
disposal facility, m yr"1
Ay/ = area of disposal facility, m2
V = groundwater velocity, m yr"1
9 = saturated zone porosity
H = leachate penetration into the saturated zone, m
CT. =• contaminant concentration in the leachate
-------
-27-
CQ = contaminant concentration in the mjocing zone
beneath the facility
If we assume that the leachate concentration, CL/ is the sane as the
maximum concentration CQ (at y = 0) of the gaussian concentration distri-
bution, then equation 14 enables direct calculation of CT given the other,
known variables. Setting CL = Co in equation 14_ simply means that the
leachate displaces the groundvBter and dilution occurs after advective
transport is initiated; a reasonable assumption given the low velocities
for leachate fluxes.
Values for q vary depending on the location of facilities, their
vertical configuration (e.g., liners, caps), and their performance over
time. The procedure used to produce a distribution for q is described
in the E. C. Jordan (1985) report. A distribution was generated from the
EPA survey of fort B permit applications fbr the area term. Ay/. Velocity,
V, and porosity, 9, and penetration depth, H, are generated as previously
discussed, fbr mathematical reasons (boundary effects) the constraint
that the ratio, H/B, where B is the saturated zone thickness, be less
than 0.5 must also be made. The minimum saturated thickness is 3 meters.
3.4.2.6 Hydrolysis Rates
Hydrolysis rate constants are unique to each chemical and will be
determined from the literature or fron laboratory experiments. All rates
(acid-catalyzed (ka), neutral (kn), base-catalyzed (kjj) are influenced by
grcundwater temperature, ka and kj-, are also influenced by pH. The pH
dependency is included directly in the grcundwater model and the rates
will be adjusted accordingly via the independently derived distribution
for pH. The temperature dependency requires further elaboration.
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-28-
Rate constants are often adjusted for temperature effects by the
Arrhenius equation. Because the rate constant values are given for a
specific temperature, the need exists to adjust these values to account
for different temperatures in the grcundwater. Using the generic activation
energy recommended by Wolfe (1985) of approximately 20 k ca I/mole, the
temperature correction factor can be written as
(15)
*an,b Tr T
wnere *a n b = second-order hydrolysis rate constants for acid,
neutral, or base conditions at temperature T
^afn.b = second-order hydrolysis rate constants for acid,
neutral, or base conditions at reference tanperature, Tr
T, Tr = temperature, "Kelvin
The tanperature can also influence the base-catalysed hydrolysis rate
through influence on autoprotolysis of water. Rarous medium properties and
groundvaters are sufficiently buffered, however, to minimize this effect.
Temperature corrections to pH are not made.
The measurement and extrapolation errors for hydrolysis mesuranents
are not yet fully developed. Once the experimental program to develop
such values is fully implemented the nature and magnitude of these errors
will be included.
3.4.2.7 Distribution Coefficient
The relationships most suited for relating the chemical distribution
coefficient, KQ, to soil or porous medium properties are discussed in
detail by terickhoff (1985). In cases where reliable relationships do
not exist, measurements are required, for many cases hydrophobia binding
-------
-29-
doninates the sorption process and it is possible to relate the distribution
coefficient directly to soil organic carbon. For these cases the dependency
is given by
KD = KOC ?oc U-6)
where KQC = normalized distribution coefficient for organic carbon
fraction organic carbon
Recall that f^, values will be generated as an independent parameter as
previously described. Equation 16 will be used to preserve dependency
between porous media properties and chemical soiptive properties. For
other binding mechanisms described by ferickhoff (1985) including those
for polar, ionizable compounds adjustments will be made on a case-by-case
basis as appropriate.
4.0 Data Generation Results
The combination of data sources and approaches described in Sections
3.3 and 3.4 were used to generate input frequency distributions for each
of the parameters and forcing f met ion variables. In some cases intermediate
or precursor variables were also generated to enable representation of
appropriate dependencies among the variables and parameters. Results for
these variables are also included in this section. Table 3 gives a
summary of the distribution types and parameters for each model parameter
or variable, fbr derived distributions, only the mean and range of the
synthesized data are given — it's not necessary to approximate these
results by a mathematical distribution function. In some cases only
single, fixed values were selected largely based upon their nature (e.g.,
a chemical-specific rate constant) or upon policy directions (e.g. , the
downgradient distance, x).
-------
-30-
Table 3. Summary of Results tor Input Data Generation
Parameter or
Variable
Temperature, °C
pH
Dissoloved
Qrganic-C, mg/1
foe
d, cm
e, cm3 nT3
P, gm on"3
Kg, cm sec"1
S
V, myr"1
B, m
*
H, m
q, m
0"* m
^L' m
^T' ra
^y m
X, m
ka MT1 yr'1
Distribution Distribution
Type Parameters
mean std. dev.
Normal 14.4 5.29
Normal 6.2 1.28
Lognormal 1.99 1.09
lognormal -5.76 3.17
LogiQuniforra .0063 —
derived fran d
derived fran e
derived fran 9, d
exponential .0309 —
derived from S, Kg, e
exponential 78.6 —
mixed; exponential
uniform
derived fran uniform 6.0 —
modeling
derived fran q, f^, V,
H, e
single values
single values
single values
single values
chemical specific value
Range
nun-ma x
(0.0 - 30.0)
(0.3 - 14.0)
(0.01 - 6.89)
( .001 - .01)
( .0004 - 0.10)
( .30 - .56)
(1.16 -1.8)
( .0001 - .48)
( .00001- 0.10)
( .01 - 9250)
(3.0 - 560)
(23 - 930,000)
(2.0 -10.0)
(0.0 - .3)
( .001 - 60,000)
chemical specific value
chemical specific value
chemical specific value
-------
-31-
4.1 Fraction Organic Carbon Content, f^.
Recall from Section 3.4.1 that f^ was generated by assuming a fixed,
low range of .001 - .01 and using the observed distribution of dissolved
organic carbon, DOC, to "shape" the foe distribution. This was done by
assuming both variables had identical distributions and scaling the f^,
by the coefficient of variation (CV) for the DOC. That is, the mean value
for ^ (based upon a lognoxnal distribution with a stated range) was multi-
plied by the DOC coefficient of variation to yield a standard deviation
for the fog. This fully specified the distribution.
4.2 Mean Particle Size, d
The distribution of d should correspond to the distribution of soil
types in the saturated zones across the country. As previously discussed
such a charactization does not exist and the mean values alone do not describe
sorted grain sites. Following the rationale developed in Section 3, the
logio uniform distribution was assumed. This distribution, shown in Figure
2, is bounded over the range fron .0004 on, corresponding to a clay
material, to 0.1 cm, corresponding to a gravelly sand. The mean is .0063
cm corresponding to a soil somewhat finer than a silty fine sand but
coarser than a clayey sandy silt. This assumed distribution is a key
component of the input because it influences 9 and V. As will be shown
the logio uniform distribution produces subsequent distributions for V that
are more consistent with observed data than alternative assumed distributions
investigated. Clearly, however, this is an area that should be more
fully investigated.
-------
175-
32
15CH
-I!:
u
c
o
•^
^*
cr
0
125H
•1
_ i
j
!OOJ
.4
- 4
I1
.Ji
i.
-j
H!!i
50-j |
J •
-i !|
25- ||
i
n ••••
0.00
1
il
illl lii ill ! : ill- HI. ! liMllM!. ,|..|.- li! ! I , -!! I- -
. . , • ; : t | , . . . , : . ; | i . . . | i . . . j . . . . j i ; . i i ; . ; . | i . . . ;
0.0' 0.02 0.03 0.04 0.05 0.06 0.07 O.OB 0.09 C.IC
Mean Particle Diameter
FIGURE 2
-------
-33-
4.3 Ebrosity (9), Bulk. Density ( p ), Hydraulic Conductivity (Ks) and
Gradient (S)
Graphical representations of frequency distributions for each of
these parameters are given in Figures 3-6. Only one distribution, S,
required a mathematical description since each data point for all others
in this group was derived through functional relationships with mean
particle size, d.
4.4 Saturated Zone Depth (B), and Facility Area
The graphical representations for these fitted distributions are
shown in Figures 7 and 8. Because Ay is used in developing for '"engineered"
facilities, Figure 8 applies only to landfills. The rationale for this
approach is the requirement that impoundments must be "closed" as if the
system were a landfill.
4.5 Percolation Flux (q) and Initial Concentration Standard Deviation
for)
The distribution for q is described in the E. C. Jordan report (1985).
Because a relatively few data points make up this distribution a direct
interpretation from the data expressed as a cumulative frequency table
was made. That is, linear interpolation for intermediate data points on
the Figure 9 developed in the E. C. Jordan report (1985) was employed.
Subsequent generation of the distributions for Aw, H, V, and 0" produced
Figures 10-12.
-------
34
7C
60-
i
. 4
5C-]
:i
*~^ "*—
^^* '•
t ^ *r\ •
c "C~
^^ * 4
1 \
i- 30-!
_i_ . ;
_j
20 H
J
1C-H
1
j
, . . . j J . . . ] i . . . ; i . . . | ; . . : j i . . . j
0.30
0.35
0.40 0.45 0.50
Porosity
055
0.60
FIGURE 3
-------
20'
35
u
c
0)
3
cr
Q)
« A .
I u —!
•1
•1
1.0
• I T
1.1
! I
I
I
I I!
I
II
• I '
1.2
•
1.3
1.4 1.5
Bulk Density
1.6
1.7
1.3
FIGURE 4
-------
36
U
c
1
90-i
sen
70-
c ^>
C 'J "
3 50 »j
D"
0)
*•*" 4C -
50
20
0-
0
I i i>
Illll.! ll. I. lM' illl!
000 0001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010
Saturated Hydraulic Conductivity
FIGURE 5
-------
45
.(I
i
35-1,,
30 H I
• I" :j < ,
jllllilil!
-Jj ! ' 1 ' I • ! I
2Hi! II
15-
-
10-1
37
0.00 0.01
0.02 0.03 0.04 0.05 0.06 0.07 0.03 0.09 010
Hydraulic Gradient
FIGURE 6
-------
O
c
C"
O
60-f
•j
j
501i
4C-i
30'
20-
:. ; i ! ! ! i ' i i
"!'Hi!'! ;!!:'ii
10-
38
iuliin.
•J;'••I•• •• i ;•••!••• M T •••i'••;j'• ••!•••• | • • • • i • ...].-.•)
50 100 150 200 250 300 350 400 450 500 550 600
Saturated Zone Thickness
FIGURE 7
-------
39
O
c
O)
13
CT
CD
70 -I
60-
50'
30-
20
10-
I !
i i
10000 20000 30000 40000 50000 60000 70000 80000 90000100000
Landfill Areas
FIGURE 8
-------
40
o
Subtitle "C* Facility
0 Subtitle *0' Facility
q. lnch««/ytar
FIGURE 3-1
ESTIMATED DISTRIBUTION OF UNIT AREA LEACHING
RATES FOR SUBTITLE C AND D FACILITIES
-——————— ECJOHW4OO
-------
41
u
c
o
D
cr
Q)
25-
20 H i
• 1
-{ , ||;
-i , i
i
H
j
H ! |
J '
"I i i
10-j
•i
*•* i
i i
••• i i
i
! t t
H I
i i '
5-i
i
i
n ....... ..J-. J,.,.. -, I.X..
U , . . . j , ; , . , ; . . . i . . . , i . . . , i .
0 1 2 3 45
i
i i
i
i i
i
6 7 8 9
t
i
i
f
J
10
Leachate Penetration Depth
FIGURE 10
-------
42
150-.
-i
14G-!
i
_4
130-j
-i
120-
11C -
100-
90-
o
c 3C_.
C" 70 -i
£ -J
-1- 60 -i
i
50 -j
30-|
20 -1
10-
n
\J
0
i
i
i .
1 ! 1 ! • i i ! 1 ! ! ! • ! - ; I 1 I 1 hi !
.. | i ... i : ... | .... j : ... j .... j .... j j !.. j ....,....,
10 20 30 40 50 60 70 SO 90 100
Groundwater Velocity
FIGURE 11
-------
3
cr
50--
40-J
3C» j
20-
43
«n_, !
|C i !
I
0.0
10.0 20.0 30.0 40.0
Standard Deviation of Gaussian
initial Concentration
50.0
FIGURE 12
-------
44
40
:|
35-
30-
25-
o
^
o J
ZS 20"
^M *
•J—
15-
-
••
-
<•.
5-
•-
.<
"•
n
w
C
i
i
!
I
i
,
!
i
; i
1 !
|
1 !
i
i
i
i
i
i
1 1
t- i
I: 1 .M . i li
1 ... J 1 .... 1 ... j .... | 1 i .. 1 . . J ; .
) 1 2 3 4 5 6
i
i
: in
1 j|
i
i
1!
i Hiii i!
in: ii >
| !i 1
III! !
1 ' :
1 li
1
H! |
j
!j ||
1
•
I
i
ii
i ! ! M
j ' 1
• '
i
i
M >i in
1 1 M
l| 1 i.
1 t
t ' t
! II II
i hllilhii
. . , . . ; | j .... j ; ... j :...;.... j . ... j
7 8 9 10 11 12 13 14
Groundwater pH
FIGURE
-------
45
50'
•
45-
.
40-
» .
»•
35-
•:
30 -
•
25-
.
20-
•1
• i
-
.1
,0-
.,
-
,
J
h
;
•
t
1
1
•
•
•
1
'
•
•
•
1
'
•
•
•
i
-
1
!
1
i i 1 : I
j
5 10 15 20 25
Groundwater Temperature
30
FIGURE 14
-------
-46-
5.0 Modeling Results
Hie groundwater model was implemented with the input data generated
by the data, assunptions, or modeling reported in the previous sections.
Two general cases are of interest: modeling results for non-degrading
chemicals, and for degrading chemicals.
5.1 Results for Nondegrading Chemicals
The behavior of all non-degrading organic chemicals will be identical
because sorption does not (as implemented in the model) influence dissolved
concentrations. Thus, it is possible to produce a single cumulative
frequency distribution for all such compounds. The resulting distribution
is given in Figure 15. In addition to the graphical results, tabulated
values for the frequency distribution are given in Table 4. Also
given in the table are results front simulations using a neutral hydrolysis
rate corresponding to a one-year half-life with no sorption.
Table 4. Model Simulation Results for Non-Degrading Chemicals
and Chemicals with a One Year Halflife
Cumulative
Percentile
0.25
0.50
0.75
0.90
0.95
*CD Value
Non-Degrading Case
<0.0 x 10~7
1.8 x 10~5
0.0044
0.043
0.09
One Year Halflife
1.0 x 10~6
2.0 x ID'5
0.0046
0.043
0.10
*CD
where C^ni = health-based threshold
C = leachate concentration
-------
47
U
M
M
U
L
R
T
I
V
E
F
R
E
Q
U
E
N
C
Y
1 -OH
0.9H
0-8H
0-0-3
MONTHS)
SUBTITLE C DKNQ = O-OGGGSll
o.o
0-1
0.2 0-3
CCNCENTRRTION
0.4
0.5
FIGURE 15
-------
-48-
5.2 Results for Degrading Chemicals
All degrading chemicals will respond to differences in both rate
constants (ka, kn, kfc>) and partition coefficients (Kj)). For this reason
no general result can be developed, rather, a unique cumulative frequency
curve exists for each individual chemical. To illustrate general
differences between behavior of chemicals that do not degrade and those
that degrade a series of simulations shown in Figures 16 - 21 were
produced representing chemicals that do not sorb but have varying
effective half-lives. These results compared to those of Figure 13
illustrate the dramatic impact that degradation can have at "fast" rates
but also show a surprisingly small effect at "slow" rates. Table 5
summarizes the results for different rate constants.
Table 5. Model Simulation Results for Degrading Chemicals
That Do Not Sorb
CD Value for Each Noted Halflife
Cumulative
Percentile 30 days 60 days 90 days 8 months 16 months 2 years
0.25 8.0x10-6 9.0x10-6 9.2xlO~6 9.7x10-6
0.50 1.7xlO-5 1.8x10-5 1.8x10-5 LSxlO'5
0.75 3.6xlO-3 4.0X10-3 4.4x10-3 4.5x10-3
0.90 3.5X10-2 3.8x10-2 3.9xio-2 4.2X10'2
0.95 7.5X10-2 8.2x10-2 8.5xlQ-2 8.6xlQ-2
1.0x10-5 i.QxlO-5
1.8x10-5 1.84x10-5
4.5x10-3 4.5xlO-3
4.3x10-2 4.3x10-2
8.7x10-2 8.8x10-2
-------
49
712 DAYS "(2 YEARS)
SUET;T[E c DKNC . o.0330435
u
L
R
T
V 0
F
F
F 0
r.
U
F
N-
C G
uo-:
:
31
O.Z
r. r _^
J • w ~i
C.i
0.2 0-3
CONCFNTRRTJON
FIGURE 16
0.5
-------
50
480 DAYS (16 MONTHS)
SUBTITLE C DKNO = 0-00005C2
1 -OH
0.9-
0.5-
0.7-
C
u
M
M
U 0.6-
L
R
T
i
V 0-5-
E
F
R
E 0.<-
Q
U
E
N
C 0.3-
Y •
0-2-
0-i-
o.o-
o.o
0-1
0-2 0-3
CONCENTRATION
FIGURE 17
0.4
0-5
-------
51
(>-; '•-' O"""T ~_;
\ ~> -'-. v./' . '• i i ]
r ,/ i ". _ •-. ~ i—••-'-. -
U' I'. l \ w — U'UOUii_i_lj
1 .0-1
0.3-
0-8-
c
LI
M
M
U 0-6-1
L
P
T
i
F
R
E 0 .4-1
Q
U
E .
N
C 0.3-1
0.2-
C.l
o.o-
n n
O • U
0.1
0.2 0.3
CONCENTRfiTjQN
0.4
0.5
FIGURE 18
-------
52
90 DAYS
SUBTITLE C DKNO - O.COC320S
1 -OH
C.9-
0.5
0.7
C
U
M
M
U 0.6
L
fl
T
I
V 0-5-
E
F
R
E 0.4-
0
U
E
N
C -0.3-
Y
0.2-
0.0-
r> n
u • u
C-l
0.2 0.3
CONCENTRRTIQN
0-4
0-S
FIGURE 19
-------
53
60 DAYS
SUBTITLE C DKNO = O.OCC4813
1 -0-1
0.9-1
0.8-1
0.7-1
U
M
M
U 0.6-
L
fl
T
i
V 0.5-
E
F
R
E 0.4-
0
U
E
N
C 0-3-
Y
0.2-1
C.U
0.0
C.I
0.2 0.3
CONCENTRRTIQN
FIGURE 20
0-4
0.5
-------
54
30. DAYS
SUBTITLE C DKNO = 0.0009525"
•OH
0.9-
0.5-
0.7-
C
U
fl
n
U 0.6-
L
fl
T
I
V 0.5-
E
F
R
E 0.4-
0
U
E.
N
C 0-3-
0-2-
0.1-
On '
• u —
o.o
0.1
0-2 0-3
CONCENTRflTJON
FIGURE 21
0.4
-------
-55-
6.0 Limitations in the Approach and Issues
The results obtained from the monte carlo simulations are intended
to represent the performance of land disposal systems as they can exist
over the entire country. Attempts have been made as presented in this
report to accurately represent the range of possible outcomes of this
process. Given the required assumptions, however (including in some
cases assumptions of independence when weak dependence is known to exist),
it is recommended that extreme values of the derived distributions be
viewed as suspect. For this reason, values in excess of the 95th percentile
level and below the 5th percentile level should not be viewed as having
the "accuracy" of those values intermediate to these extremes.
Recall from the statement of objectives the intent to include an
explicit representation of the measurement errors associted with hydrolysis
and sorption experiments. This has not yet been done but is under
development. For chemicals that do not degrade this is not a requirement.
Limited sensitivity analysis to date for degrading compounds suggests
that for certain ranges of halflives the outcomes are relatively insensitive,
especially near distribution extremes.
Increased confidence in the modeling results can be achieved by
completing the following activities:
(1) developing better distributions for subsurface properties,
particularly mean particle sizes and related phenomena based
on a more comprehensive review of subsurface data
(2) expanding the spatial and temporal extent of the HELP model
simulations (as described in the E. C. Jordan report, 1985)
for Ic^chute voluixs
-------
-56-
(3) developing a correlated distribution generation approach for
the leachate penetration depths, H, q, and V
(4) relating dispersitivities to porous medium properties (probably
hydraulic conductivities) as well as scale
(5) developing analytic expressions for the sensitivity functions
of the model
(6) conducting exhaustive sensitivity analyses to determine exact
sources of the major model sensitivity
REFERENCES
Anderson, M. P. 1979. Using Models to Simulate the Movement of Contaminants
Through Groundwater Flow Systems. CRC Critical Reviews in Environmental
Control. Vol. 9, Issue 2, pp 97-156.
Bear, Jacob. 1979. Hydraulics of Groundwater. McGraw-Hill. 569 p.
Cox, P. C. and P. Bayhutt. 1981. Methods for Uncertainty Analysis: A
Comparative Survey. Risk Analysis 1, 251-258.
Davis, S. N. 1969. Porosity and Permeability of Natural Materials. In:
Flow Through Porous Media. Ed. Roger J. M. Dewiest. Academic Press,
1969. 530 p.
E. C. Jordan Co. 1985. Analysis of Engineered Controls of Subtitle C
Facilities for Land Disposal Restrictions Determinations. Report Submitted
to EPA, Contract 68-01-7075.
-------
-57-
Freeze, R. A. and J. A. Cherry. 1979. Groundwater. Prentice-Hall Inc.
604p.
Gelhar, L. W., A. Mantoglou, C. Welty, and K. R. Rehfeldt. 1985. A
Review of Field Scale Subsurface Solute Transport Processes Under Saturated
and Unsaturated Conditions. Electric Power Research Institute, Groundwater
Studies EPRI EA-CCCC. Palo Alto, Calif. (Draft Report) 107 p.
Guven, 0., F. J. Molz, and J. G. Melville. 1984. An Analysis of Dispersion
in a Stratified Aquifer. Water Resources Research. Vol. 20, No. 10, pp
1337-1354.
Huyakorn, P. S., M. J. Ungs, E. D. Sudicky, L. A. Mulkey, and T. D.
Wadsworth. 1985. RCRA Hazardous Waste Identification and Land Disposal
Restrictions Groundwater Screening Procedure. U.S. EPA, Washington, DC.
Rarickhoff, S. W. 1985. Sorption Protocol Evaluation for OSW Chemicals.
U.S. EPA, Athens Environmental Research Laboratory, Athens, GA.
Madcay, D. M., P. V. Roberts, and J. A. Cherry. 1985. Transport of
Organic Contaminants in Groundwater. Environ. Sci. Technol., Vol. 19,
No. 5, pp 384-392.
Molz, F. J., O. Guven, and J. G. Melville. 1983. An Examination of
Scale-Dependent Dispersion Coefficients. Groundwater. Vol. 21, No. 6,
pp 715-725.
Pickens, J. F. and G. E. Grisah. 1981. Scale-Dependent Dispersion in a
Stratified Granular Aquifer. J. Water Resources Research. Vol. 17, No.
4, pp 1191-1211.
-------
-58-
Pickens, J. F. and G. E. Grisak. 1981. -Modeling of Scale-Dependent
Dispersion in Hydrogeologic Systems. Water Resources Research. Vol. 17,
No. 6, pp 1701-1711.
Rowe, William D. 1977. An Anatomy of Risk. John Wiley and Sons. 488 p.
Sauty, Jean-Pierre. 1980. An Analysis of Hydrodispersive Transfer in
Aquifers. Water Resources Research. Vol. 16, No. 1, pp 145-158.
Wolfe, N. L. 1985. Screening of Hydrolytic Reactivity of OSW Chemicals.
U.S. EPA, Athens Environmental Research Laboratory, Athens, GA.
Sudicky, E. A., J. A. Cherry, and E. 0. Frind. 1983. Migration of
Contaminants in Groundwater at a Landfill: A Case Study. Journal of
Hydrology, 63, pp 81-108.
-------
ANALYSIS OF ENGINEERED
CONTROLS OF SUBTITLE C
FACILITIES FOR LAND DISPOSAL
RESTRICTIONS DETERMINATIONS
APPENDIX D
-------
ANALYSIS OF ENGINEERED CONTROLS OF SUBTITLE C
FACILITIES' FOR LAND DISPOSAL RESTRICTIONS DETERMINATIONS
FINAL REPORT
Contract No. 68-01-7075
Work Assignment No. 24
RTI Project No. 3224
ECJ Project No. 4756-00
Contractor: Research Triangle Institute
Subcontractor: E.C. Jordan Co.
Task Officer: James Bulman
Prepared by
E.C. Jordan Co.
P.O. Sox 7050
Portland, Maine 04112
Prepared for
Research Triangle Institute
P.O. Box 12194
Research Triangle Park, North Carolina 27709
and
Office of Solid Waste
U.S. Environmental Protection Agency
Washington, D.C.
June, 1985
5.85.102
0001.0.0
-------
TABLE OF CONTENTS
SECTION
TITLE
PAGE
1.0
2.0
3.0
REFERENCES
APPENDIX
A.
INTRODUCTION 1-1
1.1 Background 1-1
1.2 Objective 1-5
1.3 General Approach 1-6
ANALYTICAL APPROACH 2-1
2.1 Leaching Process 2-1
2.1.1 Climatic Conditions 2-1.
2.1.2 Analysis Method 2-3
2.2 Climatic Data Base 2-6
2.3 Facility Conditions 2-14
2.3.1 Subtitle D Facility 2-14
2.3.2 Subtitle C Facility 2-16
CONCLUSIONS AND RECOMMENDATION'S 3-1
3.1 Leaching Rate Distributions 3-1
3.2 Sensitivity Analysis 3-4
3.3 Application of Distributions 3-7
3.3.1 Use 3-7
. 3.3.2 Limitations 3-9
3.3.3 Summary 3-10
COMPARISON OF 5 AND 30 YEAR PRECIPITATION DATA
5.85.102
0002.0.0
-------
LIST OF .FIGURES
NUMBER
2-1
2-2
2-3
2-4
2-5
2-6
2-7
2-8
2-9
2-10
3-1
TITLE
MEAN ANNUAL PRECIPITATION
AVERAGE ANNUAL LAKE EVAPORATION
LESS THAN 10" ANNUAL AVERAGE PRECIPITATION
10" TO 20" ANNUAL AVERAGE PRECIPITATION
20" TO 32" ANNUAL AVERAGE PRECIPITATION
32" TO 40" ANNUAL AVERAGE PRECIPITATION
40" TO 48" ANNUAL AVERAGE PRECIPITATION .
GREATER THAN 48" ANNUAL AVERAGE PRECIPITATION ._ . .
SUBTITLE "D" FACILITY CONDITIONS USED IN
ESTIMATING LEACHING RATES
SUBTITLE "C" FACILITY CONDITIONS USED IN
ESTIMATING LEACHING PATES , , , ,
ESTIMATED DISTRIBUTION OF UNIT AREA LEACHING
RATES FOR SUBTITLE C AND FACILITIES
PAGE
2-2
2-4
2-7
2-8
2-9
2-10
2-11
2-12
2-17
2-ia
3-3
5.85.102
0003.0.0
-------
LIST OF TABLES
NUMBER TITLE PAGE
2-1 CITIES SELECTED FOR CLIMATIC DATA 2-13
3-1 LEACHING RATES SUMMARY 3-2
3-2 SENSITIVITY ANALYSIS SUMMARY 3-5
5.85.102
0004.0.0
-------
1.0 INTRODUCTION
In accordance with recent federal legislation, land disposal of certain hazar-
dous wastes is to be banned. Short-term hazards posed by these wastes can be
controlled by specially engineered and constructed facilities. The banning of
wastes is intended to prevent hazards posed by certain wastes as the long-term
performance of the engineered facilities change. Analysis of these changes in
long-term performance provides information needed to determine which wastes to
ban.
1.1 Background
In accordance with the Resource Conservation and Recovery act of 1976 (RCRA)
and the Solid Waste Amendments of 1984 (Amendments), the U.S. Environmental
Protection Agency (EPA) must review all listed hazardous wastes and hazardous
constituents and determine which wastes should be banned from hazardous waste
land disposal facilities. The Amendments require waste to be banned for as
long as the waste is hazardous if the wastes are highly mobile, highly toxic,
persistent or bioaccumulate and pose a significant threat to human health and
the environment. Further, the EPA is developing a complementary test, EP-III,
for the toxlcity characteristic of hazardous wastes. This test, similar to the
existing test (EP-I) which screens wastes for the presence of selected mobile
heavy metals and organic compounds (40 CFR 261.24), will screen wastes for the
presence of other mobile organic constituents. Both tests are intended to be
1-1
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used by generators of solid wastes to determine if a waste is hazardous. While
specific criteria were established (i.e., 100 times National Interim Primary
Drinking Water Regulations) for the concentration of chemicals in the extract
of EP-I, new criteria need to be identified for chemicals that exceed these
criteria to determine if they should be banned from land disposal facilities.
Criteria will also be needed for waste classification and banning for chemicals
detected in the extract of EP-III.
The EPA, as part of a comprehensive regulatory development program to protect
human health and the environment from mobile and toxic wastes has identified
the following needs:
o identify wastes that should be classified hazardous and managed in Sub-
title C (hazardous waste) facilities; and
o identify those wastes that should be banned from Subtitle C land disposal
facilities.
Wastes chat are not classified as hazardous may be managed in Subtitle 0
facilities such as sanitary landfills, municipal incinerators and resource
recovery facilities.
EPA's Office of Solid Waste (OSV) is currently developing a framework for a
regulatory program to address these needs. This proposed framework is intended
to provide a generic screening procedure for all wastes generated in the United
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States. Under OSV's proposed framework, EPA will establish screening levels
for chemical constituents of wastes.
The screening levels will be transformed as maximum acceptable concentra-
tions for chemicals in air emissions, surface runoff and leachate emanating
from land disposal facilities. These transformed criteria will be established
through a back-calculation procedure. This procedure uses fate and transport
models that start from a point of potential chemical exposure at a concentra-
tion protective of public health and the environment and estimates the chemical
concentration in leachate that will not cause the criterion to be exceeded.
Wastes that yield a chemical concentration in the EP extract that exceeds the
transformed criterion will be classified as hazardous.
The transformed criteria will be further adjusted to account for the additional
control over hazardous wastes provided by engineered structures at Subtitle C
land disposal facilities. If chemical concentrations in the EP extract exceed
these adjusted criteria, then the waste would be banned from Subtitle C land
disposal facilities.
Adjustments may be based on one or more of the following:
o leaching environment and chemical flux to air, surface water or ground-
water;
o containment facilities (e.g., cover system, liner system); and
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o management controls (e.g., groundvater monitoring, operating and post-
closure care period procedures).
Leaching environments and chemical flux are highly site specific and waste
specific. Further, the interaction of wastes and mobile constituents of wastes
may significantly alter the chemical flux from a facility that occurs as
precipitation (e.g., rainfall) percolates through the waste deposit. Increases
in the chemical flux may occur by enhancing the solubility of a constituent by
the presence of a mobile chemical from another waste in percolating precipita-
tion. For example, hydrophobic chemicals may dissolve to a greater extent if
the percolating water contains sufficient organic solvents to enhance the
solubility of these chemicals. Decreases in chemical flux may occur due to
waste-waste interactions or other physicochemical or biological activity that
may occur during facility operation and containment of the waste after closure.
Examples of processes that may reduce chemical flux to the environment include:
o collection of mobile chemicals in leachate during operations and post-
closure care period (PCP):
o hydrolysis of organic wastes;
o waste/vast* interactions;
o chemical, physical and/or biological transformation or degradation of
hazardous constituents; and
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o volatilization.
Management of land disposal facilities is typically more structured and control-
led at Subtitle C facilities than at Subtitle 0 facilities. During operations,
wastes are screened, analyzed, and, if appropriate, rejected to protect the
performance of engineered containment systems and public health and the environ-
ment. Undesirable waste-waste interactions can also be avoided. Groundvater
monitoring, inspection, maintenance and reporting enhance the intended perform-
ance of the facility. Contingency plans and a regulatory program for correc-
tive action exist through the post-closure care period to prevent and control
chemical flux from the facility.
A greater degree of containment is typically provided at Subtitle C facilities
•
than at Subtitle D facilities. Installation and operation of leachate collec-
tion systems is specifically regulated. Cover and liner system components and
performance are also specifically regulated. Engineered controls are specified
in 40 CFR Parts 264 and 265 for Subtitle C and in 40 CFR 257 for Subtitle 0
land disposal facilities.
1.2 Objective
The objective of this report is to- identify how these engineered controls can
be incorporated into the back-calculation procedure. Engineered controls will
be analyzed and evaluated to factor these controls into OSW's approach for
for restricting land disposal of hazardous waste.
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The analysis takes into account the time importance of low permeable barrier
layers in cover and liner systems (e.g., polymeric geomembranes, clay), leach-
ate collection and removal systems, groundwater monitoring and corrective
action requirements of 40 CFR Parts 264 and 265. Particular emphasis is placed
on long-term events and performance of these control systems.
OSV's proposed regulatory framework is intended to provide & generic screening
procedure, independent of site specific factors and protective of human health
and the environment. The analysis and evaluation was conducted on a national
scale to incorporate engineered controls into OSV's proposed regulatory
•
framework.
1.3 General Approach
A procedure to incorporate engineering controls into OSW's proposed regulatory
framework needs to consider the following factors:
o chemical flux depends on the presence of a transport medium and the
leachability of specific chemicals in that medium; and
o performance of engineered controls depends on duration of exposure to
natural weathering processes and chemicals contained.
Chemical flux to groundwater from a land disposal facility occurs as a result
of chemicals dissolving into liquids migrating through the waste. Since bulk
and containerized liquid wastes are currently banned from land disposal facili-
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5.8S.102
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ties, chemical flux is the result of precipitation that percolates through the
waste.
Performance of engineered control structures in the short-term depends on
appropriate design, material selection and specification, construction, waste
screening, inspection, maintenance and monitoring. Over time, performance
characteristics of cover or liner system components can be expected to change.
Some components, such as polymeric geomembranes, may undergo dramatic change in
performance while other components, such as clay layers, may undergo more
limited change in performance. The effect these changes have on component and
system performance vill control the leaching rate and thus the mass and concen-
tration of chemical leached.
Duration of containment is important for evaluating the threat posed by hazar-
dous wastes if the processes identified in Section 1.1 can be reasonably
expected to significantly reduce mobility, toxicity or tendency to bioaccumu-
late during the containment period. Currently, there is insufficient informa-
tion available to accurately account for such significant reductions in waste
characteristics in a generic screening procedure. Where information is avail-
able, then the generator may seek a variance through a site-specific petition
procedure.
The back-calculation procedure proposed by OSW incorporates several important
characteristics:
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o the procedure should not be dependent on a limited mass of waste (the
procedure does not limit hazards due to the size of a facility or the
quantity of waste deposited in a facility); and
o the procedure is independent of long-term (on the order of thousands of
years) events or changes in facility performance.
These characteristics indicate that short-term performance of engineered
control, such as during operations or the typical 30 year PCP, are not import-
ant in transforming the screening levels to classification and banning
criteria. The most important characteristic is the leachate rate caused by
precipitation percolating through the waste.
Land disposal facilities typically include:
o waste piles;
o surface impoundments;
o landfill;
o land treatment; and
o subsurface injection well facilities.
Requirements of 40 CFR Parts 264 and 265 state that closure of waste piles and
subsurface impoundments must remove all hazardous waste or close in compliance
with all landfill regulations. Due to the long-term characteristic of the
screening procedure, only closed landfills are considered in assessing engin-
eered controls. Land treatment and subsurface injection well facilities
represent special cases and are not considered in this analysis.
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Analysis and evaluation of engineered controls at land disposal facilities
were incorporated into the proposed regulatory framework by the following
approach:
o identify significant mechanisms and extent of changes in leaching rates
from Subtitle C and D facilities;
o determine long-tera leaching rates representative of climatic and site
conditions within the contiguous 48 states for Subtitle C and 0 facili-
ties;
o develop an area weighted distribution of leaching rates; and
o conduct a sensitivity analysis of the parameters used to estimate the
leaching rates.
This approach was selected because the primary transport mechanism to the
groundwater is percolating precipitation, long-term performance will yield the
greatest chemical flux to the groundwater, and the procedure should be generic.
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2.0 ANALYTICAL APPROACH
The analytical approach used to incorporate engineered controls into land
disposal restrictions is based on the leaching process and anticipated long-
term conditions at the disposal facility. A standard set of conditions is used
to develop national leaching rate distributions for Subtitle C and D facili-
ties. Sensitivity analysis of the standard conditions describes the potential
variation for each distribution.
2.1 Leaching Process
Long-term chemical flux at land disposal sites is caused by precipitation
percolating through the vaste. The leaching process depends on regional
climatic conditions and site specific facility conditions. Quantitative
estimates of long-term leaching rates can be made using historic climatic and
anticipated facility conditions.
2.1.1 Climatic Conditions
Distribution of precipitation in the contiguous 43 states is shown in
Figure 2-1. Precipitation will vary from year to year, but typically will vary
less than 20 percent of the average precipitation. Precipitation in the form
of rainfall will initially enter or infiltrate the cover soil of a disposal
t
facility until the precipitation rate exceeds the infiltration rate and will
then drain from the facility as surface runoff. Water that infiltrates the sur-
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k.MU.fT.M)HUII.*M>MM.NU*.MnMaLOS> KM (NGtMCf WS.McfilMI HB.L.
FIGURE 2-1
MEAN ANNUAL PRECIPITATION (IN INCHES)
r.C.JORDANCO
-------
face soil is stored in the soil and transmitted to lower, less moist soils.
Infiltrating water is .removed from the soil through evaporation and transpira-
tion. Average evaporative losses are shown in Figure 2-2. Evaporative losses
from pans or lakes are used because of the difficulty in directly measuring
evaporation and transpiration losses from soil. Areas with high evaporative
losses are also found to have high evaporative-transpiration (E-T) losses.
Actual E-T losses will depend on such factors as solar radiation, wind speed,
humidity, plant type, (including leaf area and root zone) texture of surface
soil, and availability of water.
Precipitation in excess of losses due to surface runoff and E-T will result in
net infiltration or deep percolation to soils below the root zone. This net
infiltration is considered comparable to the long-term leaching rate at land
disposal facilities. Site specific facility conditions such as low permeable
layers or drainage layers may cause the leaching rate to be less than net
infiltration since these layers may divert percolating water from underlying
waste.
2.1.2 Analysis Method
Quantitative estimates of leaching rates are typically calculated using the
Hydrologic Evaluation of Landfill Performance (HELP) model or the Water Budget
(WATBUG) model. The HELP model relies on the Penman technique to estimate net
infiltration and was developed by EPA in 1980 (Perrier and Gibson, 1980) and
most recently revised in 1984 (Schroeder, et al., 1984) specifically for
hazardous waste landfills. The WATBUG model relies on the Thornthwaite method
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5.85.102
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MMP1CO »MH.
IWitC V MM tMMIIIMI. •>IM KISOXCIS
MtSMMI MH.l-.Mt* f««.»f», C.
FIGURE 2-2
AVERAGE ANNUAL LAKE EVAPORATION (IN INCHES)
L C.O J )/\NCO
-------
(Thornthwaite and Mather, 1957) of estimating net infiltration and has been
used for landfill applications in automated form since 1980 (Mather, et a_l.,
1980) and manual form since 1975 (Fenn, et al., 1975). The HELP model conducts
the water balance computations on a daily time step, but relies on average
monthly temperatures; and the WATBUG model relies on a monthly time step.
The HELP model was adapted from similar models developed by the US Department
of Agriculture and incorporates analytical modules that account for drainage
barrier layers that can be installed in cover or liner systems. The VATBUG, in
the form presented by Mather, does not account for such drainage layers.
The HELP model is readily available through a National Technical Information
Service (NTIS) time-share computer and includes the most recent 5 years of
climatic data at more than 100 reporting stations. The WATBUG uses a 25-year
average of climatic conditions and requires that precipitation data be entered
into the computer for each station.
The HELP model was chosen to conduct this analysis of the leaching rate for the
following reasons:
o the ood«l is currently being validated and documented by the EPA for land
disposal sites; whereas a comparable validation and documentation is not
available for the WATBUG model;
o ease of access to the large number of reporting stations compared to
manual entry for WATBUG;
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5.85.102
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o 5 years of data was not considered 'to be an overly restrictive data base
compared to 25 years (see Appendix A); and
o barrier and drainage layer performance is already incorporated into the
HELP model.
2.2 Climatic Data Base
The precipitation data, Figure 2-1, and evaporation data, Figure 2-2, were used
to identify ranges of conditions that may be encountered in the contiguous
48 states. These conditions are summarized in Figures 2-3 through 2-8. Six
precipitation ranges were selected as representative of the U.S. and three E-T
conditions were selected. A total of 18 climatic conditions were identified
for developing the national leaching rate distributions. Greater definition of
the distribution is possible by selecting a larger .number of precipitation
and/or evaporation conditions. If greater definition is desired, emphasis
should be placed in areas of the country where precipitation is greater than
C-T because these areas yield the larger leaching rates.
A reporting station of climatic data was selected in each of the 18 areas shown
in Figures 2-3 through 2-8. Stations were selected from the more than 100
cities included in the HELP model.data base. Cities selected are listed in
Table 2-1. Since some areas selected are larger than others, it may be desir-
able to relate the estimated leaching rate to the percent of the total area of
the contiguous 48 states.
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ADATIfP «NOM
I AM (WttAAIION- lINSHf AND fHANIUII. «B>lfl» III SuKCCIV tNCIMCCMINC; MtOHAHI KILI .MB (OMI.im; P 12
ti» fat*.11*2,p. r«
FIGURE 2-3
LESS THAN 10* ANNUAL AVERAGE PRECIPITATION
EC JOKI )ANCO
-------
O
it Si TWIN M'MMUM mtiucc CWKMAIUN
| JO" 1O 4O~MMUM. MflUCf tWPOHAIION
I OXIAIth TNM 4O"*MMMt »VEIUC( EtMnMATlOM
MMPItO (MM
IMVtl «M> flUN/IHI. mliH HtSOUMCIS mtUHtHUX.. M»6«U1II MUL .Mt» »OM«.l»t»: P
tK (OMK.IM2.P. ?•
FIGURE 2-4
10' TO 20' ANNUAL AVERAGE PRECIPITATION
1C JCM WM (X)
-------
o
US* THMI «O'»Nm»l AVtNMi f WVOIUIKM
4O" 1O Mt'MMUtt ACIUGt tVWUMION
THAN M>"*NMUAL Avtfuct
AUAflfU >NOM
t*M CWKMOOI- IMSlO AMI rwHIWI.
tMC.MtHaW,.>kUWU»IIILI..Nt» >bM.I»r»; K 12
» naw.iMt.i*. T*
FIGURE 2-5
20' TO 32* ANNUAL AVERAGE PRECIPITATION
rc.xjki >ANCX>
-------
C ) itSS fIMN 3O" ANNUM. MCMMiC f WOIIA1ION
^ »" 1O «O" ANNUM. (WIIUCC
CWMIH IIMN 4ONMK>N
UMICtMWRMIM lIMlt I *MOf**N2«l. »«H» MSOUBU
. MttMMt IM.I . M* lONK.Ktt, f U
FIGURE 2-«
32" TO 40' ANNUAL AVERAGE PRECIPITATION
rCJUKDANCO-
-------
o
if ss IHMI JU'MMUM. tintatx CMPOIWIION
JO" IO 4O" ANNUM. AVCNAGC {WkfOMATlON
CMMCM IHAN 4O"ANNUM. WltUOt (VAfCMAIKM
I Mi{n ^^^aJ^^tts
. giQIIM.UCl.
MI MM HUI .HIM fO»n.i»/».r
, VlUKM nil I ,M« »O«t>l. I»»^ . P
FIGURE 2-7
40* TO 48* ANNUAL AVERAGE PRECIPITATION
LCJOM)ANCO
-------
CftfOTfft
f f *M> >*U t(* tMHMm4».Mim«»l lint Htm KM»,I9B.*,P I*
FIGURE 2-8
GREATER THAN 48* ANNUAL AVERAGE PRECIPITATION
fC.IORDANCO
-------
TABLE 2-1
CITIES SELECTED FOR CLIMATIC DATA2
PRECIPITATION EVAPORATION
RANGE0 POTENTIAL
CLIMATOI.OG1CAL
CENTER
AVERAGE 5-YEAR
PRECIPITATION0
PERCENT OF
TOTAL AREA4
<10
10-20
20-32
32-40
40-48
>48
a
b
c
Low
Meditui
High
Low
Medium
High
Low
Ned ilia
High
Low
Medium
High
Low
Medium
High
Low
Hediua
High
Based on USEPA HELP model
Inches per year (assumes
Percent of total area of
Pocatello, ID
Cedar City, UT
Las Vegas, NV
Great Falls, MT
Rapid City, SO
Midland, TX
St. Cloud, HN
Grand Island, NE
Oklahoma City, OK
Hontpelier, VT
Cleveland, Oil
Columbia, MS
Boston, MA
Indianapolis, IN
Charleston, SC
Astoria, OR
Knoxville, TN
Tallahassee, FL
unit area).
contiguous 48 states.
9.8
9.8
5.3
17.9
15.4
16.3
25.8
22.2
30.4
34.5
36.7
37.1
40.9
40.3
48.3
65.6
48.1
68.4
,
3
2
3
3
18
11
9
4
5
3
5
3
3
7
5
2
3
11
5.85.102
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2.3 Facility Conditions
The design conditions used in predicting the leaching rate are based on current
state and federal regulations, and guidance criteria from EPA documents. The
major design conditions considered in analyzing engineered controls include:
cover and liner configuration (e.g., slope, soil types, barrier layer mater-
ials), type of vegetative cover and depth of root (evaporative) zone. The
standard set conditions used in the analysis of Subtitle 0 and Subtitle C
facilities are discussed below.
2.3.1 Subtitle D Facility. Subtitle D facilities are typically municipal
solid waste landfills. These types of landfills are regulated by state
agencies. These regulations include specific design requirements as veil as
site location, operating and other requirements. In addition, federal guide-
lines for Subtitle D facilities are found at 40 CFR 257. A review of state
regulations concerning cover and liner requirements found the following:
1. 90 percent of the 30 states require a minimum of 2-feet of cover
soil; and
2. 90 percent of the 50 states have no specific requirements for liner
systems beneath Subtitle D facilities.
The type of soil selected for use in the cover must be able to support vegeta-
tion and to minimize infiltration. Soil textures, as classified by the U.S.
Department of Agriculture (USDA), commonly used to meet this requirement
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include loamy sand, loam and clayey loam. A 24-inch thick loam soil
placed on a slope of 2 to 5 percent will comply with the regulations found in
over 90 percent of the 50 states and was selected for the standard conditions
of this analysis. The type and condition of vegetative cover at the Subtitle D
landfill influences the leaching rate by controlling infiltration rates,
evapotranspiration and surface runoff. Landfill covers are usually seeded with
a mixture of grass to control erosion. Because the cover soils required are
expected to be conducive to grass growth, complete coverage or a good grass
stand would be expected shortly (several years) after seeding the cover. The
root zone of grass species can extend to 36 inches and more. However, the root
zone is not expected to penetrate the waste layer, which is at a depth of 24
inches, due to unsuitable growing conditions in the waste layer. Vaste mater-
ial in sanitary landfills will decompose (e.g., production of acids, methane
and carbon dioxide), creating an unsuitable growing condition which would
inhibit the roots from penetrating below the cover soil layer.
Vegetative cover may progress to other species in the long-term, depending on
the climatic conditions, indigenous species in the vicinity of the landfill,
and growth conditions prevalent in the landfill cover. This long-term vegeta-
tive species progression was not considered since such a long-term vegetative
species progression is highly sensitive to site-specific conditions, it may
also be expected at Subtitle C facilities, and the greatest chemical flux at
sanitary landfills occurs in the first several years after waste placement.
Based on the above information, the conditions used in analyzing long-term
Subtitle D facility performance using the HELP model included:
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o 2-feet of cover soil consisting of a loam texture and a good grass
stand on a 2 to 5 percent slope;
o root zone of 24 inches; and
o no liner system beneath the site.
These conditions are depicted in Figure 2-9. A sensitivity analysis of soil
texture and root zone depth is discussed in Section 3.0.
2.3.2 Subtitle C Facility. Subtitle C facilities are regulated by federal
regulations for the disposal of hazardous wastes. Specifically, the regula-
tions cited in the 40 CFR Parts 264 and 265 and requirements of the Amendments
provide the framework for engineered controls. In addition, the EPA has issued
guidance to owners and operators of land disposal facilities (Lutton, 1980;
EPA, 1932; EPA, 1983; EPA, 1984; EPA, 1985). These engineered controls for
disposal facilities include multi-layered cover/liner systems consisting of
drainage layers, geooembrane barriers and soil barriers. Several cover/liner
system configurations that will meet the regulations are depicted in Figure
2-10. The configurations include on* cover system and three liner systems.
The cover system consists of a 2-foot cover soil layer above a 1-foot drainage
layer, a geooembrane liner bedded with filter fabric, followed by a 3-foot clay
layer.
The liner systems shown on Figure 2-10 all include leachate collection and
detection layers. The difference between the liner systems is the combination
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COVER SYSTEM
COVER
SOIL
_L
GOOD GRASS CONDITION
ROOT ZONE
LINER SYSTEM
NO FLOW
IMPEDANCE
FIGURE 2-9
SUBTITLE "D"
FACILITY CONDITIONS USED IN
ESTIMATING LEACHING RATES
ECJORDANCQ
-------
GEOMEMBRANE-
FILTER FABRIC
LCS
LO/CS
CLAY
NO FLOW
IMPEDANCE
LEGEND
LCS LEACHATE COLLECTION
LO/CS LEACHATE DETECTION/COLLECTION SYSTEM
GEOMEMBRANEt ASSUMED TO FAIL
AND NO FLOW IMPEDANCE)
I
CLAY
GOOD GRASS CONDITION
ROOT ZONE
CLAY
I
(SAME IMPEDANCE
AS COVER SYSTEM)
UNER SYSTEMS
LONG TERM
FIGURE 2-10
SUBTITLE mC'
FACILITY CONDITIONS USED IN
ESTIMATING LEACHING RATES
ECJORDANCO
-------
of barrier layers used. The combinations, include the use of two geomembranes
separated by a drain layer, a geomembrane separated from a clay layer, and a
geotnembrane separated from a geomembrane-clay composite layer.
Since the analysis of engineered controls is intended to evaluate long-term
performance (e.g., several centuries.), the leaching rate of configurations
described above is expected to change.
The principal change affecting leaching rate is expected to be the degradation
of the geomembranes to a point where they are no longer effective in control-
ling water movement. In addition, the leachate collection/detection systems
that remove leachate from the facility are not expected to be operating over
this period. The clay liners are expected to have greater hydraulic conduc-
tivity as a result of geologic change (e.g., weathering) and exposure to
chemicals.
Practical experience with the performance of polymeric geomembranes as barriers
to water flow is limited to a few decades. Use of geomembranes to contain
mobile wastes in landfill environments is limited to less than 20 years. An
assessment was made of the service life of geomembranes used to contain hazar-
dous wastes at land disposal facilities (Lyman, et al.. 1983) this assessment
indicated there is limited data available on which to project long-term service
life but containment may be expected over several decades and could possibly
extend over 100 years. Since the long-term analysis of engineering controls
considers performance over several centuries and the service life of geomem-
branes is estimated to be a fraction of this period, the effectiveness of
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geomembranes barriers to control leaching rates is expected to be equal to or
less than clay barriers.
Clays are residual soils created through physical and chemical weathering of
rocks and minerals such as feldspars in granite and pegmatites. The silicon-
oxygen sheet structures of these minerals combine with aluminum, sodium,
calcium, potassium and magnesium cations, some iron oxides and hydroxl mole-
cules from water to form hydrous silicates -- mainly Icaolinite, illite and
montmorillinite clays. Clays are relatively stable, although they exchange
cations and dehydrate and hydrate to variable extents.
Clays are regionally distributed in the U.S. and are susceptible to specific
geologic weathering processes. In general, the most important long-term
weathering process of clay barriers at waste disposal facilities is the develop-
ment of soil structure (fabric). Soil fabric may result from wetting and
drying in response to percolating precipitation. Clay particles tend to
flocculate and clump together in aggregates, or peds, when the clay dehydrates.
The formation of peds is a slow gradual process that transforms the clay
barrier into blocks of soil. These blocks of soil cause an increase in the
hydraulic conductivity of the clay barrier. The extent of this increase
depends on th« extent of dehydration. Clay barriers in cover and liner systems
are not as susceptible to formation of peds as similar clays at the ground
surface since they are less susceptible to large fluctuations in moisture
content caused by evapotranspiration of percolating water.
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Naturally occurring clay soils near the ground surface can be considered
representative of the extent of geologic weathering to which clay barriers in
Subtitle C facilities will be exposed. A Soil Conservation Service survey of
clay soils for states across the U.S. indicates hydraulic conductivity ranged
from 1.4 x 10~* to 4.3 x 10~* cm/sec for soils at depth of 30 to 80 inches.
It is anticipated that natural clays with an in-situ hydraulic conductivity on
the order of 10 * cm/sec can be compacted to achieve the 10 T cm/sec required
by the Amendments. Therefore, the slower hydraulic gradient (4.3 x 10~*
cm/sec) is probably representative of the upper limit for hydraulic conductiv-
ity that may result from geologic weathering of clay barriers in 'engineered
controls at Subtitle C facilities. An even slower hydraulic conductivity may
be more typical of the long-term clay performance of clay barriers since some
weathering processes, such as transport of fines by percolating water from the
soils overlying the clay barrier tends to reduce hydraulic conductivity by
plugging pores of the clay soil.
The use of clay soils as barrier layers in cover or liner systems is subject to
both geologic weathering and alteration of the clay soil structure on exposure
to chemicals. These alterations can lead to increased hydraulic conductivity.
Alteration of the clay soil structure may be caused by dissolving constituents
of the clay mineral, including aluminum, iron and silica (Brown and Anderson,
1983). Changes in the colloidal characteristics of the clay mineral may cause
flocculation and increased hydraulic conductivity. The extent of alteration is
controlled by such factors as type of clay mineral, waste constituent, mixture
of chemicals and concentration of chemicals. As these alterations progress
increased flow of percolating liquids may cause piping. These alternations may
2-21
-------
cause the hydraulic conductivity of some clay soils to increase by a factor of
100 (Anderson, 1982). While much of the current knowledge of chemical inter-
actions with clay is based on laboratory studies with concentrated
chemicals, there is a potential for increased hydraulic conductivity to occur
under field conditions. Additional information is needed to determine the
increase in hydraulic conductivity caused by aqueous solutions of chemicals
under field conditions. The increase, however, is not expected to be greater
than the 100 fold increase observed for concentrated chemicals under laboratory
conditions. A hydraulic conductivity range of 5 x 10*( to 5 x 10"T cm/sec
appears to be reasonable to estimate long-term performance of clay barriers
exposed to chemicals.
Based on the above information, the conditions used in analyzing long-term
Subtitle C facility performance using the HELP model included:
o 2 feet of cover soil consisting of a loam texture and good grass
stand;
o 1-foot drainage layer at a two percent slope to free drain at toe of
slope;
o root zone of 36 inches; and
o 3-foot clay layer with a hydraulic conductivity of 1 x 10 ' cm/sec.
2-22
5.85.102
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A bottom liner system was not included in^ the design because the clay layer in
the bottom liner is subject to similar conditions as the clay layer in the
cover system and is also exposed to chemicals leaching from the waste. There-
fore, the hydraulic conductivity of the bottom clay liner is expected to be
equal to or greater than the clay layer in the cover and is not expected to
control the leaching rate.
A sensitivity analysis was conducted to determine the variation in estimated
leaching rates by varying the cover soil texture, clay hydraulic conductivity
and root zone depth. The results of this analysis is presented in Section 3.2.
2-23
5.85.102
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3.0 CONCLUSIONS AMD. RECOMMENDATIONS
3.1 Leaching Rate Distributions
Leaching rates for Subtitle C (hazardous) and Subtitle D landfill facilities
were estimated with the HELP model for conditions considered representative of
long-term performance. Leaching rates were estimated for 18 climatic condi-
tions encountered in the contiguous 48 states. A summary of leaching rates is
provided in Table 3-1. This information is expressed as percent of area in the
contiguous 48 states where leaching rates may be expected to equal or be less
than the rate shown.
Estimates of leaching rates suggest the rates are not randomly distributed in
the contiguous 48 states, but are highly dependent on the annual precipitation.
Leachate was estimated for all chosen locations of Subtitle D facilities.
These leaching rates ranged approximately 2 orders-of-magnitude (100 fold) from
Pocatello, ID to Astoria, OR (35.9 inches per year), while precipitation ranged
over one order-of-magnitude. Long-term leaching was not estimated to occur at
Subtitle C facilities receiving less than 20 inches per year of precipitation
(with one exception). Where leaching was estimated to occur at Subtitle C
facilities, the rate was generally 2 to 3 times less than for Subtitle D
facilities.
The distributions of leaching rates shown in Figure 3-1 indicate Subtitle C
facilities are expected to leach at a rate less than for Subtitle D facilities.
3-1
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TABLE 3-1
LEACHING RATES SUMMARY*
PRECIPITATION
RANGE0
<10
10-20
20-32
32-40
40-48
>48
EVAPORATION
POTENTIAL
Low
Medina
High
Low
Medium
High
Low
Medium
High
Low
Medium
High
Low
Medium
High
Low
Medium
High
LEACHING
"C"
0.0
0.0
0.0
0.0
0.0
0.4
0.3
0.5
0.5
3.6
3.7
2.9
7.0
3.3
2.5
11.9
7.1
6.9
RATE"
"D"
0.1
0.3
0.2
0.8
0.6
1.2
1.5
1.5
2.4
7.2
6.8
4.8
12.1
6.8
5.8
35.9
12.2
12.1
CLIHATOLOGICAL
CENTER
Pocatello, ID
Cedar City, UT
Las Vegas, NV
Great Falls, MT
Rapid City, SD
Midland, TX
St. Cloud, MN
Grand Island, NE
Oklahoma City, OK
Montpelier, VT
Cleveland, OH
Columbia, MS
Boston, MA
Indianapolis, IN
Charleston, SC
Astoria, OR
Knoxville, TN
Tallahassee, FL
AVERAGE 5-YEAR
PRECIPITATION11
9.8
9.8
5.3
17.9
15.4
16.3
25.8
22.2
30.4
34.5
36.7
37.1
40.9
40.3
48.3
65.6
48.1
68.4
PERCENT OF
TOTAL AREAC
3
2
3
3
18
11
9
4
5
3
5
3
3
7
5
2
3
11
b
c
Based on USEPA HELP model estimates. Estimates for Subtitle C 'facilities assume an evapotranspiration
zone of 36 inches and 24 inches for Subtitle 0 facilities.
Inches per year (assumes unit area).
Percent of total area of contiguous 48 states.
5.85.102
0055.0.0
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I
o
o
a
CB
O
>
«
Subtitle 'C' Facility
D Subtitle-D* Facility
10
FIGURE 3-1
ESTIMATED DISTRIBUTION OF UNIT AREA LEACHING
RATES FOR SUBTITLE C AND D FACILITIES
ECJORDANCO
-------
The distributions may be better defined if more climatological centers are
evaluated (up to 100 reporting cities are included in the HELP data base), but
the basic trends and differences are not expected to change dramatically.
3.2 Sensitivity Analysis
Since the leaching rates shown in Table 3-1 and Figure 3-1 were estimated for a
standard set of conditions, an analysis was conducted to determine the effect
on leaching rate over a range of conditions that may be encountered. This
analysis was conducted using Indianapolis, IN. Other climatological centers
would be expected to respond in a similar manner. Conditions that were varied
included cover soil texture, hydraulic conductivity of the barrier layer and
evapotranspiration zone.
Cover soil texture effect on estimated leaching rates was analyzed for loamy
sand and clayey loam. These soils are considered reasonable substitutes for
the loam soil that was used in the standard conditions. As may be expected,
use of more permeable loamy sand in the cover to support vegetation was found
to yield more leachate than loam. The leaching rate was almost doubled for the
Subtitle C facilities while it was tripled for Subtitle 0 facilities. The
leaching rat* was less affected by use of clayey loam instead of loam
(<10 percent at Subtitle C facilities and <20 percent at Subtitle 0 facili-
ties). This suggests that the use of cover soils less permeable than loam will
have a minor effect on the estimated leaching rate whereas the use of more
permeable cover soils will increase leaching rates more at Subtitle D facili-
ties than at Subtitle C facilities.
3-4
5.85.102
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TABLE 3-2
SENSITIVITY ANALYSIS SUMMARY
LEACHING RATE3
CONDITION
Standard Conditions 3.3 6.8
Soil Texture
Loamy Sand 6.11 19.71
Clayey Loam 2.97 5.22
Hydraulic Conductivity, k
5 x lO", cm/sec 4.3
5 x 10"' cm/sec 2.2
Evapotranspiration (E-T) Zone
Depth = half of standard condition 7.34 11.6
a inches per year (assumes unit area) for Indianapolis, IN
location: q,, = Subtitle C facility
q|j = Subtitle D facility
Standard Conditions included:
cover soil texture _6 loam
barrier layer hydraulic conductivity 10" cm/sec
evapotranspiration zone 36 inches for Subtitle C facility
24 inches for Subtitle D facility
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3 Hydraulic conductivity in barrier layers in cover or liner systems was varied
from 5xlO~* to 5xlo"7 cm/sec to determine the effect on leaching rate from the
standard condition of 10 ' cm/sec. Since Subtitle D facility cover systems
were not assumed to provide such a barrier layer, the analysis was limited to
Subtitle C facilities. The analysis indicated changes in leaching rates on the
order of approximately 50 percent.
Reducing the depth of the zone where evapotranspiration may occur increased the
Subtitle C leaching rate by a factor of almost 2.5, while the Subtitle D
leaching rate increased by a factor of 1.7. This difference in effect on
leaching rates caused by reducing the evapotranspiration zone suggests that the
greater depth used for the Subtitle C facility (36 inches) provides more
control over leaching rates than the shallower depth (24 inches) used for
Subtitle D facilities.
Comparison of the relative importance of the conditions analyzed indicated the
evapotranspiration depth is the most important condition for estimating Sub-
title C leaching rates followed by use of more permeable soils for barriers and
cover systems. The same two conditions, but in reverse order, were the most
important in affecting Subtitle 0 leaching rates. In all cases, Subtitle D
leaching rates were greater than for Subtitle C.
The sensitivity analysis was conducted over a reasonable range of long-term
conditions. The estimated leaching rates over these ranges therefore provide a
means of estimating the range of leaching rates that may be expected for these
facilities under climatic conditions represented by Indianapolis, IN. Sub-
3-6
5.85.102
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title C facilities in Indianapolis may leach at a rate ranging from 2.2 to
7.34 inches per year, whereas, a Subtitle D leaching rate may range from 5.22
to 19.71 inches per year. The range of leaching rates may be greater if more
than one standard condition is varied.
3.3 Application of Distributions
3.3.1 Use. Leaching rates and their frequency of occurrence in the contiguous
48 states were estimated for use in developing a generic procedure to classify
wastes as hazardous and determine hazardous wastes to be banned from Subtitle C
land disposal facilities. The leaching rates provide a means of estimating the
chemical flux (mass rate of chemical release) from both Subtitle C and D
facilities. The volumetric flux (volumetric rate of leachate production)
identifies the transport rate which is leaching mobile chemicals out of the
facility. When leaching rate is multiplied by concentration of chemicals in
the leachate, then the chemical flux is described on a unit area basis. It is
appropriate to express this flux on a unit area to maintain the generic appli-
cation of the procedure.
The generic procedure is to be used to select chemical concentration criteria
for use with a simple extraction procedure (e.g., Extraction Procedure III -
organics). The EPA must ultimately select a specific leaching rate to deter-
mine the chemical concentration criterion that is protective of human health
and the environment. Maximum protection is provided by selecting the greatest
leaching rate.
3-7
5.85.102
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Selection of an appropriate chemical concentration may be a complex task. An
upper concentration limit may be identified as the solubility of the chemical
in an aqueous solution. This assumes that vastes placed in the facility are
not, or do not, contain free liquids and must dissolve into precipitation that
percolates through the wastes. This approach to identifying a chemical concen-
tration has several limitations:
o not all chemicals have solubility limits in water (i.e., some chemicals
are miscible in water);
o solubility concentrations are rarely attained because of the inherent
kinetics of the leaching process and chemical equilibria; and
o may far exceed actual leachate concentrations.
Alternatively, an appropriate concentration can be estimated by an iterative
process to determine the concentration that, when released to an underlying
groundwater system and transported downgradient to a receptor, does not cause
adverse human health or environmental effects. This iterative process can be
conducted after a specific leaching rate is selected or can be conducted on a
mass flux basis (e.g., product of leaching rate and chemical concentration).
The appropriate leaching rate and concentration that meets the chemical flux
criterion can then be selected.
3-8
5.85.102
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3.3.2 Limitations
Limitations of the leaching rate distributions and their use may be described
as:
o analytical assumptions; and
o geographical distribution of leaching rates.
The analytical approach has several limitations that were described in
Section 2. These limitations relate to the data base used to project long-term
performance. Use of the HELP model is based on 5 consecutive years of climatic
data. Although an assessment was made that suggested limited differences in
average precipitation for the 5-year and 25-year periods, the significance of
several years of abnormally high precipitation or permanent shift in climatic
conditions has not been evaluated.
The conditions projected to prevail in the long-term are not based on an
extensive long-term data base. Reasonable assumptions were made to identify a
range of conditions that may prevail in the future. A particularly important
assumption was that performance is controlled by natural activities and not by
human disturbance of the low permeable barrier.
Geographical distribution of the estimated leaching rates presents a limitation
to its use in the generic procedure. Low leaching rates prevail in certain
areas of the nation and high leaching rates in other areas. If a leaching rate
3-9
5.85.102
0044.OiO
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is selected in establishing criteria for'specific chemicals, then two undesir-
able effects may occur:
o over-regulation of wastes in areas with low leaching rates; and
o under-regulation of wastes if the leaching rate is larger than the rate
selected for the criterion.
Under-regulation of wastes can be avoided by using the maximum estimated
leaching rate for selecting chemical concentration criteria. Both limitations
can be avoided by establishing land disposal banning criteria expressed as a
mass flux (e.g., the product of leaching rate and concentration). The owner/
operator of a specific facility could readily identify if a waste with appropri-
ate testing results (i.e., EP-III) is banned. This approach allows higher
concentrations in areas with low leaching rates and requires low concentrations
in areas with high rates. Using the mass flux rate approach, the rule or
classification procedure becomes national in scope, avoids over- or under-
regulation, protects human and the environment, and allows climatic conditions
and costs to control where wastes are deposited in a protective manner.
3.3.3 Summary
The analysis of engineered controls for land disposal of wastes yielded distri-
butions of leaching rates (Figure 3-1) for the contiguous 48 states. The
Subtitle C distribution yielded estimated leaching rates that were always less
(generally 1/2 to 1/3) than the Subtitle D leaching rates. The depth of the
3-10
5.85.102
0045.0.0
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evaporative zone was found to be the most sensitive long-term site condition
used to estimate leaching rates at Subtitle C facilities. Soil texture was
found to be the most sensitive long-term site condition for Subtitle D facili-
ties.
The distributions are useful in developing a generic procedure for classifying
hazardous wastes and banning wastes from land disposal facilities. The EPA may
use the distributions to develop chemical criteria in one of the following
approaches:
o select a leaching rate and then determine an appropriate chemical concen-
tration criterion; or
o determine an appropriate chemical mass flux rate from a facility by
back-calculation from a health/environmental based criterion; and estab-
lish a mass flux criterion with regional maps of leaching rates for use by
owners/operators of disposal facilities; or
o establish a concentration criterion using the maximum leaching rate and
over-regulate wastes in low leaching rate areas; or
o establish a concentration criterion using a leaching rate that will
under-regulate higher leaching rate areas and over-regulate lower leaching
rate areas.
3-11
5.85.102
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REFERENCES
Anderson, D., 1982. "Does Landfill Leachate Make Clay Liners More Permeable?"
Civil Engineering, September, pp 66-69.
Brown, K.W. and D.C. Anderson, 1983. "Effects of Organic Solvents on the Per-
meability of Clay Soils." EPA-600/S2-83-016, April.
Environmental Protection Agency, 1982. "Draft RCRA Guidance Document: Land-
fill Design, Liner Systems and Final Cover." Washington, D.C.
Environmental Protection Agency, 1983. "Lining of Waste Impoundment and Dis-
posal Facilities." SW-870. Revised Edition. Washington, D.C.
Environmental Protection Agency, 1984. "Permit Applicants' Guidance Manual
for Hazardous Waste Land Treatment, Storage, and Disposal Facilities Final
Draft." EPA 530 SW-84-004. Washington, D.C.
Environmental Protection Agency, 1985. "Minimum Technology Guidance for Double
Liner Systems." Washington, D.C.
Environment Reporter. State Solid Waste-Land Use Bureau of National Affairs.
Perrier, E.R., and A.C. Gibson, 1980. "Hydrologic Simulation on Solid Waste
Disposal Sites (HSSWDS)." SW-868, U.S. Environmental Protection Agency,
Cincinnati, OH.
Fenn, D.G., K.J. Hanley and T.V. DeGeare, 1975. "Use of the Water Balance
Method for Predicting Leachate Generation from Solid Waste Disposal
Sites". EPA/630/SW-168, U.S. Environmental Protection Agency, Cincinnati,
OH.
Lutton, R.J., 1980. "Evaluating Cover Systems for Solid and Hazardous
Waste." SW-867. U.S. Environmental Protection Agency. Washington, D.C.
Lyman, W.J., et al., 1983. "Expected Life of Synthetic Liners and Caps."
Draft Final Report. Contract 68-01-6160. Arthur D. Little, Inc. for U.S.
Environmental Protection Agency, Washington, D.C.
Mather, J.R., and P.A. Rodriquez, 1980. "The Use of the Water Budget in
Evaluating L«aching Through Solid Waste Landfills." PB 80-180888,
National Technical Information Service, Springfield, VA.
NOAA 1980. Climates of the States. National Oceanic and Atmospheric Admini-
stration, Second Edition.
Schroeder, P..R., et al., 1984. "The Hydrologic Evaluation of Landfill Per-
formance (HELP) Model: Volume I - User's Guide for Version I and
Volume II - Documentation for Version I." EPA/530-SW-84-009 and -010,
U.S. Environmental Protection Agency, Washington, D.C.
5.85.102
0047.0.0
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Thornthwaite, C.W., and J.R. Mather, 1957. "instructions and Tables for Com-
puting Potential Evapotranspiration and the Water Balance" in Publica-
tions in Climatology, Volume X, No. 3. Laboratory of Climatology, Drexel
Institute of Technology, Elmer, New Jersey.
5.85.102
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APPEiNDIX ,'A
COMPARISON OF 5 AND 30 YEAR PRECIPITATION DATA
5.85.102
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APPENDIX A
COMPARISON OF 5-YEAR AND 30-YEAR
PRECIPITATION DATA
Analysis of the long-term performance of engineered controls at waste disposal
facilities relied on the 5-year precipitation data base used in the HELP model.
The appropriateness of using a 5-year data base was assessed by comparing the
5 year average annual precipitation to an average from a longer period.
Average annual precipitation collected over a 23- to 30-year period for the
climatological centers used in the analysis of engineering controls compiled
from "Climates of the States" (NOAA, 1980). These data are presented in
Table A-l along with the 5-year annual average precipitation computed for the
HELP model data base. Comparison of the two averages for each center showed
differences in averages from less than 1 percent to 27 percent. The larger
differences tend to occur in the low precipitation ranges. Two-thirds of the
centers exhibited average annual precipitation differences of less than
5 percent. The 5-year HELP averages for those centers in the higher precipita-
tion ranges (>32 inches per year) were generally greater than for the 30 year
average. This general trend was reversed for the lower precipitation ranges.
In addition, the larger differences (>5 percent) were generally because the
HELP data base provided a larger average annual precipitation than the 30-year
average.
Based on the above assessment of average annual precipitation, the following
observations are made:
5.85.102
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TABLE A-l
COMPARISON OF 5 AND 30 YEAR
AVERAGE PRECIPITATION
PRECIPITATION" EVAPORATION
RANGE POTENTIAL
<10
10-20
20-32
32-40
40-48
>48
Low
Medina
High
Low
Medium
High
Low
Medium
High
Low
Medium
High
Low
Medium
High
Low
Medium
High
CLIMATOLOGICAL AVERAGE PRECIPITATION"
CENTER 5 -YEAR 30-YEARC
Pocatello, ID
Cedar City, UT
Las Vegas, NV
Great Falls, MT
Rapid City, SO
Midland, TX
St. Cloud, MN
Grand Island, NE
Oklahoma City, OK
Montpelier, VT
Cleveland, OH
Columbia, MS
Boston, MA
Indianapolis, IN
Charleston, SC
Astoria, OR
Knoxville, TN
Tallahassee, FL
9.8
9.8
5.3
17.9
15.4
16.3
25.8
22.2
30.4
34.5
36.7
37.1
40.9
40.3
48.3
65.6
48.1
68.4
10.8.
9.97d
4.16
14.99
17.55
13.31
26.84
23.41
31.73
33.23e
34.93
37.39
41.50
39.90
48.73
66.34
46.18
61.58
PERCENT
DIFFERENCE
9
1
27
19
12
22
3
5
4
3
5
0.7
1
0.8
0.8
1
4
11
a Inches per year (assumes unit area)
b Based on HELP model, May, 1985.
c Based on "Climates of the States".
d 24-year
e 23-year
average.
average.
5.85.102
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o distribution of leaching rates estimated using the HELP model tend to
over-estimate the long-term performance of land disposal facilities;
o the larger differences between the two precipitation averages are associ-
ated with the lower precipitation ranges (<20 inches per year) which were
estimated to yield small leaching rates.
5.85.102
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APPENDIX E
ANALYSIS OF ENGINEERED
CONTROLS OF SUBTITLE C
FACILITIES FOR LAND DISPOSAL .
RESTRICTIONS DETERMINATIONS
REVISED DISTRIBUTION OF LEACHING RATES
9.35.124
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TABLE OF CONTENTS
SECTION
1.0
2.0
3.0
4.0
TITLE
INTRODUCTION
REVISED LEACHING RATE DISTRIBUTIONS
2.2 Climatic Data Base
2.3 Leaching Rate Distribution
COMPARISON OF 5-YEAR AND 20-YEAR PRECIPITATION
DATA
CONCLUSIONS
PAGE NO.
1-1
2-1
2-1
2-1
2-3
3-1
4-1
REFERENCES
9.85.124
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1.0 INTRODUCTION
As part of recent federal legislation, the U.S. Environmental Protection Agency
(EPA) must review all listed hazardous wastes and determine which wastes should
be banned from land disposal facilities. The general approach for identifying
such wastes was developed by EPA's Office of Solid Waste (OSW). OSV's analyti-
cal procedure includes credits for engineering controls that are designed into
Subtitle C facilities. These engineering controls are used to determine
leaching rates from Subtitle C facilities based on long-term performance (e.g.,
beyond anticipated design life). An analysis of leaching rates from Subtitle C
facilities and Subtitle D facilities was performed and reported in June and
August of 1985 (Jordan, 1985). Jordan's analysis evaluated 18 climatic centers
throughout the contiguous 48 states. Recommendations for future studies
included 1) an increase in the number of cities evaluated; and 2) comparing
leaching rates based on the 5-year HELP1 model data base to a long-term (i.e.,
20-years) precipitation data base. This report presents the results of the
additional analyses conducted in accordance with those recommendations.
1 Hydrologic Evaluation of Landfill Performance (Schroeder, et. al., 1984)
9.85.124
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2.0 REVISED LEACHING RATE DISTRIBUTIONS
2.1 Analytical Approach
The analytical approach used for this evaluation is identical to that used in
the June 1985 study in which a standard set of design and long-term conditions
was used to estimate the leaching rates for Subtitle C and D facilities. In
both studies these standard sets, along with climatological data, were entered
into the HELP model resulting in a calculated leaching rate.
2.2 Climatic Data Base
In the June 1985 study a total of 18 climatic centers were identified for
developing the national leaching rate distribution. As fifty percent of these
locations yielded leaching rates of less than one inch for Subtitle C facili-
ties, few data points were provided to establish the upper end of the leaching
rate. To obtain more data for the higher leaching rates, 12 additional clima-
tic centers with precipitation averages of greater than 20 inches were evalu-
ated in the September 1985 study. The combined list of cities selected for
evaluation is presented in Table 2-1. Included in the group are cities with an
extended data base of up to 20 years that were also used for a sensitivity
analysis (Section 3.0) of the leaching rate based on a comparison of the 5-year
and 20-year climatic data.
2-1
9.85.124
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TABLE 2-1
LEACHING RATES SUMMARY*
PRECIPITATION EVAPORATION
RANGE POTENTIAL
LEACHING RATE
"C" "D"
CLINATOLOGICAL AVERAGE 5-YEAR PERCENT OF
CENTER PRECIPITATION TOTAL ARF.AC
(20-YEAR)
<10
10-20
20-32
32-40
40-48
>48
b
C
.
Low
Hedium
High
Low
Hedium
Hedium
High
Low
Low
Hedium
Hedium
High
Low
Hedium
Hedium
High
Low
Low
Low
Low
Low
Medium
Medium
Medium
High
High
Low
Medium
High
High
Based on USEPA HELP model
zone of 36 inches and 24
Inches per year (assumes
Percent of total area of
11 years of precipitation
0.0 0.1
0.0 0.3
0.0 0.2
0.0 0.8
0.0 0.6
0.02(0.04) 0.04
0.4 1.2
0.3 1.5
3.1 (3.4) 3.4
3.4 3.4
0.5 1.5
0.5 2.4
3.6 7.2
3.7 6.8
2.7 5.4
2.9 4.8
7.0 12.1
6.6 12.8
4.6 (5.3) 10.0
5.5 14.2
5.7 13.0
(5.2)
6.6 10.6
3.3 6.8
2.^ 5.8
6.4 11.4
11.9 35.9
7.1 12.2
6.9 12.1
9.8(5.9) 16.7
estimates. Estimates
inches for Subtitle 0
unit area); number in
contiguous 48 states.
data.
Pocatello, ID
Cedar City, UT
Las Vegas, NV
Great Falls, HT
Rapid City, SD
Denver, CO
Midland, TX
St. Cloud, HN
Milwaukee, WI
Sao Francisco, CA
Grand I a land, HE
Oklahoma City, OK
Montpelier, VT
Cleveland, OH
E. St. Louis, IL
Columbia, MS
Boston, MA
Providence, RI
Hartford, CT
Worcester, HA
Portland, HE
Newark, NJ
Philadelphia, PA
Indianapolis, IN
Charleston, SC
Norfolk, VA
Astoria, OR
Knoxville, TN
Tallahassee, FL
New Orleans, LA
9.8
9.8
5.3
17.9
15.4
13.0 (14.9)
16.3
25.8
34.1 (33.1)°
(19.7)
22.2
30.4
34.5
36.7
16.2
37.1
40.9
46.7
41.1 (44.1)
46.5
45.5
(40.4)
43.7
40.3
48.3
44.4
65.6
48. 1
68.4
70.1(56.7)
3
2
3
3
13
5
11
7.8
2.2
2
2
5
3
2
:»
3
0.4
0. 1
0.2
1 .6
0.8
o.:»
1 .4
5.2
4.6
0.4
2
3
5
5
for Subtitle C facilities assume an evnpotranspj rat ion
facilitiea.
parenthesis indicates average based on 20 year database.
-------
2.3 Leaching Rate Distribution
In both studies leaching rates for Subtitle C and Subtitle D landfill facili-
ties were estimated with the HELP model. Leaching rates were estimated in the
September 1985 study for 30 climatic centers in the contiguous 48 states. A
summary of the leaching rates is provided in Table 2-1. This information is
expressed as percent of area in the contiguous 48 states where leaching rates
may be expected to equal or be less than the rate shown.
The distributions of the leaching rates shown on Figure 2-1 do not indicate a
significant change from the June 1985 distribution. The maximum leaching rates
for Subtitle C and D facilities repeated the pattern of the initial study in
that the Subtitle C leaching rates were generally 50 percent less than those
for Subtitle D facilities. The distribution represents the estimated leaching
rates based on the 5-year precipitation data base with the exception of New
Orleans (Louisiana), San Francisco (California) and Newark (New Jersey) which
were based on a more extensive data base. The 5-year precipitation data for
New Orleans is substantially greater than the 20-year average (70.1 inches
versus 56.7 inches); therefore, the 20-year leaching rate was selected to
estimate long-term conditions. San Francisco and Newark were not available in
the 5-year data base, but estimated leaching rates for both cities are pre-
sented using the 20-year data base.
With the inclusion of the 12 additional climatic centers, the greatest change
in the leaching distributions was observed for Subtitle 0 facilities with
estimated leaching rates greater than 7 inches. The leaching distribution from
2-3
9.85.124
0007.0.0
-------
o
2
o
a
a>
3
10
0
+ SUBTTTLE X* FACBJTY
Q SUBTITLE "D* FACBJTY
0
10
REVISED 9/17/85
I
20
q, inches/year
T
30
40
FIGURE 2-1
ESTIMATED DISTRIBUTION OF UNIT AREA LEACHING
RATES FOR SUBTITLE C AND D FACILITIES
• ECJORDANCQ
-------
that point is shifted to the right an average of 35 percent compared to the
previous distribution submitted in August 1985. While the Subtitle C distri-
bution did not change to any extent, the additional data more clearly defines
the 4 to 7 inches/year rate range in estimated leaching rates.
2-5
9.85.124
0009.0.0
-------
3.0 COMPARISON OF 5-YEAR AND 20-YEAR PRECIPITATION DATA
A 5-year precipitation data base is typically used in the HELP model. Jordan's
initial comparison provided a sensitivity to the duration of precipitation used
in the HELP model based on a comparison of average annual precipitation for 5
years and 30-years of record. The assessment concluded that the HELP model
would tend to over-estimate the long-term performance of land disposal facili-
ties by an unknown percentage.
In the September 1985 study, to analyze sensitivity of leaching rates to
duration of precipitation, a 20-year data base consisting of eight cities was
loaded into the HELP model. The data base was obtained from the Waterways
Experiment Station, U.S. Army Corps of Engineers. Half of the cities loaded
were not in the original 5-year HELP data base, therefore the nearest climatic
center was used to allow a comparison of leaching rates. However, for three
cities the nearest climatic center was not appropriate and only five cities
were finally used in the analysis. The cities are listed in Table 3-1.
Comparison of the two annual precipitation averages (5-year and 20-year) for
each city showed differences ranging from 1 percent to 19 percent (Table 3-1).
In contrast to the June 1985 findings, the largest difference occurred in the
highest precipitation range, greater than 48 inches. In this case the 5-year
average was considerably greater than the 20-year average. The remaining
differences were not significant in relation to the range of precipitation.
3-1
9.85.124
0010.0.0
-------
TABLE 3-1
COMPARISON OF 5 AND 20-YEAR
CLIMATOLOGICAL DATA BASE
AVERAGE
I'KKCJI*
KANGK
10-20
20-32
40-48
>48
Notes :
1 TAT ION EVAPORATION CLINATOLOGICAL
POTENTIAL CENTER
Medium Denver, CO
Low Milwaukee, WI
Low Hartford, CT
Low Seattle, WA
High New Orleans, LA
1. Inches per year (assuaes unit area).
2. Based on HELP Model, May 1985.
3. Nearest clinatic center Chicago.
4. 11 years of precipitation data.
PRECIP
5 YR.2
13.0
34. 13
41.1
35.6
70.1
ITATION1
20 YR.
14.9
33. 14
44.1
35.8
56.7
PERCENT
DIFFERENCE
15
3
7
1
19
LEACHING
5 YR.
0.02
3.1
4.6
8.1
9.8
RATE "C"1
20 YR
0.04
3.4
5.3
8.7
5.9
PERCENT
DIFFERENCE
100
9
15
11
40
5.85.102
0058.0.0
-------
A HELP model was run for the 5-year and 20-year data bases utilizing standard
conditions for Subtitle C facilities. The results of the 5-year and 20-year
leaching rates, shown on Table 3-1, showed differences ranging from 9 percent
to 100 percent. However, the difference of 100 percent occurred in the lowest
precipitation range and is not considered a significant increase. The next
largest difference, 40 percent for New Orleans, is considered significant as it
occurred in the highest precipitation range. In contrast to the initial
findings, the 5-year leaching estimate for New Orleans is greater than the
long-term average. Generally, the remaining data agree with our original
findings that the 5-year data base will tend to over-estimate the long-term
performance of land disposal facilities.
The results of the additional study point to an apparent relationship between
the percent differences of the precipitation and leaching rates in that the
percent difference of the leaching rate appears to be approximately twice the
percent difference of the precipitation data for moderate to high precipitation
areas.
3-3
9.85.124
0012.0.0
-------
4.0 CONCLUSIONS
The evaluation of 12 additional climatic centers yielded distributions of
leaching rates (Figure 2-1) very similar to the original distribution presented
in the June 1985 study. In both studies the Subtitle C distribution yielded
leaching rates that were always less, generally 50 percent, than the Subtitle D
leaching rates. The inclusion in the September 1985 study of additional
climatic centers did provide better definition of the leaching curves for the
moderate precipitation ranges.
Comparison of 5-year and 20-year climatological data bases for the moderate to
high rainfall ranges indicated a general correlation between the precipitation
and leaching rate differences: the percent difference of the 5-year and
20-year leaching rate is approximately twice the percent difference of the
5-year and 20-year precipitation averages. Using this assumption, a review of
the percent differences of the 5-year and 30-year average precipitation data
presented in Table A-l of the June 1985 report shows that the percent differ-
ences for the rainfall ranges greater than 20 inches are very small. This
would indicate that the 18 climatic centers chosen for the initial study are
appropriate for use in determining the national leaching distribution rates for
Subtitle C facilities.
9.85.124
0013.0.0
-------
REFERENCES
E.G. Jordan Co., June 1985. "Analysis of Engineered Controls of Subtitle C
Facilities for Land Disposal Restrictions Determinations." EPA Contract
No. 68-01-7075. Revised August 1985.
Schroeder, P.R., et al., 1984. "The Hydrologic Evaluation of Landfill Perfor-
mance (HELP) Model: Volume I - User's Guide for Version I and Volume
II - Documentation for Version I." EPA/530-SV-84-009 and -010, U.S.
Environmental Protection Agency, Washington, D.C.
9.85.124
0014.0.0
-------
DRAFT
APPENDIX F
Analysis of th« "infinite Source* AssuBption
Osad in tha Groundwater Nodal for Land
Disposal Banning Evaluation
La* A. Mulkey
BnvlronBental lasaareh Laboratory
Oollaga Station load
Athens, Osorgia
-------
34»1A:07:29
A key assumption of the ground water fate and transport model is that the
mass of each individual Qienaical constituent deposited in the facility is
sufficiently large to justify the mathematical assumption of an infinite source.
In addition to the mathematical convenience resulting from such an assumption,
the desire to regulate on leachate concentration values rather than total waste
characteristics (e.g., mass loading to the facility) makes the assumption appealing.
The purpose of the following analysis is to evaluate the physical significance
of the "infinite source" assumption and its impact on the outcomes of the ground
water model. The results demonstrate that the "infinite source assumption" of
the model is a physically realistic part of the approach and not- overly conservative.
The groundwater fate and transport equations are solved for the steady-state
case which requires an evaluation of the solution at infinite tine. Obviously, the
source term under these conditions must also be infinite. The resulting solution
allows the plume to fully develop in the grcundwater system and the desired
•maximum concentration at the plume center line along the x-axis (see Figure 1) is
achieved. A useful graphical depiction as CX£&CH is the assumed, constant, and
infinite source tern that produces the down-gradient exposure concentration,
The tine period,^^ is the travel tins to the downgradient exposure point and
is the approximate tine required for the plums shown in Figure 1 to fully develop.
The result for the infinite source of leachate is represented by Figure 2. The
difference between Cjyji and Crja&rH results from the combined effects of dispersion,
• dilution from recharge, and degradation.
The corresponding result for a finite source of the leachate is represented
Figure 3. This results in a pulse input moving through the groundwater system.
tnding on the duration of the pulse, the dawngradient exposure concentration
value (set to the fix value of C^j in the rule) may be different than that given
by the solution in Figure 2. In any case, the duration of the exposure value,yc,
is largely determined by the duration of the pulse input, y^. The differences
between exposure and C^^oi •** ft*-*9 related to dispersion, dilution and degradation,
but their relative effects nay be different than that from the infinite source
case. If the input duration is short (i.e.,Vi is small), corresponding to a
relatively small amount of mass available for transport, then the down-gradient
concentration may not reach the levels obtained for the infinite source case. If
the input duration is sufficiently long, corresponding to a relatively large
amount of mass available foe transport, then the down-gradient value will reach
the same level as in the infinite source case albeit for a finite period of time,
e, and the assumption of an infinite source is most likely to be met. The exact
mathematical solution for the pulse-load case and its sensitivity to the pulse
input tine, Y^, is not now implemented for the decision rule. Me can, however,
approximate the impact of the pulse duration via the steady-state solution by
noting that this will yield the maximun values for the down-gradient concentration
in the pulse load
Another useful characteristic shown in Figure 3 is the exposure time,ye.
Because the reference dose masses for carcinogens are based upon a seventy-year life
span it follows that a minimum value for¥e is 70 years. Simply stated, the idea
is that the leachate must be emitted at a minimum for a tine sufficient - to produce
the 70-year exposure period. Full development of the plume may or may not actually
s**** achieved depending on the value foryt. If Ye »Tt then the plums is fully
' jveloped, the requirements for the steady-state solution are met, and a pulse
-------
UNSATURATED
20NE
LAND DISPOSAL
UNIT
/
SATURATED
ZONE
•.MEASUREMENT
^ftn!«*OINT
9ft J J * ,< / ,
CROSS SECTION
PLUME BOUNDARY
PLAN VIEW
Figure 1. Schematic description of contaminated groundwater system.
-------
2 77/vr Ms
-------
DRAF
-------
load of duration, Ye , can be accurately evaluated via the current- model. If
ye
-------
Equation (3) can now be used to calculate the total trass of each specific chanical
constituent required to be present in the waste material for any tine, , of interest.
A more useful measure of the mass corresponding to the tine periods depicted
in Figure 2 and 3 is concentration in the waste. That is, the concentration of
each constituent of the waste that if made totally available for leaching would
produce a sufficient mass of material at the leachate concentation, CTp^rw • to yield
the exposure values, CADI« Consider the mass of the waste, MW, in the facility.
By coribining this total waste mass with the constituent mass expression fron
equation (3), we obtain
SM Q * AW * Y *
Mrf CD * EW * r^ * AW
* or iwc - Q *y* CAM/CD * uw * 'w (4)
where IMCv - leachate concentration of the constituent in the waste
material for leach time,Y,
ON - depth of the waste material in the facility, m
Py - density of the waste material, gra/cm3
Bjuation (4) requires two new parameters not heretofore needed. Fortunately,
both will vary over relatively narrow ranges and can be either fixed at man
values or can be allowed to vary according to some distribution. Interestingly,
the facility area (which varies widely) cancels in the equation and does not
influence the result except through the values for CD taken from the groundwater
modal.
Equation (4) enables us to calculate tor any desired value of CD (say that
corresponding to the 90th par cant ils level) the required ocjuceuiration level
in the waste (assuming all can be leached) for any given duration,^Recall
that at the minimum y must be 70 years. Thus, a minimum waste concentration
for any constituent is given by
- 70 * Q * CADI/CD * DW * /?, (5)
The value obtained from equation (5) can be viewed as the mininum constituent
ntration in the waste (assuming it is all leachable) required to insure that
the conditions represented by the ground water model are physically possible. If
the actual concentration is greater than LWC^n. then the outcome of the ground
water model is also physically possible. If the actual concentration is less than
IWCrcin, then the ground water model overestimates the dcwngradient concentration
""^ecauae the assumed source terra is greater than the waste can provide.
-------
Another useful waste charact eristic to consider is the concentration of
constituent required to fully develop the plane corresponding to the travel time,
M This value can be determined from
Vt « X (1+ KD /«)/V (6)
where X » distance downgradient to the exposure point, m
KD « partition coefficient, on3/gm
PB « soil bulk density, gra/cra3
• » porosity, cm3 /cm3
V * groundwater flow velocity, m/yr
By containing aquation (6) and (4) we obtain
Q * x(i + KD /e)/v* CD* EW* (7)
Where IWDp can be interpreted as the minimum constituent concentration in the
waste required to insure that the decision rule outcome is derived from a fully
developed plume. If the actual waste concentration is greater than UNDp, then
"the assumptions become more nearly those of an infinite source and the rule
outcomes are accordingly correct . If the actual waste concentration is less than
LWGj., then the plume is not fully developed and the source is exhausted before
the dcwngradient concentration, Cjg)X' is reached* Note also that if
X(l + Kb B/&/V <70 (8)
then the minimum exposure time of 70 years will not be achieved by exposure to
the mass resulting from the fully developed plume. Thus, IMGp only has moaning
if the travel time is given by equation (6) is greater than 70 years.
Consideration of equations (IK (8) leads to a useful additional concept in
regulating land disposal via leachate concentrations. We can now specify for any
given allowable leachate level the associated mininum applicable constituent
concentration given as
Max tUCroin, DrfCjO
This value can be interpreted as the constituent waste concentration below
which land disposal is acceptable regardless of the results from the leach test.
These values can be viewed as bench-mark measures of the reasonableness of the
infinite source assumption embedded in the decision rule.
-------
The problem retains to calculate the IW^nin **& ^^T values for any percentile
LLevel chosen from the frequency distribution generated by the rente carlo runs.
Note from equations 5 and 7 that each monte carlo run (i.e., single values for
each variable and parameter in the model) will have a unique set of values for
all defined variables except the two new waste parameters, DW and fy. Thus, if
these are Known we can calculate LWCjri.n and LWCj. values for each data point on
the curve and hence the one ultimately chosen for regulation. Example calculations
for a non-degrading, sorbing constituent (NX « 1000.0) with an assumed facility
depth of 5 meters, a waste density of 1.0 and CN)I of 1.0 are given in the attached
figures. Subtitle C facility results are presented in Figure 4-7 and Subtitle D
facility results art presented in Figures 8-11.
The figures denonstrate several important outcomes. First, the magnitudes
of both concentration level* (IMCMIN, UfCTOT) and the required masses (SMMIN,
SMTCT) are quite reasonable and thus the "infinite source" assumption of the
model remains a physically realistic part of the approach. For example, at the
• 90th percentile level for the Subtitle C facility, DO-ON ranges fron 7-90 mg/Jcg
and SttUN ranges from 500-50,000 kg if the reference dose is 1.0 mg/1.
Second, pursuing further the ideal of specifying an additional "critical
value," the figures suggest that if the 90th percentile is chosen for regulation
one can further state that if the constituent concentration in the waste is less
than 7 mg/kg than land disposal is safe regardless of the leachate test values.
8
-------
5-
o.s
Mass Balance Analysis of the
Infinite Source Assumption
0.6
0.7
0.6
0.9
Empirical Cumulative Frequency
y
T
"I
1.0
-------
DE/
Mass Balance Analysis of the
Infinite Source Assumption
5--
10*s?
5-
5--
5-:
ftCMS
0.5
0.6
0.7
0.8
0.9
1.0
Empirical Cumulative Frequency
fact Ii tu -h Prvtlncc.
it,
-------
C-
>:
Mass Balance Analysis of the
Infinite Source Assumption
10
5-
?> 40'
5-a*.
.10
5*
io-y .
si * . *
3
IO;T »
1 *
10~T
51
•*U 1 ' 1 ' 1 ' |
0.5 0.6 0.7 0.8
., m iff
• m
IK
» J T 1
0.9 1.0
Empirical Cumulative Frequency
-------
Mass Balance Analysis of the
Infinite Source Assumption
.*.
*-. n« "* •
10
Empirical Cumulative Frequency
Mass *f
lZ
-------
D!
Mass Balance Analysis of the
Infinite Source Assumption
10
0.5
Empirical Cumulative Frequency
/
Q
*v
-------
DRAFT
a*
s
CO
Mass Balance Analysis of the
Infinite Source Assumption
10
"» *"m *
. ««l? " •
* . * • •
• K •
«»
« **«
k\f5i &r^|
IMJI" ^fiV* "B"1 r "" " "" "«« . r
W*£i« s."^ ".. .y «***% a? ».
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TM i
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i*»
0.
1
5
1 1 '
0.6
1 I '
0.7
1 1
0.8
1 I
0.9
1 I
1.
Empirical Cumulative Frequency
"7
-------
Mass Balance Analysis of the
Infinite Source Assumption
•* s
* * •
10<
6-
u_ „ • K
V**
Jrmr*
J^ww IUK •%,
i * x43**r/.
5J»oi •^-*fe*9?*Sji
r ^»..:/..*--*fe4ffl*|Srf.*
rJ^V^/l|t^
Mf,j
* *
"^
0.6
Empirical Cumulative Frequency
Minimum ConcenknctfoiX't'f
<7i (Of54 9^ frvoiuu, fully
-------
Mass Balance Analysis of the
Infinite Source Assumption
0.5
Empirical Cumulative Frequency
Mass *f
f+ci/iJy
Its
-------
APPENDIX G
FORTRAN LISTING
GROUND WATER SCREENING PROCEDURE
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560 WRITE! 6,565) 00001110
MS FORMAT! ' Enter OKOC > 'I 00001 ItO
READ (5,3S5,ERR*560,END*t300) OKOC 00001130
IF (OKOC .LT. 0.0001 80 TO 3M 00001148
60 TO 100 80001188
C 888011*8
600 WRITE!6,60SI 88081178
605 FORMATI////,1 Enter UMAX Inueber off 0euM potato) > 'I 88881188
READ l5,3*5.ERR**OO.EM)*t300> MtAX 80001190
00 610 I » 1,9 88881188
610 IF C »8UX .EQ. NMAXCKII) I 80 TO COO OOOOltlO
WRITE (6,615) NNAX 80001 MO
615 FORMATI//,' You entered ',19,'. Pleese roonter',/, 00001(30
x ' 4, 5, 6, 10, 15, t8, 60, 104, t56',///, 00001 CM
x 'Hit Carriage Return to Continue') 8000 It 50
READ (5,315,ERR*366,END>t300> MENU OOOOlt**
60 TO 380 88801178
C OOOOltOO
640 WRITE! 6,6451 OOOOU90
645 FORMATI////,' Enter HPROB (nueber of Plot potato) > ') 88881188
READ (5.365,ERR'640,END«t300) NPROB 88881118
IF (NPROB .LT. 108) 60 TO 388 66681116
60 TO tOO 66661138
C 00001340
660 NRITE(6,665) 60661316
685 FORMAT(' Enter TCOHV > •) 686611*6
READ (5,355,ERR*680.END:t300) TCOHV 66661178
IF (TCONV .LE. 6.000) 60 TO 366 66681166
60 TO tOO 86661196
C 66681466
720 NRITE(*,7t5) 66661416
7t5 FORMATC Enter T[ ') 000014tO
READ <5,355,ERR*7tO,END't300) TR 66661416
IF (TR .LE. 6.806 .OR. TR .6T. 50.000) 00 TO 166 66001446
•0 TO tOO 00001450
C 000014*6
760 HRITE16.765) 00*61476
765 FORMATI' Enter XX > •) 60061466
READ (5,355,ERR'760,END*t300) XX(1) 66661496
IF (XXII) .LE. 6.0DO) 60 TO 366 00001100
60 TO tOO 00001510
C OOOOlftO
600 I LEACH « 3 - I LEACH 66661S36
GO TO tOO 00061146
C 68661556
AtO WRITE!6,8111 666615*6
811 FORMATI' Enter OF > ') 66001570
READ (5,355,ERR-810,END=t300) OF 60061588
IF (OF .LE. 0.000) 60 TO 300 60001590
C M T° "°
880 MBIT" 4,821)
V0UV19VW
Wffl
]
-------
821 FORMAT!' Entar RHOH > ') 00001*30
READ (5,355.ERR*620,END*2300) RMOM 00001640
IF (RHOH .11. 0.000) M TO MO 00001*50
BO TO 100 OOOOIMO
C 00001*70
C Perform calculations 00001*69
C 00001*90
640 CALL CLSCR 00001700
C OPEN(UNU*IUNITl,rUE*>HCARLO.DAT'.3TATU3».INP',3TATUS*'NEN') 00001730
C 00001740
C Hrlta Inforsatlon 00001750
C 000017*0
WRITE (2,2150) AOI,DIUO,DKBO,DKNO,DKOC.NNAX,NPROB, 00001770
x TCQNV.TR,XX(1),LEACH(ILEAC1O.DF.RHOM 000017M
8150 FORMAT (/,tX,'A - ADI (Valua •'.Bit.*,* I'./. 000017*0
x tX,'8 - DKAO (Valua -'.Bit.*,'IS/, 00001600
x tX.'C-DKBO (Valua •',812.*,*)',/, 00001610
x tX.'O - DKNO (Valus »*.Bit.*,')'./, OOOOlOtO
x tX.'I - OKOC (Valua "'.SK.*,')*,/, 00001636
x 2X,'F - NMAX (Valua >M1(.*) 6 of Bauss points*,/, 00001640
x tX.'B - NPROB IValua -'.lit.1I 0 of plot points*,/, 00001610
x tX.'H - TCONV IVslus •*••».*,*IS 600016*6
x • Unite srs par y*«r for rsto constants',/. 66001676
x ZX.'I - Tlrofl IValus •',Bit.*.')',/, 60001666
x tX.'J - XX (Value s>,fit.*.')',/, 600616tO
x tX.'K - I SU»titl« *,A1,* Itaod I*. 66661*66
x * Laachlng Rat* Distribution',/, 00001910
x tX.'L - DF (Valua-'.611.§.')',/, 000019M
x tX.'N - RHOU (Valua •*,Ml.f.•>•,/! 00001930
CALL CLSCR 00001940
URITE(*,tl*0) 000019S6
tl*0 FORMAT (101/),1§X,'Calculations ar« bsing Psrfonssd1,//) 000019*6
SEED1 • It3457.000 66001970
SEEOt » lt34S7.0DO 00001966
SEE03 • 115457.000 00061996
8EE04 • 113457.000 OOOOtOOO
IX • 1235 OOOOtOlO
IY • 67*5 OOOOtOtO
00 ttOO I>1, NPROB OOOOtOM
C 0000(040
C NSM coda OOOOtOSO
C 000020*0
2170 OOLMIN • DL0610(4.00-4) 00002070
DOLHAX • DLOS10(1.00-1) 00002000
CALL RANDUMIDDLraN.DDUUX.ODI 00002090
00 • 10.000IWOD 00002100
TMETA « 0.261 - 0.0365 • ( OLOB(DO) I 60001110
RMOB • 2.65 s | 1.000 - TMETA ) 60002120
OK3 * 476.0 • ITHETAM3.000 « DQMI2.000 0000(136
x / (1.00 - THETA)Mt.000) 00002140
CCCCC CALL RANDUHd.OD-S.O.lOOtSS) 00002150
21BO CALL EXRAMMO.0309,1,SSI 6006(1*6
IP ( 35 .LT. 1.00-5 .OR. SS ,8T. 1.00-1 ) 80 TO 1166 6000(170
VH(1) « (3.163*05 * DKS • 8S) / THETA 6000(166
IP I VM(1) .6T. 9250.000 I 60 TO (176 6006(196
\ COP. .do- 0*/05/65
TRK • TR • (73.000
-------
C190 CALL RANNOR C 14.400, 27.9500. T ) 00002240
IF ( T .LT. 0.000 .OR. T .ST. 30.000 I 6O TO t!9* 000022SO
T * T « 273.000 00002260
C 00002270
OKA * OKAO « I OEXPI 1.004 • I 1.000 / TRK - 1.000 / T III 00002260
DKN * OKNO • I DEXPt 1.004 • I 1.000 /TRK - 1.000 / T III 00002290
0KB * OKBO • I OEXFI 1.004 • I 1.000 / TRK - 1.000 / T III 00002300
C 00002310
219* CALL RANNOR I 6.6200. 1.6*00. PH ) 0000232*
If ( PH .LT. 0.300 .OR. PH .BT. 14.000 I CO TO tl9» 00002330
C 00002340
C CODE ADDED 0/26/65 0T JEROME COLEfUN 000023*0
C QC IS THE 9 VALUE FOR SUBTITLE C 00002360
C 00 IS THE 0 VALUE FOR SUBTITLE D 00002370
C 00002300
C 00002390
IFf ILEACH.EQ. 1 ITHEH 00002400
C 00002410
C Call Rudy's subroutines 00002420
C 00002430
CALL TBLC(QC,QD,XX.XY> 00002440
IF ( QC .LE. 0.0100 I QC • 0.0000100 000024SO
QC * QC • 0.02B400 000024*0
IF ( 00 .LE. 0.0100 I 00 • 0.0000100 00002470
00 • 00 * 0.02*400 00002460
QsQC 00002490
ELSE 00002SOO
C , 00002S10
C Cell Rudy's sUbroutinee 00002520
C 00002530
CALL TBLDfQC.QD.IX.lY) 00002*40
IF ( QC .LE. 0.0100 I QC • 0.0000100 000025*0
QC * QC • 0.02*400 00002*60
IF I 00 .LE. 0.0100 I 00 • 0.0000100 00002*70
00 • 00 • 0.02*400 00002*00
Q*OD 00002*90
ENDIF 00002*00
C 00002*10
CALL EXRANH 76. 600.1. BAQFR I 00002*20
BAQFR « BAOFR * 3.000 00002*30
C MRITEI2.111I' BAOFR- •.BAQFR 00002*40
Clll FORIUTIlX.A10tFlf.7l 00002***
C 000026*0
C B2 edded eedsd en */10/6*. 00002*70
C 00002*60
CALL RAMNM I2.00.10.00.HIHXTI 00002*90
IF I HDUT / BAOFR .«T. O.WO I THEN 00002700
HSOURC • O.MO • BAOFR 00002710
ELSE 00002720
HSOURC • HIMIT 00002730
END XF 00002740
C 000027*0
CC 000027*0
CC ADDITION 06/19/6* BT JEROME COLEHAN 00002770
CC 0000276*
ROME! 1 IBQD/HSOURC 00002790
C 00002000
C 00002611
1
199
-------
UU » UU / 0.9107100
AH > -85752.ODO • OL06 ( 1.000 • UU I
IF I AH .LT. O.OOO .OR. AH .0T. 1.505 I 80 TO 2199
ELSE
CALL RANDUH 10.000.1.000,UUI
AH = 1.505 » 7.790* * UU
END IF
C
C
C
C
C
SIGMA!1) • ( 9 • AH ) /
x ( THETA • VWdl • 094RTITMDPI) • HSOURC
IF I Q .LE. 0.02MOO I U8HAUI • 0.00100
cc
CC CODE ADDED 08/28/85 iY JEROME COLEIUN
CC
SAU * 034RTIAHI
IF I 3I6MAI1) .6T. SAM I THEN
3I6MAI1) a SAH
VHI1I • t9*AHI/ITHETA«SI6HAtllHO80JITITHOrai«NSOUM;)
S3 * IVHI1>*THETA)/(3.1SO5«OK8>
IFI9S .LE. 1.00-1I6OTO 2189
1.00-1I60TO 2178
CC
CC
CC
CC
CC
CC
CC
CC
CC
CC
CC
CC
C
C
2185
2200
2205
IFISS .ST.
ENDIF
Coda addad 04/20/8*
ALFAL • 0.100 •XXII)
ALFAT * ALFAL / 3.00OO
RCH6EI1I =0.00
CALL LN06EN (-5.200.2.840.FOCI
ALZLO • 0.02500 • ALFAL
ALZHI • 0.10* • ALFAL
CALL RANDUN I ALZLO* ALZHI. ALFAZ I
CALL CAD
IF II .19. 1 .OR. I .E«. NPROB)
x MRITE 12,22051 I,ALFAL,ALFAT,ALFAZ,AH,BAQFR,COI 1,1,11.
x DKAO.MUM.OKNO.FOC.HIMIT.HSOURC.
x PH,RHOB,8I6tUll).T.THETA,VHIl),XXIl).
x DF.RHOM
CONTINUE
FORMAT l/»T3.'P*u
MS,/,
K
X
X
x
X
X
X
X
x
x
X
X
T5 .
T55.
T5 ,
T55.
T5 ,
T55.
T5 ,
T55.
T5 ,
«•
*
5.
ALFAL
ALFAZ
AH
CO
OKAO
OKNO
FOC
HSOURC
PH
SI8KA.
VH i
i •
i •
i •
.812.4.T30.' ALFAT • ',812.4,
BAQFR •
,812.4,T30.'
,812.4,X.
.81C.4.T30.'
.812.4.X,
.8I2.4.T30.'
.812.4.X,
OKM • ',•11.*.
HWIT • •••!!. 4,
00002850
00002860
00002870
00002880
00002890
00002900
00002910
00002920
000029M
00002940
00002950
00002940
00002970
•0002980
00002990
OOOOMOO
OOOOM10
OOOOS020
OOOOS030
00003040
00001050
00003040
00003070
00003080
00003090
00003100
00003110
•0003IEO
•00031M
•00031*0
•0003150
••••314*
••••SIT*
••••318*
••••319*
•0003200
•0003210
•0003220
•0003230
•00032M
•0003250
••003240
••003270
00003280
••••329*
•••03300
••••3318
•0003320
00003330
00003340
•00033N
••••3348
••003378
••••3388
8800339*
•0003400
•0003418
0000342*
THETA • ',812.4,
-------
x TS ,' XX a ',612. 6. /. 00003460
x 15 .' Of « S6U.4.T30.' RHOM « '.Sit.*./! 00003470
C CLOSE1UNIT=IUNIT1) 00003400
C CLOSEIUNIT'IUNITC) 00003490
C 00003SOO
2220 CALL CLSCR 00003310
WRITE(6,t225> 000033ZO
ties FORMAT!/////////. 00003530
x • Do you Mnt to Mk« another run IT/HI > 'I 00003540
READI5,315.ENDs*300.ERR>ttt01HENU 00003550
IF I INDEX I •YNyn'»HENU I .19. 0 I THEN 00003540
CALL CL8C* 00003570
WRITE <«.tt3S) NENU 000035M
t£35 FORMAT I* You antarad <'.A1.'>. Plaaaa raantar') 00003590
00 TO CttS 00003400
ENDIF 00003410
IF I MENU .E«. 'Y* .«. MENU .E0J. *y' I 90 TO tOO 000034(0
X300 CONTINUE 00003430
STOP 00003440
END 00003450
00003440
BLOCK DATA 00003470
IMPLICIT REAL** IA-M.O-Z) 0000340*
REAL«« UCraNrUCTOT 00003490
INTE6ER«t IIMITI.nMZTt.IUNITS.IPSKC. 00003700
x N8I«U.NLAHOA.M(,NVM.IFCAL.nCH»E,NnAX,CHOICf 00003710
CHARACTER TERN 000037CO
COTflON/CLEARS/ TERH 00003730
COMMON/INTEfia/ IP8PEC»N8IGnA.NLAMDA.NX.NVM,IFCAL>IRCHei,NriAX 00003740
8I8HAI 1 ).RHOB.THETA.TCONV.OKA.OKB.OKN,m,OKOC,FOC,00003750
AOI.XXIll.ALrAL.ALrAT.VMfll.IICN8iai.OKS. 00003740
HSOURC.BAQFR.AH.ALFAZ 00003770
COmON/IO/ nMTl.IUNITC.IUNXTf 00003700
COmON^LOCKA^OCl.l.tl,XOat.«LAHBfl).iOCll,ZZIlI.O)lAfNII 00003790
,11 .OLFACI i . i . 1 1 00003*00
fTOT.iHC9UN.ucTjOT.or.RMOM.«j OOOOMIO
C 0«el«r* all data stataiwito. 000036*0
DATA IUNITl.IUNITC.IUNIT5.TERn/ I. C. 5. 'I* / OOOOM30
DATA XPSPEC.NiZ0NA.NUNOA.NX.NVM.ZPCAL.IKHM / 00003640
K 1. 1, t. 1. 1. 1. I / 00003650
DATA NMAX.SICNA.RNOB.TNETA.TCONV / 00003640
K IS. 15.0. 1.*. S.SS. 1.0 / 00003670
DATA PH. OKOC. FOC. AOI. XX. ALTAL.ALTAT, VH. ROMC / 0000366*
x 7.0. 100.0. 0.01. 1.0. 1B0.0. 10.0* 1.0, 0.0. 0.* / MOOM90
DATA OF.RHOM / S.0. 1.0 / 000039**
END C0003910
01003920
SUBROUTINE CLSCR 90003930
C CHARACTER CUJ11 101. CLRCI 1*1, TERH M003940
C INTEBEWf IlMITI.IUNITt.IUNITS C0003950
C COMMOM/IO/ IUNIT1.IUNZTI.ZUNZTS M003940
C COMMON/CLEARS/ TERH 00003970
C OATA CLR1 / • •.tT.'I'.'l'.'l'.'I'.'f'.tT.M'.'J* / ••003900
C DATA CLRt /4«' •,t7.J' / «0003990
C IF ( TERH .E«. •!• I MRITEf«.l*ICLRI 00004000
C IF I TERH .E«. 'f I NRITEI4.10ICLRC M004010
C 10 FORMAT tlOAll 00004010
00 10 I'l.M 0000403*
.11
JJ
-------
RETURN 00004070
END 000040BO
C TBLC.FTN - 9/31/89 00004100
C 00004110
C ROUTINE TO PRODUCE A RANDOM NUMBER OH THE BASIS OF A 000041 tO
C TABLE-SPECIFIED EMPIRICAL DISTRIBUTION 00004130
C 00004140
£&»•»••••••••••••••••*••••••••••••••••••••••*••••••••••••••••••••• . 000041S0
C 000041*0
SUBROUTINE TBLC IRESC,RESO,IX,XY) 00004170
C 00004100
IMPLICIT REALMS (A-M.O-ZI 00004190
INTEGERS IX,IY 000*4200
DIMENSION TABLECt13,tI 00004tlO
DIMENSION TABLED! IS,11 00004220
C 00004230
DATA TABLEC/.01,.3,.4,.>,2.1,2.9,3.3,3.*,3.7.*.9,7.0,0.0,11.9. 00004240
• .t9,.3B,.49,.M,.*3,.*«,.73,.7*..S1..9t,.99..90,1.0/ 00004tSO
C 00004MO
C 00004170
DATA TABLEO/.l,.2,.3,.ft,.S,l.2,1.0,t.4,4.0,0.0,*.*,7.t.lt.l,lt.t. 000042SO
• 39.9, .03..0«,.OS,.tt,.t9,.40,.93,.90,.*l..**,.70,.01,.W..90, 00004t90
• l.O/ 00004100
C 00004110
CALL RANDUIIX.IY.VFL) 00004UO
C 00004310
C CHECK VS TABLEC 00004340
IF!YFL.0T.TABLEC!l.t))00 TO 100 000043SO
C 000043*0
RESC'TABUCtl.ll 00004370
•0 TO 101 00004100
C 00004190
C DO TABU LOOKUP. INTERPOLATION 00004400
C 00004410
100 DO 101 I«t,13 000044S0
IFIYFL.0T.TABLECII.tn00 TO 101 00004410
SLOPE • !TABLECII,t)-TABUC!I-l,t))/(TABLIC(I,l)-TABLICII-l,l)l 00004440
RESC • TABLECtI-t.l) «
-------
201 CONTINUE 00004660
C 00004690
RESD • TABLED!IS.II 00004700
C 00004710
C99 RETURN 000047X0
END 00004750
Cs*==tmm*f*msmmmmfas**mmm*mmmmmm*mmmmmmmmmmmmmm*ummmmmmmmmmmmmmmmmmm 00004740
C TBLD.FTN - S/31/6S 000047SO
C 000047*0
C ROUTINE TO PRODUCE A RANDOM NUMBER ON THE BASIS Of A 00004770
C TABLE-SPECIFIED EMPIRICAL DISTRIBUTION 00004780
C 00004790
C=fssm*mttmmm*fmmmmmmmmmmmmmmmmmmmmmmmmmmmmfmmmmmmmmmfmmmmmnmmmmfmmmm 00004600
C 00004010
SUBROUTINE TBLO IRESC.RE8O.IX,IY | 000046X0
C 666646S6
IMPLICIT REALMS IA-H.O-ZI 00004640
INTEGER** IX.IY 666646*6
DIMENSION TABLECflS.tI 600046*0
DIMENSION TABLED!IB.tI 60004670
C 66004SS6
DATA TABLEC/.01,.3..4,.*.C.S.t.9.I.3,I.*.1.7,*.9.7.*.*.6.11.9. 66604696
* .C9,.36..49,.ft6,.43..6«..71..7*,.*1..9X..9S,.96,l.*/ 66664906
C 66664916
C 66664916
DATA TABLEO/.l,.t..3..*..6.I.C.l.f,t.4.4.6.S.6.«.*.7.t,lf.l,lt.t, 66664996
• 35.9, .OS..06,.06..C4,.t9..40,.»S,.B6..*l,.66..76,.61,.9»..96, 66604946
» l.O/ 666649M
C 666649*6
C 6ENERATE A UNIFORM 16.11 66664976
C 66664966
CALL RAMMIIXX.IY.YFL) 00004996
C 00001000
C not* for 0 6666S6I6
C 6666S6S6
C CHECK VS TABU 6666SOM
C 00000*40
IFIYFL.eT.TABLEOIl.tMBO TO tOO 6666S6B6
C 6606*6*6
RESO*TABLEO(1.1I OOOOM7*
SO TO 199 00000060
C 6666S096
C DO TABLE LOOKUP, INTERPOLATION 0666SI66
C 0*001116
too oo tot i«i»is oooosito
IF160 TO tOl OOOOflM
SLOPE • (TABLEO(I,t)-TABLEDII-l.tn/fTABLEDII,l)-TASLSDII-l.in 0000014*
RESO • TABLE01I-l.il « IYFL-TABLE0!I-1.CII/SU)PI OOOOIIS6
BO TO t99 666011*6
E01 CONTINUE . 00001170
C 0600S166
RESO • TABLEOIlB.il 00000190
c oooostoo
899 CONTINUE OOOOSE16
C OOOOSEtO
C now for C OOOOStM
C OOOOSI40
C CHECK VS TABLEC OOOOIMI
IFIYFL.ST.TABLECIl.SIISO TO 100
RESC"TABLEC(1,1I
-------
GO TO lOt 00005290
C 00005300
C DO TABLE LOOKUP. IMTERPOUTION 00005310
C 00005310
100 00 101 1*8,13 00005330
IFtYFL.GT.TABLECtl.tnGO TO 101 00005340
SLOPE • (TABLEC(I.t)-TABLECII-l.t)>/(TABLEC(I.i)-TABLECIl-i,t>) 00005350
RESC • TABUCII-1,1) « (YFL-TABLECIX-LEU/SLOPE 00005360
GO TO lOf 00005370
101 CONTINUE 00005360
C 00005390
RESC • TABLECItS.l) 00005400
lOt RETURN OMOS410
END 00005410
C**s=sxm*amammMmmm*mmmmmm»mmmmmmm*mmmmmmmmmmmmmmmmmmmmnummmm»mmmmmmm 00005430
C TBLINTRP.rTN > 5/31/65 00005440
C 00005450
C ROUTINE TO PRODUCE A RANDOM NUMBER ON THE BASIS Of A 000054*0
C TABLE-SPECIFIED EMPIRICAL DISTRIBUTION 00005470
C 00005460
•••••••••••••••M ••••MM
. •••05100
SUBROUTINE TBLINT IRESULT.IX.ITI 00005510
C M0055M
IMPLICIT REALM (A-H.O-Z) 999991M
INTEGERS IX.IT 00005540
DIMENSION TABLE! 13. t> 00005550
C M005MO
DATA TABLE/.01..3,.4,.5.t.l.t.9.I.3,3.*.3.7.«.9,7.«,B.«.il.f. 00005B70
• .E9,.M,.49,.M,.«1,.M».73,.7*».BI,. ft*.«*».«•»!.•/ ••••5BM
C 000051*0
C DO COO 1-1.13 00005400
C 9000M10
C GENERATE A UNIFORM (0,1) ••••MM
C ••••MM
CALL RANDU(IX.IY.YFL) •••OM40
C ••••MM
C CHECK VS TABLE M005440
IF(YFL.«T.TABLEIl.t))GO TO !•• MMM7*
C •0005460
RESULT'TABLEIl.l) MMMM
GO TO »» •0005700
C •MOI7I*
C DO TABLE LOOKUP. INTERPOLATION . OOOOSTtO
C M0057M
100 00 I I«t,13 •••0574*
IFIYFL.BT.TABLEII.tMGO TO 1 90005750
SLOPE • (TABLEII.t)-TABLE(I-l.t»/ITABLE(I.l)-TABLE(I-l.l)l (OOOSTOO
RESULT » TABLE! 1-1.1} * IYFL-TABLEd-1.ED/SLOPE 90005770
GO TO »» ' M005706
1 CONTINUE 90005790
C ••••MO*
RESULT • TABLEI11.1) MOOM10
C ••••ME*
9* RETURN COOOMM
END 90005640
^•••••••••"•'•••••••••••••••mmmm*mmm*mm*mmmm»mmmmmmmmmm»mmmmmmmmmm ••••MM
C TBLINTRPD.FTN - •7/10/61 ••00M«9
^ SUBROUTINE TBLINt CRESULT,XX.XTI
II
-------
IMPLICIT REAL«0 IA-H.O-Z) 00005900
INTEGER«2 IX.IY 00005910
DIMENSION TABLE! 15,El 00005910
C 00005990
DATA TABLE/.l,.E..3..*..8.1.t.l.5,t.4.4.a.5.B,*.8.7.E.lt.l.lE.C, 00005940
• 35.9. .03,.0*,.M,.E*,.E9,.4*..S3,.M,.*l,.**..7a,.ai,.95,.9a. 00005950
• l.O/ 000059*0
C 00005970
C GENERATE A UNIFORM (0,1) 00005900
C 00005990
CALL RANDUIIX.IY.VPL) 00004000
C 00004010
C CHECK VS TABLE 000040CO
IPITPL.tT.TABLCIl.tn00 TO 100 00004030
C 8000*040
RESULT-TABLE!1,11 00004050
80 TO 99 8000*0*0
C •000*070
C 00 TABU LOOKUP. INTERPOLATION 00004000
C 00004090
100 00 1 I^t,15 00004100
IFIYFL.eT.TABLEII.EMW TO 1 00004110
SLOPE • (TABLE(I,tl-TABLE(I-l.M>/ITABLEII.l)-TABLEiI-l.l)> 00004ItO
RESULT • TABLE!1-1.II » IVFL-TABLEII-l.tll/SLOPf 00004130
60 TO 99 0000*140
1 CONTINUE ' 0000*150
C . 0000*1*0
RESULT • TABLEI15.il 0000*170
C 0000*100
99 RETURN 0000*190
END OOOMtOO
€*•*•*••»•••*•••»«*•••••••••••••••••*•••••••••»•••••••••••••••••••• 0000*E10
SUBROUTINE RANDUIIX.IY.YPLI BOOMCM
OOOME30
IMPLICIT REAL«*B f A-N.O-ZI 0000*140
INTEBER't IX,IY 00004EM
DATA IA.IB.SCVE89,St7*7.l/ BOOB*t*0
00004C70
IT-IX-IA 88SME80
IFIIYIB,*.* 00004C90
5 IY»(IY«IB)«IC 00004300
* TPL-IY 0000*110
YFL-VFLV.M510509E-4 0000*310
IX-IY 0000*330
RETURN 0000*340
END 0000*350
0000*3*0
C LHMCN.PTN 0000*370
C OOOOA3B*
SUBROUTINE LN08EN IHEAN.VARI.VALUEI 0000*390
IMPLICIT REALM f A-H.O-ZI 0000*400
DOUBLE PRECISION VALUE.SEEDl.SEEOE,SEED5ttCE04 0000*410
COMMON/SEEDS/ SEE01.SEEOt.SEE03,SEEO% 0000*410
REAL MEAN. VARI. VALUES!E) 0000*430
10 CALL BOOB I8EEOI. I. MEAN, VARI, VALUESI 0000*440
VALUE • VALUES! 1) 0000*450
IP I VALUE .IT. 1.000-3 .01. VALUE .«T. 1.000-EI BO TO 10 000064*0
gCJUBN 0000*470
END ~
C RANNOR.PTN
-------
12.
C 00006S10
SUBROUTINE RANNORIMEAN.VARI,VALUEDI 00006310
IMPLICIT REAL** IA-H.O-ZI 00006510
DOUBLE PRECISION VALUED,3EED1,3EED2,BEE01.SEE04 00006540
COMMON/SEEDS/ SEEOl.SEEOt.SEEDS,8EED4 00006550
REAL HEAN. VARI. VALUE!1) 00006560
CALL CGNHL I SEED*, 1. VALUE!1) I 00006570
VALUED • MAN » MRTIVARI) • VALUE! II 000065M
RETURN 0000659*
END 00006600
00006610
C RANDUH.PTN 000066(0
C 000066M
SUBROUTINE RANDUMILOHER,UPPER.VALUED) 00006640
IMPLICIT REAL** IA-H.O-Z) 00006650
DOUBLE PRECISION VALUEO.SEE01.SEEOt.SEE01.SEEM 0000666*
COmON/SEEDS/ SEE01.SEEOt.3EEOS.8EEM 00006670
REAL LOWER. UPPER. VALUE 000066*0
VALUE • S8UBPSISEEOSI lOOOMt*
VALUED « LONER * VALUE • I UPPER - LONER) 00006700
RETURN 00006710
END M0067C*
0000673*
C EXRAND.FTN 00006740
C 00006750
SUBROUTINE EXRANDIXH.NR.VALUED) 0000676*
IMPLICIT REAL** IA-H.O-Z) 9000677*
DOUBLE PRECISION VALUEO.SEEOl.SEEOt.KEOB.SEEM 000067M
COMMIN/SEEDS/ SEED l.KEDt.tCEDl. SEEM *00067«*
REAL XH, VALUE M006M*
CALL C6EXN ( SEEM. XN. NR, VALUE ) **006*l*
VALUED • VALUE 00006BC*
RETURN ***06*S*
END 00006*4*
•0006*50
SUBROUTINE CAD *0006*60
C EPASNOO-lt COMPUTES SUOIOCT'* STEADT-STATE ANALYTICAL SOLUTION*0006*7*
C DISTRIBUTION OP CONCENTRATION AT X " *. THE CODE •0006MO
C DETERMINES OMIT CONCENTRATION VALUE* ALON* TNI X-AXI*00006*9*
C INSERT STKOn>ERRO.P *0006900
C INSERT SYSCOH>KEYS.P ••••691*
IMPLICIT REALM0IA-H.O-Z) ••••6ft*
INTEOER*! ZUNITl.ZUNITE.IUNZTI, M00691*
x IPSPEC,NSIOnA»NLAHDA.NX.NVM,IPCAL.IRCH0E.NHAX MCMfM
CHARACTER MENU.ANS.TITLE«60,TERH **006*50
REAL** KRO.KROSTO.KRON.LMCraN.UCTOT 00006*60
DIMENSION RETARD!1) 00006970
COMMON/INTE89/ IPSPEC.NSISMA.NLAnDA.NX.NVM.IPCAL.ZRCINM.NNAX M0069M
COMMON/10/ ZUNITl.IUNITt.IUNIT5 00006990
COMMON/REALS/ SlfiHAI D.RHOB.THETA.TCONV.OKA.DKB.OKN.m.DKOC.POCi **007000
x AOI.XXIl).ALPAL.ALPAT.VHIl).RCHMIl)fDM. 00007010
x HSOURC.BAQFR.AH.ALFAZ 00007010
COMMaN^LOCKA/COIl.l,l),XD!l).0LAnDll),SOIl)» 00007010
1 ZZI1).0LAH!1) 00007040
COttlON/BLOCKP/CPril.l.tl.OLFACil,!,!) 00007050
COMMON^ICMOUT/SNUN.SMTOT.LNCraN.LHCTOT.OP.RNOU.*. 00007MO
c 0*007070
C CALL SRCHOIIMREAO.'IPEPAHS'^.l.ITT.ICOD) 00007080
-------
C [[[ CARD TYPE 00007110
IF(NMAX.E4.0> HtAX=l(K 00007130
C ..... READ PARAMETER VALUES 00007140
C [[[ CARD T00007150
C 00007160
VS « VHI1) • 0000717*
C 0000710*
ISPEC=IPSPEC 0000719*
IFIIPSPEC.EQ.il 60 TO 10 00007100
C ..... FOR IPSPEC=0, READ IN OIMEN3IONLES8 VALUES OF OOOOTtl*
C STANDARD DEVIATION. DECAY CONSTANT AND DISTANCE 00007MO
C — — — ———————— 00007CM
C [[[ CARD 00007C40
ALFAL'0.9 00007CSO
ALFAT'O.I 00007ti*
V3M. MOOTtT*
DO It JM.NSI6HA 00007IM
IX SIGMAIJI'SOUI **007t9*
00 14 J=1.NX 0000710*
14 XX(J)*XDIJI 90007S1*
60 TO CO *00071t*
10 CONTINUE 00007SM
C ..... FOR IPSPECal. READ IN REAL VALUES OF 00007S40
C STANDARD DEVIATION. DECAY CONSTANT AND DISTANCE M0071M
C ................................... . .......................... CARD TY00007SA*
C --------------------------------------- ••••717*
IF(IPCAL.E9.0) 60 TO 1C* 00007SM
C ........ , [[[ -0 TV 0000719*
IFIOABSITCONVI.LE.l.O-CO) TCONV1.00 *00*740*
DO 149 Jsl.NLAHDA 9000741*
OKO » OKOC • FOC *00074CO
C .................................. . ........................... CARD TY0000741*
POH»I4.-PM 0000744*
PH--PH *00074f*
POH--POH ••••744*
6LAH1*DKAH( 10.MPM)*OKN«OKB«(10.*«POH> 0000747*
6LAnt3tO.«OKA«(10.MlpH)*OKN . 0000740*
6LAH1*6LAN1«TCONV 0000749*
6LArtts6LAHC*TCONV COOOTfO*
eUUII J )«( eLAHl»THETA»6LAHt*OKO«mOB )/l TNETA*OKD«RND1I 00007S1*
RETAROUI'l.tRHOBMOKO/THETA 00007SI*
149 CONTINUE ••••TIM
119 CONTINUE **0*7f4*
It FORHATI//10X.'BULK DENSin •>,Elt.4.«X. 'HATER CONTENT -'.Elt.4, OOOOTfM
1 *X.'TinE CONVERSION FACTOR ••.E1C.4//1M. MOOTS**
t 'LIST OF CHENICAL PROPERTIES OF SOLUTE SPECIES'// *0**797*
1 5X. 'SPECIEM'.TX, 'CONSTANT KA «. IX, 'CONSTANT KB '.IX, 00007SO*
4 'CONSTANT KN'.SX.' FH-VALUE '. IX.' CONST. 6LAH1', 00007S9*
S IX. 'CONST. 6LAIUV) 00007*00
t7 FORMATIlX.».OX.*tE14.4.1X)I 00007*10
B4 FORMAT! //10X.' LIST OF RETARDATION VALUES'/ I ****7*t*
c -------------------------------------- *0*07*M
IFINZ.E4.0I NZ>1 *0007*40
C ..... FOR IPSPEC • 1. READ IN VALUES OF LONBITUDINAL AND TRANSVERSE 00007AM
C OISPERSIVITIES, HATER VELOCITY. AND RECHARtt PARAHETCR INDEX *0007**0
-------
00 .A J*1,N3IGHA 00007730
101 3D(J)-316(1*(J» 00007740
00 102 JM.NLAHDA 000077SO
102 6lAMO(J)*6LAmJI 000077*0
DO 104 J»1,NX 00007770
104 XOU)=XXIJI 00007766
IFdRCHBE.EQ.OI 60 TO 49 00007790
48 CONTINUE 00007806
C CAM 00007816
DO 69 J*1,NLAHDA 60007810
RFAC3l./(THETA«RETARDIJI) 00007838
69 6LAn(J)*6LANUI*RCH6EUI«RPAC 60007846
49 CONTINUE 60067886
1032 FORHATI/10X,'SOLUTE VELOCITY «',Elt.3l 606678*8
1034 FORHATf/lOX.'BROUNDHATER SEEPA8E VELOCin • SElt.l) 08667676
103 FORIUTC//10X.' LONBITUDINAL DISPERSIVITY «'.tlt. 1/X 66867686
10X,' TRANSVERSE DISPERSIVin •'.Elt.3// 66667896
IOX,• VERTICAL OISPERSIVITY •',Elt.3// 00067966
10X,' AQUIFER THICKNESS •',Elt.3// 66667916
IOX,' SOURCE THICKNESS •MIt.3// 66667916
16X,' PENETRATION RATIO •'.tit.I/I 00007930
tO CONTINUE 66667946
C 666679S6
c . 666679*6
IPRCHM1 60067976
C .—. 66667986
DO 40 1316=1.N3I6MA 66667996
SsSIBHAdSIB) 60008666
C ' 66668816
DO 38 ILAH'l.NLAMDA 600060tO
C 66668636
JsILAM 66688846
IFIISPEC.EQ.OI RETAROUI'l. 666688B6
IFd3PEC.EQ.il KRO*6LAmiLAMI 666888*6
VX^VSyDETAROIJI 66068676
DX«ALFAL»VX 66668686
OY*ALFAT«VX 66668896
DZ«ALFAZ«VX 66668166
DO 36 IX'l.NX 66668116
XPrXX(IX) OOOMltO
IPdSPEC.NI.il KRO*6LANIdLAHI/XP 66666116
KRDSTOsKRD 66666146
C FULL PENERATION EVALUATION 666661B6
OELCCP'O. 666661*6
CALL 6HP200CXP,3.0X,DY,VX,KRD,CCFI 60668176
IPIOABSICCFI.LT.l.O-tOI CCMl.O-tO 66668166
C PARTIAL PENETRATION EFFECT 66666196
00 294 IZ-l.NZ 66668C66
ZP>ZZdZI 66666116
IFJXP.LE.0.01) 60 TO 409 66668116
IFIHONB.LT.0.99001 CALL 6HP3DPIXP,ZP,i,OX,OY,OZ,VX,IWOSTO, 00008E36
1 BAQFR,HONB,OELCCP,NKEEPI 86686E46
COdX,ILAN,ISI6lCCP 00008270
60 TO 43 00006260
409 CONTINUE 00006290
NKEEP'O 60006300
-------
CPFIIX.IUM,ISIGIM. 00006340
IF(ZP.LT.HSOURC) 60 TO 45 00000350
DIFAC(IX,ILAM.ISIO>*0. 00000160
CPF(IX.ILAM,ISIO)«0. 00006370
45 CONTINUE 00006500
C 00000190
C cod* adcfad 10/07/OS by II. Neon 0000O400
C 00000410
STtUN » 14 • AM » 70.000 " ADI • 10.00-041 / COIIX.ILAM.ISIO) 000004EO
TAU • IXXdl • I 1.000 * t DKOC • FOC • MOB I / TNITA )) 0000O4SO
K / VM11) 00000440
SltTOT • 10 • AM • TAU » ADI • 10.00-041 / COIXXiILANiXSIO) 000004M
LNCMIM « 10, • 70.000 • ADI) / !CO!IX,ILAM.ISIO) • OT * RMOM) 000004*0
LMCTOT • IQ • TAU • ADD / ICOIIX.ILAH.ISIO) • Of • WON) 00000470
C 00000400
IFIIPRCHK.NE.O) MRITEI1,4991)C0IXX»XLAH,XS10)>. 000004*0
K UOUN OOOOOBOO
4993 FORMAT IF10.7.1X.611.5) 00000510
90S FORMAT!//10X.'MINT CHECKlXP-ZP-OX-Or-OZ-KRO-CO-CPF-OLFAC'. 00000510
1 '- NKIEPV) 00000590
1091 FORHAT(lX,II4i'-')) 00000540
995 FORNAT(9eit.4,X7t 00000550
C54 CONTINUE 000005*0
56 CONTINUE 00000570
50 CONTINUE 00000500
40 CONTINUE 00000590
CALL OUTPUT 00000*00
100 CONTINUE 00000*10
C FORMATS OOOOMtO
1 FORMAT!1*151 00*00*50
11 FORMATICOA4) 00000*40
C9 FORMAT!1E10.5.15.3E10.3) 00000*50
3 FORMAT!//lOX.'MfBER OF PROBLEMS TO OK SOLVED •SIS//) 0*000*60
13 FORMAT1///10X.'PROBLEM NUMBER »'tI5// 00000*70
1 10X. 'NUMBER OF OAUSS POINTS FOR NUMERICAL XMTEORATXON -'.IS/I 00000*00
C3 FORMATI/10X.'PARAMETER SPECIFICATION INDEX ••.I5//IOX* 00000*90
1 'NUMBER OF STANDARD DEVIATION VALUES "'.HX/IOX. 00000700
E 'NUMBER OF OECAT COEFFICIENT VALUES •'.XS//10X. 0000071*
3 'NUMBER OF X-COOROINATE VALUES -M5//10X. 00000710
4 'NUMBER OF Z-COORDINATE VALUES «',I5I 00000730
El FORMATIOE10.3) 00000740
35 FORMAT!//10X.'LIST OF STANDARD DEVIATION PARAMETER VALUES'/I 00000750
43 FORMAT!OE1C.3I 000007*0
53 FORMAT!//10X,'LIST OF DECAY PARAMETER VALUES*/) 00000770
63 FORMAT!//10X,'LIST OF DISTANCE PARAMETER VALUES*/) 00000700
RETURN 0000600*
END 00000010
00006610
SUBROUTINE OUTPUT 00000030
IMPLICIT REAl«6IA-H,0-Z) 00006640
INTEOER'E IUNITl,IUNITt.IUNIT5. 00006650
x IP3PEC,NSIWU,NLAMDA,NX,MVH.IPCAL,1RCHBE.M1AX 000060*0
CHARACTER MENU.ANS.TITLE«60,TERM 00006070
REAL«0 KRD,KR03TO.KRDN,LHCHIM,LMCTOT 00006000
DIMENSION RETARD! 1) 00006690
COMMON/INTESV IPSPEC.NSIOMA.NLAHDA.NX.NVM.IPCAL.XSXHM.NNAX 00006900
COMMON/10/ IUNIT1.IUNITE.IUNIT5 00000910
COMMON/HEALS/
x
X
-------
/I/
COMnON/BUXXA/CO«UH( 11 00006961
COMMON/BLOCKP/CPFf1,1,11.OLFACI 1.1.11 00008970
COrtWN/t«MOUT/3MniM,SNTOT,UCmN,LHCTOT,DF.RHOM,e. 00008980
NCOL=5 00008990
ITABL'O 80009000
oo 10 isiesi,NsieMA 80009010
9160-50(1816) 600090CI
ILST»1 80009030
ILEND*IL9T*NCOL-I 00009040
IF(UEND.6T.NUMDA) IUND-NUIDA 80009011
14 CONTINUE 800098*0
ITABL°ITABU1 88889870
IFIIPSPEC.E6..0) 60 TO 19 60069880
133 FORHAT(/18X,6('RCNM>'.116.3.1X1) 60069890
60 TO 69 66669160
19 CONTINUE 66669110
69 CONTINUE 66669110
00 16 IXs1,NX 66669138
IFICOIIX.IL8T,I8I6).LT.l.E-7) 60 TO 18 66669140
16 CONTINUE 660691N
It3 FOmUTItX»93( •-•)///) 60009160
39 FORHAT(///tX,'TABLE',I3,'l>.tX.'X VM9U9 CO FOR 9I6HA • ', 66669178
1 E11.V/CX.93I'-')) 66069188
49 FORMAT(/ltX,9f•LANDA*'.E16.3.1X)) 60009190
89 FORMAT!SX.'X-VALUE'.OX.'CO-VALUES 68009C66
1 4(6X. 'CO-VALUE' )//*X.93< •-•)/) 66689110
ILST'ILENO^l 66689186
ILEND*IL9T*NCOL-1 60009S30
IFIILST.6T.NUIOA) 60 TO 16 60009140
IFIILENO.OT.NUtfBA) ILCM)«NUHDA 6000n60
60 TO 14 60009160
16 CONTINUE 66089(76
10 CONTINUE 60009166
C FORMATS 60009(90
3 FORrUT(///tX,'TABlEM3,'l',eX.(XD VEMU9 CD FOi 9X60 •', 68669366
1 Ell.V/tX.9311-1)) 66669316
13 FORHATI/ltX.fl'UN)«*.E16.3.CX)) 60009310
113 FORHATtSX.'XO-VALUE'.OX,'CO-VALUE',4(6X.'CO-VAUJI*)//tX.9SI •-•)/) 60009330
t3 FORMAT! 1X.E16.3.814X.E11.3)) 66669346
RETURN 66669396
END 668693*6
66669376
SUBROUTINE 6MPtOO(X.9.0X,OY.VX.KM.CCP) 96689388
IMPLICIT REAL»8IA-H.O-Z) 66669398
INTE6ER»t IUNITl,IUNITt.IUNXT9. 96669468
» IPSPEC,NSI6MA.NLAItOA.NX,NVM,IPCAL.I*CH6E,NHAX 66669418
REAL*8 KRO.KRD9TO.KRDN 60009410
COMMON/10/ IUNIT1,IUNITC,IUNXT9 66669436
COMMON/INTE6S/ iraPEC.N8I6m.N1JUt)A.NX,NVM.IPCAL.nCH6<.M1AX 66609446
DIMENSION Z(t96).HIC96) 60009498
TLRNCE'1.0-06 600094*6
CO FORMAT!////50X,'ERROR IN SUBROUTINE eHPt06'//f8X. 66669476
1 'THE PARAMETERS OX.OY.9 MU9T ALL BE 6REATER HUN ZERO BUT YOU', 66009498
C ' 9ETV//40X.' DX •<.ElC.4.fOX.'OY "'.EU.4/ 68609498
3 tlX.'9 • '.E1C.4//) 00069909
IFIDX.LE.O..OR.OV.LE.0..01.B.LI.6.) 9TOP 90009919
PI«3.1419926939997900 000099|0
-------
A=O.DO 00009560
8=1. 0*20 00009970
CALL 06AUSS(A.B,Z.N> •0009MO
8UH=0.00 00009*90
Exo=vx»x/ie.oo»ox) 00009*00
00 100 I*1.NHAX 00009*10
ze=zm»zm ••••9*t«
ACCELERATE THE INTE6RATIOM BY LETTINB Y«Z»Z«OS«T< 1 1/9 ••••9»M
Z4=Zt*Zt ••009*40
EX*EXO-Z4-X*OS4RT(t.OO«OY*Z4/IOX«8«8>*ALmA/DX) ••••MM
TERN*0.0« M089MI
IF(EX.8T.-7t.) TEim • Z(I)«NXH«EXPI.NTERM 8M099M
800099t«
ZPARG*EN«PI*ZP/BA9FR 800099M
ATERHBOSIN(AR6l«OC08(ZPARfl/EN 8I00994*
KRON'KROSTO*EN«EN«OZCONB 00«»99M
CALL 8HPtOOIXP,8,OX,OY,VX.KRON.OCTEim} 80009988
OELCCP*OELCCP«OCTERHNATERn 88809970
CTOLsERROR«OAB3(OELCCP) - 88809988
IFtOABSIDCTERHI.LT.CTOLI 80) TO t88 80009990
100 CONTINUE 98018888
COO CONTINUE 88018818
NKEEPsN 80010818
DELCCP*OELCa»*CON9T 888I88M
RETURN 00010844
KND 88818880
880108*8
88010*70
•••10088
80C18098
•8010188
80010118
80010MO
SUBROUTINE 06AUSSI A,B,Z.H) OOOfOU
-------
C F0« -THE SOLUTION OP INTEGRALS OP THE FORM 00010170
c oooioiao
C INTEGRAL OP FtZ)«OZ • SUN OP M(I)»P(Z(I» 00010190
C AS Z " 1.... MfAX 00010200
C IKTEGRATEO PRON A TO • 00010210
C 0001 OttO
C OOOlOtM
IMPLICIT REAL*6fA-H,0-Z) 00010140
INTECER»t IUNITl,IUNITt.IUNIT§, OOOlOtM
» IPSPEC,rmem,NLAMDA,HX,NVN.IPCAL,ZRCH8C.NHAX 00010MO
DIMENSION HltM).Z(tM) OOOlOtTO
COMMON/10/ lUNITItlUNZTt.ZUNZTS OOOlitM
COMMON/INTESS/ IP8PEC.NSISW,NUMDA.NX,NVN.IPm.IIKH6E.MUX OOOlOtM
C 00010MO
C A LONER LIMIT OP ZHTEBRATZON 00010310
c oooiosto
C B UPPER LIHIT OP INTIMATZON 00010330
C 00010340
C Z ROOTS OP TNI LE8MMI POLYNOMIALS PIN+llfZ) 00010UO
C 00010MO
C N HEI8HT FACTORS PW THE •AUM-UCQMI «MDRATUM 00010170
C 000103M
C UMAX NUMBER OP INTE8RATION POINTS 00010390
C NMAX CAN ONLY HAVE THE VALUE OP EITHER 4,1,4,10,11 ,tO,«0,104.tM 00010400
C 00010410
C 000104tO
c eeesstM
C , 00010440
C THE ROOTS AND MEIfiHT PACTORS POR THE NORMALIZED XNTEMAL ARE TAKEN000104M
C PROM : 00010460
C APPLIED NUMERICAL METHODS OOOI047S
C BY i B. CARNAHANt N.A. LUTHER AND J.O. WLKES 000104M
C JOHN HILEV AND SONS. INC. » 19*9 00010490
C AND IN ADDITION t SOOIOSOS
C 8AUSSIAN QUADRATURE FORMULAS 00010S10
C BY i A.H. STROUD AND DON SECREST OOOlOStO
C PRINTICE-HALL. INC. 19** 00010BM
C 00010S40
c oooiosso
C 00010MO
C PROGRAMME HAS MRZTTEM BY t MICHAEL J. UNSS JULY, 197* 00010S70
C 00010SBO
C 00010S90
C CHECK IP A > B 0001MM
IFtB.LT.AI HRITEI2,!) A.B.NNAX OOOlMtO
PORMATi/////////tSOX.>M«M ERROR IN SUBROUTINE OBAUSS •*•*•>, ///HOIMM
t .40X.-THB POLUMINB VALUES WHERE SPECIPIED',//. MX, •LONER LIMIT 000010*40
IP INTEGRATION A • ', DEO. tt,/,30X, 'UPPER LIHIT OP INTE0RATION B0001MSO
4 * '.DtO.lt.AlTX, 'NUMBER OP BAUMIAN INTEORAnON POINTS NHAX • 'S0010MS
S. I5,//,35X,'YOU VIOLATED THE CONDITION THAT UNIT • MUST BE 6REAT00010*70
«ER OR E4UAL THEN UNIT A* .//.SOX. 'PROORAH SHALL STOP AfTER POJMATOOOI06M
7 1 IN SUBROUrnC DSAUSS'I 011106*0
IFIB.LT.AI STOP 00010700
00010710
NORMALIZED ROOTS AND HEIONTS SOOI07IS
S001S7M
IFIMUX.NE.4I 60 TO SO S0010740
mm
-------
H( 3 1= . 34 76548451 37453800 00010700
60 TO 10000 0001079*
50 IFINTUX.N!.*) SO TO 60 00010801
Z<1)=0. 0001081*
Z(2)>.5384«9310105683000 00010810
2(4)3.906179845938663900 00010838
M(l)». 568888888888888800 00010840
M(2)». 478628670499366400 0001085*
H( 4)*. 236926885056189000 0001086*
60 TO 1000* *0010*7*
60 IFIM1AX.NC.6) 60 TO 100 0001088*
Z(l)«. 238619186083196900 0001089*
Z( 3 )=. 66120938646626450* 0001090*
Z( 5 >*. 932469514203152000 *001*91*
M( I)*. 467913934572691000 M01092*
Ml 3 )=. 36076157304813860* *001093*
M(5)c. 17132449237917*30* ***1094*
60 TO 10000 *00109M
100 IF(MUX.NE.IO) 60 TO 150 *0*1*96*
Z( 1 )« . 1488743389816310* *0*1097*
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•••14050
00014540
•••14170
M014SM
•0014590
•0014*10
•••14*10
•0014*20
•••14*30
•0014*41
•••14*50
•••14*60
•••14*70
•0014*80
•••14*90
•••14700
•••14710
••mm
•0014730
•••14741
M0147M
•••14740
•••14771
•M147M
•0014790
•••14800
•••14610
•••14621
•••14630
•••14640
•••14650
•••146*0
•••14670
•••14660
•0014690
•••14900
00014910
000149*0
00014930
•0014940
•0014950
•00149*0
••014970
•0014980
••014990
•0013000
00015010
mm
-------
HI 1231*
HI 1251*
HI127I*
Ml 1291*
MI131I*
HI 1331*
HI 1351*
Mil 37)'
HI 1391*
MI 1411*,
HI143I*,
Ml 1451*.
Ml 1471*,
HI 1491*
MUSI)*.
Ml 1531*.
HI 1851*.
HI 1571'.
HI 1591*.
HI 161)«.
HI 1631*.
HC165I*.
HI 1671".
HI 169)*
Ml 171»«.
HI 1731*.
Ml 1751*.
M1177I*.
HI 1791*.
Ml 1011*.
MI1S31*.
Ml 1651*.
Ml 1671*.
Ml 1691*.
Ml 1911*.
Ml 193)*.
Ml 1951«.
Ml 1971*.
Ml 1991*.
Ml 2011*.
Ml 2031*
Ml 2051*
Ml 2071*.
Ml 2091*.
Ml 211)"
MI213I*
HI 2151*
MI2171*.
MI219I*
Ml 221)*
Ml 2131*
Ml 2251*
MI227I*.
HI 2291*.
HI 2311*
HI233I*
Ml 2351*
.90364315406626730-02
.09344947037502070-02
.88312177572407500-02
.07266159616900070-02
.06207050004010140-02
.05135010250224900-02
.04050190532215350-02
.02952770462352250-02
.•1042914664302690-01
.00720773620734990-02
.79506523607143400-02
.70440334909397110-02
.77202379473015550-02
.76112030045456590-Ot
.74931064540050030-02
.73739657730123460-02
. 72536309250339130-02
.71322239610753900-01
.70097390929690220-02
,60062026954463200-02
67616333001737900-02
,66 360495937010450-02
.65094704150536600-02
.63019147521070000-01
, 62534017395424010-02
,612 39306555679320-02
.59935009191153300-02
.50623120069226530-02
.57301430306014370-02
.55971560336029100-01
54433065006443100-02
53206415939159300-02
.51931752300692000-02
.50569290007060420-02
.49199259210130650-02
,47621039250926910-02
46437245556000600-02
.45045605014470970-02
.43647360779600560-02
.42242504213015360-02
. 40031302060326600-02
.39413976414000330-02
.37990737407662570-01
. 36561799501425020-02
. 35127377050563070-02
.33607605073155510-01
.32242939617941900-02
.30793357411993370-02
.29339155900297160-02
.27000553253277060-02
.26417768254274900-02
.24951020347037060-02
.23400529563273120-02
.22006516490399100-02
.20529202279661430-02
.19040000534997100-02
.17565557363307290-02
.16079671307493270-02
00015050
00015060
00015070
00015000
00015090
00015100
00015110
00015120
00011130
•0011140
00015150
00015140
00015170
00015100
•0015190
•0015200
00015210
00015220
00015230
•0015240
00015250
00015260
00015270
•0011200
•0015290
•0015300
00015310
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•0015330
•0015340
•0015350
•0015360
•0015370
•0015300
•0015390
•0015400
•0015410
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•0015430
•0015440
•0015450
•0015460
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•0015400
•0015490
•••15500
•0015510
•0015520
•0018530
•0015540
00015550
•0015560
•0015570
•0015500
0001859*
•0015600
00018610
00018620
MM
II
-------
H(243J=.10114243932084400-02 00019660
HI245)=.8618537014200890D-03 00019670
HI 247 IB.71215416547332060-03 00015680
HI249)>.56234895403140980-03 00015690
H( 251)3.41246325442617630-03 0001570*
HI 253)*. 26253494429644590-03 00019710
HI 255>s.11278901782227110-03 00015720
60 TO 10000 00015730
3000 CONTINUE 00011740
HRITE<2,4000)NMAX 00011750
4000 FORMAT!/////.40X,'WHHHi EURO* FLAB FROM SUBROUTINE D8AUSS MMHM>,000197*0
2//.20X,'SUBROUTINE D8AU3S MIS NOT CONTAIN TNI NMAX" ', II, 00011770
0* ROOTS AND HEI8HT FACTORS', 000197M
3 /, MX,'FOR THE 6AUS3-LE0ENDRE 0JUADRADURE INTEMOO19790
4RATION SCHEME. THEY MUST BE AWED •,/, SOX.'PROBRAH SHAU END AFTEOOO11800
SR FORMAT 4000 IN SUBROUTINE OSAUSS'I 0001M10
STOP 0001B820
10000 CONTINUE 0001S8M
C 00019040
C CONSTRUCT THE REMAUONS COEFFICIENTS FROM TNI UVEN ONES OOOIMfO
C 000198*0
N0=0 0001M70
NF=NHAX/t MOIM6S
IF(Z(1).EQ.O.) N0»l 0001M90
NJ=NO 00019900
00 10100 J*1,NF 00011910
NJ=NJ»2 000199M
ZINJ)«-Z(NJ-1> 0001I9M
10100 MINJI*HtNJ-ll • 0001*940
C 0001I9M
C CHECK IF LONER AND UPPER INTE8RATION UHTTt ARE FDOTI OOOIIHO
C OR INFINITE 00011970
IFIA.LE.-1.0*10) 90 TO 30000 0001S9M
IFIB.0E.1.0*10) 00 TO MOM 00011990
C 00014000
C ADJUST THE COEFFICIENTS TO ACCOUNT FOR TNI NDN NORJIAUZEO 0001*010
C LIMITS OF INTEMATION 0001*0(0
C HHERE OOOIAOM
C HID HNtI)«(B-A)/E 0001*040
C OOOIAOM
C ZII) IZNII)MB-A)*a»A)/C 0001*0*0
C 0001*070
C WERE HMII) AND ZN(I) ARE TNI NnRMALIffO OOOIAOM
C RAUMIAN HEIOHTS AND ROOTS 0001*090
C SEE PAM 104 AND E« E.M IN THE " APPLIED NUMERICAL METHODS" 0001*100
C 0001*1IB
00 tOOOO I=1,NNAX OOOU1CO
HII)*HII)«IB-A)/C.DO 0001*130
EOOOO Z(I»IZII)«IB-A)*B*A)/E.Ot 0001*140
RETURN 0001*100
30000 CONTINUE 0001*1*0
C 0001*17*
C SPECIAL CASE WEN A — > - INFINITY 0001A1M
C 0001*190
DO 40000 ICI.NMAX 0001*100
H(I):Hm/IZ(I)*l.DO) 0001*210
40000 ZII)=B*OL06IIZII)«1.DO)/2.DO) 0001*220
C CHECK IF THIS INTE6RAL HAS INFINITE UPPER AND LONER UNITS OOOU23C
c 111 M T°
-------
SOOOC'dlNTINUE 00016270
C 00016180
C SPECIAL CASE WHEN B—> INFINITY 00016290
C 00016300
00 60000 IM.NMAX 00016310
H(ii=um/izm*i.DO) ooei63te
60000 Zm=A«DL06(t.OO/(Z(I)*l.DOn 00016330
C CHECK IF ONE IS TRYINB TO SOLVE THE INFINITE ZNTEMAL 00016340
IFU.LE.-1.0*10) 80 TO 00000 00016350
RETURN 00016360
80000 CONTINUE 00016370
II«0 00016380
C 00016390
C IF ME MANT TO SOLVE A PROBLEM KITH A~> - INFINITY AND 00016*00
C B —> » INFINITY, THEN BREAK TNI INTE6RATION INTO TMO 00016410
C SEMI-INFINITE INTEMALS 00016420
C THUS t FIXIMOX f-INF.tlMF) • F(X)*OX f-INF,0) « F(X)«OX (0,«INP) 00016430
C 00016440
MRITEI2, 90000) A.B.MUX 000164BO
90000 FORHAT(//////////.30X,'MHHHI ERROR IN SUBROUTINE 08AUSS WHHM00016460
2',//. 30X,'DBAUSS MAS CALLED MITH A • ', OtO.lt.X, B4X,'B • ', 00016470
3020.U,/, SIX,' HAMX- ', I3,///,10X,*THIS SUBROUTINE CAN NOT HANDL000164BO
4E AN INTEGRAL NHERE BOTH THE UPPER AND LONER LIMITS OP INTEMATIONOOO16490
S ARE INFINITE', ///. COX.'HHAT TO 00 ...DEFINE A MEM PROBLEM SUCH 00016BOO
6THAr,//,20X. 'FIXMttX <-INF,«INPI • F(Xi«OX I-INP.SI • F(XI«000165IO
TDK te,»INF) NHERE INF * l.D»20 ',//,tOX,'PRO8RAH SMALL END APTE00016BM
8R FORMAT 90000 IN SUBROUTINE DBAUSS' I 00016S30
IFIII.EQ.OI STOP 00014S40
1 RETURN 00016SBS
END 00016B60
-------
D032
0032
0032
0032
0032
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0032
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END
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END
END
END
END
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END
END
END
END
END
END
,END
END
END
END
END
END
END
END
END
END
END
END
END
END
END
END
END
END
END
END
END
END
END
END
END
END
END
END
END
END
END
TSU 4430 66C
TSU 4430 BSE
TSU 4430 BSE
TSU 4430 BBC
TSU 4430 G6C
TSU 4430 BBC
TSU 4430 BBC
TSU 4430 BBC
TSU 4430 BBC
TSU 4430 BBC
TSU 4430 BBC
TSU 4430 BBC
TSU 4430 BBC
TSU 4410 BBC
TSU 4430 BBC
TSU 4410 BBC
TSU 4410 BBC
TSU 4430 BBC
TSU 4430 BBC
TSU 4430 BBC
TSU 4430 BBE
TSU 4430 BBC
TSU 4430 BBC
TSU 4430 BBC
TSU 4430 BBC
TSU 4430 BBC
TSU 4430 BBC
TSU 4430 BBC
TSU 4430 BBC
TSU 4410 BBC
TSU 4430 BBC
TSU 4410 BBC
TSU 4430 BBC
TSU 4430 BBC
TSU 4430 BBC
TSU 4410 BBC
TSU 4430 BBC
TSU 4410 BBC
TSU 4410 BBC
TSU 4430 BBC
TSU 4430 BBC
TSU 4430 BBC
TSU 4410 BBC
TSU 4430 BBC
TSU 4430 BBC
TSU 4430 BBC
TSU 4430 BBC
TSU 4430 BBC
TSU 4410 BBC
TSU 4410 BBC
TSU 4430 BBC
TSU 4430 B0C
TSU 4410 BBC
TSU 4410 BBC
TSU 4410 HI
TSU 4410 HI
TSU 4410 BBC
TSU 4430 G6C
ACCT CAEO
ACCT CAEO
ACCT CAEO
ACCT CAEO
ACCT CAEO
ACCT CAEO
ACCT CAEO
ACCT CAEO
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CACD
ACCT CACD
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CAEO
ACCT CAEO
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CACD
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CACD
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CAEO
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CACO
ACCT CAEO
ACCT CACO
ACCT CAEO <
ACCT cStff '
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.01.14 m
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.09.94 m
.09.94 m
.09.94 PH
.09.94 m
.09.94 m
.09.94 PH
.09.94 m
.09.94 m
.09.94 m
.09.94 m
.09.94 m
.01.94 m
.09.94 PH
.09.94 m
.09.94 m
.09.94 PH
.09.94 m
.09.94 PH
.09.94 m
.09.94 m
.09.94 PH
.09.94 FN
.09.94 m
.09.94 m
.09.94 m
.09.94 m
.09.94 m
.09.94 m
.09.94 PH
.09.94 m
.09.94 m
.09.94 PH
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.09.94 m
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l:H:» EH \
DEC 09 L20.8R1
DEC 0S LC0.8R1
DEC 01 LC0.SRI
DEC 0* 120. Ml
DEC 05 LC0.SRI
DEC 0S LC0.SRI
DEC 01 UO.SRI
DEC 09 L20.SR1
DEC 0S L20.8R1
DEC 0S L20.SR1
DEC 0S U0.SR1
OEC 0S U0.SRI
DEC 0S LC0.M1
OEC 0S UO.SRI
OEC 0S U0.SRI
OEC 0S 1*0. SRI
OEC 0S U0.SRI
OEC 0S UO.SR1
OEC 0S 120.8*1
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DEC 0S U0.SRI
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DEC 0s 120. SRI
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PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HBC1
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTCRC HSCI
PRINTER* HSCt
PRINTER* HSCI
PRINTCRC HSCI
PRINTER* HSCI
PRINTCRC HSCI
PRINTER* HSCI
PRINTCRC HSCI
PRINTCRC HSCI
PRINTER* HSCI
PRINTERS HSCI
PRINTER* HSCI
PRINTER* HSCI
PRINTER* HSCI
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PRINTCRC HSCI
PRINTCRC HSCI
PRINTCRC HSCI
PRINTER* HSCI
PRINTCRC HSCI
PRINTCRC HSCI
PRINTER* HSCI
PRINTCRC HSCI
PRINTCRC HSCI
PRINTER* HSCI
FUNfffii BSi
DP
OP
DP
DP
OP
OP
OP
OP
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OP
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RH 001*
RH 003*
RH 003*
RH 003*
RH 003*
RH 003*
RH 003*
RH 003*
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RH 001*
RH 001*
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RH 001*
RH 001*
RH 001*
RH 001*
RH 001*
RH 001*
RH 001*
RH 001*
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RH 001*
RH 003*
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RH 009*
RH 001*
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RH 001*
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RH 001*
RH 009*
RH 003*
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6(18011
------- |