FINAL REPORT
        THEORETICAL EVALUATION OF
SITES LOCATED IN THE ZONE OF SATURATION
            STATE OF WISCONSIN
         Contract No. 68-01-6438
               Task No. 012
              Prepared for:

             Mr. James Bland
         Project Officer (5  AHWM)
   U.S.  Environmental Protection Agency
                 Region V
         Chicago, Illinois  60604
               Prepared by:

               Versar Inc.
            6850 Versar -Center
              P.O. Box 1549
       Springfield, Virginia  22151

                   and

              JRB Associates
           8400 Weatpark Drive
         McLean, Virginia  22102
              Date Prepared:

             August 29, 1983

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                            TABLE OF CONTENTS


1.0  INTRODUCTION 	     1

2.0  DRAIN THEORY 	     4

     2.1  Drain Spacing and Head Levels	     4

          2.1.1   Drains On Impervious Barriers 	     5
          2.1.2   Drains Above Impervious Barriers	     7
          2.1.3   Drains On Sloping Impervious Barriers 	    11

     2.2  Drain Pipe Sizing	    13

          2.2.1   Hydraulic Gradient (i) and Roughness Coefficient   14
          2.2.2   Discharge (Q)	    17
          2.2.3   Pipe Size	    21

     2.3  Filters and Envelopes	    23

          2.3.1   Function of Filters and Envelopes	    23
          2.3.2   Design of Sand and Gravel Filters	    24
          2.3.3   Design of Sand and Gravel Envelopes	    26
          2.3.4   Synthetic Filters 	    26

3.0  DESIGN AND CONSTRUCTION	    28

     3.1  Hypothetical Site	    28
     3.2  Sensitivity Analysis  	    31

          3.2.1   Drains On Impermeable Barriers  	    31
          3.2.2   Drains On Sloping Impervious Barriers 	    34
          3.2.3   Drains Above An Impervious Barrier  	    40

     3.3  Application	    40

          3.3.1   Parameter Estimation	    43
          3.3.2   Landfill Size	    44
          3.3.3   Example Problem	    45

     3.4  Application	    47

          3.4.1   Construction Inspection 	    47
          3.4.2   Drain System Maintenance	    48
          3.4.3   Future Operating Conditions 	    49
                                    ii

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                            TABLE OF CONTENTS
                               (Continued)
4.0  FLOW NET ANALYSIS	     50

     4.1  Introduction	     SO
     4.2  Initial Conditions  	     52
     4.3  Parameter Analysis  	     55

5.0  MODELS	     60

     5.1  Release Rate Models	     60

          5.1.1   Fundamentals	     60

                  5.1.1.1  Leachate Generation  	     60
                  5.1.1.2  Leachate Constituent Concentrations. .     66
                  5.1.1.3  Leachate Release 	     66

          5.1.2   Selected Release Rate Models  	     69

     5.2  Solute Transport Models 	     77

          5.2.1   Fundamentals	     77

                  5.2.1.1  Analytical Models  	     80
                  5.2.1.2  Numerical Models 	     81

          5.2.2   Selected Solute Transport Models  	     82

                  5.2.2.1  Analytical Models  	     86
                  5.2.2.2  Numerical Models 	     90

     5.3  Model Limitations  	     94

6.0  RECOMMENDATIONS	     95

7.0  BIBLIOGRAPHY	     97

APPENDIX A - Flow Net Construction	    A-l
                                   iii

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                          LIST OF TABLES


2-1  Values for the Equivalent Depth d of Hooghoudt 	    10

2-2  Minimum Hydraulic Gradients for Closed Pipes  	     IS

2-3  Drain Grades for Selected Critical Velocities 	     16

3-1  Range of Site Variables	     30

3-2  Drain Length Spacing (m) for Drains on an Impermeable
     Barrier	     32

3-3  Values of h/L for Various C=q/k! and Angles a	     36

3-4  Drain Spacing (m) for Head Maintenance Levels of 2 Meters   38

3-5  Drain Spacing (m) for Drains Above an Impermeable Barrier   41

3-6  Example Data Set	     46

5-1  Major Factors Affecting Leachate Generation 	     62

5-2  Factors Affecting Leachate Constituent Concentrations .     67

5-3  Factors Affecting Leachate Release  	     68

5-4  Release Rate Models	     70

5-5  Solute Transport Models 	     83
                                iv

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                         LIST OF FIGURES


1-1  Typical Stratigraphic Column of Zone of Saturation
     Sites in Wisconsin  ..................       2

2-1  Drains Resting on an Impervious Barrier ........       6

2-2  Flow to Drains Above an Impervious Barrier  ......       8

2-3  Drains on Sloping Impermeable Barrier .........      12

2-4  Flow Components to a Landfill .............      18

2-5  Division of a Symmetrical Drawdown Drain Problem Into
     Two Equivalent Fragments ................      20

2-6  Capacity Chart  n = 0.013 ...............      22

3-1  Hypothetical Zone of Saturation Landfill ........      29

3-2  Drain Length versus Flow Rates for Head Levels Equal to
     1 Meter ........................      33

3-3  Plot of h/L versus h/I = tan a for Drain and Sloping
     Impervious Layers ...................      37
3-4  Drain Length (L) versus c - q/ki  ...........     39

3-5  Drain Spacing (L) versus Inflow rates (q) .......     42

4-1  Cross Section of Typical Zone of Saturation Landfill   .     51

4-2  Inflow With Typical Landfill Cell ...........     54

4-3  Flow Nets With Different Leachate Levels  .......     56

4-4  Flow Nets With Different Vertical Gradients ......     57

4-5  Flow Nets With Different Numbers of Drains .......     58

5-1  Major Components of Groundwater Transport Equations .  .     79

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                             ACKNOWLEDGMENTS
    This report was prepared by Dr. Edward Repa, Ms. Kathi Wagner, and
Mr. Roger Wetzel of JRB Associates, and Mr. Michael Christopher of Versar
Inc., under the direction of Dr. G. Thomas Farmer, Task Manager, and
incorporates numerous useful suggestions and comments by Mr. Peter Kmet
and Mr. Paul Huebner of the State of Wisconsin's Bureau of Solid Waste
Management.  This report was prepared for the Wisconsin Department of
Natural Resources under the U.S. EPA's Technical Assistance Project
sponsored by U.S. EPA, Region V.
                                    vi

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                             1.0   INTRODUCTION

    The State of Wisconsin and much  of EPA Region V are located  in a
portion of the United States characterized by thick surficial deposits of
saturated glacial till and lacustrine deposits underlain by fractured
sedimentary or crystalline rock.  A  typical stratigraphic column for
Wisconsin is shown  in Figure 1-1.  Landfill site design in this part of
the country is complicated by the hydrology of the zone of saturation.
At these sites, the glacial clay deposits into which the landfills are
built act as limited unconfined aquifers.  Hydraulic conductivities of
                        _c
the clays range from  10   cm/sec, where the clays are fractured, to
10   cm/sec, where the clays are unfractured (Newport, 1962).  Locally
higher permeabilities may be present due to inclusion of silt, sand, and
gravel.  Although saturated, because of the overall highly impermeable
nature of these deposits, water supply wells are usually not developed in
them.   Underlying the clays are thick units of dolomite and sandstone
which act as semi-confined aquifers.  Confining pressures in these units
can bring groundwater to the land surface in drilled wells.  Recharge of
these underlying units occurs at or near outcrops and from the overlying
glacial deposits.
    Siting landfills in this region, especially those which will accept
hazardous wastes, is a problem because the base grade of the facility is
typically below the water table (i.e., in the zone of saturation).   As a
result of having the base grade below the groundwater table, the
potential for accelerated leachate generation and contaminate release is
greatly enhanced.  To alleviate this problem,  landfill operators are
required to manage groundwater and leachate in the landfills so that
inward hydraulic gradients are constantly maintained,  thereby limiting
                                   -1-

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         Geologic
            Log
           \ \ \ \ \
             \  \ \ \
           v \ \ \  \
           \ \ \  V Y~\
            \ \  V \V
           \ \  \  \ \
           \ \ \ \ \
            .v .^ . V
           v\ \ \ \\
            A \  \  \ \
Rock Unit
       Aquifer
                       Glacial deposits
                         Red Clay
                             Limited Unconfined
                                 Aquifer
Galena Dolomite and
  Platteville Formation
Confined Aquifer,
solution cavities
                       St. Peter Sandstone



                       Trempealeau Formation

                       Franconia Sandstone


                       Galesville Sandstone
                             Confined Aquifer
                          •
   Vertical Scale 1"»200'
Figure 1-1.  Typical Stratigraphic Column of Zone of Saturation
             Sites in Wisconsin 
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the possibility of contaminant escape.  The method utilized to maintain
inward hydraulic gradients is a drainage collection system installed on
the base of the landfill.  The drainage system allows for the maintenance
of landfill head levels which are lower than the natural groundwater
table (i.e., inward hydraulic gradients).
    The purpose of this study was to perform a theoretical evaluation of
the validity of the presently used landfill management schemes for
groundwater and leachate at sites located in the zone of saturation.
This evaluation included flow net and parameter sensitivity analyses.
The key parameters that were evaluated include:
    o  Drain spacing.
    o  Hydraulic conductivities of the landfill and natural soils
       surrounding the site.
    o  Inflow rates resulting from groundwater infringement and leachate
       generation.
    o  Head maintenance levels within the landfill.
    o  Pipe sizing.
    o  Drainage blanket use.
Other parameters addressed include landfill dimensions, construction
inspections, and future operating conditions.  Drainage theory and
selected models for predicting release rates and solute transport are
also described.
    The results of this study should assist permit writers in determining
engineering design modifications and site monitoring requirements, as
well as aid in establishing a basis for future design protocols for zone
of saturation landfills.
                                      -3-

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                             2.0  DRAIN THEORY

    There  are  three major elements  to consider  in  the design of  a
subsurface drainage system  suitable for zone of saturation landfills:
    o  The drain  spacing required to achieve the desired head maintenance
       levels.
    o  The hydraulic design  of the  conduit, including the pipe diameter
       and gradient.
    o  The properties of the drain  filter and envelope.
    This section  briefly describes  the principles  involved in determining
a desirable drain slope and  spacing, and in selecting appropriate drain
materials.
2.1  Drain Spacing and Head  Levels
    There are numerous analytical solutions and models that have been
developed for estimating the drain spacing required to maintain head
levels at a predetermined height in saturated media.  This section
presents the analytical solutions for determining drain spacing based on
maintenance head levels, permeabilities, and flow rates for:
    o  Drains resting on an  impermeable barrier
    o  Drains installed above an impermeable barrier
    o  Drains resting on an  impermeable barrier that slopes symmetrically
       at an angle to the drains.
    The equations presented here assume that steady state conditions
exist, that recharge distribution and leachate generation over the area
between the drains is uniform, and that the soil is homogeneous.   Most
real world situations do not fully meet these criteria; therefore, the
results obtained should be considered approximate.   In using the
equations for designing a landfill drain system, a conservative approach
                                    -4-

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should be taken to ensure that head maintenance levels are at or below
the desired height.
2.1.1  Drains on Impervious Barriers
    Groundwater flow to drains resting on a horizontal (flat) impervious
barrier can be represented (Van Schlifgaarde, 1974; Wesseling, 1973) by
the equation:

    L = t(8KDh + 4Kh2)/ql°'5                                      (1)
where:
    L = drain spacing (m)
    K = hydraulic conductivity of the drained material (m/day)
    D = distance between the water level in the drain line and the
        impermeable barrier (m)
    h = water table height above the drain levels at the midpoint between
        two drains (m)
    q = leachate generation rate (m/day) [equal to total inflow
          3                                 2
        (m /day) divided by landfill area (m )]
Figure 2-1 illustrates the relationship between these terms.  When two
parallel drain lines are installed properly, each line causes the
establishment of a drawdown curve that, in theory, will intersect midway
between the two drain lines.  In solutions to gravity flow problems, the
distance from the drain to a point where the drawdown can be considered
insignificant (Ah = 0) is equal to half of the drain spacing (L/2).
This distance, L, is commonly referred to as the "zone of influence" of
the drain.
    For a pipe drain resting on an impermeable barrier, the parameter D
approximately equals the radius of the pipe and hence can be very small
in comparison to h (the water table height above the drain).  Then, since
the term SKDh becomes very small (=0), equation 1 can be simplified to:
             2    0.5
    L =» [(4Kh )/q]                                               (2)
Equation 2 represents horizontal flow to the drains above the drain level.
                                    -5-

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Figure 2-1: Drains Resting On An Impervious Barrier
                            -6-

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    Drain spacing (L) and hydraulic head level (h) in the equations are
interdependent design variables which are a function of the leachate
generation rate (q) and hydraulic conductivity (K) of the drained
material.  Assuming a constant leachate generation rate and hydraulic
conductivity, the closer two drains are spaced the more their drawdown
curves will overlap and the lower the hydraulic head levels between the
drains will be.  Therefore, in order to space the drains at the required
distance to achieve the desired head maintenance levels, the hydraulic
conductivity of the landfill material and the quantity of leachate
generated must be determined to a reasonable degree of accuracy.
2.1.2  Drains Above Impervious Barriers
    Equations 1 and 2 are suitable for estimating drain spacing and head
levels if the drains are located on an impervious barrier, as is the case
with most landfill operations.  In using drainage system design
equations, a layer is generally considered impervious if it has a
permeability at least 10 times less than the overlaying layer (i.e.,
K  t   /K .  ,   >10).  The clay base of a landfill may not act as an
  above   below
impermeable layer in the design equations if:
    o  Clays are not adequately compacted to produce the desired
       permeability
    o  Clays are fractured (naturally or during placement)
    o  Clays are not uniform (e.g., contain sandy zones)
    o  Landfill material has a permeability comparable to the clay liner.
    Where drains are not installed on impermeable barriers, flow to the
drains is radial (as illustrated in Figure 2-2).  In this case the drains
are considered to be installed at the interface of a two-layered soil
with hydraulic conductivities of K  and K  (as shown in Figure 2-2).
Substituting the hydraulic conductivity of the material below the drain
(K ) into the first term of the right hand side of equation 1
  2
compensates for radial flow to the drain system, and gives:
                      2    0.5
    L =  l(8K2Dh + AK-jh )/q]                                         (3)

                                    -7-

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•°. -V •••*.' •• ?• •• • • .' ~.v .• •• ...••«••,<>'• ..»•, • :.'o; "••.' ••.• •• • • o *. •. ,• .-•'..;.•. • •.. •.. .' . • .'• °. •
 r_-_-_-^Xr_-_-_-_-_-_^-_-_-_----~-~^-~-~-~-^^^       	1	[
 	>_j	T-^- ~~~~~iniiiri'      -I-I-I-£





   Figure  2-2:  Radial Flow to Drains Above An Im-


                     pervious  Barrier
                                  -8-

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 However, the drain spacing calculated by equation 3 does not take into
 account the fact that flow velocity in the vicinity of the drain is
 higher than elsewhere in the flow region.  If the flow velocity was
 uniform, the reduction in hydraulic head caused by the drain would be
 distributed evenly around the drain.  But, because of the non-uniform
 velocity,  a proportionally higher loss of head occurs close to the drain,
 and the actual water table elevation (h) will stand higher than expected
 with drains spaced according to equation 3.
     To account for the increase in h caused  by radial flow, Hooghoudt
 (1940) introduced a reduction of the parameter D to a smaller equivalent
 depth, d.   The equation that was developed to take into account radial
 flow can be rewritten as:

     L = [(8K2dh + AKxh )/ql  '                                        (4)
 where the  new term d is  the  equivalent depth (m)
     Equation  4 shows  the drain  spacing L is  dependent on  the equivalent
 depth d.   But the value  of d is calculated from a specified value  for L,
 so  equation 4 cannot  be  solved  explicitly in terms  of L.   The  use  of  this
 equation as a drain spacing  formula  involves either a trial and error
 procedure  of  selecting d and L  until both sides of  the  equation are equal
 or  the use  of nomographs which  have  been  developed  specifically for
 equivalent  depth  and  drain spacing.  Table 2-1  gives  values  of  the
 equivalent  depth  (d)  as  a function of  drain  spacing  (L) and  saturated
 thickness below the drains (D).  This  tables  show values of  d for  a drain
 pipe  with a radius  (r  )  of 0.1 meter.  Similar  tables have been
 prepared for  other  values of r  .  For  saturated thicknesses  (D) greater
 than  10 meters, the equivalent depth can be  calculated  from  drain spacing
 using  the following equation:
    d  - 0.057  (L) + 0.845                                           (5)
This equation was developed by linear regression  from the values given in
Table 2-1.
                                    -9-

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        L-«  S
                            20
                                    30
O
I
D
0.5 • 0.47 0.48 0.49 0.49 0.49 0.50 O.SO 	 	 ^
0.75 0.60 0.65 0.69 0.71 0.73 0.74 0.75 0.75 0.75 0.76 0.76
1.00 0.67 0.75 0.80 0.86 0.89 0.91 O.93 0.94 0.96 0.96 0.96
1.25 0.70 0.82 O.B9 1.00 1.05 1.09 1.12 1.13 1.14 1.14 1.15
l.SO
1.75
2.00
2.75
1.50
J.75
1.00
3.25
3.50
3.75
4.00
4.50
5.00
i.50
6.00
7.00
8.00
f».OU
10.00
0.88 0.97 1.11 1.19 1.25 1.28 1.11 1.34 1.35 1.36
0.91 1.02 1.20 1.30 1.19 1.45 1.49 1.52 1.55 1.57

















1.08 1.28 1.41 1.5 1.57 1.62 1.66 1.70 1.72
1.11 1.14 1.50 1.69 1.69 1.76 1.81 1.84 1.86















1.38 1.57 1.69 1.79 1.87 1.94 1.99 2.02
1.42 1.63 1.76 l.C
8 1.98 2.05 2.12 2.18
1.45 1.67 1.81 1.97 2.08 2.16 2.23 2.29
1.48 1.71 1.8B 2.04 2.16 2.26 2.35 2.42
l.SO 1.75 1.91 2.11 2.24 2.1i 2.45 2.54
1.52 1.78 1.97 2.17 2.31 2.44 2.54 2.64









1.61 2.02 2.22 2.17 2.51 2.62 2.71
1.85 2.08 2.31 2.50 2.63 2.76 2.87
1.88 2.15 2.38 2.58 2.75 2.89 1.02






0.71 0.93 1.14 1.53 1.
2.20 2.41 2.65 2.84 1.00 3.15





B9 2.
2.48 2.70 2.92 3.09 3.26
2.54 2.81 3.03 3.24 1.43
2.57 2.85 3.11 1.15 3.56


24 2.
2.89 3.18 3.41 3.66
1 3.23 3.48 3.74
58 2.91 3.24 3.56 3.88
U r JU IJ WW «J

D
0.5 0.50 	
I 0.96 0.97 0.97 0.97

2 1.72 1.80 1.82 1.82

3 2.29 2.49 2.52 2.54

4 2.71 3.04 1.08 3.12

5 3.02 3.49 l.SS 3.61

6 3.21 3.85 3.91 4.00

7 3.43 4.14 4.21 4.33

8 1.56 4.38 4.49 4.61

9 3.66 4.57 4.70 4.82
10 3.74 4.74 4.89 5.04
12.5

IS
17.5

20

25
3O
35
40

45
50
60
5.02 5.20 5.38

5.20 5.40 5.60
5.30 5.51 5.76

5.62 5.87

5.74 5.96







1.88 5.18 5.76 6.00



cr
O t-1
P »
M
C 1
0.98 0.98 0.99 0.99 O.99 »-• M
P P •
1.81 1.85 1.00 1.92 1.94 O f+
O. (D
2.56 2.60 2.72 2.70 2.8] Q. <
M P
1.16 1.24 1.46 1.58 1.66 P «> (-•
rr O C
3.67 1.78 4.12 4.11 4.41 e 1 »
l-| M
4.08 4.21 4.70 4.97 5.15 p O
ff t-** M>
4.42 4.62 5.22 5.57 5.81 rt> rt> O
a "> n
4.72 4.95 5.68 6.11 6.41 O
HIM
4.95 5.21 6.09 6.63 7.00 =T O J3
5.18 5.47 6.45 7.09 7.51 O Jr M-
5.56 5.92 7.20 8.06 8.68 3 < p
m ra i— i
5. gO 6.25 7.77 8.84 9.64 in M (D
5.99 6.44 8.20 9.47 10.4 W {j jj.
nrt tfl
6.12 6.60 8.54 9.97 11. I » O
1— * O A
6.20 6.79 8.99 10.7 12.1 O «> -O
9.27 11.3 12.9 * a £f
9.44 11.6 13.4 ° 2 0-
11.8 13.8 P. a* ^
12 0 11 a 3 n>
(0 M O
12.1 14.3 ^"2 **
| 14.6 0 0 H
1 ^^- i-i. Q
6.26 6.82 9.55 12.2 14.7 3 ..
OM II
*^ O
r1 •
          Source:  Wesseling, 1973.

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2.1.3  Drains on Sloping Impervious Barriers
    Typically, landfill cells are designed so that the compacted base of
the cell slopes symmetrically at an angle towards the drains.  A
cross-section of such a design is shown in Figure 2-3.  By designing the
drain system on sloping barriers, the flow of water towards the
collection system is accelerated, thus decreasing the steady-state head
maintenance levels.  This allows the drains to be spaced further apart or
the heads to be lowered if the other parameters in the equation are held
constant.
    Drain spacing can be calculated for landfills designed with an
impervious layer sloping towards the drains at an angle by the following
equation (Moore, 1980):

    L = <2h    /c°'5)/[tan2a/c) +1 - (tan a/c) (tan2o + c)°'5]         (6)
            max
where:
    c » q/K (dimensionless)
    a = slope angle (degrees)
    nmax = maximum allowable head level above impervious layer (m)
Note that because the "peak" formed by the two slopes between the drains
intrudes on the saturated mound between the drains, h    is not found
                                                     max
directly above this peak (midway between the drains) but at some distance
to either side of this point.
    For example, consider a landfill to be constructed in glacial till
with bottom drains constructed of a material with a hydraulic
                          -4               -6
conductivity (K) of 2 x 10   cm/sec (2 x 10   m/sec).  The fill will
have slopes toward the drains of 2% (1.1°), has an estimated leachate
generation rate of 6 inches per year (4.2 x 10   m/day)  based on water
calculations, and must maintain the leachate level at a maximum elevation
of 2 m above the drains.  The drain spacing is calculated using
equation 6:
                                    -11-

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                Infiltration  (q)
Figure 2-3: Drains on  Sloping Impervious Barriers
                           -12-

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    L = <2h    /c°'5>/[tan2a/c) +1 -  (tan a/c)  (tan2<* + c)°'5]          (6)
            max
                                       -4
          .     _     .„   	4.2 x  10   ro/day	   _  .„   „ -3
         where C = q/K = 	r	*	 = 2.43 x 10
                         2 x 10~  m/sec x 86,400 sec/day

    T      (2 x 2 m)      /[(3.69 x 10~4>   .    (1.92 x 10~2
                  -3 0 5 /            -3      ~           -3
        (2.43 X 10  )    I [(2.43 X 10 )        (2.43 X 10  )

      + (3.69 x 10~4 + 2.43 x 10~3)°

      = 	—	 /[(1.52 x 10"1) + 1 - (7.90) (5.29 x 10~2)]
        4.93 x 10"*
                        -1
      * 81.1 ra/7.34 x 10

      = 110.6 m
    These drainage system design equations assume that the drain pipe
will accept the drainage water when it arrives at the drainline and that
the drain pipe will carry away the water without a buildup in pressure.
To meet the second assumption, the pipe size and drain slope must be
adequate to carry away the water after it enters the drain pipe.  The
following sections describe the methods utilized to ensure that these
assumptions are valid.
2.2  Drain Pipe Sizing
    The design diameter of a drain pipe is dependent on the flow rate,
the hydraulic gradient, and the roughness coefficient of the pipe.  The
roughness coefficient, in turn, is a  function of the hydraulic resistance
of the drain pipe.  The formula for the hydraulic design of a drain pipe
is based on the Manning formula for pipes which is:

    QT - (R0'67)(i°-5> A/n                                          (7)
                                    -13-

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where:
    QT = design discharge (m^/sec)
    R  = hydraulic radius of the pipe (m), which is equal to the wetted
         cross-sectional area divided by the wetted perimeter, or is
         equal to 1/4 of the diameter of a full flowing pipe
    i  = hydraulic gradient (dimensionless)
    A  = cross-sectional area of flow (m2)
    n  = roughness coefficient (dimensionless).
Each of the above factors is described in further detail in the following
sections.
2.2.1  Hydraulic Gradient (i) and Roughness Coefficient (n)
    Subsurface drains are generally installed on a gradient (i) that is
sufficient to result in a water velocity within the pipe that will
prevent silting, but is less than the velocity which will cause turbulent
flow.  Turbulent flow will cause abrasion within the pipe and ultimately
result in the pipe being destroyed.  Past experience has shown that
non-silting velocities occur above 1.4 feet per second (Soil Conservation
Service, 1973).  In situations where silting may be a problem and
velocities are less than 1.4 ft/sec, filters and traps can be utilized to
prevent the drains from clogging.  The minimum hydraulic gradients
required to prevent siltation in three sizes of closed pipe are listed in
Table 2-2.  However, steeper gradients are generally desirable provided
they are less than the gradients which would result in turbulent flow.
    To prevent turbulent flow, the hydraulic gradients should result in
velocities that are less than critical velocities.  Table 2-3 gives
critical velocities for various drain sizes, gradients, and roughness
coefficients.  For smooth perforated concrete or plastic pipes, roughness
coefficients can be assumed to be equal to 0.013 (Soil Conservation
Service, 1973).  Knowing the velocity which results in siltation and that
which results in turbulent flow, the design engineer can select a
gradient which results in a velocity somewhere between the two extremes.
                                    -14-

-------
TABLE 2-2.  MINIMUM HYDRAULIC GRADIENTS  FOR CLOSED PIPES
        Pipe Diameter                   Grade
       Inches       Cm                    %

         4         10.2                   0.10

         5         12.7                   0.07

         6         15.2                   0.05
        Source:   Soil Conservation Service,  1973
                            -15-

-------
           TABLE 2-3.  DRAIN GRADES FOR  SELECTED  CRITICAL  VELOCITIES
Drain Size
laches
1.4 fps
(1) 3.5 fps
V E L 0 C
5.0 fps
I T Y
6.0 fps
7.0 fps
9.0 fps
Grade - feet per 100 feet
For drains with "n" •

4
5
6
8
10
12

Clay
4
5
6
8
10
12

Clay Tile,
.28
.21
.17
.11
.08
.07

Concrete Tile,
1.8
1.3
1.0
0.7
0.5
0.4
For drains
Tile, Concrete Tile, and
.41
.31
.24
.17
.12
.09

2.5
1.9
1.5
1.0
.8
.6
For drains
0.011<2)

and Concrete Pipe (with good
3.6
2.7
2.1
1.4
1.1
0.8
with "n"
Concrete
5.2
3.9
3.1
2.1
1.6
1.2
with "n"
Corrugated Plastic
4
5
6
8
10
12
.53
.40
.32
.21
.16
.13
3.3
2.5
2.0
1.3
1.0
.8
6.8
5.1
4.0
2,7
2.0
1.6
5.1
3.9
3.1
2.1
1.5
1.'2
• 0.013
Pipe (with
7.5
5.6
4.4
3.0
2.2
1.8
- 0.015
Pipe
9.8
7.3
5.8
3.9
2.9
2.3
7.0
5.3
4.1
2.8
2.1
1.6


alignment)
11.5
8.7
6.9
4.6
3.5
2.7

fair alignment)
10.2
7.7
6.0
4.1
3.0
2.4


13.3
9.9
7.9
5.3
4.0
3.1
16.8
12.7
10.0
6.8
5.0
3.9


21.9
16.6
13.2
8.8
6.6
5.1
(1)—Feet per second
(2)—"n" is  the roughness  coefficient

Source:   Soil Conservation Service, 1973.
                                       -16-

-------
 For example, for a 6" drain pipe with roughness coefficient of 0.013 and
 a velocity of 5 ft/sec, a grade of 3.1 feet per 100 feet would represent
 the maximum gradient possible prior to creating turbulent flow.
 2.2.2  Discharge (0)
     The design discharge of a pipe, Q  is equal to the sum of the
 individual discharges which impinge upon the drain.  Figure 2-4  shows the
 various flow components that could contribute to a drain discharge within
 a landfill.   These flow components can be broken into two major
 categories—flow from within the site and flow from the surrounding
 aquifer.
     In  most  instances the flow rates  are estimated for design purposes  so
 that the  drain spacing can be determined using the previously presented
 equations.   Estimates of discharge can be obtained using two simplified
 methods—the water balance method and the method of fragments.   The water
 balance method is  used to calculate the amount of the percolation that
 can  recharge the water table between  the lines of drains.   This  flow must
 be removed to maintain steady state conditions.   A simple  water  balance
 equation  is  as  follows:
     qp  =  P-RO-ST-ET                                                 (8)
     where:
     q_  =  percolation  rate:   amount  of  water  that  must be removed  by
         drainage  system (in/day)
     P   = precipitation  (m/day)
     RO  =  surface water  runoff  (m/day)
     ST  = change in  soil  (refuse) moisture  storage  (m/day)
     ET  - evapotranspiration  rate  (m/day)
Once the percolation  rate has been  calculated, discharge can be obtained
by multiplying the percolation rate by the drainage area (i.e., Q
  32
(m/day) = q  (m/day) Area (m  )).
                                    -17-

-------
CD
I
                                              Lateral flow
                                                  in waste
                          Figure 2-4s  Flow Components to a Zone of Saturation Landfill

-------
    When using the water balance method to calculate flow rates or

discharges for landfills, the following points should be considered:

    o  Precipitation values for those time periods with high intensity
       rainfalls should be used to ensure percolation values are
       maximized and drainage design is adequate to handle these
       discharges.

    o  Soil (refuse) moisture storage changes can be significant as new
       refuse is placed into the landfill; once field capacity of the
       materials is attained the SI term can be considered zero.

    o  Variations in cover depths and the absence of vegetation can have
       significant effects on percolation rates; these effects will
       probably be greatest during the active operational phase when
       shallow covers are presented and drainage is inadequate.

    The method of fragments is used to calculate the flow rates that are

derived from the aquifer that borders the outermost drains,  this flow

component is not considered in the drain spacing equations but could
significantly affect the pipe sizing of the border drain.  Discharge of
the border drains can be derived exclusively from horizontal flow or
through a combination of horizontal and radial flow.  Figure 2-5 shows
the division of the border drain flow into two fragments that can be

calculated separately and summed.

    The quantity of flow into fragment 1 (Figure 2-5) can be estimated

(Moulton, 1979) from the equation:


    Q_. » K(h )x/2(R.-b)                                            (9)
     V»i             0
where:

        - Pi?® discharge (m3/day)

    K   = hydraulic conductivity (m/day)

    h   = height of the water table above the drain (m)

    x   = length of the drain (m)

    Rd-   distance of the drain's influence (m)

    b   = half the width of the drain and the trench (ra).
                                    -19-

-------
i
r-o
O
I
                     Impervious Boundary
                                                            Fragment No.  I
                                                                       Impervious
Fragment  No.  2
V
t

H


D
RH

! <
i
<
Y,
T
^
^
VvV^V^<^X
-2b
'.
\
I
Impervious
           Figure 2-5»  Division of  Symmetrical Drawdown Drain Problem  into Two


                           Equivalent Fragments  (Moulton, 1979)

-------
 In order to solve the equation, the value of R. must be known or
                                               a
 estimated.  Typically, the value of R. is estimated using an equation
                                      a
 such as the Sichardt (1940) equation:

     Rd = C(h)(K>°'5                                                 (10)
     where h and K are as specified as above, and C is a constant that
 Sichardt set equal to 3; however,  most drainage engineering books now
 recommend this constant be set at  1.5-2 for "realistic" results.
     The quantity of flow into fragment 2 can be estimated (Moulton,  1979)
 from the equation:
     (J   = (K(H-D)x)/[RJ/D)-(l/ir)(log 0.5(sinh «/D)l                  (11)
      GZ                u
where the new terms  are:
     H =  height of water table  above  impervious barrier  (m)
     D =  height of the  drain  above  impervious  barrier  (m)
Once the individual  discharges  for the  segments  are calculated, the  total
discharge is  the sum of the  individual  discharges.  For sites on
impervious barriers, the  total  discharge  is equal to  Q  ; for sites
                                                      Gl
with drains above an impermeable barrier  the  total discharge is the  sum
of Qcl plus QG2.
2.2.3  Pipe Size
     Once  the  total discharge (Q )  has been determined, an appropriate
grade selected, and the appropriate roughness  coefficient determined, the
minimum drain diameter  can be determined.  Nomographs such as the one
shown in  Figure 2-6 are typically  utilized to  obtain pipe diameters.
Because the nomographs  are based on the Manning formula (Equation 7),
this formula can be used directly  to obtain pipe size.  Rearranging
Equation  7, pipe diameter (d) can be found from:

    d = 4(QTn/i°' )  '                                               (12)
                                    -21-

-------
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r -
i
        n
        3
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        "i
        -
        D
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         .
        Q
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        .,
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         .
       •••
       r-
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       -
 1

:-
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 :

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 i

 i

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               .
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                    D

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                                                                                                                        13

                                                                                                                         II


                                                                                                                        O


                                                                                                                        O

                                                                                                                        OJ
                               0.o^o
                                                                     (0 Q         t)         O



                                                                      (cub/'c feet per SHCO/TC/)

-------
    A margin of safety is usually incorporated  in the selected drain
diameter which will account for the reduction in drain capacity caused by
siltation over time and for any discharge in excess of the design
capacity.  Because the nomographs and Manning formula estimate drain
diameter without accounting for a margin of safety, the drain diameter is
typically chosen as the next larger size.
2.3  Filters and Envelopes
    Performance of a drainage system is based on the assumption that the
pipe will accept all inflow without a pressure build-up.  Filters and
envelopes are used to ensure that this requirement is met.
2.3.1  Function of Filters and Envelopes
    The primary function of a filter is to prevent soil particles from
entering and clogging the drain.  The function of an envelope is to
improve water flow into the drains by providing a material that has a
higher permeability than the surrounding soil.  Envelopes may also be
used to provide suitable bedding for a drain and to stabilize the soil
material on which the drain is being placed.  The filter's function and
the envelope's function are somewhat contradictory because filtering is
best accomplished by fine materials, and coarse materials are more
appropriate for envelopes.
    As percolating water approaches a subsurface drain,  the flow velocity
increases as a result of convergence towards the perforations or joints
in the pipe.  This increase in velocity is accompanied by an increased
change in hydraulic gradient.   As a result,  the potential for soil
particles to move towards the drain is increased.  By using a highly
permeable envelope material around the pipe, the number of pore
connections at the boundary between the soil and the envelope will
increase, thereby decreasing the hydraulic gradient.
    A filter should prevent the entry of soil particles,  which could
result in sedimentation and clogging of the  drains,  blocking of
                                    -23-

-------
perforation or tile joints, or blocking of  the envelope.  The  filter
materials should not, however, be so fine that they prevent all soil
particles from passing through.  If silts and clays are not permitted to
pass through, they may clog the envelope resulting in  increased entrance
resistance which can cause the water level  to rise above the drain.
    Although filters and envelopes have different distinct functions, it
is possible to meet the requirements of both a filter  and an envelope by.
using well-graded sands and gravels.  The specifications for granular
filters, however, are more rigid that those for envelopes.  It is usually
necessary for filter materials to be screened and graded to develop the
desired gradation curves.  Envelope materials, on the  other hand, may
have a wide range of allowable sizes and gradings (Soil Conservation
Service, 1973).
2.3.2  Design of Sand and Gravel Filters
    Detailed design procedures are available for both  gravel and sand
envelopes.  The Soil Conservation Service (SCS) (1973) has distinct
design criteria for filters and envelopes, whereas the Bureau of
Reclamation (1979) has developed one set of standards  for a well-graded
envelope which meets the requirements of both a filter and an envelope.
The separate SCS design criteria will be considered below for the
following reasons:
    o  Site specific conditions may warrant the use of only a filter or
       an envelope, but not both.
    o  Where both a filter and an envelope are needed, the SCS design
       criteria for a filter can generally be used.
    o  It may be desirable to use a fabric filter with a gravel envelope.
    The approach recommended by SCS is to determine whether the drainage
system needs a filter and then determine the need for an envelope.
Generally, this sequence is performed because a well-graded filter can
also function as an envelope.
                                    -24-

-------
    The general procedure  for designing  a gravel  filter  is  to  (1) make  a
mechanical analysis of both the soil and the  proposed  filter material;
(2) compare the two particle distribution curves;  and  (3) decide by  some
set of criteria whether the envelope is  satisfactory.  The  Corps of
Engineers and the Soil Conservation Service (1973) have  adopted similar
criteria which set size limits for a filter material based  on  the size  of
the base material.  These  limits are:
    50 percent grain  size  of the filter
     SO percent grain size of the base
    15 percent grain  size  of the filter
     ,_ 	7"	:	:	T~7T—T	  = 12  to 40
     IS percent grain size of the base
Multiplying the SO percent grain size of the  base material  by  12 and 58
gives the limits within which the SO percent  grain size  of  the filter
should fall.  Multiplying  the IS percent grain size of the  base material
by 12 and 40 gives the limits within which the IS percent grain size of
the filter should fall.
    All of the filter material should pass the l.S inch  sieve, 90 percent
of the material should pass the 0.76-inch sieve, and not more  than
10 percent of the material should pass the No. 60 sieve.  The  maximum
size limitation aids  in preventing damage to  drains during  placement, and
the minimum size limitation aids in preventing an excess of fines in the
filter which can clog the  drain.  When the filter and base materials are
more or less uniformly graded, a generally safe filter stability ratio  of
less than 5 is recommended.
    15 percent filter grain size   ,_ .   _„
    __  	.  ...,.	—:	:— » 12 to 58
    85 percent filter grain size
    Consideration must also be given to  the relationship between the
grain size of the filter and the diameter of  the perforations  in the
pipe.  In general, the 85  percent grain  size  of the filter should be no
smaller than one-half the  diameter of the perforations.  SCS recommends a
minimum filter thickness of 8 cm (3 inches) or more for sand and gravel
envelopes (Soil Conservation Service, 1973).
                                    -25-

-------
2.3.3  Design of Sand and Gravel Envelopes
    The first requirements of sand and gravel envelopes is that the
envelope have a permeability higher than that of the base material.  SCS
(1973) generally recommends that all of the envelope material should pass
the 1.5-inch sieve, 90 percent should pass the 0.75-inch sieve, and not
more than 10 percent should pass the No. 60 sieve (0.25 millimeter).
This minimum limitation is the same for filter materials; however, the
gradation of the envelope is not important since it is not designed to
act as a filter.
    The optimum thickness of envelope materials has been a subject of
considerable debate.  Theoretically, by increasing the effective diameter
of a pipe, the amount of inflow is increased.  If the permeable envelope
is considered to be an extension of the pipe, then the larger the
envelope's thickness the better.  There are, however, practical
limitations to increasing envelope thickness.  The perimeter of the
envelope through which flow occurs increases as the first power of the
diameter of the envelope, while the amount of the envelope material
required increases as the square of the diameter.  Doubling the diameter
of the envelope (and consequently decreasing the inflow velocity at the
soil-envelope interface by half) would require four times the volume of
envelope material with an attendant increase in costs.  Recommendations
for drain envelope thickness have been made by various agencies.  The
Bureau of Reclamation (1978) recommends a minimum thickness of
10 centimeters (4-inch) around the pipe.  SCS (1973) recommends an
8 centimeter (3-inch) minimum thickness.
2.3.4  Synthetic Filters
    For synthetic materials, the suitability of a filter can be
determined from the ratio of the particle size distribution to the pore
size of the fabric.  The accepted design criterion for geotextile filters
is:
                                    -26-

-------
      P85 (85% pore size of the filter fabric)
    D85 (85% grain size of the subgrade material)' ~
    or P85 < D85
Using this equation, the P85 of the filter fabric can be determined from
the D85 of the subgrade soil.  Manufacturers of geotextile fabrics can
then be consulted to select the proper filter type (DuPont Co., 1981).
Compatibility of the filter fabric with site waste and leachate must be
considered in selecting the proper filter fabric.
                                    -27-

-------
                        3.0  DESIGN AND CONSTRUCTION

     This chapter presents an analysis of a hypothetical zone of
 saturation landfill site that is based on data provided by the State of
 Wisconsin.  A sensitivity analysis was performed for the site (based on
 the equations presented in Chapter 2) using the following parameters:
     o  Groundwater/leachate generation rates,  q
     o  Hydraulic conductivity of waste materials,  K^ and native soils,
        K2
     o  Head maintenance levels within the site,  h
     o  Drain spacing, L
Also included in this chapter are  design  and construction  considerations
which may  be  incorporated  into a zone  of  saturation  landfill.
3.1   Hypothetical Site
     A hypothetical zone of  saturation  landfill site was developed using
available  data from similar sites  located  in Wisconsin.  A cross-section
of this site  is  presented  in  Figure 3-1.  Table 3-1 presents some of the
typical ranges of values that may be encountered at similar sites.  The
hypothetical  site and the accompanying site data are used in the next
section as the basis for the  sensitivity analysis.   Assumptions made to
simplify the  site conditions  include:
    o  Landfill materials and soils are homogeneous and isotropic.
    o  Water tables within and outside the site are drawn down to drain
       level.
    o  Groundwater system is at equilibrium (steady state) conditions.
    o  Groundwater pressures in the underlying  (dolomite) aquifer do not
       affect groundwater movement into the bottom  of the pit.
                                    -28-

-------
                                                 Final Clay Cover
i
ro
                                            Landfill Material (K, = IO"3to IO"5)
                                              Base  grades = I %
                             •PVC Pipe

                             in pea gravel
   Original

#   water table
      r25ft
                                                                   Recompacted Clay
          125  25Oft
                                          Clay
                                                                                     Dolomite-
           Figure 3-h  Cross  Section  of  Hypothetical  Zone  of  Saturation  Landfill

-------
                   TABLE 3-1.  RANGE OF SITE VARIABLES
         Parameter
           Range of Values
Cell Dimensions

   o  Depth of cell


   o  Thickness of compacted clay
      beneath drains

   o  Thickness of compacted clay
      sidewalls

   o  Thickness of clay till below
      base grade

   o  Drain spacing

Hydraulic Data

   o  Depth to water table

   o  Permeability of:

        Clay till

        Refuse

        Compacted clay

   o  Drain diameters

   o  Slope of base
20 to 30 feet (average)  up to
60 feet

3 to 5 feet
5 feet (average)
20 to 30 feet (minimum)  sometimes
greater than SO feet

200 to 400 feet
10 feet (average)



10~5 to 10~7 cm/sec

10"2 to 10"^ cm/sec

<. 10~7 cm/sec

4 to 6 inches

1% (average)
                                    -30-

-------
If these assumptions are invalid, the drain equations will predict drain
spacings that are too large.  The degree to which these equations
over-predict will be directly related to the degree the assumptions are
invalid.
3.2  Sensitivity Analyses
    Sensitivity analyses were performed on the drain equations for:
    o  Drains on impervious barriers
    o  Drains on sloping impervious barriers
    o  Drains above impervious barriers.
The variables in the sensitivity analyses include head maintenance
levels, hydraulic conductivities, flow rates, drain spacing and barrier
slope.
3.2.1  Drains on Impervious Barriers
    The equation for drains placed on an impervious barrier is
(Equation 2, Chapter 2):

    L = (AK^/q)0'5                                                (2)
When using this equation, a barrier is usually considered impervious if
the barrier material has a permeability (K ) at least 10 times less
than the overlying material 
-------
                        TABLE 3-2.   DRAIN LENGTH SPACING  (m) FOR DRAINS ON AN  IMPERMEABLE BARRIER
w
to
k-6(.)
q
(•/djy)
IO'2 10° I0~4 I0~5 IO"2
1
0.5 15; 50 '.6 SI 105
I 	
0.01 353 111 35 II 235
0.005 499 15; 1 50 16 333
1
I
0.001 1115 353 | 111 35 744
1 	
0.0005 15;; 499 is; 50 1052
*
0.0001 352; 1115 353 III 2352
1 	

0.0(1005 4989 157; 499 15; 3328



h-4(«) k-2(i) h-K«)

((ca/tec)
,0-' ,.-* ,o-5 ,o-2 ,.-> ,.-* ,.-» ,o-2 ,o-> ,o-' ,o-5
1
33 II 3 1 52 i; 5 2 26 8 3 1
1
! 74 23 7 1 118 37 12 4 59 19 6 2
I 1
| 105 33 11 166 | 52 17 5 83 26 8 3
L__ _ , L 	 _,
235 j 74 23 371 1 118 37 12 186 | 59 19 6
! 1 	 T 1
333 1 105 33 525 166 I 52 17 263 I 83 26 8
»---1 I I
7U 235 H II74 371 1 118 37 588 1 186 59 19

fc- — — — | — — -^
1052 333 105 1661 525 166 1 52 831 263 1 83 26
| 	 1 	 1 	


t.-0.b(.)


,o-2 ,o-J ,o-*

13 4 1

29 9 3
42 13 4

93 29 9

131 42 13

294 1 93 29
1
I
416 131 42






,o-5

> i

1
1

3

<,

9


13




-------
 1000,
     9
     e
     7
                 3  4567891
                                        3  4567891
                                                                                                           3  4 5 6 7 691
  ioo«
      g
      7
      o
      5
LO
ji
I
fffi
 111!
 nil
    lOi

      3
      /
   11




                  if



                    0.00005  0.0001     0.0005     .001            0.005   0.01           0.05


                                                           (q(m/day)


                         Figure  3-2.   Drain Length  versus Flow Rates  for 1'ead Levels F.qual to 1-meter

-------
    Leachate  generation  rate  (q)  and  landfill  permeability (K_)  are the
most  important parameters  to  determine  accurately when designing  a
landfill, not because they are  the most  sensitive,  but because they are
the most difficult  to determine accurately.  Head maintenance levels  are
usually predetermined in the  landfill design and therefore are not
sensitive even though they potentially  can have the greatest effect on
drain spacing.
    One aspect of the equation  for drains on impervious barriers  that is
not readily apparent is that  this equation can also be used for
determining the depth of drainage blankets.  When the equation is
utilized for this purpose,  the  height of the water  table  is designed  to
remain within the blanket.  Permeabilities of the drainage blanket
materials are also  generally  known with some accuracy, which is not the
case with most landfill materials.  Table 3-2 also  shows  the combination
of flow rates, hydraulic conductivities, and head maintenance levels  that
yield drain spacings that  are equal to or less than the maximum spacing
used in the hypothetical site (i.e., 400 ft).  Generally, when flow rates
are large and hydraulic conductivities are low, the theoretical upper
limit of 400 feet on drain  spacing is too large to  accomplish the
intended design.   It is, therefore, important to quantify  the values
associated with leachate generation rates and landfill permeabilities to
determine drain spacing; drain  spacing should not be specified
arbitrarily.
3.2.2  Drains on Sloping Impervious Barriers
    Drains that are placed on sloping impervious barriers are governed by:

    L = (2h/c°'5)/[(tan2a/c) + 1 - (tan a/c)(tan2a+c)°'5]           (6)
As discussed in the previous section,  the underlying drain material is
typically considered impermeable if its permeability is at least ten
times less than the permeability of the overlying material.  This
situation is typical of landfills  that have compacted clay bases.
                                    -34-

-------
    Table 3-3 gives solved values of h/L for  selected values of  c  = q/K-
and barrier slope angles, a.  Figure 3-3 presents  a  plot of h/L  versus
I = tan a for selected values of c = q/K .  This graph  shows how h/L
is indirectly related to the barrier slope angle and directly  related to
c = q/K .  Generally, the greatest decrease in h/L occurs when the
barrier angle increases from zero to five degrees  (i.e., up to
approximately 10% slope).  Angles greater than five  degrees cause
decreasingly smaller changes in h/L.  For design purposes, this  means
that increasing the angle above five degrees  has little effect on head
maintenance levels (h) and drain spacing (L).
    Using the values of h/L presented in Table 3-3,  drain spacing was
solved while holding head maintenance levels  (h) constant at two meters.
Table 3-4 presents the results of this analysis, and Figure 3-4  shows a
plot of drain length versus c = q/K  for barrier angles of 0°, 1* and
5°.  These data show that if h is held constant, the barrier angle has
the greatest effect on increasing drain spacing length at lower  values of
c = q/K  (i.e., low leachate generation rates divided by high
permeabilities).
    The equation for drains on an impermeable sloping barrier  can also be
utilized for determining the thickness of a drain  blanket by substituting
h for the thickness of the drain blanket (i.e., so that the maintenance
head level is designed to be within the blanket) and K  for the
permeability of the drain blanket.   For example, consider a landfill
without a drainage blanket with the following parameters:  q =
0.0005 m/day,  K., = 0.00864 m/day (i.e.,  10**  cm/sec), a = 1°,  and
h = 2 meters.   Based on these figures,  drains would  have to be spaced at
intervals of L = 18 meters to maintain a 2-meter head level.    If a
drainage blanket that has a permeability of K  = 0.864 m/day
   -3
(10   cm/sec)  is installed at the site and the values of q and L remain
unchanged,  the thickness of the blanket  and hence the corresponding
height of the  head levels would be  0.14  meters.  This is a substantial
reduction in head levels for a relatively thin drain layer.   The
advantage to lowering the head level within the site is that less
leachate is likely to be released from the site.

                                    -35-

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I
u>
                             TABLE 3-3  VALUES OF h/L FOR VARIOUS C=q/l^ AND ANGLES a
«-,/«,
5.787
0.5787
0.05787
0.005787
0.0005787
0
1.203
0.380
0.120
0.038
0.012
a (degrees)
0.5 1
1.198
0.376
0.116
0.034
0.009
1.194
0.372
0.112
0.031
0.008
2
1.186
0.364
0.105
0.027
0.007
3
1.177
0.356
0.101
0.024
0.006
5
1.161
0.341
0.092
0.022
0.006

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    0.10
    0.08
    0.06
    0.04
    0.02
                                             .001
                                              .0001
                    0,1
   0.2
la to n<*
0.3
0.4
Figure 3-3.  Plot of h/L versus  I™tar. a for
             drain and sloping impervious layers
             (Moore, 1980)
                           -37-

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TABLE 3-4  DRAIN SPACING (m) FOR HEAD MAINTENANCE LEVELS OF 2-METERS
c-q/K.. a (degrees)

5.787
0.5787
0.05787
0.005787
0.0005787
0
1.66
5.26
16.67
52.63
166.67
1
1.68
5.38
17.86
64.52
250.00
3
1.70
5.62
19.80
83.33
317.40
5
1.72
5.87
21.74
90.91
326.60
                                  -38-

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                                                                                         3   4  567891

5.787(10
                                                                                              5.787
                                        c=q/K,
                                                                   O  ,0
             1-4.  Drain Length  (L) versus c=q/Kj  for  a  equal  to  0 ,  1  ,  and 5 .

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3.2.3  Drains Above  an  Impervious Barrier
    The governing equation for a drain system above  an  impervious  barrier
is:
    L =
    where the parameters are as defined previously in Chapter 2.
    This equation takes into account radial flow to the drains through
the material underlying the drain.
    Solutions to the equation are shown in Table 3-5 for a head
maintenance level (h) of two meters, a permeability (K ) of the
                                            _5        1
landfill material of 0.00864 m/day (i.e., 10   cm/sec), and a depth to
the impermeable layer (D) of 30.4 meters.  Figure 3-5 shows a plot of
drain spacing (L) versus inflow rates (q) for various permeabilities of
underlying material (K ).  These presentations show that when the
permeabilities of the overlying (K ) and the underlying (K ) material
are the same, the drain spacing (L) increases.  This phenomenon is caused
by the introduction of radial flow to the drains rather than straight
lateral flow.
    When the permeability of the underlying material (K )  is an order
of magnitude (0.1)  less than the overlying material (K ),  the
calculated drain spacing does not differ significantly from a drain on an
impermeable barrier.  If the underlying material has a permeability that
is two orders of magnitude (0.01)  less than the overlying material, the
drain spacing is identical to a drain on an impermeable barrier.   This
occurs because the  term 8K dh does not significantly affect the results
of the drain spacing equation.   Consequently,  the "rule of thumb" for
designing drains is that if the underlying layer has a permeability at
least 10 times less than the overlying material, the underlying material
can be considered impermeable.
3.3  Application
    The basic premise behind the use of a landfill located in the zone of
saturation is that  if the head maintenance levels within the site are
                                    -40-

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TABLE 3-5  DRAIN SPACING (m) FOR DRAINS ABOVE AN IMPERMEABLE
           BARRIER (h-2m, K^O.00864 m/day (lO-Son/sec), D=30.4m)
q
(m/day)
0.05
0.01
0.005
0.001
0.0005
0.0001
0.00005

io-5
2
5
7
19
31
114
212

ID'6
2
4
5
12
18
43
64
K9 (cm/sec)
io-7
2
4
5
12
17
37
52

Impermeable
2
4
5
12
17
37
52
                              -41-

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                                                                                                       3  4567891
111
                  I       I
               0.0005 0.0001
0.0005  0.001
0.005    n.oi
0.05
                           Figure 3-5.  Drain  Sparing  (1.)  versus inflow rates (q) where
                                        li = 2 meters and  K  = 10~^  cm/sec.

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less than  the groundwater levels  outside  the  site,  then  hydraulic
gradients  should be  into the  site, thus minimizing  the likelihood of
contaminant release.  Basic hydraulic principles  show this to be the case
as long as (1) the landfill materials and soils are homogeneous and
isotropic, (2) water tables are drawn down to drain levels, and (3) the
groundwater system is at equilibrium.  In reality, these conditions
rarely exist at a landfill site.  For these real-world situations, the
Wong (1977) model can be used to  predict releases.
3.3.1  Parameter Estimation
    In order to utilize the drain spacing equations, the input parameters
must be known with some accuracy.  The two parameters which are the most
difficult to estimate accurately  are leachate generation rate (q) and
hydraulic conductivity (K).  Head maintenance level (h) and barrier slope
angle (a) are typically chosen by the designer and are not estimated.
    Total inflow rates to the drains can be estimated through the use of
water balance equations (equation 8) and the method of fragments
(equations 9 and 10).  These equations, however, do not take into account
the volume of liquid that is added to the site as landfill material
(e.g., paper waste sludges).  Estimating this volume is very specific to
a landfill.  Once the total volume is estimated, the value should
probably be increased to take into account variations that were not
anticipated (e.g., acceptance of more liquids, unseasonably high
precipitation) and to add a margin of safety to the design.
    Determining the hydraulic conductivity of the landfill material with
any accuracy is very difficult because, typically, the material is a
mixture of wastes and daily covers which tends to create discrete cells.
Waste mixtures tend to cause the landfill to be very heterogeneous and
anisotropic, making estimations of permeabilities difficult.   Here, as
before, the hydraulic conductivity selected should probably be the
highest value found for the waste materials to determine a worst-case
situation.  The problems associated with daily cover can be minimized if
the cover is removed each day, allowing old and new fill materials to be
                                    -43-

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hydraulically connected.  As daily removal of the cover is often
impractical at some sites, use of a granular soil cover to provide
hydraulic connection is recommended.
    The use of drainage blankets in a landfill effectively eliminates the
problem associated with determining conductivities.  Hydraulic
conductivities for the drainage blanket can be determined easily in the
lab and most blanket materials are relatively homogeneous and isotropic.
A blanket layer covering the bottom of the cell and the sidewalls
provides a hydraulic connection between the leachate generated and the
drains.  A drainage blanket also aids in the prevention of leachate
pooling, accelerates leachate removal times, and allows for lower head
maintenance levels with the same drain spacing.
    Wisconsin landfills presently have nearly vertical sidewalls.
Installation of drainage blankets would necessitate cutting these
sidewalls back to a maximum of 3:1 side slopes.  Cutting back the
sidewalls and installing drainage blankets would result in greater
confidence in landfill design.
3.3.2  Landfill Size
    Zone of saturation landfills are depth-limited by the following
factors:
    (1)  Slope stability decreases with depth.
    (2)  Leachate generation increases with depth.
    (3)  Probability of interconnections with major underlying aquifer
         increases with depth.
    (4)  Difficulty of sealing off permeable zones increases with depth.
    (5)  With increasing depth more soil is removed from above the
         underlying aquifer decreasing the amount of protective covering
         over the aquifer.
    (6)  With increasing depth, hydraulic gradients into the landfill
         increase resulting in larger quantities of groundwater that must
         be removed from the site (See Section 4.3).
                                    -44-

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    (7)  With increasing depth there is greater chance of  intercepting
         water which will cause quick conditions in the base.  If quick.
         conditions occur, extensive dewatering may be necessary to
         maintain a stable base.
3.3.3  Example Problem
    An example of the use of the drain equations for the hypothetical
site developed in Section 3.2 is presented here for illustrative
purposes.  Table 3-6 presents the data utilized in the example.  For the .
example, the recompacted clay base and sidewalls were assumed to have the
same permeabilities as the saturated clay aquifer.
    To calculate the drain spacing needed at the site, the equation for
drains on sloping barriers (equation 6) can be used because the
underlying clay material has a permeability of 10 times less than the
fill material.  Solving equation 6 for drain spacing (L) :

    L = (2h/c°'5)/[(tan2o/c) + 1 - (tan a/c) (tan2a+c)°'5]
        = 0.0007(m/day)/0.0086A(m/day)
        - 0.08102
                       0.5     2
    L » (2(3. 0)/0. 08102   /[tan 0.6/0.08102)+l-( tan 0.6/0.08102)

        [(tan20. 6+0.008102 )°'5]
      = ( 21. 079) /[(0.00135)+1-(0. 12926) (0.28483)]
      = 21.85m(71.89 ft)
The value obtained for drain spacing using these parameters is
significantly less than the currently specified allowable upper limit
(about 400 ft).  However, this solution would not be considered
conservative for an actual site where (1) conductivities of the fill may
not be a uniform 10   cm/sec, (2) inflow rates may be higher than
expected; for example, when the site is not capped, and (3) materials
with high water content may be landfilled.
    An appropriate pipe size can be selected by calculating the system's
expected discharge and considering the factors described in Section 2.
Total flow along any single collector pipe can be calculated by:
                                    -45-

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               TABLE 3-6.  EXAMPLE DATA  SET
 Parameter
          Value
Cell Dimensions

 o Width
 o Length
 o Depth
1000 ft (304m)
1000 ft (304m)
  30 ft (9.1m)
Clay Thickness Below Base
  50 ft (15.2m)
Hydraulic Conductivities

 o Fill (KL)

 o Clay (Kj)

   - compacted or natural
10~5 cm/sec (0.00864 m/day)

10~7 cm/sec (0.0000864 m/day)
Base Grade
1% (0.6 degrees)
Water Table (b.l.s.)
10 ft (3.0m)
Head Maintenance Levels
10 ft (3.0m)
Inflow (q) From Percolation    10 in/yr  (0.0007 m/day)
                             -46-

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    Q1 - qA
where q, inflow, is 0.0007 in/day and A, area, is the area drained by each
drain line-22m x 304m (drain spacing times length)
    Q  = (0.0007 m/day)(22m)(304m)

       =4.7 m3/day (0.002 ft3/sec)
Using Figure 2-6 for plastic pipes with a roughness coefficient of
n = 0.013 and a design velocity of 1.4 ft/sec, a 4-inch drain pipe should
be sufficient to handle the discharge.  Total discharge from the main
header pipe is:
    QT = qA
       = (0.0007 m/day)(304m)(304m)

       = 64.7 m3/day (0.026 ft3/sec or 17,094 gal/day)
Using Figure 2-6 again, a 4-inch pipe should be sufficient to handle the
flows.  A larger size pipe may be selected as a margin of safety.
3.4  Construction Aspects
    Previous discussions related the application of the design criteria
for zone-of-saturation landfill leachate collection systems to a
hypothetical site.   Some aspects of construction of these sites are
important but do not fall within the focus of the other sections.  These
considerations are described in the following sections and include:
    o  Construction inspection
    o  Collector drain maintenance
    o  Future operating conditions
3.4.1  Construction Inspection
    Construction inspections are important to ensure the specified design
criteria are implemented in the field.  Some criteria which are important
for zone of saturation landfills are:
    o  Moisture of clays when compacted on bases and sidewalls
    o  Placement of drain pipe and filter envelopes, and their protection
       while exposed
                                    -47-

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    o  Compliance with specified design criteria  for slopes, and drain
       blanket thickness and gradation
    The clay tills associated with the zone of  saturation landfills can
easily exceed the moisture content at which maximum density can be
achieved.  Trying to compact these excessively  wet clays on the base and
sidewalls of the landfill is a wasted effort, and in many instances,
causes the soil to shear.  Shearing of the clays may result in planes of
weakness and cracks throughout the layer which  can easily transmit
leachate out of the cell.  Construction inspections can identify when the
soils exceed the optimum moisture content for compaction and prevent
their placement until the clays have dried to within an acceptable
moisture content range.
    Construction inspections should be performed during drain pipe and
filter envelope placement.  Inspections can ensure that these operations
are performed as specified in the designs and that:
    o  Drain pipes are not damaged during placement
    o  Filter materials are kept free of fines  and are graded and
       installed properly
    o  Drains are protected after placement so  that fines do not clog
       drains before wastes are placed
    Slopes specified within a cell are generally just enough to prevent
pooling of leachate on the compacted clay base  (i.e., 1% slope).  With
these gentle slopes, there is a very small margin for error that would
still ensure that leachate moves freely towards the drain.  Inspections
performed during the grading of the base can verify proper construction.
Inspections should also be performed during the placement of a drain
blanket to ensure adequate blanket thickness and proper gradation of the
blanket material.
3.4.2  Drain System Maintenance
    Proper maintenance of a drain system is a critical element in
ensuring its continued performance.  The initial design of the system
must allow for adequate access to the drain system components both for
inspections and cleanings.  Regular maintenance inspections should be
                                    -48-

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 performed to assess  the  system's performance  and  to plan cleaning and
 repairing activities.  Additionally, maintenance  inspections should be
 performed when an unexplained reduction in flow occurs to sumps or
 increased head levels are observed within the cell.
 3.4.3  Future Operating Conditions
     Landfill designs should anticipate and account for the type of waste
 disposal operations planned.  As mentioned previously, hydraulic
 conductivities of the wastes placed in a cell are critical to the design
 of the leachate collection system.   Conductivities used for design
 purposes are frequently estimates based on the experience  of the designer
 or are averages that represent the  range of conductivities  that could  be
 found throughout  the cell.   If the  landfill will  be accepting balings,
 shreddings,  large solid objects,  or separations of particular wastes
 during its operational  life,  the  conductivities used  in the  drain  designs
 should be adjusted to reflect  the hydraulic  conductivity of  these
 materials and  their  volume  in  relation  to  the  remainder of  the  fill
 material.
    The  total quantity  of water that must  be extracted from  zone of
 saturation landfills  can  vary widely.   Water can be derived  from
 percolating  rainfall, groundwater infiltration, and from sludges or
 liquids brought into  the  site.  Underestimating the amount of water that
must be removed will  result in rising internal head levels and the
eventual release of generated leachate.  Therefore, care must be
exercised to ensure that water removal capabilities specified in the
landfill design realistically represent the eventual landfill operations.
                                   -49-

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                          4.0  FLOW NET ANALYSIS

4.1 Introduction
    Water flow through porous media is governed by several physical
relationships (e.g., Darcy's Law) that can also be represented
mathematically.  The equations used to represent this flow can be
arranged so that they apply to certain physical conditions.  The
solutions to the equations can then be obtained through numerical or
graphical means; the graphical solutions are called flow nets.  In this
case, the flow nets are graphical representations of two-dimensional
equations of continuity for water flow.
    The generation and application of a flow net requires certain
assumptions and simplifications.  Most of these are common to any
representation (model) of a natural physical system and include the
assumptions of aquifer homogeneity, water incompressibility and laminar
Darcian flow.  Consideration of site conditions at each of three
Wisconsin landfills reveals several features which are common to all, so
that the flow nets can be constructed for a generic site that
incorporates these common features (Figure 4-1) and also includes some
simplifications.  These include:
    a) elimination of small heterogeneities in the clay around the site,
       since they are discontinuous and not well-mapped.
    b) treatment of the underlying dolomite as an impermeable boundary.
       It is recognized that recharge to the clay probably does occur
       from the dolomite; however, the vertical permeability of the clay
       is low enough that this recharge can be considered negligible for
       the purposes of constructing a flow net,
    c) treatment of all landfill surfaces as orthogonal to ground surface.
    d) assuming that the landfill excavation can be treated as a circular
       well so that water flows radially to it.
                                    -50-

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                  LEACHATE MAINTENANCE LEVEL
                                                                  WATER TABLE
                                     REFUSE
V


K * 1 x 1 0 cm sec
	 J_ _T 	
O 0 O '
DRAINS
YTILL

r o c
V 1
i


1
k


<* 70 -80 FEE!
                                                 h 5=50-75 FEET
          .-1
DOLOMITE,
  /   /   /    /    /././/   /    /.   /    /   /    T
  /   /   /    /    /    /   /    /   /    /   /    /   //
                                                  ?  20  40  60 FEET
0

10 FEET
  FIGURE 4-1.  CROSS SECTION OF TYPICAL ZONE-OF-SATURATION LANDFILL
                                   51

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    e) assuming that the water table aquifer can be treated as a line
       source of seepage beyond 250 feet from the landfill.
The flow nets are composed of two families of lines that intersect at
right angles.  Flow lines show paths along which water can flow;
equipotential lines represent lines of equal hydraulic head.  The flow
nets constructed for the generic site indicate the approximate
arrangement of flow lines and equipotential lines around the landfill for
different physical conditions, as explained below.  Instructions on flow
net construction techniques are contained in Appendix A.

4.2 Initial Conditions
    Three points need to be made about the flow nets before examination.
First, by treating the excavation as a circular well, some idea of the
radius of influence (R ) and equivalent well radius (R ) can be
obtained.  These are defined by:
               where L = length of landfill
                     w = width of landfill
    Values of L and W were chosen equal to 300 ft. so that R,, = 169 ft.
             nr~
   R  = C&h..  /      where C = a constant ranging from 1.5 to 3
           ^10         Ah = drawdown expected in "well"
                         K = hydraulic conductivity in cm/ sec"
    Values chosen for Ah (30 feet) and K (1 x 10   cm/sec  )
represent typical values for these parameters at each site.  Several
references used suggested setting C =» 2.0 for typical results.  This
gives R  a 19 feet.
    Second, there is a difference between the horizontal and vertical
hydraulic conductivities at these sites because of the layered nature of
the till deposits.  Average values for horizontal K and vertical K used
here were 1 x 10   cm/ sec   and 2 x 10   cm/ sec  , respectively.
Construction of flow nets for anisotropic media requires that the
horizontal and/or vertical dimensions be transformed to offset the effect
of different horizontal and vertical hydraulic conductivities.
                                    -52-

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    The transformation factor used in this case is   K^/K^, which
resulted in a vertical exaggeration of approximately 7 times in the cross
sections, which have not been "re-transformed".  This exaggeration must
be kept in mind when interpreting the flow nets.
    Third, during the construction of extremely accurate flow nets, each
four-sided figure developed by the intersection of the two families of
lines should approximate a square or curvilinear square.
    The plan view flow net (Figure 4-2) indicates nearly symmetrical
inflow, as would be expected from any roughly square excavation in an
aquifer acting as a line source of seepage on all sides.  Due to the low
hydraulic conductivity, the amount of inflow is relatively small.  This
can be approximated (using the parameters given in Figure 1) by:
          2  2
  Q = irK(H -h )   where H - total saturated thickness of clay = 75 feet
      In  (R/r )
                        h = saturated thickness beneath "well" = 65 feet
                        R = radius of influence = 188 feet
                        r = effective radius of "well" = 169 feet
                         w
                        K = hydraulic conductivity  in ft/sec"  =
                            3.3 x 1
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                                LANDFILL CELL
                       300 FEET •
                                              AQUIFER ACTS AS LINE SOURCE
                                              OF SEEPAGE BEYOND THESE LINES
FIGURE 4-2.  INFLOW TO TYPICAL LANDFILL CELL (PLAN VIEW)

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4.3 Parameter Analysis
    Examination of the effect of leachate maintenance levels
(Figures 4-3A, B, C) indicate that the most favorable situation in terms
of collecting lower amounts of leachate is when the maintenance level is
relatively high.  This causes redistribution of the equipotential lines
in the aquifer around the drains such that the contribution of inflow
from the aquifer is small compared to that from the leachate.  However,
this does not leave much of a safety margin and also enhances the
susceptibility for outward leakage along permeable sandy lenses in the
sides of the landfill.
    Analysis of the effect of vertical gradients (Figures 4-4A, B)
indicates that, in comparison to sidewall inflow and leachate from the
refuse, the amount of inflow at the base will be small regardless of the
direction of gradient.  This is predominantly due to the low vertical
hydraulic conductivity of the clay till in contrast to the more permeable
sidewalls.
    Analysis of the effect of drain spacing (Figure 4-5) shows that the
drains tend to depress equipotential lines between their centers,
bringing higher head levels closer to the bottom of the excavation.  In
the presence of a local downward gradient, this might enhance the
possibility of diffusion of contaminants through the base of the fill,
although most movement would be horizontal because of aquifer
anisotropy.  As the number of drains increases, this effect becomes less
noticeable, and at some point would be offset by inflow through the base
of the excavation.
    The effect of the depth of excavation below the water table can also
be examined by using some of the assumptions and site dimensions given
earlier and treating the excavation as a well.  If the leachate
maintenance level is set at the base of the fill, the amount of inflow in
relation to excavation depth varies as follows:
                                    -55-

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      A)  LEACHATE LEVEL AT (H-h)

                           t
(7)
          LEACHATE LEVEL AT (H-1)
      C)  LEACHATE LEVEL AT (H-.Sh)
                                                 SCALE:

                                                           r°
                                                           L-10FT.

                                                 VERTICAL EXAGGERATION - 7x
FIGURE 4-3.  FLOW NETS WITH DIFFERENT LEACHATE LEVELS
                       56

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        A   DOWNWARD GRADIENT
         B   UPWARD GRADIENT
FIGURE 4-4. FLOW NETS WITH DIFFERENT VERTICAL GRADIENTS
                         57

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      A)  TWO CORNER DRAINS
      B)  THREE DRAINS
        r
~i
       C) SIX DRAINS
FIGURE 4-5.  FLOW NETS WITH DIFFERENT NUMBERS OF DRAINS






                         58

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          Depth Below Water                Approximate
          Table Excavated.  Ft.              Inflow. GPM
                   10                           8.8
                   20                          16.7
                   30                          23.8
                   40                          29.8

These inflows need to be considered in comparison to the capacity of the

drain system and the possible inducement of heaving or buckling because
of the artesian head in the underlying dolomite.  Rough calculations
indicate that 40 feet is about the maximum depth that should be
excavated, less if the remaining depth to the dolomite is below about 50
feet.
                                    -59-

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                               5.0  MODELS

    This chapter characterizes some commonly accepted models that can be
utilized in the design and performance evaluation of waste disposal
sites, and in the tracking of pollutants released from these sites.
These models are divided into two major groups:  (1) release rate models
and (2) solute transport models.  Typically, estimates of leachate
quantity and quality released from a site are obtained from a release
rate model and are used as input to a solute transport model.  The theory
behind some of the models is very complex and readers should refer to
other sources such as Bachmat et. al. (1980), Mercer and Faust (1981),
Anderson (1979), and Weston (1978) for in-depth discussions of modeling.
5.1  Release Rate Models
    The first and probably the most crucial step in waste site modeling
is to obtain accurate estimates of the quantity and quality of leachate
that will be released into the subsurface environment.  Only after
adequate determination of leachate release can a solute transport model
be performed.  This section briefly describes the theory behind release
rate models and presents those models that can potentially be utilized in
obtaining release rates from landfills.
5.1.1  Fundamentals
    Most release rate models are based on dividing the problem of
prediction into three separate components—leachate generation,
constituent concentrations, and leachate release rates from the site.
Combining the three separate components allows for prediction of the
quantity and quality of leachate that can be expected to be released from
the site.
                                    -60-

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5.1.1.1  Leachate Generation
    Leachate generation refers to the quantity of fluid within the site
available to leach and transport waste constituents.  The major factors
that directly influence leachate generation are listed in Table 5-1.
Probably the most important factors for zone-of-saturation landfills are
infiltrating precipitation and groundwater intrusion.  There are
currently two main approaches for predicting leachate generation—the
water balance approach and the use of bounding assumptions.
    Fenn, Hanley, and DeGeare (1975) pioneered the use of water balances
to predict leachate generation from solid waste disposal facilities based
on the earlier work of Thornthwaite (1955).  Several authors have since
updated and modified Fenn, et al.'s., work for application to other types
of waste disposal sites.  Basically, water balances numerically partition
the amount of fluid moving into, around, and through the cap of a land
disposal facility by utilizing the equation:
                         Perc = P - RO - ST - ET
where:
Perc   = percolation rate; the portion of precipitation which infiltrates
         the surface and is not taken up by plants or evaporated
     P = precipitation rate
    RO = surface water runoff; the portion of the precipitation which
         does not infiltrate into the ground but instead moves overland
         away from the site
    ST = change in soil moisture storage
    ET = Actual evapotranspiration; the combined amount of water returned
         to the atmosphere through direct evaporation from surfaces and
         vegetative transpiration.
                                    -61-

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     TABLE  5-1    MAJOR FACTORS AFFECTING LEACHATE GENERATION
      Primary Factors
      Secondary Factors
Precipitation


Liquid Content of Wastes



Liquids from Waste Decomposition


Groundwater Intrusion



Soil Moisture Storage


Evapotransp iration



Runon/Runoff Control



Operation Mode

Surface/Cap Conditions
quantity, intensity, duration,
frequency, seasonal distribution

type, quantity, moisture content,
and moisture storage capacity
(field capacity)

waste composition, waste environ-
ment , and micro-organism populations

flow rates into pit, seasonal
distribution of water table, head
levels, liner materials

field capacity of materials,
seasonal fluctuations

temperature, wind velocity,
humidity, vegetation type, solar
radiation, soil characteristics

diversions, crowning of surface
cap, permeability and integrity
of cap, depression storage

open versus closed, coverage

permeability, integrity, surface
contour, runoff underdrain
systems, subsidence
                                  -62-

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    Values for the parameters needed for such an analysis can be found in
a variety of sources or estimated using a variety of techniques.
Precipitation values for a given location are available from a number of
sources including the National Weather Service.  Runoff is very site
specific and difficult to measure.  Most release rate models use one of
the following methods to estimate runoff:
    •  Rational Formula—utilizes empirical runoff coefficients based on
       vegetative type, soil type, and slope.
    •  SCS Curve Numbers—utilizes empirical coefficients which relate
       runoff to soil type, land use, management practices, and daily
       rainfall.
    •  Green-Ampt Equation—approximates runoff based on soil properties,
       initial water content and distribution, surface conditions, and
       accumulative infiltration.
Both evapotranspiration and soil moisture storage can be estimated using
empirical soil moisture retention relationships such as those developed
by Thornthwaite (1955).  Some models require that evapotranspiration be a
measured site specific input, while others do not specify a method to
obtain values.  Some models relate evapotranspiration to physical
parameters such as temperature, solar radiation, and the leaf area index
(LAI), while others store evapotranspiration and soil moisture
information for various locations on a national data base that can be
accessed by the model.  One model also makes simplifying assumptions to
estimate soil moisture storage either by apportioning soil moisture into
a "wet" zone and a "dry" zone or by using the method of depth-weighted
fractional water content within the soil profile.
    Release rate models also allow the user to set surface conditions and
cover  liner characteristics for the site with varying degrees of
flexibility.  Some methods allow multiple clay-synthetic liners, others
only clay liners, while still another can only be applied to open sites
                                    -63-

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without covers.  Cover vegetation, slope, contour, and soil properties

can also be specified in all but the most simplistic models.

    When cover liners are used to impede percolation to waste cells,

excess water moves away from the site through subsurface lateral drainage

above the liner.  Models estimate this lateral drainage by:

    •  Approximate methods (utilizing correction factors) derived from
       the Boussinesq equation for lateral saturated flow.

    •  Empirical methods development by Moore (1980) which calculate the
       maximum hydraulic head above the liner and then the upper bound of
       the quantity of liquid flowing into tile drains.  The liner  is
       assumed to be impermeable for these calculations.

    •  Empirical methods which calculate percolation through the liner
       and soil moisture storage; then extrapolate lateral drainage as
       the remaining excess water.

    The next step is to predict the flow rate through the top liner.

This  is ultimately the major contributing factor  in leachate generation.

Numerous methods are used to predict this percolation rate and they can

be divided into methods for clay liners and those for synthetics.

Methods used for clay liners include:

    •  Darcy's Law for saturated conditions, which relates flow velocity
       to hydraulic conductivity, effective porosity, hydraulic head, and
       travel distance using the following general equation:

                                V = Kh/nx

       where:   V is flow velocity, K is hydraulic conductivity, n  is
                effective porosity, h is hydraulic head difference, and
                x is travel distance

    •  Approximations of saturated Darcy flow as proposed by Wong (1977).

    •  Soil storage routing techniques through multiple soil layers which
       relate liner permeability to inflow rate, time interval, hydraulic
       conductivity, soil water storage, and evapotranspiration.

    •  Darcy's Law with provisions to arbitrarily increase liner
       permeability assuming that certain events occur (e.g., burrowing
       animals or equipment breach of the liner).
                                    -64-

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    o  Prediction of unsaturated flow driven by capillary forces
       utilizing the Green-Ampt approximation of the wetting front
       assuming a constant capillary head.
Methods to predict flow through synthetic liners include:
    o  Darcy's Law as described above and based on hydraulic head and
       liner thickness.
    o  Power Law relationships for estimating the aging of a liner based
       on the life expectancy of the liner.
    o  Arbitrary methods such as assuming that the liner will be
       impermeable for 20 years and then will fail completely (i.e.,
       after 20 years the model treats the facility as if it were
       unlined).
    o  Stochastic (Monte Carlo) simulation for liner failure due to aging
       and installation problems.
    The amount of water percolating through the cover liners and into the
waste cells is either adjusted according to the moisture content of the
wastes and fill materials in the facility, or the wastes and fill
materials are assumed to be at field capacity and, therefore, the amount
of water percolating into the waste cells is also the total quantity of
leachate generated.
    Water balances for waste disposal sites produce only relative
solutions to leachate generation for comparing different designs or
sites.  The high degree of uncertainty that exists in these solutions has
led to the use of bounding assumptions.  Bounding assumptions are based
on the knowledge that the quantity of leachate generated at a given
facility falls between 0% and 100% of the maximum potential amount (based
on total possible leachate), such that upper and lower bounds for
leachate generation volume can be established.  Using assumptions and
empirical data, the bounds can be narrowed to produce best- and worst-
case scenarios which can, in turn, be used to design the landfill based
upon performance goals.
                                    -65-

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5.1.1.2  Leachate Constituent Concentrations
    For a release rate model to be useful, it must not only estimate the
quantity of leachate produced, but it also must estimate the quality
(i.e., leachate constituent concentrations).  The quantitative simulation
of the processes and interactions occurring within a landfill to produce
leachate are very complex, and therefore most available models do not
attempt to simulate all these processes.  Table 5-2 lists some of the
factors affecting leachate constituent concentrations that would have to
be considered.
    Because of the complexity of the interdependent interactions
occurring within a disposal site and our inability to accurately
characterize these interactions, simulations of the processes are
extremely difficult, if not impossible.  Consequently, release rate
models do not address the factors which govern constituent
concentrations.  Rather, the models make assumptions to greatly simplify
the complexities of the real world.  These assumptions are:
    •  Constituents are at the saturation solubility concentration levels
       in leachate.
    •  Constituents exist at equilibrium concentrations between the
       aqueous and sorbed phases.
    •  Bounding assumptions are used in a similar manner as described for
       leachate generation.
5.1.1.3  Leachate Release
    Leachate release is defined as the escape of any contaminants beyond
the containment boundary of a land disposal facility.  The type and
magnitude of release depends upon the presence of a liner system, the
type of liner employed, the presence and efficiency of a leachate
collection system, and the occurrence and magnitude of any system
failures.  Table 5-3 lists some of the factors affecting leachate release
from a land disposal site.
                                    -66-

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TABLE  5-2    FACTORS  AFFECTING  LEACHATE  CONSTITUENT CONCENTRATIONS
       Major  Components
   Primary Factors
        Secondary  Factors
    Waste  Composition
    Fhysicochemical
    Properties
    Contact  Time
    Chemical Reactions
    and Interactions
    Chemical Reactions
    and Interactions
    (continued)
Volume

Constituents
Constituent
Concentrations

Solubility


Mobility


Persistence
                             Volatilization
Phase/State

Conditions of Waste
Environment
    Facility Age
Hydrolysis


Oxidation



Reduction



Photolysis



Microbial Degradation



Microbial Acclimation

Changes in Waste
Environment
pH; temperature;  composition of
liquid phase

Viscosity;  temperature;  density;
sorption; complexation

pH; temperature;  presence  of catalysts;
chemical degradation (e.g. oxidation,
reduction,  hydrolysis, photolysis);
biological degradation

t'ugacity; constituent vapor pressure;
temperature

Temperature; pressure

Flow rates through wastes, fill
materials and drain layers; waste
permeability; waste porosity;
particle size: site heterogeneities:
capillary action; piping through
wastes; ponding in waste cells;
plugging of pore  spaces

pH; temperature;  soil pH,  catalysts
Presence and type of oxidants;
catalysts; oxygen concentration; pH:
temperature

Oxygen concentration;  conplexation
state; concentration and type of
reducing agents:  pU; temperature

Solar radiation;  transmissivlty of
water; presence or  sensitizens and
quenchers

Microbial population;  soil moisture
content; temperature;  pH, oxygen
concentration,  redox potential
                                                      oh:  temperature;  removal of most
                                                      soluble constituents
                                           -67-

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      TABLE 5-3    FACTORS  AFFECTING LEACHATE  RELEASE
  Major Components
   Primary Factors
        Secondary Factors
Synthetic  Liners
Physical Factors
                          Chemical Factors
Clav Liners
                          Leachace Collection
                          Physicochemical Factors
                          Chemical Factors
                          Physical Factors
                          Biological Factors
                          Leachace Collection
Aging; human activities;  Internal
loading stresses; hydrogeology;
bathtub effect; weather resistence;
deep root growth, burrowing animals;
installation and design problems
(e.g., subsidence from improper
siting, improperly prepared seams);
uplifting by gasses or liquids
under pressure; impingment rate;
temperature

Chemical disintegration:  weather,
ultraviolet radiation, chemical
and microbial attack from the soil
atmosphere: waste-linear compata-
bility: nature soil chemistry; pH,
temperature

Efficiency, maintenance;  design

Chemical dehydration, flocculacion/
dispersion, alteration of shrink/
swell properties; soil piping;
leachate characteristics; pore  size
distribution

Dissolution of c.hemical species,
adsorpsion properties; chemical
disintegration, native soil chemistry

Internal loading stresses; dehydration;
hydrogeology; weathering; erosion;
bathtub effect; aging; impingment
rate; hydraulic head; structural and
design considerations (e.g., proper
siting and design to handle
differential subsidence

Microbial population; burrowing
animals; deep root growth, human
activities

Efficiency; maintenance;  design
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    Prediction of leachate releases  involves the estimation of leachate
quantity escaping from the site over time, which is combined with
constitutent concentration.  The major drawbacks in predicting releases
are obtaining realistic estimates of liner lifetime, estimating  the
probability of liner failure, and establishing cause and magnitude of
failure if it occurs.  The methods employed to predict releases  parallel
those used to estimate flow rates through cover liners (described
previously as part of the water balance approach).
5.1.2  Selected Release Rate Models
    Five release rate models and one series of simple calculations chosen
for their potential applicability to Wisconsin zone of saturation
landfills are discussed below and summarized in Table 5-4.
    DRA1NMOD (1980) is a computer model developed to predict the response
of water in both the unsaturated and the saturated zones to rainfall,
evapotranspiration, specified levels of surface and subsurface drainage,
and the use of water table control or subirrigation practices.  DRAINFIL
(1982) is an adaptation of DRAINMOD for landfills which considers
drainage from a sloping layer underlain by a tight clay liner and seepage
through the cap.  DRAINFIL can also quantify drainage to the leachate
collection system and through the underlying clay liner during the time
the landfill is open.  A water balance for the soil water profile is used
to calculate the infiltration rate, vertical and lateral drainage,
evapotranspiration, and distribution of soil water in the soil profile
using approximate solutions to nonlinear differential equations.   The
prohibitive cost of using numerical methods to finding solutions to
equations of this sort requires that approximate methods be used.  Checks
of solutions obtained through these methods suggest, however,  that
satisfactory results can be consistently obtained.
    The minimum data required for these models include precipitation
(amount,  distribution,  intensity,  and duration),  water table elevation,
daily potential evapotranspiration (PET),  net solar radiation,
temperature,  humidity,  wind velocity, soil moisture content, soil profile
                                    -69-

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                                 TABLE 5-4
                            RELEASE RATE MODELS
MODEL

DRAINMOD/
DRAINFIL
ADVANTAGES

Predicts response
of water in un-
saturated zones
to rainfall
DISADVANTAGES

High cost
REFERENCE

Skaggs (1982)
HELP/
HSSWDS
LSIPE
PCLTF
LTTM
Requires minimum
amount of data.
Estimates vertical
and lateral
percolation.

Evaluation
efficiency of
liner design in
controlling
leachate release.
Addresses all factors
necessary to predict
a mass load release.

Accounts for
moisture content
of wastes and fill
material.  Includes
both gravitational
and capillary forces.
Simple and easy to
use.
Ignores rainfall
intensity, duration,
and distribution.
Accuracy is
questionable

Estimates release
in a single
modular waste cell.
Based on assump-
tions of good
engineering design
(rare in older
landfills)

Unsaturated zone
Currently being
developed.  All
elements have not
been tested.
Perrier and
Gibson (1980)
Moore (1980)
U.S. EPA (1982)
Pope-Reid Assoc,
(1982) (Unpub.)
Release
Rate
Computa-
tions
A series of simple
calculations
Some assumptions
are questionable.
SCS Engineers
(1982)
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depth, surface compaction, vegetation, depth of root zone, hydraulic
conductivity (saturated and unsaturated), and pressure head.  Most of the
data are readily available, though some difficulty may exist in obtaining
reliable unsaturated hydraulic conductivity and pressure head data.  In
addition, to simplify calculations, the models assume:
    •  One-dimensional, saturated flow in the bottom liner.
    •  Infiltration rates for uniform deep soils with constant initial
       water content expressed in terms of cumulative infiltration alone,
       regardless of the rate of application.
    •  Drainage is limited by the rate of soil water movement to the
       lateral drains and not by the hydraulic capacity of the drain
       tubes or outlet.
    DRAINMOD is currently being used in assessing agricultural drainage
systems and has been field-verified in a variety of locations.  DRAINFIL,
however, has not yet undergone the final changes needed for its use in
assessing infiltration at waste disposal sites, and therefore remains
untested.
    These models are similar to other release rate models in that they
use a water balance approach, do not consider leachate constituent
concentrations, and do not consider any processes occurring within the
waste cell that may affect leachate quantity or quality.  Some unique
features of DRAINMOD/DRAINFIL are their ability to predict the upward
movement of water, and the precision of their hydraulic head estimates.
Hydrologic Evaluation of Landfill Performance (HELP/HSSWDS)
(Perrier and Gibson. 1980)
    The hydrologic evaluation of landfill performance (HELP, formerly
HSSWDS) is a one-dimensional, deterministic water balance model modified
and adapted from the CREAMS (Chemical Runoff and Erosion from
Agricultural Management Systems) soil percolation model for use in
estimating the amount of water that will move through various landfill
covers.  This model can simulate daily, monthly, and annual values for
runoff, percolation, temperature, soil-water characteristics, and
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evapotranspiration with a minimum of data (e.g., percipitation, mean
temperature, solar radiation, leaf area index, and characteristics of the
cover material).  Should data be unavailable, the model provides default
values for such parameters as soil-water characteristics, precipitation,
mean monthly temperature, solar radiation, vegetative characteristics and
climate based on the location of the site.  The model is portrayed by its
developers as "no more complex than a manual tabulation of moisture
balance."
    The HELP model ignores rainfall intensity, duration, and distribution
and considers only mean rainfall rates, which could somewhat limit the
accuracy of the estimates.  It also does not evaluate leachate quality.
However, it can estimate percolation through up to eight drainage layers
including through the waste cell itself, and estimate lateral drainage
through any or all of these layers.   Some other features of the HELP
model include the ability to provide estimates of the impingement rate of
leachate entering the bottom liner collection system,  predict the seepage
rate through a saturated clay liner, and estimate evapotranspiration and
runoff using a minimum of data.
    The HSSWDS model has been successfully field verified by Gibson and
Malone (1982) and many others.  Those HSSWDS users contacted for comments
and opinions believed that HSSWDS was very useful in comparing sites or
cover designs, but that the accuracy or validity of the outputs could not
be determined.  HELP is currently undergoing refinement and has not yet
been tested.
Landfill and Surface Impoundment Performance Evaluation (Moore. 1980)
    The Landfill and Surface Impoundment Performance Evaluation (LSIPE)
model attempts to determine the adequacy of designs of hazardous waste
surface impoundments and landfills in controlling the amount of fluid
released to the environment.  LSIPE utilizes a series of linearized
equations and simplified boundary conditions to evaluate the efficiency
of a proposed liner design in terms of:
                                    -72-

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    •  Horizontal flow through sand and gravel drain layers.
    •  Vertical flow through low permeability clay liners.
    •  Efficiencies of liner-drain layer systems.
    •  Seepage through the bottom liner.
    LSIPE has the advantage of allowing for nonlinear equations and more
complex boundary conditions to be employed if needed.  Only transport of
liquids through a single modular waste cell can be estimated; however,
modules can then be arranged in the proposed configuration for analysis.
The LSIPE approach also possesses the unique capability of allowing for
leachate releases to be measured indirectly through the efficiency of the
leachate collection system.
    In order to provide estimates of the above mentioned parameters, this
approach requires:
    •  Liquid routing diagram for the site.
    •  Water balance for the site.
    •  Slopes in the routing system.
    •  Hydraulic conductivities.
    •  Service life of any synthetic liners.
    The LSIPE model also makes the general assumption that the operating
conditions for a waste landfill or surface impoundment meet the basic
requirements of good engineering design, including:
    •  Surface water runon has been intercepted and directed away from
       the site so that only the rainfall impinging directly on the
       landfill needs to be accounted for.
    •  Proper precautions have been taken to prevent erosion of the cover
       soils which would degrade cover performance.
    •  Synthetic liners have been installed properly to ensure their
       integrity for design life.
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Post-Closure Liability Trust Fund Model (PCLTF) (U.S. EPA 1982)

    This model is being developed to assess the adequacy of the

Post-Closure Liability Trust Fund established as the result of the

passage of CERCLA in 1980.  The fund will provide for liability claims

resulting from failure of RCRA permitted sites after proper closure.  The

analytical approach involves:

    •  Assessing failure probabilities of facilities.

    •  Determining environmental exposure.

    •  Assessing damage potential.

    •  Quantifying damages, and assessing costs for clean-up, remedial
       action, damage to natural resources, personal injury and economic
       loss.

    PCLTF is the only model reviewed which addresses all three components

necessary to predict a mass load release from a land disposal site.  The

model can be applied to open or closed facilities with both clay and/or
synthetic liners.  The user can specify one of seven generic site types

from a variety of cover and bottom liner and leachate collection

configurations.  The components of the model  consists of:

    •  User-supplied inputs which characterize the site design and
       operation, and identify the wastes placed within the fill.

    •  A data base of physical and chemical characteristics of waste
       constituents which relate to their solubility, toxicity,
       persistance, and mobility as well as their effect on synthetic
       liner performance.

    •  A data base of climate, soils, and the geology of various regions
       of the U.S.

    •  A baseline analysis with which to set initial site conditions.

    •  Water movement simulation which uses Monte Carlo simulation
       techniques to generate values for seepage velocity, effective
       porosity, dispersion, and liner failure to route leachates through
       the layers of the landfill, including liners and drain layers.
       Adjustments to leachate quantity are made based on moisture
       content of wastes and fill materials.
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This model's output is a two-dimensional, uniformly distributed, leachate
discharge estimate (concentration and flux) to the unsaturated soil
column beneath the site.  The output provides the source term for a mass
transport module for the unsaturated zone.
Leachate Travel Time Model (LTTM) (Pope-Reid Associates. 1982)
    The Leachate Travel Time Model (currently under development by
Pope-Reid Associates) combines several analytical techniques and
previously developed models to evaluate the performance of landfills of
various designs in a variety of climatic settings.  The model consists of
a monthly, quarterly, or annual hydrologic and waste budget which is used
to calculate leachate volume in the active fill area, leachate head in
drain layers, containment time and seepage rate through the bottom liner,
and travel time and seepage rate in the unsaturated zone below the
landfill.  The model possesses the unique feature of accounting for the
moisture content of wastes and fill materials.  Actual measured values or
estimations of moisture content can be input.  Also, the model includes
both gravitational and capillary forces to calculate seepage rates
through liners.
    The Leachate Travel Time Model does not include a specific cover
liner option, although the user can incorporate a cover liner by altering
the hydrologic budget.  Like other models, the current program does not
address constitutent concentrations of contaminant mass transport, but
the authors do intend to incorporate constituent transport in the
future.  The model does, however, address both leachate generation and
release in a relatively simple and easy-to-use program which incorporates
many interesting features.
Release Rate Computations for Land Disposal Facilities (SCS Engineers.
1982)
    This approach consists of a series of simple calculations to predict
the quantity of leachate generated and released from landfills and
surface impoundments which will be incorporated into EPA's RCRA Risk/Cost
                                    -75-

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Policy Model Project (ICF Incorporated, Clement Associates, Inc., and SCS
Engineers, Inc., 1982).  The approach assumes that:

    •  Synthetic liners last for 20 years, after which liquid moves
       freely through them.

    •  Clay liners retain their integrity for longer than 100 years.

    •  The only sources of liquids are infiltration from the surface and
       free liquids in waste.  Only saturated flow takes place through
       the liner in the absence of free liquids.

    •  Infiltration through the cover system after closure is less than
       or equal to leachate movement through the liner system.

    •  Synergistic effects do not occur.

    The time required for leakage to appear beneath the bottom of a clay

liner is given by:


    t = Tird2/4D

where:

    t = time to first appearance of leakage (sec)
    d = thickness of clay liner (cm)
                                            2
    D = linearized diffusivity constant, (cm /sec) assumed to be
          5   2
        10  cm /sec.

    The volume of leachate release over time is given by:
    q = Ks(dh/d )A(At)
where:
    q  = volume of leachate released over time

    Ka = saturated permeability coefficient
    dh = hydraulic gradient
    dz
    A  = Area at base of facility

    At = length of time over which leachate releases.
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5.2  Solute Transport Models
    Once the quantity and quality of a release from a land disposal site
has been determined, this estimate can be used as the input for a solute
transport model.  Solute transport models predict the migration of
chemical constituents away from a source over time in one, two, or three
dimensions.  A brief discussion of the principles used in transport
modeling and descriptions of several transport models are contained in
the following sections.
5.2.1  Fundamentals
    The transport models presented in this section are all mathematical
models, rather than rating or ranking type models (e.g., the MITRE
Model).  The mathematical approach to modeling involves applying a set of
equations, based on explicit assumptions, to describe the physical
processes affecting pollutant transport from a site.  These models can be
divided into two types—deterministic and stochastic.  Deterministic
models attempt to define the shape and concentration of waste migration
using the physical processes (e.g., groundwater flow) involved, while
stochastic models attempt to define causes and effects using probablistic
methods.  Models presented in this report are generally deterministic.
    Deterministic mathematical models can be further divided into
analytical models and numerical models.  Analytical models simplify
mathematical equations, allowing solutions to be obtained by analytical
methods (i.e., function of real variables).  Numerical models, on the
other hand, approximate equations numerically and result in a matrix
equation that is usually solved by computer analysis.  Both types of
deterministic models address a wide range of physical and chemical
characteristics but the analytical models usually simplify the
characteristics by assuming steady state conditions.  The physical and
chemical characteristics considered by these models include:
    •  Boundary Conditions—hydraulic head distribution, recharge and
       discharge points, locations and types of boundaries.
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    •  Material Constants — hydraulic conductivity, porosity,
       transmissivity, extent of hydrogeologic units.
    •  Attenuation Mechanisms — adsorption-desorption, ion exchange,
       complexing, nuclear decay, ion filtration, gas generation,
       precipitation-dissolution, biodegradation, chemical degradation.
    •  Hydrodynamic Dispersion — diffusion and dispersion (transverse and
       longitudinal) .
    •  Waste Constituent Concentration — initial and background
       concentrations, boundary conditions.
    Both mathematical model types incorporate two sets of equations to
define transport; a groundwater flow equation and a mass transport
equation.  Figure 5-1 illustrates the relationship between these
equations.
    A general form of the water momentum balance equation for
nonhomogeneous anisotropic aquifers (Pope-Reid Associates (1982)) is:
        axi   ij axj       at
where :
    h = hydraulic head
    K = hydraulic conductivity
    S = storage coefficient
    W 5 volume flux per unit area (e.g., pumping or injection wells,
        infiltration, leakage)
    x a distance
    t = time
The Darcy equation is generally represented as:
         v  .
         Vi "  n
where:
    V = groundwater velocity
    n = porosity
    K a hydraulic conductivity
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             Mass Transport
               Equations
Groundwater Flow
   Equations
              Mass  Balance
              for Chemical
                Species
     Water
   Momentum
    Balance
                                                     Darcy's
                                                    Equation
                                 Transport
                                 Equation
Figure 5-1.   Major  Components of Groundwater Transport Equation
             (after Mercer and Faust, 1981)
                                 -79-

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    The mass transport side of the model, which describes the
concentrations of a chemical species in a flow pattern in general form is:
    3c    3         9C      3          C'W
    W = ^7 (Dij '  ^? - ^ (CV -  n  + R
where:
    C' = concentration of solute in the source or sink fluid
    C  = chemical species concentration
    D  = dispersion tensor (i.e., hydrodynamic dispersion)
    V  = groundwater velocity (i.e., convection transport)
    R  = rate of chemical species attenuation/transformation
    These equations are coupled to provide predictions of solute
transport in the groundwater system with chemical reactions considered.
For analytical models, these equations are simplified to explicit
expression.  For either type of model, a sensitivity analysis of model
results can be performed by varying the input characteristics singularly
or in combination.  One type of sensitivity analysis that could be
performed involves changing single parameters (within known values of
occurrence) to demonstrate the effects that variations in individual
parameters have on model output.  This analysis helps identify those
parameters which have the greatest influence on model results.  A second
type of sensitivity analysis involves a series of trial runs of the model
using an array of input parameters which vary in accordance with the
expected errors associated with each parameter (i.e., Monte Carlo
simulation techniques).  This method provides a general assessment of the
overall model sensitivity and intrinsic precision by providing a range of
variations of the model outputs as a function of the error bars
associated with the input parameters (e.g., mean values, maximum values,
minimum values).
5.2.1.1  Analytical Models
    Analytical models provide estimates of waste constituent
concentrations and distributions using simplified, explicit expressions
                                    -80-

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generated from partial differential equations.  The mathematical
expressions are usually simplified by assuming steady  state  conditions
relative to fluid velocity, dispersion dynamics, and other physical
parameters.  For example, groundwater flow equations can be  simplified  if
the aquifer is assumed to have infinite extent.  Governing equations
characterize both groundwater flow and mass transport, and may also
address dilution, dispersion, and attenuation.  These  models can simulate
plume migration from the source to a utilized groundwater system allowing
for attenuation and dispersion.  The method provides a quick and
inexpensive solution with minimal amounts of data as long as the
simplifying assumptions do not render results invalid.
5.2.1.2  Numerical Models
    Numerical models characterize groundwater contamination  processes
without the simplification of complex physical and chemical
characteristics required by analytical models.  The numerical models
reduce the partial differential equations to a set of  algebraic equations
that define hydraulic head at specific points (i.e., grid points).  These
equations are solved through linear algebra using matrix techniques.
    The numerical methods most commonly used to simulate groundwater
transport problems can be divided into four groups:  finite difference
(FD); finite element (FE); method of characteristics (HOC);  and discrete
parcel random-walk (DPRW).  In each method, the governing equations
(e.g., groundwater flow equations) are solved by subdividing the entire
problem domain into a grid system of polygons.  Every  block has assigned
hydrogeologic properties (e.g., transmissivity) associated with it that
define the aquifer.  Accompanying each grid is a node  point that
represents the position of an equation with unknown values (e.g., head).
For the finite difference method, the derivatives of the partial
differential equations are approximated by linear interpolation (i.e.,
the differential approach).  In the finite element method the partial
differential equations are transformed to integral form (functionals) and
minimized to solve the dependent variables.  The algebraic equations for
each node point, derived by the FD or FE methods, are then combined to
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form a matrix equation which is solved numerically.  The FE method is
better suited for solving complex two- and three-dimensional boundary
conditions than the FD method.   When using FD or FE methods for solving
contaminant transport problems, results are subject to numerical
dispersion or numerical oscillation.  Numerical dispersion causes answers
to be obscured because of accumulated round-off error at alternating time
steps.  Numerical oscillation causes answers to overshoot and undershoot
the actual solution at alternating time steps.  Numerical oscillation is
generally associated with FE methods, while numerical dispersion is
generally associated with FD methods.
    The method of characteristics and discrete parcel random-walk models
were developed to minimize the numerical difficulties associated with the
FE and FD methods.  Both the method of characteristics (HOC) and discrete
parcel random walk method analyze temporal changes in concentrations by
tracking a set of reference points that flow with the groundwater past a
fixed grid point.  In the HOC method, points are placed in each finite
difference block and allowed to move in proportion to the groundwater
velocity at the point and the time increment.  Concentrations are
recalculated using summed particle concentrations at the new locations.
The random-walk method varies from the HOC method because, instead of
solving the transport equation, a random process defines dispersion.
Reference points move as a function of groundwater flow, consistent with
a probability function related to groundwater velocity and dispersion
(longitudinal and transverse).   The methods provide comparable results
but the HOC method is time consuming, expensive, and requires
considerable computer storage.
5.2.2  Selected Solute Transport Models
    Eight analytical models and nine numerical models are presented in
the following sections.  Each has characteristics that make it unique;
therefore, selection of a model should be based on making the best use of
available data given the desired output.   These models are summarized in
Table 5-5.
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                       TABLE  5-5  SOLUTE TRANSPORT MODELS
  MODEL

 (Analytical)

 SESOIL
PESTAN
ADVANTAGES
"User-friendly",
addresses numerous
processes.
Calculates pollutant
velocity, length of
pollutant slug,
contamainant concentra-
tions.  Easy to use,
inexpensive, can be
used as a screening
model.  Can be coupled
with PLUME.
DISADVANTAGES
Field and analytical
verifications not
yet performed.
Designed for un-
saturated zone
simulations.

One dimensional
through un-
saturated zone.
REFERENCE
Bonazountas and
Wagner  (1981)
Enfield, et
al.,  (1982)
PLUME
Leachate
Plume
Migration
Model
Cleary
Model
A saturated zone model.
Provides 2-dimension-
al plume traces.
Predicts plume migra-
tion and mixing in
saturated zone.
Methods of use are
simplified.

10 different models
using a variety of
boundary conditions.
Little information
available.
Effects of adsorp-
tion and degrada-
tion ignored in
testing.
Wagner (1982)
                       Kent, et al.,
                       (1982)
                       Cleary
                       (1982)
                                    -83-

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                 TABLE 5-5  SOLUTE TRANSPORT MODELS (Continued)
  MODEL

(Analytical)

AT123D
Screening
Procedure
PATHS
ADVANTAGES
Estimates waste trans-
port in saturated and
unsaturated zones.
Computer coded,
available, valuable
for preliminary
assessments.

Assesses transport
and degradation
in saturated zone
of specific chemicals.
Provides quantitative
and qualitative
screening based on
estimates of exposure.

Used for saturated
flow.  Estimates
single contaminant
transport.  Fast,
inexpensive.
DISADVANTAGES
Appears to have
not been field
verified.
REFERENCE
Yeh (1981)
Does not address
synergistic effects.
Unpublished and not
available to public.
Falco, et.
al. (1980)
Ignores dispersion
effects.  Has not
been field verified
Nelson and
Sheen (1980)
(Numerical Models)

MMT/VTT/       Used for saturated or
UNSAT I D      unsaturated zone.
               Computer package
               available for
               graphic displays.
                         As with all
                         numerical models,
                         costs are high as
                         are requirements
                         for accurate
                         geohydrologic data.
                       Battelle
                       (1982)
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                 TABLE 5-5  SOLUTE TRANSPORT MODELS (Continued)
  MODEL
ADVANTAGES
DISADVANTAGES
REFERENCE
(Numerical Models)
CFEST/
UNSAT ID
Pollutant
Movement
Simulator
FEMWASTE
Random Walk
Solute
Transport
Model
CFEST predicts fluid
pressure, temperature,
and contaminant con-
centrations in
saturated zone.

Three-dimensional
model for coupled
saturated-unsaturated
zone.

Two-dimensional model
for coupled saturated-
unsaturated zones.
Utilizes FEMWATER.

Saturated zone model.
Concentrations can be
specified in any segment
of model.  Documented,
available to public,
and verified.
Presently being field
verified.  Model
documentation in
preparation.
Has not been
tested for
landfills.
Battelle
(1982)
Khaleel and
Reddell,
                       Yeh (1981)
                       Prickett, et
                       al., (1981)
SWIFP
Solute
Transport/
Groundwater
Flow Model
Saturated zone models
three-dimensional. Field
and analytically verified,
well documented.
                       USGS (1982)
Saturated zone.
Analytically and
field verified.
Ignores dispersion,
Colder
Associates
(1982)
Leachate
Organic
Migration
and Attenua-
tion Model
Coupled saturated-
unsaturated zones.
Specifically designed
for landfills.
Currently being
revised.
Sykes, et
al. (1982)
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5.2.2.1  Analytical Models
    The eight analytical models characterized in this section do not
address cases involving secondary porosity, immiscible liquids, or more
than one contaminant.  Only one model, AT123D developed by G.T. Yeh
(1981), considers both the saturated and unsaturated hydrologic zones;
the other models are restricted to modeling only one hydrologic zone.
SESOIL (Bonazountas and Wagner. 1981)
    SESOIL, a seasonal soil compartment model, was developed by A.D.
Little Inc. for the U.S. EPA Office of Toxic Substances.  The model is
described as a "user-friendly" statistical/analytical mathematical model
designed for long term environmental pollutant fate simulates.
Simulations are performed for the unsaturated zone and are based on a
three-cycle rationale—the water cycle, the sediment cycle, and the
pollutant cycle.  SESOIL addresses numerous processes including
diffusion, sorption, chemical degradation, biological degradation, and
the complexation of metals.  The model is presently being updated and is
available for limited use although field or analytical verifications have
not yet been performed.
PESTAN (Enfield. et al.. 1982)
    PESTAN was developed at the EPA Robert S. Kerr Environmental Research
Laboratory.  The model calculates the movement of organic substances in
one dimension through the unsaturated zone based on linear sorption and
first order degradation (i.e., hydrolysis and biodegradation).
Calculated outputs include pollutant velocity, length of the pollutant
slug, and contaminant concentrations.   Pollutant application rates to
the soil surface can be changed to determine the effect of the number of
applications, application period, and number of days before
reapplication.  This model is best classified as a screening model
because it provides for a rapid evaluation of chemicals without the
sophistication of numerical models.  The model is also easy to use and
inexpensive.  PESTAN can be coupled with PLUME, a saturated zone
analytical model.  PESTAN has been field verified for the chemicals DDT
and Aldicarb, and the model is being used by EPA-Athens.
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PLUME (Wagner. 1982)
    PLUME is a steady state analytical model developed at Oklahoma State
University to model contaminant transport in the saturated zone.
Themodel provides two-dimensional plume traces from a continuous source
and allows for first order degradation and linear sorption (i.e., organic
pollutants) with dispersion.  The model was verified using a case history
of groundwater contaminated with hexavalent chromium, although the
effects of adsorption and degradation were ignored.
Leachate Plume Migration Model (Kent, et. al. 1982)
    The Leachate Plume Migration Model was developed as an analytical
technique for the hazard evaluation of existing and potential, continuous
source waste disposal sites by predicting plume migration and mixing in
the saturated zone.  Predictions can be made from nomographs, hand-held
calculators, or a large scale computer.  The model allows for degradation
(i.e., radioactive and biological) of constituents and for the effects of
dispersion and diffusion.  The predictive methods presented are
simplified so that a strong background in mathematics and computer
programming are not required for their use.  The model has been verified
using data from a chromium plume at Long Island and is presently being
tested against other case studies.
Clearv Model (Cleary. 1982)
    The Cleary Model consists of ten different analytical models that
describe mass transport and groundwater flow, with dispersion, under a
variety of boundary conditions.  The model addresses conservative
constituents (i.e., without degradation).  The ten available models are:
    •  1-dimensional, mass transport; 1st type boundary conditions.
    •  1-dimensional, mass transport; 3rd type boundary conditions.
    •  2-dimensional, mass transport; strip boundary, finite width.
    •  2-dimensional, mass transport; strip boundary, infinite width.
    •  2-dimensional, mass transport; Gaussian source, infinite width.
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    •  3-dimensional,  mass transport; patch source, finite dimensions.

    •  3-dimensional,  mass transport; 5 area Gaussian source.

    •  2-dimensional,  groundwater flow; infinite dimensions, recharge
       boundary.

    •  2-dimensional,  groundwater flow; finite dimensions, recharge
       boundary.

    •  2-dimensional,  groundwater flow; infinite dimensions, no recharge,

These models were not available for review and R. Cleary (developer)

could not be contacted; information concerning these models was,

therefore, very limited.

AT123D (Yeh. 1981)

    AT123D, developed by G. T. Yeh at Oak. Ridge National Laboratory, is a

generalized transient, one-, two-, or three-dimensional analytical

computer model for estimating waste transport in both the unsaturated and

saturated zones.  The model is flexible, providing 450 options: 288 for

the 3-dimensional case; 72 for the 2-dimensional case in the x-z plane;

72 for the 2-dimensional case in the x-y plane; and 18 for the

1-dimensional case in the longitudinal direction.  AT123D models all of

the following options:

    •  Eight sets of source configurations (i.e., point source; line
       source parallel to x-, y-, or z-axis; area source perpendicular to
       the x-, y-, or z-axis; and a volume source).

    •  Three kinds of source releases (instantaneous, continuous, and
       finite duration releases).

    •  Four variations of the aquifer dimensions (finite depth and width,
       finite depth and infinite width, infinite depth and finite width,
       infinite depth and infinite width).

    •  Modeling of radioactive wastes, chemicals, and head levels.
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The transport mechanisms addressed are advection, hydrodynamic
dispersion, adsorption, decay/degradation, and waste losses to the
atmosphere from the unsaturated zone.  The model is computer coded and
publicly available, making it a potentially valuable tool for preliminary
assessment of waste disposal sites.  Fifty sample problems (simulations)
have been performed but actual field verification appears to be lacking.
Screening Procedure (Falco et al.. 1980)
    A screening procedure for assessing the transport and degradation of
solid waste constituents in the saturated zone as well as surface waters
was developed by Falco et al., (1980).  The procedure estimates the
movement and degradation of chemicals released from landfills and lagoons
based on the physical and chemical properties of the compound and a
defined range of environmental conditions that the compound would be
expected to encounter in groundwater.  The procedure developed involves
two parts, a mathematical model to obtain quantitative estimates of
exposure and a logic sequence that assigns qualitative descriptors of
behavior (e.g., low, significant, high) based on the quantitative
estimates of exposure.  Quantitative estimates are based on hydrolysis,
biological degradation, oxidation, and sorption.  The results of using
this procedure indicate that it provides a means of qualitatively
screening organic chemicals when specific process rates are available.
PATHS (Nelson and Schur. 1980)
    The PATHS groundwater model is a hybrid analytical/numerical model
for two-dimensional, saturated groundwater flow that estimates single
contaminant transport under homogeneous geologic conditions.   The model
also considers the effect of equilibrium ion exchange reactions for a
single contaminant at trace ion concentrations.  Dispersion effects are
not considered by the model.  The model provides a fast, inexpensive,
first-cut evaluation consistent with the amount of field data Usually
available for a site.  Analytical verifications have been performed but
field verifications have not.
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5.2.2.2  Numerical Models
    The nine numerical models characterized in this section generally
address the following characteristics:
    •  Coupled saturated/unsaturated zones.
    •  Primary porosity.
    t  Heterogeneous, anisotropic aquifers.
    •  Miscible constituents.
    •  Dispersion.
    •  Attenuation/degradation.
    This group of models represents the most flexible approach to
modeling a wide range of hydrogeologic conditions and contaminant types
because the governing equations are not simplified as they are for the
analytical models.  These models generally involve greater costs and
require accurate geohydrologic data for a given site.
MMT/VTT/UNSAT1D (Battelle. 1982)
    MMT (Multicomponent Mass Transport) is a one- or two-dimensional mass
transport code for predicting the movement of contaminants in the
saturated or unsaturated zone.  The MMT model utilizes the discrete
parcel random-walk method and was originally developed to simulate the
migration of radioactive contaminants.  The model accounts for
equilibrium sorption, first-order decay and n-members radioactive decay
chains.  A velocity field (i.e., groundwater flow equations) must be
input to the model and this  is generally accomplished by coupling with
the VTT (Variable Thickness Transient) model for the saturated zone and
UNSAT1D (One-Dimensional Unsaturated Flow) model for the unsaturated
zone.  A computer package facilitates interpretation of results by
providing graphic data displays.  The model has been used at the Hanford,
Washington, site to predict  tritium concentrations.
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CFEST/UNSAT1D (Battelle. 1982)
    CFEST (Coupled Fluid Energy and Solute Transport) predicts fluid
pressure, temperature, and contaminant concentrations in saturated
groundwater systems.  Coupling the model with UNSAT1D allows for modeling
the unsaturated zone.  The model applies finite element techniques to
solve equations.  The flow system may be complex, multi-layered,
heterogeneous and anisotropic with time-varying boundary conditions and
time-varying areal sources and sinks.  Sorption and contaminant
degradation are presently being incorporated into the model.  The model
is presently being field verified for EPA at the Charles City, Iowa, site
for arsenic and pharmaceutical chemical waste (organics).  Model
documentation is in preparation.
Pollutant Movement Simulator (Khaleel and Reddell. 1977)
    The Pollutant Movement Simulator is a three dimensional model
describing the two-phase (air-water) fluid flow equations in a coupled
saturated-unsaturated porous medium.  Flow equations are solved by finite
difference methods.  A three dimensional convective-dispersive equation
was also developed to describe the movement of a conservative,
noninteracting tracer in nonhomogeneous, anisotropic porous medium.
Convective-dispersive equations are solved by the method of
characteristics.  Attenuation processes have been incorporated into the
model since its original release.  The model has been tested for salt
(NaCL) movement in sample plots and is presently being used in coal mine
contamination studies.
FEMWASTE (Yeh. 1981)
    FEMWASTE, developed by G. T. Yeh at Oak Ridge National Laboratory, is
a two dimensional, finite element, mass transport model for the coupled
saturated-unsaturated hydrologic zones.  This model utilizes FEMWATER,
also developed by Yeh, to provide the groundwater flow field allowing for
a variety of boundary conditions and initial moisture conditions.
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Additionally, FBMWASTE incorporates the effects of convection,
dispersion, chemical sorption and first order decay in the mass transport
equations.  FEMWASTE/FEMWATER is computer coded and available to the
public.  This model has been field verified and is presently being used
by the Carson City office of the USGS.
Random Walk Solute Transport Model (Prickett et al.. 1981)
    The Random Walk Solute Transport Model, developed by Prickett,
Naymik, and Lonnquist (1981), predicts the transport of chemical species
(e.g., organics, metals, inorganics) in the saturated zone by the random
walk or particle-in-a-cell method.  Mass transport equations include
provisions for dispersion and chemical reactions (attenuation).  The
model also accounts for time varying pumpage, injection by wells, natural
or artificial recharge, water exchange between surface water and
groundwater, and flow from springs.  Chemical constituent concentrations
in any segment of the model can be specified.  Flow equations are solved
by finite difference methods.  The model has been documented and made
available to the public.  Analytical and field (i.e., fertilizer plant,
Meredosia, Illinois) verifications have been performed.
Solute Transport and Dispersion Model (Konikow and Bredehoeft. 197A)
    The Solute Transport and Dispersion Model simulates the movement of
conservative chemical species in a two dimensional, coupled
unsaturated-saturated hydrologic zone.  Flow equations are solved using
the finite difference method while mass transport equations are solved by
the method of characteristics.  The model allows for the incorporation of
pumping or recharging wells, diffuse infiltration, and for varying the
transmissivity, boundary conditions, contaminant concentrations, and
saturated thickness.  Analytical and numerous field verifications have
been performed for the model (e.g., Hanford Reservation, Washington for
radioactives; Rocky Mountain Arsenal, Colorado for pond leachate).
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SWIFP (USGS. 1978)
    The SWIFP model simulates the movement of nonconservative
constituents through the saturated zone in three dimensions.  The model
incorporates dispersion processes and also allows for deep well injection
predictions.  Flow and transport equations are solved by the finite
difference method.  This model is well documented and maintained, and has
been field and analytically verified.  Presently field verifications are
being performed in New Jersey for sea-water intrusion, in Carson City for
geothermal transport, and in Minnesota for coal tar residues.  A version
of SWIFP has also been developed for the Nuclear Regulatory Commission to
handle radioactive materials.
Solute Transport/Groundwater Flow Model (Colder Associates. 1982)
    This model simulates the movement of multiple conservative
constituents without dispersion in the saturated zone.  Flow and mass
transport equations are solved using finite element techniques.  The
model has been analytically and field verified.
Leachate Organic Migration and Attenuation Model (Sykes et al.. 1982)
    The Leachate Organic Migration and Attenuation Model simulates the
movement of nonconservative organic solutes through the
saturated-unsaturated zone.  The model is generally run in one or two
dimensions but can be modified for three dimensional analysis.  Flow and
mass transport equations are solved by finite element techniques.  This
model is specific to sanitary landfills because it measures organics as
chemical oxidation demand, and addresses biodegradation, adsorption,
convection, and dispersion processes.  The model is currently being
revised.  Field verification has been performed for the model at the
Borden Landfill, Ontario, Canada for chloride and potassium, at granite
sites for nuclear wastes, and for aldicarb.
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5.3  Model Limitations

    The following issues provide a context for considering the

limitations inherent in the application of models to evaluate or predict

groundwater problems.

    •  Modeling results represent approximations of the actual movement
       of contaminants and groundwater; results should be used to
       estimate the comparative magnitude of a problem and to assign
       priorities.

    •  Models should be verified against actual field observations to
       determine how closely they simulate real world situations;
       verification should be performed in the actual hydrogeologic
       system to which the model is to be applied.

    •  Model accuracy may vary dramatically when models are applied to
       situations for which they have not been verified.

    •  Models presently do not simulate all the processes that control
       contaminant movement; the equations that describe attenuation and
       dispersion are especially weak in most models.

    •  Generally, the capacity of a model to simulate field situations is
       a function of its complexity; the more complex the model, the more
       data are required.  Model reliability becomes a function of data
       accuracy, i.e., "garbage in, garbage out".

    •  Models for which sensitivity analyses have not been conducted may
       generated mathematical errors when parameters are changed and
       assumptions modified.

    Because of the complexity and limitations of models, assertions

determined through the use of models should not be interpreted as actual

values but only as estimates.

    For Wisconsin zone of saturation landfills, those models which

address leachate production, such as DRAINMOD/DRAINFIL and LSIPB, are

applicable.  LTTM may be useful when fully documented and verified.

Solute transport models, such as SUIFP and the Random Walk Solute

Transport Model, may be applicable if leachate migration from existing

landfills is detected or suspected.
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                           6.0  RECOMMENDATIONS


    Zone of saturation landfills are by nature very susceptible to

contaminant releases because of the large amounts of water, both

groundwater inflows and leachate, that must be removed by the drainage

system.  If the only sites available for construction of the landfills

are in the saturated zone, the following recommendations may help limit

the probabilities of leachate release:

    •  Determine as accurately as possible the values of inflow rates (q)
       and hydraulic conductivities (K) of both landfill material and
       soils because these values have a major impact on drain system
       design,  especially drain spacing.

    •  Determine the hydrogeology of the site accurately so that
       groundwater level variations throughout the year are known and
       conservative head maintenance levels can be specified (i.e.,
       always maintaining inward hydraulic gradients).

    •  Design the landfill base so that it slopes toward the drains, thus
       allowing for lower head maintenance levels and more rapid leachate
       removal.

    •  Specify low head maintenance levels within the fill, thus reducing
       the hydraulic head capable of discharging leachate (i.e., for
       hazardous waste sites, EPA regulations require heads less than
       1-foot).

    •  Select the proper drain equation for system design and allow for a
       margin of error in the results obtained (i.e., design
       conservatively).

    •  Design filters and envelopes for drain pipes that prevent silting
       and allow for free flow of liquids.

    •  Remove daily fill covers from cells or ensure by some other means
       that the cells are hydraulically connected to the drainage system
       thus allowing free flow of water between cells and drains.
                                    -95-

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    •  Incorporate drain blankets into landfill designs to reduce head
       maintenance levels without decreasing drain spacing and improve
       the overall efficiency of leachate collection.

    •  Compact clay base and sidewall layers at optimum working moisture
       conditions so that high density, low permeability barriers are
       created without shearing or fracturing the clay.

    •  Provide construction inspections to ensure that critical
       operations such as placement of leachate collection drain and
       filter envelopes, base gradings, and clay recompaction are
       performed as specified.

    •  Design leachate collection system so that routine maintenance and
       inspections can be performed to adequately maintain flows.

    •  Provide for continuous monitoring of leachate collection volumes
       and head levels so that problems can be identified quickly.

    •  Design landfill drainage systems to incorporate anticipated future
       operations such as the acceptance of large quantities of liquids.

Understanding the drain equations and the theory behind them and

incorporating the above recommendations into the original landfill design

can substantially reduce the chances of leachate release.  However,

unless the designs are incorporated properly during construction, the

system will fail to meet its intended purpose.
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                            7.0  BIBLIOGRAPHY
7.1  Background

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.  U.S.EPA-S30/SW-168, Cincinnati, Ohio.  40 pp..

Fungaroli, A.A.  1971.  Pollution of subsurface water by sanitary
landfills.  U.S.E.P.A. Solid Waste Management Series, SW-12rg.  Vol. 1.
132 pp.

Fungaroli, A.A. and R.L. Steiner.  1979.  Investigation of sanitary
landfill behavior.  Volume 1.  U.S.E.P.A. 600/2-79-053a.

Gerhart, R.A.  1977.  Leachate attenuation in the unsaturated zone
beneath three sanitary landfills in Wisconsin.  University of Wisconsin.
Wisconsin Geological and Natural History Survey.  Info. Circular No. 3.
93 pp.

Green, J.H. et al.  1965.  Groundwater pumpage and water level changes in
Milwaukee-Waukesha area, 1950-61.  USGS Water Supply Paper 1809-1.
                                                         »
Harr, C.A., L.C. Trotta, and R.G. Borman.  1978.  Ground-water resources
and geology of Columbia County, Wisconsin.  University of Wisconsin -
Extension.  Geological and Natural History Survey.  Info.  Circular
No. 37.  30 pp.

Holt, C.L.R., Jr.  1965.  Geology and water resources of Portage County,
Wisconsin.  USGS Water Supply Paper 1796.  77 pp.

Huebner, Paul. 1982.  Personal Communication.

Hughes, G.M. et al.  1971.  Hydrogeology of solid waste disposal sites in
Northeastern Illinois.  U.S.E.P.A. Publication No. SW-12d.  154 pp.

LeRoux, E.F.  1957.  Geology and ground water resources of Outagamie
County.  USGS Water Supply Paper 1604.

Newport, T.G.  1962.  Geology and ground water resources of Fond du Lac
County, Wisconsin, USGS Water Supply Paper 1604.

Olcott, P.G.  1966.  Geology and water resources of Winnebago County,
Wisconsin.  Geological Survey Water Supply Paper 1814.
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Sherrill, M.G.  1978.  Geology and ground water in Door County,
Wisconsin, with emphasis on contamination potential in the Silurian
Dolomite.  Geological Survey Water Supply Paper 2047.

Soil Conservation Service.  1980.  Ground water resources and geology of
Washington and Ozaukee Counties, Wisconsin.  University of Wisconsin -
Extension.  Geological and Natural History Survey.  Inform Circular
No. 38, 37 pp.

Young, H.L. and Batten, W.G.  1980.  Soil Survey of Winnebago County,
Wisconsin.  U.S. Department of Agriculture.

7.2  Drains

Bureau of Reclamation.  1978.  Drainage Manual.  Water Resource Technical
Publication.  United States Government Printing Office, Washington, D.C.
286 pp.

DuPont Company.  1981.  Designing and Constructing Subsurface Drains.
DuPont Company, TYPAR Sales, Wilmington, Delaware.

Hooghoudt, S.B.  1940.  Bijdragen tot de kennis van enige natuurkundige
grootheden van de grond.  No. 7.  Versl. Landbouwk.  46:515-707.

Kmet, P.  1982.  Personal Communication.

Kmet, P., K.J. Quinn and C. Slavik.  1981.  Analysis of design parameters
affecting the collection efficiency of clay lined landfills.  In;
Proceedings of Fourth Annual Madison Conference of Applied Research and
Practice on Municipal and Industrial Waste.  September 28-30, University
of Wisconsin Extension, Madison, WT.

Moore, C.A.  1980.  Landfill and Surface Impoundment Performance
Evaluation.  U.S. Environmental Protection Agency, SW-869, Office of
Water and Waste Management, Washington, D.C.

Moulton, L.K.  1979.  Design of subsurface drainage systems for the
control of groundwater.  Presented at;  58th Annual Presentation of the
Transportation Research Board, Washington, D.C.

Powers, J.P.  1981.  Construction Dewatering.  John Wiley and Sons.  New
York.  484 pp.

Sichardt, W. and W. Kyrieleis.  1940.  Grundwasserabenkungen bei
Fundierungsarbeiten.  Berlin, Germany.

Soil Conservation Service.  1973.  Drainage of Agricultural Land.  Water
Information Center, Inc.  Syosset, New York.  430 pp.

Van Schlifgaarde, J.  1974.   Drainage for Agriculture.  American Society
of Agronomy 17,  Madison, Wisconsin.
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Wesseling, J.  1973.  Theories of Field Drainage and Watershed Runoff:
Subsurface Flow into Drains.  In:  Drainage Principles and Applications.
International Institute for Land Reclamation and Improvement.  P.O.
Box 45, Wageningen, The Netherlands.

Winger, R.J. and W.F. Ryan.  1970.  Gravel Envelopes for Pipe
Drain-Design.  American Society of Agricultural Engineers.  Chicago,
Illinois, December 8-11.

7.3  Flow Nets

Bennett, R.R.  1962.  Flow Net Analysis.  In:  Ferris, J.G., D.B.
Knowles, R.M. Brown, and R.W. Stallman.  1962.  Theory of Aquifer Tests:
U.S. Geological Survey Water Supply Paper 1536-E, pp. 139-144.

Bennett, R.R., and R.R. Meyer.  1952.  Geology and Groundwater Resources
of the Baltimore Area.  Maryland Department of Geology, Mines, and Water
Resources.  Bulletin 4, 573 p.

Cedergren, H.E.  1977.  Seepage, Drainage, and Flow Nets  (2nd Edition).
John Wiley and Sons, New York.  534 p.

Freeze, R.A. and J.A. Cherry.  1979.  Ground Water.  Prentice-Hall,
Englewood Cliffs, New Jersey,  pp. 168-191.

Lohman, S.W.  1979.  Ground Water Hydraulics.  U.S. Geological Survey
Professional Paper  708.  70 p.

Mansur, C.I. and R.I. Kaufman.  1962.  Dewatering.  In;   Leonards, G.A.
(Ed.).  1962.  Foundation  Engineering.  McGraw-Hill, New  York.
pp. 241-350.

Powers, J.P.  1981.  Construction Dewatering - A Guide to Theory  and
Practice.  John Wiley and  Sons, New York.  484 pp.

7.4  Models

7.4.1  Release Rate  Models

Ali, E.M., C.A. Moore,  and I.L. Lee.   1982.  Statistical  Analysis of
Uncertainties of Flow of Liquids  Through Landfills.  Proceedings  of the
Eighth Annual Research  Symposium:  Land Disposal of Hazardous Wastes.
EPA-600/9-82-002; U.S.  Environmental  Protection Agency, Cincinnati, OH.
pp. 26-52.

Anderson, D., K.W.  Brown and T. Green.  1982.  Effect of  Organic  Fluids
on  the Permeability  of  Clay Soil  Liners.  Proceedings of  the Eighth
Annual Research Symposium:  Land  Disposal of Hazardous Wastes.
EPA-600/9-82-002; U.S.  Environmental  Protection Agency, Cincinnati, OH.
pp. 174-178.
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Bailey, G.  November 1982.  Personal communication.

Barrier, R.M.  1978.  Zeolites and Clay Minerals as Sorbents and
Molecular Sieves.  Academic Press, New York.  497 pp.  As cited in Haxo
et al., 1980.

Brady, N.C.  1974.  The Nature and Property of Soils.  Macmillan
Publishing Co., Inc.  New York, N.Y.

Brenner, Walter and Barry Rugg.  1982.  Exploratory Studies on the
Encapsulation of Selected Hazardous Wastes with Sulfur Asphalt Blends.
Proceedings of the Eighth Annual Research Symposium:  Land Disposal of
Hazardous Waste.  EPA-600/9-82-002; U.S. Environmental Protection Agency,
Cincinnati, OH.  pp. 315-326.

Burns, J., and G. Karpinski.  August 1980.  Water Balance Method
Estimates How Much Leachate Site Will Produce.  Solid Wastes Management.
pp. 54-86.

Chou, Sheng-Fu J., Robert A. Griffin, and Mei-In M. Chou.  1982.  Effect
of Soluble Salts and Caustic Soda on Solubility and Adsorption of
Hexachlorocyclopentadiene.  Proceedings of the Eighth Annual Symposium:
Land Disposal of Hazardous Waste.  EPA-600/9-82-002; U.S. Environmental
Protection Agency, Cincinnati, OH.  pp. 137-149.

D'Appolonia, D.J. and C.R. Ryan.  1979.  Soil-Bentonite Slurry Trench
Cutoff Walls.  In:  Geotechnical Exhibition and Technical Conference
Proceedings, Engineered Construction International, Inc., Chicago, IL.

Dragun, James and Charles S. Helling.  1982.  Soil and Clay Catalyzed
Reaction:  I.  Physicochemical and Structural Relationships of Organic
Chemicals Undergoing Free - Radical Oxidation.  Proceedings of the Eighth
Annual Research Symposium:  Land Disposal of Hazardous Waste.
EPA-600/9-82-002; U.S. Environmental Protection Agency, Cincinnati, OH.
pp. 106-121.

Falco, J.W., L.A. Mulkey, R.R. Swank, Jr., R.E. Lipcsei, and S.M. Brown.
A Screening Procedure for Assessing the Transport and Degradation of
Solid Waste Constituents in Subsurface and Surface Waters.  (Unpublished
paper)

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/530/SW-168, Solid Waste Information, U.S.
Environmental Protection Agency.  Cincinnati, OH.  40 pp.

Freeze, R.A. and J.A. Cherry.  1979.  Groundwater.  Prentice-Hall, Inc.,
Englewood Cliffs, N.J.  604 pp.
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Fuller, W.H.   1982.   Methods for Conducting Soil Column Tests to Predict
Pollution Migration.   Proceedings of the Eighth Annual Research
Symposium:  Land Disposal of Hazardous Wastes.  EPA-600/9-002; U.S.
Environmental Protection Agency, Cincinnati, OH.  pp. 87-105.

Garrett, B.C., J.S.  Warner, M.P. Miller, and L.G. Taft.  1982.
Laboratory and Field Studies of Factors in Predicting Site Specific
Composition of Hazardous Waste Leachate.  Proceedings of the Eighth
Annual Research Symposium:  Land Disposal of Hazardous Wastes.
EPA-600/9-82-002; U.S. Environmental Protection Agency, Cincinnati, OH.
pp. 67-86.

Gibson, A.C.  and P.G. Malone.  1982.  Verification of the U.S. EPA HSSWDS
Hydrologic Simulation Model.  Proceedings of the Eighth Annual Research
Symposium:  Land Disposal of Hazardous Wastes.  EPA-600/9-82-
002; U.S. Environmental Protection Agency, Cincinnati, OH.  pp. 13-25.

Giroud, J.P.  and J.S. Goldstein.  1982.  Geomembrane Liner Design.  Waste
Age, September 1982.

Glaubbinger,  R.S., P.M. Kohn, and R. Ramirez.  1979.  Love Canal
Aftermath:  Learning from a Tragedy.  Chemical Engineering.  October 22.

Guerero, P.,  November 1982.  Personal Communication.

Hardcastle, J.H. and J.K. Mitchell.  1974.  Electrolyte Concentration
Permeability Relations in Sodium Illite-Silt Mixtures.  Clays and Clay
Minerals.  22(2):143-154.  As cited in. Haxo, et al., 1980.

Haxo, H.E. et al.  September 1980.  Lining of Waste  Impoundment and
Disposal Facilities.  EPA/530/SW-870c, U.S. Environmental Protection
Agency, Cincinnati, OH.  385 pp.

Haxo, H.E., Jr.  1981.  Testing Materials for Use in the Lining of Waste
Disposal Facilities, Hazardous Solid Waste Testing:  First Conference.
ASTM STP 760, American Society for Testing and Materials,  pp. 269-292.

Haxo, H.E.  1982.  Effects on Liner Materials of Long-Term Exposure in
Waste Environments.  Proceedings of the Eight Annual Research Symposium:
Land Disposal of Hazardous Waste.  EPA-600/9-82-002; U.S. Environmental
Protection Agency, Cincinnati, OH.  pp. 191-211.

Huck, P.J,  1982.  Assessment of Time Domain Reflectrometry and Acoustic
Emission Monitoring; Leak Detection Systems for Landfill Liners.
Proceedings of the Eighth Annual Research Symposium:  Land Disposal of
Hazardous Waste.  EPA-600/9-82-002; U.S. Environmental Protection Agency,
Cincinnati, OH.  pp. 261-273.
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Hughes, J.  1975.  Use of Bentonite as a Soil Sealant for Leachabe
Control in Sanitary Landfills.  Soil Lab. Eng. Report Data 280-E.
American Colloid Co., Skokie, IL.  As cited in Haro et al., 1980.

Hung, Cheng Y.  1980.  A Model to Simulate Infiltration of Rainwater
Through the Cover of a Radioactive Waste Trench Under Saturated and
Unsaturated Conditions.  Draft submitted to AGU for "Role of the
Unsaturated Zone in Radioactive and Hazardous Waste Disposal," to be
published by the Ann Arbor Science Publishers in 1983.

ICP Incorporated, Clement Associates, Inc., and SCS Engineers, Inc.,
1982.  RCRA Risk/Cost Policy Model Project, Phase 2 Report.  Submitted
to:  Office of Solid Waste, U.S. Environmental Protection Agency,
June 15, 1982.  Draft internal agency document.

JRB Associates, Inc.  1982.  Techniques for Evaluating Environmental
Processes Associated with the Land Disposal of Specific Hazardous
Materials, EPA Contract No. 68-01-5052, DOW No. 36, Task 1.

Kinman, Riley N., Janet I. Rickabaugh, James J. Walsh, and W. Gregory
Vogt.  1982.  Leachate from Co-Disposal of Municipal and Hazardous Waste
in Landfill Simulators.  Proceedings of the Eighth Annual Research
Symposium:  Land Disposal of Hazardous Waste.  EPA-600/9-82-002; U.S.
Environmental Protection Agency, Cincinnati, OH.  pp. 274-293.

Krisel, W.J., Jr., Editor.  1980.  CREAMS, a Field Scale Model for
Chemical Runoff and Erosion from Agricultural Management Systems.  Vols.
I, II, and III.  Draft copy.  USDA-SEA, AR, Cons. Res. Report 24.

Kumar, J. and J.A. Jedlicka.  1973.  Selecting and Installing Synthetic
Pond Linings.  Chemical Engineering. February 5, 1973.

Lee, J.  1974.  Selecting Membrane Pond Liners.  Pollution Engineering.
6(1):33-40.

Lentz, J.J.  1981.  Apportionment of Net Recharge in Landfill Covering
Layer into Separate Components of Vertical Leakage and Horizontal
Seepage.  Vol. 17, No. 4, Water Resources Research, American Geophysical
Union,  pp. 1231-1234.

Lu, J.C.S., R.D. Morrison, and R.J. Stearns.  Leachate Production and
Management from Municipal Landfills:  Summary and Assessment.  Calscience
Research, Inc.  (Unpublished paper)

Lyman, W.J., W.F. Reehl. and D.H. Rosenblatt.  1982.  Handbook of
Chemical Property Estimation Methods;  Environmental Behavior of Organic
Compounds.  Prepared by Arthur D. Little, Inc. for the U.S. Army
Bioengineering Research and Development Laboratory,  Fort Detrick,  MD.  As
cited in JRB Associates, 1982.
                                     -102-

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Mabey, W. and T. Mill.  1978.  Critical Review of Hydrolysis of Organic
Compounds in Water Under Environmental Conditions.  J. Phys. and Chem.
1(2):383, 1978.  As cited in. JRB Associates, 1982.

Mielenz, R.C. and M.E. King.  1955.  Physical-Chemical Properties and
Engineering Performance of Clays.  Bulletin 169.  California Division of
Mines,  pp. 196-254.  As cited in. Haxo, et al., 1980.

Mingelgren, U. et al.  1977.  A Possible Model for the Surface-Induced
Hydrolysis of Organophosphorus Pesticides on Kaolinite Clays, Soil
Science Society of America J. 41.  As cited in. JRB Associates, 1982.

Mill, T.  1980.  Data Needed to Predict the Environmental Fate of Organic
Chemicals.  In;  Dynamics, Exposure and Hazard Assessment of Toxic
Chemicals.  Rizwanul and Hague, Eds.  As cited in JRB Associates, 1982.

Montague, P.  1982.  Hazardous Waste Landfills:  Some Lessons from New
jersey.  Civil Engineering.  ASCE.  September 1982.

Moore, C.A.  September 1980.  Landfill and Surface Impoundment
Performance Evaluation.  SW-869, U.S. Environmental Protection Agency,
Cincinnati, OH.  63 pp.

Moore, C.A. and M. Roulier.  1982.  Evaluating Landfill Containment
Capability.  Proceedings of the Eighth Annual Research Symposium:  Land
Disposal of Hazardous Wastes.  EPA-600/9-82-002; U.S. Environmental
Protection Agency, Cincinnati, OH.  pp. 174-178.

Moore, C.A. and E.M. Ali.  1982.  Permeability of Cracked Clay Liners.
Proceedings of the Eighth Annual Research Symposium:  Land Disposal of
Hazardous Wastes.  EPA-600/9-82-002; U.S. Environmental Protection
Agency, Cincinnati, OH.  pp. 174-178.

Perrier, E.R., and A.C. Gibson.  September 1980.  Hydrologic Simulation
of Solid Waste Disposal Sites.  EPA/530/SW-868c, U.S. Environmental
Protection Agency, Cincinnati, OH.  Ill pp.

Peters, W.R., D.W. Shultz, and B.M. Duff.  1982.  Electrical Resistivity
Techniques for Locating Liner Leaks.  Proceedings of the Eight Annual
Research Symposium:  Land Disposal of Hazardous Wastes.
EPA-600/9-82-002; U.S. Environmental Protection Agency, Cincinnati, OH.
pp. 250-260.

Pohland, Frederick G., Joseph P. Gould, R. Elizabeth Ramsey, and Daniell
C. Walters.  1982.  The Behavior of Heavy Metals During Landfill Disposal
of Hazardous Wastes.  Proceedings of the Eight Annual Research
Symposium:  Land Disposal of Hazardous Wastes.  EPA-600/9-82-002; U.S.
Environmental Protection Agency, Cincinnati, OH.  pp. 360-371.
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Pope-Reid Associates, Inc.   1982.   Hazardous Waste Landfill Design, Cost
and Performance Modelling.   Unpublished draft report.

Prickett, T.A.  July 1982.   Personal Communication.

Rosenbaum, M.S.  1976.  Effect of Compaction on the Pore Fluid Chemistry
of Montmorillonite.  Clays and Clay Minerals.  24:118-121.  As cited in.
Haxo, et al., 1980.

SCS Engineers, Inc.  1982.  Release Rate Computations for Land Disposal
Facilities.  Currently under development for EPA.

Shuckrow, Alan J. and Andrew P. Pajak.  1982.  Studies on Leachate and
Groundwater Treatment at Three Problem Sites.  Proceedings of the Eighth
Annual Research Symposium:  Land Disposal of Hazardous Waste.
EPA-600/9-82-002; U.S. Environmental Protection Agency, Cincinnati, OH.
pp. 346-359.

Shultz, David W. and Michael Miklas.  1982.  Procedures for Installing
Liner Systems.  Proceedings of the Eighth Annual Research Symposium:
Land Disposal of Hazardous Waste.  EPA-600/9-82-002; U.S. Environmental
Protection Agency, Cincinnati, OH.  pp. 224-238.

Silka, L.R., and R.L. Swearingen.  1978.  A Manual for Evaluating
Contamination Potential of Surface Impoundments.  EPA-570/9-78-003; U.S.
Environmental Protection Agency, Cincinnati, OH.  73 pp.

Skaggs, R.W.  1980.  Combination Surface-Subsurface Drainage System for
Humid Regions.  Journal of the Irrigation and Drainage Division, ASCE,
Vol. 106, No. 1R4, Proc. Paper 15883, pp. 265-283.

Skaggs, R.W.  1980.  A Water Management Model for Artificially Drained
Soils.  Tech. Bui. No. 267, North Carolina Agricultural Research
Service.  54 pp.

Skaggs, R.W.  1982.  Modification to DRAINMOD to Consider Drainage from
and Seepage Through  a Landfill.  I.  Documentation.  Unpublished EPA
Document, August 26, 1982.

Skaggs, R.W., A. Nassehzadeh-Tabrinzi, and G.R. Foster.  1982.
Subsurface Drainage  Effects on Erosion.  Paper No. 8212, Journal Series,
North Carolina Agricultural Research Service, Raleigh,  pp. 167-172.

Skaggs, R.W., N.R. Fausey, and B.H. Nolte.  1981.  Water Management Model
Evaluation for North Central Ohio.  0001-2351/81-2404-0929, American
Society of Agricultural Engineers,  pp. 922-928.

Skaggs, R.W., and J.W. Gillian.  1981.  Effect of Drainage System Design
and Operation on Nitrate Transport.  0001-2351/81-2404-0929, American
Society of Agricultural Engineers,  pp. 929-940.
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Skaggs, R.W.  1982.  Field Evaluation of a Water Management Simulation
Model.  0001-2351/82/2503-0666, American Society of Agricultural
Engineers,  pp. 666-674.

Spooner, P.S., et al.  1982.  Draft Technical Handbook on Slurry Trench
Construction for Pollution Migration Control.  EPA Contract
No. 68-01-3113.

Thornthwaite, C.W. and J.R. Mather.  1955.  The Water Balance.
Centerton, N.J.  104 p.  (Drexel Institute of Technology.  Laboratory of
Climatology.  Publications in Climatology, V. 8, No. 1.)  As cited in
Fenn, Hanley, and DeGeare, 1975.

Thornthwaite, C.W. and J.R. Mather.  1957.  Instructions and Tables for
Computing Potential Evapotranspiration and the Water Balance.  Centerton,
NJ.  pp. 185-311.  (Drexel Institute of Technology.  Laboratory of
Climatology.  Publications in Climatology, V. 10, No. 3.)  As cited in.
Fenn, Hanley, and DeGeare, 1975.

Tolman, A.L., A.P. Ballestero, Jr., W.H. Beck, Jr., and G.H. Emrich.
1978.  Guidance Manual for Minimizing Pollution from Waste Disposal
Sites, EPA-600/2-78-142.  U.S. Environmental Protection Agency,
Cincinnati, OH.  83 pp.

U.S. Environmental Protection Agency.  1981.  Land Disposal of Hazardous
Waste:  Summary of Panel Discussions, (SW-947).  U.S. EPA, Washington,
D.C., May 18-22, 1981.  Contract No. 68-01-6092.

U.S. Environmental Protection Agency.  June 1982.  Post-Closure Liability
Trust Fund Model Development.  Unpublished internal report.

U.S. Environmental Protection Agency.  1982.  Hazardous Waste Management
System:  Permitting Requirements for Land Disposal Facilities, (40 CFR
Parts 122, 260, 264, and 265).  Federal Register, Vol. 47, No. 143,
July 26, 1982.

Waller, Muriel Jennings and J.L. Davis.  1982.  Assessment of Techniques
to Detect Liner Failings.  Proceedings of the Eighth Annual Research
Symposium:  Land Disposal of Hazardous Waste.  EPA-600/9-82-002; U.S.
Environmental Protection Agency, Cincinnati, OH.  pp. 239-249.

Weber, W.J.   1972.  Physiochemical Processes for Water Quality Control.
As cited  iii JRB Associates, 1982.

Wong, J.  1977.  The Design of a System for Collecting Leachate from a
Lined Landfill Site.  Water Resources Research, V. 13, No. 2,
pp. 404-410.  As cited  in. Moore, 1980.
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7.A.2  Transport Models

Anderson, M.P.  1981.  Groundwater Quality Models - State of the Art.  In
Proceedings and Recommendations of the Workshop on Groundwater Problems
in the Ohio River Basin.  Cincinnati, OH.  ppp. 90-96.

Anderson, M.P.  1979.  Using Models to Simulate the Movement of
Contaminants through Groundwater Flow Systems.  CRC Critical Reviews in
Environmental Control 9(2):97-156.

Bachmat, Y., J. Bredehoeft, B. Andrews, D. Holtz, and S. Sebastian.
1980.  Groundwater Management:  The Use of Numerical Models.  Water
Resources Monograph S.  American Geophysical Union, Washington, D.C.
127 p.

Bachmat, Y., B. Andrews, D. Holt, and S. Sebastian.  1978.  Utilization
of Numerical Groundwater Models for Water Resources Management.
Robert S. Kerr Environmental Research Laboratory, U.S. EPA, EPA-600/8-78-
012.

Battelle Pacific Northwest Laboratories.  1982.  Personal communication.

Bibby, R.  1981.  Mass Transport of Solutes in Dual-Porosity Media.
Water Resources Research 17(4):1075-1081.

Bonazountas, M. and J. Wagner.  1981.  "SESOIL":  A Seasonal Soil
Compartment Model.  Arthur D. Little, Inc., Cambridge, MA.

Chang, S., K. Barrett, S. Haus, and A. Platt.  1981.  Site Ranking Model
for Determining Remedial Action Priorities Among Uncontrolled Hazardous
Substances Facilities.  The MITRE Corporation, Working Paper to EPA,
Contract No. 68-01-6278.

Charbeneau, R.J.  1981.  Groundwater Contamination Transport with
Adsorption and Ion Exchange Chemistry:  Method of Characteristics for
Case Without Dispersion.  Water Resources Research 17(3):705-713.

Chou, S.J., B.W. Fischer, and R.A. Griffin.  1981.  Aqueous Chemistry and
Adsorbtion of Hexachlorocyclopentadiene by Earth materials.  In;
Proceedings of the Seventh Annual Research Symposium on Land Disposal of
Hazardous Waste.  EPA-600/9-81-0026, p. 29-42.

Chu, S. and G. Sposito.  1980.  A Derivation of the Macroscopic Solute
Transport Equation for Homogeneous, Saturated, Porous Media.  Water
Resources Research 16(3):542-546.

Cleary, R.  1982.  Personal communication.
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Dettinger, M.D.  and J.L. Wilson.  1981.  First Order Analysis of
Uncertainty and Numerical Models of Groundwater Flow.  Part 1.
Mathematical Development.  Water Resources Research 17(1):149-161.

Dragun, J. and C.S. Helling.  1981.  Evaluation of Molecular Modeling
Techniques to Estimate the Mobility of Organic Soils:  II.   Water
Solubility and the Molecular Fragment Mobility Coefficient.  In;
Proceedings of the Seventh Annual Research Symposium on Land Disposal of
Hazardous Waste.  EPA-600/9-81-0026, p. 58-70.

Duffy, J.J., E.  Peake, and M.F. Mohtadi.   1980.  Oil Spills on Land as
Potential Sources of Groundwater Contamination.  Environment
International 3(2):107-120.

Enfield, C.G., R.F. Carsel, S.Z. Cohen, T. Phan, and D.M. Walters.
1982.  Approximating Pollutant Transport to Ground Water.  U.S. EPA.
RSKERL.  Ada, OK.  (Unpublished paper)

Falco, J.W., L.A. Mulkey, R.R. Swank, R.E. Lipcsei, and S.W. Brown.  A
Screening Procedure for Assessing the Transport and Degradation of Solid
Waste Constituents in Subsurface and Surface Waters.  (Unpublished paper)

Faust, C.R.  The Use of Modeling in Monitoring Network Design.
Unpublished

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/530/SW-168.  U.S. EPA, Office of Solid Waste,
Cincinnati, OH.

Fuller, W.H.  1982.  Methods for Conducting Soil Column Tests to Predict
Pollutant Migration.  In;  Proceedings of the the Eighth Annual Research
Symposium on Land Disposal of Hazardous Waste.  EPA/600/9-82-002,
p. 87-103.

Fuller, W.H.  1977.  Movement of Selected Metals, Asbestos, and Cyanide
in Soil:  Applications to Waste Disposal Problems.  MERL, ORD, U.S. EPA,
EPA/600/2-77-020.  243 p.

Fuller, W.H., A. Amoozegar-Fard, E. Niebla, and M. Boyle.  1981.
Behavior of Cd, Ni, and Zn in Single and Mixed Combinations in Landfill
Leachates.  In;  Proceedings of the Seventh Annual Research Symposium on
Land Disposal of Hazardous Waste.  EPA/600/9-81-0026, p. 18-28.

Gorelick, S.M. and I. Remson.  1982.  Optimal Dynamic Management of
Groundwater Pollutant Sources.  Water Resources Research 18(l):71-76.

Grisak, G.E. and J.F. Pickens.  1980.  Solute Transport through Fractured
Media.  1.  The Effect of Matrix Diffusion.  Water Resources Research
16(4):719-730.
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Grisak, G.E., J.F. Pickens,  and J.A. Cherry.  1980.  Solute Transport
through Fractured Media.  2.  Column Study of Fractured Till.  Water
Resources Research 16(4):731-739.

Colder Associates.  1982.   Personal Communication.

Grove, D.B.  1977.  The Use of Galerkin Finite-Element Methods to Solve
Mass-Transport Equations.   USGS, Water Resource Division, Denver, CO.
USGS/WRI-77-49.

Haque, R.  1980.  Dynamic Exposure and Hazard Assessment of Toxic
Chemicals.  Ann Arbor Science Publishers, Inc.  496 pp.

Haxo, H., Jr., S. Dakessian, N. Fong, and R. White.  1980.  Lining of
Waste Impoundment and Disposal Facilities.  U.S. EPA, MERL, Cincinnati,
OH.

Intercomp Resource Development and Engineering, Inc.  1978.  A Model for
Calculating Effects of Liquid Waste Disposal in Deep Saline Aquifer.
Part I - Development.  Part II - Documentation.  USGS, Water Resources
Division, Reston, VA.

Jones, C.J.  1978.  The Ranking of Hazardous Materials by Means of Hazard
Indices.  Journal of Hazardous Materials 2:363-389.

Jury, W.A.  1982.  Simulation of Solute Transport Using  a Transfer
Function Model.  Water Resources Research 18(2):363-368.

Kent, D.C., W.A. Pettyjohn, F. Witz, and T. Prickett.  1982.  Prediction
of Leachate Plume Migration and Mixing in Ground-Water.  Solid and
Haqzardous Waste Research and Development Annual Symposium Proceedings,
pp.  71-82.

Khaleel, R. and D.L. Reddell.  1977.  Simulation of Pollutant Movement  in
Groundwater Aquifers.  Technical Report No. 81.  Texas Water Resources
Institute, Texas A&M University.

Konikow, L.F.  and J.D. Bredehoeft.  1974.   Computer Model of
Two-Dimensional Solute Transport and Dispersion in Groundwater.  In:
Techniques of  Water Resource Investigation.  Book  7, Chapter C2.

Krisel, W.J.,  Jr., Editor.  1980.  CREAMS,  A Field Scale Model for
Chemical Runoff and Erosion from Agricultural Management Systems.
Vols.  I, II  and III.  Draft copy.  USDA-SEA, AR, Cons. Res. Report 24.
                                     -108-

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Kuczera, G.  1982.  On the Relationship Between the Reliability of
Parameter Estimates and Hydrologic Time Series Data Used In Calibration.
Water Resources Research 18(1) : 146-154 .

Larson, N.M. and M. Reeves.  1979.  ODMOD.  Union Carbide Corp., Nuclear
Division.  Oak Ridge, IN.

LeGrand, H.E.  1964.  System for Evaluation of Contamination Potential of
Some Waste Disposal Sites.  Journal of the American Water Works
Association 56(8) :959-967 , 969-970, 974.

Lentz, J.L.  1981.  Apportionment of Net Recharge in Landfill Covering
Layer into Separate Components of Vertical Leakage and Horizontal
Seepage.  Water Resources Research 17(4) -.1231-1234.

Maslia, M.L. and R.H. Johnston.   1982.  Simulation of Groundwater Flow  in
the Vicinity of Hyde Park Landfill, Niagra Falls, New York.  USGS Open
File Report 82-159.

Mercer, J.W. and C.R. Faust.  1981.  Ground-Water Modeling.  National
Water Well Association.  60 p.

Moore, C.A.  1980.  Landfill and Surface Impoundment Performance
Evaluation Manual.  U.S. EPA, Office of Water and Waste Management,
Washington, D.C.  SW-869.  63 p.

Nelson. R.W. and J.A. Schur.  1980.  Assessment of Effectiveness of
Geologic Oscillation Systems:  PATHS Groundwater Hydrologic Model.
Battelle, Pacific Northwest Laboratory, Richland, WA.

Perrier, E.R. and A.C. Gibson.  1980.  Hydrologic Simulation on Solid
Waste Disposal Sites (HSSWDS).  U.S. EPA, MERL, ORD.  SW-868.  Ill p.

Pettyjohn, W.A. , T.A. Prickett, D.C. Kent, and H.E. LeGrand.  1981.
Prediction of Leachate Plume Migration.  In:  Proceedings of the Seventh
Annual Research Symposium on Land Disposal of Hazardous Waste.
EPA/600/9-81-0026,  p. 71-84.

Pickens, J.F. and G.E. Grisak.  1981.  Modeling of Scale-Dependent
Dispersion  in Hydrogeologic Systems.  Water Resources Research
Pickens, J.R. and W.C. Lennox.  1976.  Numerical Simulation of Waste
Movement in Steady Groundwater Flow Systems.  Water Resources Research
12(2):171-180.

Pope-Reid Associates, Inc.  1982.  Leachate Travel Time Model.
(Unpublished)
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Pope-Reid Associates, Inc.  1982.  Technical Review of Groundwater
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Rao, P.V., K.M. Portier, and P.S.C. Rao.  1981.  A Stochastic Approach
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Sagar, B. and A. Runcal.  1982.  Permeability of Fractured Rock:  Effect
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Silka, L.R. and T.L. Sweringen.  1978.  A Manual for Evaluating
Contamination Potential of Surface Impoundments.  U.S. EPA, Groundwater
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Smith,  L.  and F.W.  Schwartz.   1981.   Mass Transport.   3.  Role of
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Tang, D.H., E.G. Frind, and E.A.  Sudicky.  1981.  Contaminant Transport
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Tang, D.H., F.W. Schwartz, and L.  Smith.  1982.  Stochastic Modeling of
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Personal communication.

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Wagner, J.  1982.  Personal communication.

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L.B. Baskin.  1982.  Transport and Fate of Selected Organic Pollutants in
a Sandy Soil.  U.S. EPA, RSKERL,  Ada, OK.  (Unpublished report)

Wyrick, G.G. and J.W. Borchers.  1982.  Hydrologic Effects of
Stress-Relief Fracturing in an Appalachian Valley.  USGS Water Supply
Paper 2177.

Yeh, G.T.   1981.  AT123D:Analytical Transient One-, Two-, and
Three-Dimensional Simulation of Waste Transport in the Aquifer System.
Oak Ridge National Laboratory. Environmental Science Division.
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Yeh, G.T.  and D.S.  Ward.  1981.  FEMWASTE:  A Finite-Element Model of
Waste Transport Through Saturated-Unsaturated Porous Media.  Oak Ridge
National Laboratory, Environmental Science Division.  Publication
No. 1462.   ORNL-5601.  137 p.
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Yeh, G.T. and D.S. Ward.  1980.   FEMWATER:   A Finite-Element Model of
Water Flow Through Saturated-Unsaturated Porous Media.  Oak Ridge
National Laboratory, Environmental Science Division.  Publication
No. 1370.  ORNL-5567.  153 p.
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                                APPENDIX A

                          FLOW NET CONSTRUCTION


    Plow nets provide a useful tool that can aid in the interpretation of
groundwater flow through permeable earth materials.  At present, by far
the most useful reference for flow net construction (including over 100
examples) is Cedergren (1977) upon which much of the discussion in this
Appendix is based.
    A first step in the understanding of flow net construction is the
careful study of well-constructed flow nets.  This can lead to an
appreciation of what can be learned from flow nets.  Careful study of the
examples and suggestions given in Cedergren (1977) is recommended.
    Prior to constructing flow nets, the following steps are essential:
    o  Thorough field investigations which provide soil and lithologic
       data from the site.
    o  Thorough experienced evaluation of field conditions by personnel
       preferably familiar with what data are required for flow net
       construction.
    Types of Flow Nets
    There are several types of flow nets which can be constructed, based
on the nature of the materials through which water is flowing at the
site.  Flow conditions at the site can usually be categorized as one of
the following:
    o  Confined flow in single permeability geologic units.
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    o  Confined flow within units having two or more permeabilities.
    o  Unconfined flow in single permeability geologic units.
    o  Unconfined flow within units having two or more permeabilities.
    As discussed in Chapter 4.0, flow nets are composed of two families
of lines that intersect at right angles - flow lines which show paths
along which water flows (flow directions) and equipotential lines which
represent lines of equal hydraulic head.  Groundwater flows away from
high hydraulic head equipotential lines toward those of lower hydraulic
head along the paths represented by the flow lines.
    Flow nets can be constructed in a variety of ways after the field
data have been collected and thoroughly evaluated.  Hydraulic head data
must be known from numerous points distributed throughout the site and
the equipotential lines may be drawn from this data similar to the way
one would manually draw contour lines on a topographic map.  (The flow
nets presented in Chapter 4, as they were dealing with hypothetical
situations, used assumed but realistic head data).  Once the
equipotential lines are drawn and knowing that equipotential lines and
flow lines must intersect one another at right angles, the flow lines can
then be drawn.  Flow nets in plan view (e.g., Figure 4-2) are generally
constructed in this manner for flow in a single aquifer of constant
permeability.
    The most common ways of constructing flow nets can be characterized
as follows:
    o  Immediately sketching both flow lines and equipotential lines,
       working from one part of the flow net into another.
    o  Sketching  a plausible family of flow lines prior to sketching
       equipotential  lines.
   o   Sketching a plausible  family  of  equipotential  lines prior to
       sketching flow lines.
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    Examples  of  Construction  of  a Flow Net  for Confined Flow in  a  Single
    Permeability Aquifer  - Cross-Section View
    Steps
    (1)   Identify prefixed conditions  (water table  elevations, hydrologic
         barriers,  etc.}.
    (2)   Identify starting directions  of  lines  (either equipotential  or
         flow).
    (3)   Draw a  trial family  of  flow lines  (or  equipotential lines)
         consistent with  prefixed conditions.
    (4)   Draw in the other family of lines.
    (5)   Ensure  all lines intersect each  other  at 90°.
    (6)   Erase and redraw all lines until all  figures between lines are
         square.
    (7)   Subdivide as desired for detail  and accuracy.
    By repeatedly erasing and redrawing portions of lines and studying
the overall pattern and individual parts, a finished flow net can be
developed.
    The hydrogeologist or engineer using  flow nets to interpret
groundwater flow patterns must keep in mind that flow net analysis of a
hydrogeologic situation is an approximation of  the actual situation at
the site.   Flow nets are  a tool, a graphic  approximation of a natural
situation, and are only as  accurate as:
    (1)   The  amount and accuracy of the data used as control points on
         the  flow net.
    (2)   The  ability of the  person constructing the flow net.
    (3)   The  care exercised  by the person during construction of the flow
         net.
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