Vcrsai
inc.
       TECHNICAL EVALUATION OF
   SITES LOCATED IN THE ZONE OF SATURATION
6621 Electronic Drive, Springfield, Virginia 22151 - Telephone (703) 750-3000

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          DRAFT FINAL REPORT
             DRAFT
       TECHNICAL EVALUATION OF
SITES LOCATED IN THE ZONE OF SATURATION
       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
            Date Prepared:

            March 14, 1983

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                             ACKNOWLEDGMENTS
    This report was prepared by Dr. Edward Repa, Ms. Kathi Wagner, and
Mr. Rodger Wetzel of JRB Associates, and Mr. Michael Christopher of
Versar Inc., under the direction of Dr. G. Thomas Fanner, Task Manager.
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.

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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 	    10

     2.2  Drain Pipe Sizing	    13

          2.2.1   Hydraulic Gradient (i) and Roughness Coefficient   14
          2.2.2   Discharge (Q)	    14
          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	    25
          2.3.4   Synthetic Filters 	    26

3.0  DESIGN AND CONSTRUCTION	    27

     3.1  Hypothetical Site	    27
     3.2  Sensitivity Analysis  	    30

          3.2.1   Drains On Impermeable Barriers  	    30
          3.2.2   Drains On Sloping Impervious Barriers 	    34
          3.2.3   Drains Above An Impervious Barrier  	    37

     3.3  Application	    40

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

     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	    50
     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

          5.1.2   Selected Release Rate Models  	    69

     5.2  Solute Transport Models 	    76

          5.2.1   Fundamentals	    76

                  5.2.1.1  Analytical Models  	    80
                  5.2.1.2  Numerical Models 	    80

     5.3  Model Limitations 	    90

6.0  RECOMMENDATIONS	    92

7.0  BIBLIOGRAPHY	    94
                                   iii

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                          LIST OF TABLES


2-1  Values for the Equivalent Depth d of Hooghoudt 	    11

2-2  Minimum Hydraulic Gradients for Closed Pipes  	     IS

2-3  Drain Grades for Selected Critical Velocities 	     16

3-1  Range of Site Variables	     29

3-2  Drain Length Spacing (m) for Drains on an Impermeable
     Barrier	     31

3-3  Values of h/L for Various C=q/k1 and Angles a 	     35

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	     45

5-1  Major Factors Affecting Leachate Generation 	     62

5-2  Factors Affecting Leachate Constituent Concentrations  .     67

5-3  Factors Affecting Leachate Release  	     68
                                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  	      9

2-3  Drains on Sloping Impermeable Barrier 	     12

2-4  Flow Components to a Landfill	     17

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	     28

3-2  Drain Length versus Flow Rates for Head Levels Equal to
     1 Meter	     32

3-3  Plot of h/L versus h/I = tan a for Drain and Sloping
     Impervious Layers 	     36

3-4  Drain Length (L) versus c - q/kj	     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 .  .     78

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                               1.0   INTRODUCTION

     The Scare of Wisconsin and much of EPA Region V are  located in a
portion of the country characterized by thick surficial deposits of saturated
glacial till underlain by fractured sedimentary or crystalline rock.
A typical stratigraphic column for Wisconsin is shown in  Figure 1-1.
Landfill sice 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 the clays range from 10   cm/sec,
where the clays are fractured, to 10   cm/sec, where the  clays are unfrac-
tured.  Underlying the clays are chick units of dolomite  and sandstone
which act as confined aquifers.  Confining pressures in these units can
bring groundwater to the land surface in drilled wells.   Recharge of the
underlying units occurs at or near outcrops.

     Siting landfills in this region, especially chose for accepting hazard-
ous 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
accelerate leachate generation and contaminate release are greatly enhanced.
To alleviate this problem, landfill operators are required to manage ground-
water and leachate in the landfills so that inward hydraulic gradients
are constantly maintained, thereby limiting the possibility of contaminant
escape.  The method utilized to maintain inward hydraulic gradients is
a drainage collection system on the base of the landfill.  The drainage
system allows for the maintainance 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
groundwarer 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:
                                                                      , JRB Associates _

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                Geologic
                   Log
            Rock Unit
       Aquifer
                  \\v\\
                  \ \  V \\
                  \ \ \  \ \ \
                   \ \  v \T
                        "
                  \ \ \
                  \ \  V \ "\ \
                  _n_C3-£

.*J__—1—^.
                              Glacial deposits
                                Red Clay
                                         Limited Unconfined
                                             Aquifer
            Galena Dolomite and
              Platteville Formation
Confined Aquifer,
solution cavities
                              St. Peter Sandstone



                             ZTrempealeau Formatior

                              Franconia Sandstone


                              Galesville Sandstone
                                         Confined Aquifer
          Vertical Scale 1"-200'
Figure 1-1.  Typical Stratigraphic Column of Zone of Saturation
             Sites in Wisconsin (City of Fond du Lac)
                                                                    , JRB Associates.

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     o  Drain spacing
     o  Hydraulic conductivities of the  landfill and natural  soils  sur-
        rounding the site
     o  Inflow rates resulting from groundwater infringement  and  leachace
        generation
     o  Head maintenance levels within the  landfill
     o  Pipe sizing
     o  Drainage blanket use.

Other parameters addressed include landfill dimensions, construction in-
spections, and future operating conditions.  Drainage  theory  and  selected
models for predicting release rates and  so  solute transport are also de-
scribed.

     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.
                                                                      .JRB Associates.

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                              2.0  DRAIN THEORY

     There are three major elements to consider in the design of a sub-
surface 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 deisrable 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.  This section presents the analytical  solutions
for determining drain spacing based on maintenance head levels, permeabil-
ities, 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, recharge distribution and leachate generation  over the area between
the drains is uniform, and the soil is homogeneous.   Most real world  situ-
ations do not fully  meet  these criteria, therefore, results obtained  should
                                                                      .JRB Associates.

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 be considered approximate.   In  using  the  equacions  for  designing a  landfill
 drain  system, a  conservative  approach  should  be  taken  to  ensure  chat  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) impervi-
 ous barrier  can  be represented  by the  equation:

        L =  [(8KDh + 4Kh2)/q]°'5
                                                                            (1)
 where:

                 L = drain spacing (m)
                 K = hydraulic conductivity of the drained material  (m/day)
                 0 = 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)

 Figure 2-1 illustrates the relationship between  these terms.  When  two
 parallel drain lines are installed  properly,  each line exerts a drawdown
 curve that,  in theory, will intersect midway  between the two drain  lines.
 In solutions to  gravity flow  problems, the drain spacing (L) is the distance
 from the drain to a point where the drawdown  car. be considered insignificant.
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 is very small
 in comparison to h (the  water table height above the drain).  This allows
equation 1 to be simplified to:
        L = [(4Kh2)/q]°-5
                                                                           (2)
                                                                      . JRB Associates —

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                Impervious Layer
                	  L  	
Figure 2-1 Drains Resting on an Impervious Barrier
                                                        JRB Associates —

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where:
                8KDh = 0

Equation 2 represents horizontal flow to the drains above the drain level.

     Drain spacing (L) and hydraulic head level (h) in the equations are
interdependent design variable which are a function of the leachate gener-
ation rate (q) and hydraulic conductivity (K) of the drained material.
 Assuming a constant leachate generation 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.  There-
fore, 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 less
than 0.1 of the overlying layer (i.e., Kbelow/Kabove! 0<*•>•  The clay
base of a landfill may not act as an impermeable layer in the design equat-
cions 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 that is close to the  clay
        liner.
                                                                      .JRB Associates —

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     Where drains are not  installed on an  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 permeabilities  of  K  and K. (as  shown  in  Figure  2-2).   Substituting
 the permeability (K_) of  the material below the  drain  into the first  term
 of the right hand side of  equation 1  compensates  for  radial  flow to the
 drain system,  as given by:

        L = [(8K2Dh + 4K1h2)q]°'5
                                                                            (3)
 Radial flow to the drains  causes a convergence  of  flow lines near the
 drains which in turn causes  the flow  lines to lengthen.  This process
 results in a more than proportional loss of hydraulic  head because  the
 flow velocity  in the vicinity of the  drains is  larger  than elsewhere  in
 the flow region.  Consequently, the elevation of  the water table  and  drain
 spacing would  be larger than those predicted using  equation 3.

     To account for the extra resistance caused by  radial  flow,  Kooghoudt
 (1940) introduced a reduction of the  depth, D,  to a smaller equivalent
 depth, d.   The equation that was developed to take  into account  radial
 flow can be rewritten as:

        L = [(8K2dh + 4K1h2)/q]
                                                                            (4)
where the new  terms are defined as;

         d = equivalent depth (m)
        K  = hydraulic conductivity of the layer above  the drain  (m/day)
        K_ = hydraulic conductivity of the layer below  the drain  (m/day)

     Because the drain spacing, L,  is dependent on the equivalent depth,
d, which in turn is a function of,  L, equation 4 can not 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
                                                                      . JRB Associates —

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Figure 2-2.  Flow to Drains above a  Impervious  Barrier
                                                          , JRB Associates-.

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of che equacion are equal or che use of nomographs which have been developed
specifically for equivalent depth and drain spacing.  Table 2-1 gives
values for che equivalent depth (d) as a function of drain spacing (L)
and depth below the drains (D), where r ,  the radius of the drain pipe
equals 0.1 meter.  Similar tables have been prepared for other values
of r .  For depth (i.e., D valves) 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 equacion was developed by linear regression fprm che values given
in Table 2-1.                                     ^

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-sec-
tion of such a design is shown in Figure 2-3.  By designing che drain
system on sloping barriers, che flow of wacer cowards che collection system
is acceleraced thus decreasing the steady-state head maintenance levels.
This allows either the drains to be spaced further apart or the heads
to be lowered if the other parameters in the equation are held constant.

     Head levels and drain spacing can be calculated for landfills designed
with an impervious layer sloping cowards the drains at an angle ofa by
the following equation:

        1/L = (c°'5/2 h   )[(tan2a/c) -r 1 - (cana/c) (can2a+ c)0'3]
                       max
                                                                         .  (6)
where:

                c = q/K (dimensionless)
                a = slope angle (degrees)
                                      ^___^^__^________ JRB Associates —
                                       10

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                     TABLE: 2-1.
                VALUES FOR THE EOUIVALENT DEPTH d OF HOOHHOUDT  (r   =  0.1  m,  D and L in m)
                                                                 o
3J
CD
>
a
g.
a
£
VI
L— S n 7.5 10 IS 20
D

0 3 IB 0 6 * 0.48 049 0 49 0. 49
0.75 0.60 0.65 0.69 0 71 0 73
1 00 0.67 0.75 O.BD 0.86 O.B9
1.25 0 70 0.82 0.89 1 00 1.05
1.50
1.75
2.00
2.75
;.5o
V.75
3 00
3.2S
3 50
3 )5
4 00
4 50
5.00
5 50

6 00

7 00

8 00
t 00
10 00
0.88 0.97 l.ll 1.19
0.91 1.02 1.20 1 30




















1.08 1.28 1 41
1.13 1.34 1.50


















1.38 1.57
1 42 1.63
1.45 1.67
1.48 1 71
1.50 1.75
1.52 1.78
I 81
1.85
1.88









0 71 0.93 l.lt 1 53 1.B9


25 30 35 40 45 50 L — . 50 75 80 85 90 100


D

0 74 0.75 fl 75 0.75 0.76 0 76 °'5 0-i°
0.91 093 0.94 096 0.96 096 l °-96 0'" 0'9' «•" °'»8 0'»8
1.09 1.12 1.13 1.14 1.14 1 15 J '-» l-«° '•« >•« '•" « 8S
1.25 1.28 1 31 1.34 L35 1 36 J J-" 2.49 2-52 2.54 2.56 2.60
1 39 1.45 1 49 1.52 1 55 1.57 4 2.71 3.04 3.08 3.12 3.16 3.24
1.5 1.57 1.62 1.66 1 70 1 72 5 3.02 3.49 3.55 3.61 3.67 3.78
1.69 1.69 1.76 1.81 1.84 1.86 6 3.23 3.85 3.93 4.00 4. OB 4.23
1.69 1.79 1.87 1.9« 1.99 2.02 7 3.43 4.14 4.23 4.33 4.42 4.62
1.76 1.88 1.98 2 O5 2.12 2 IB g 3.56 4.33 4.49 4.61 4.72 4.95
1.83 1.97 2 08 2.16 2.23 2.29 9 ,.66 4.5, 4.70 4.82 4.« 5.23
1.88 2 04 2.16 2 26 ! 35 2.«2 lo J-74 4 „ 4-8, 5-{M j.,8 5.47
1 93 2.11 2.24 2.35 2.45 2.54 12 5
1.97 2.17 2.31 2.44 2.54 2.64 (J
2.02 2.22 2 37 2.51 2.62 2.71 ^ ^
2.08 2.31 2.50 2.63 2.76 2.87
2.15 2.38 2 58 2.75 2.89 3.02
2.20 2 43 2.65 2 84 3 00 3.15
30
2.48 2.70 2 92 3.09 3.26
35
2.54 2 81 3 03 3.24 3 43
4O
2.57 2 85 3.13 3.35 3.56
12.89 3.18 3 43 3.66 *S
1 3.23 3.48 3.74 w
2 24 2 58 2.91 3.24 3 56 3.88 <>0
— ]

5.02 5.20 5.38 5.56 5.92
5.20 5.40 5.60 5.80 6 25
5.30 5.53 S.76 5.99 6.44
5.62 3.87 6.12 6.60
5.74 S.96 6.20 6.79










3B 5.38 5.76 6.00 6.26 6.82
150 200 250





0.99 0.99 0.99
1.00 1.92 1.94
2.72 2.70 2.83
3.46 3. SB 3.66
4.12 4.31 4.43
4.70 4.97 5.15
5.22 5.57 S.Bl
5.68 6.13 6.43
6.09 6.63 7.00
6.45 7.09 7.53
7 20 8.06 8.68
7 77 8.84 9.64
8.20 9.47 10.4
8 54 9.97 11.1
B.99 10.7 12.1

9 27 11.3 12.9

9 44 11.6 13.4

11.8 13.8

12 0 13.8
12 1 14.3
14.6
9 55 12.2 14.7
Source:  Wesseling, 1973.

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                                                      Impermeable
Figure 2-3. Drains on Sloping  Impermeable Barriers
                                                       , JRB Associates _
                       12

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As in the previous equations, h     is the hydraulic head above the impervious
layer, but this  level does not occur midway between the drains.  Rather
it occurs at some point along the sloping impervious  layer.

     These drainage systems 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 meec 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 Mannings formula for pipes which is:
                                                                           (7)
where:

                Q  = 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 k of the diameter of a full
                    flowing pipe
                i = hydraulic gradient (dimensionless )
                n = roughness coefficient (dimensionless).
                                     _____^______^__— JRB Associates _
                                      13

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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 non-silting water velocity within the pipe,
but is less than the velocity which will cause turbulent flow.  Past ex-
perience has shown that non-silting velocities are about 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 some where between the two extremes.

2.2.2  Discharge (Q)

     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.
                                      _^-^— JRB Associates _
                                      14

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TABLE 2-2  MINIMUM HYDRAULIC  GRADIENTS FOR CLOSED PIPES
       Pipe Diameter                    Grade

      Inches       Cm                     Z

        4         10.2                   0-10


        5         12.7                   0.07


        6         15.2                   0.05
 Scource:   Soil  Conservation Service, 1973
                       ______^______—^^-^— JRB Associates _
                        15

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          TABLE 2-3.   DRAIN GRADES FOR SELECTED CRITICAL  VELOCITIES
Drain Size
Inches
1.4 fp8(1) 3.5 fps
VELOCITY
5.0 fps 6.0 fps
7.0 fps 9.0 fps
                           Grade - feec per 100  feet

                        For drains with "n" - 0.011
Clay Tile, Concrete Tile,
4
5
6
8
10
12

Clay Tile,
4
5
6
B
10
12

.28
.21
.17
.11
.08
.07

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

2.5
1.9
1.5
1.0
.8
.6
For drains
and Concrete Pipe (with good alignment)
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

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
(D—Feet per second
(2)—"n" is the roughness coefficient

Source:  Soil Conservation Service, 1973.
                                    ________________ JRB Associates _
                                     16

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     Lateral Flow  in

     Surrounding Material
                                       Lateral  Flow  in  Waste
Radial Flow from Below Site
30
09
                                           Figure 2-4.  Flow Components to a Landfill

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     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 percolation that can
recharge the water table between the lines of drains.  This flow must
be removed to maintain steady stae conditions.  A simple water balance
equation is as follows:

        q  = P-RO-ST-ET
         P                                                                 (8)
        where:

          q  = percolation rate: amount of water that must be removed
               by the drainage system (m/day)
           P = precipitation (m/day)
          RO = surface water runoff (m/day)
          ST = Change in soil moisture storage (m/day)
          ET = Evapotranspiration rate (m/day)

Once the percolation rate has been calculated, discharge can be obtained
by multipling the percolation rate by the drainage area (i.e. Q   (m /day)
                    2
= q  (m/day) Area (m )).

     When using the water balance method to calculate flow rates  or dis-
charges 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 moisture storage changes can be  significant as new refuse
        is placed into the landfill; once field capacity of the materials
        is attained the ST term can be considered zero
                                        ________^__^^_^^__—^_ JRB Associates —.
                                        18

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     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 broader the outermost drains.  This
flow component is not considered in the^drain spacing equations but could
signicantly affect the pipe sizing of the boarder  drain.  Discharge to
the boarder 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 boarder 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
from the equation:
              K(h2)x/2(Rd-b)
                                                                           (9)
where:
        Q_, = pipe discharge (m /day)
         Gl
          K = hydraulic conductivity (m/day)
          h = height of the water table above the drain (m)
          x = length of the drain (m)
         R. = distance of the drain's influence (m)
          d
          b = half the width of the drain and the trench (m),
In order to solve the equation, the value of R, must be known or estimted.
Typically the value of R, is estimated using an equation such as the Sichardt
(1940) equation:
        R. = 3(h)(K)°'5
         a
                                                                          (10)
                                      ______„.^— JRB Associates -_
                                       19

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[
1
4 T*n 	
v» J }
1 "
•
"X.
^~^^— ^\ r^ \,
"Xl I T 	
j-— 1-lJ
i U
p T 7i, , ,*, ;
v-zb I » J
1 ?
^t\x->x\v- \\o ^ — 1 — /.v \wv-^>.-:,-
Impervious Boundary H 4
i '
? "'
Rd-«»

\. FRAGMENT NO, 1
~Zj^^k£ ,
X^N^V/ V*v'//N>VX'-*''**X/N^'X'''''>'%V "*' | Nx
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     The quality of flow into fragment 2 can be estimated from the equation:

        Q_, = (K(H-D)x)/[(R./D)-(l/f)(log 0.5(sinh 1 /D)]
                                                                          (11)
where the new terms are:

        H = height of the 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 with drains above
an impermeable barrier the total discharge is the sum of QGI 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:
                                                                           (12)
     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 capa-
city.  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.
                                        ______^^_i^_ JRB Associates _
                                        21

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              DRAIN  CAPACITY CHART - n = 0.013

     «  «; «j   o
               HYDRAULIC GRADIENT (feet per- foot)
REFERENCE: Thit CMn was
d«v«iOD*d bv Guv •• Fa«k«n.
  U S. DEPARTMENT OF AGRICULTURE
  SOIL CONSERVATION SERVICE
ENGINEERING DIVISION - DRAINAGE SECTION
STANDARD DWG. NO.
tS • 7J1
SHEET 2 OF 3
DATI (-3-70
                   Figure 2-6.  Capacity  chart  -  n  =  0.013
Source:  Soil Conservation Service, 1973.
                                22
                                                                . JRB Associates _

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2.3  FILTERS AND EVELOPES

     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 per-
meability 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, whereas, filtering is best accomplished  by
fine materials, coarse materials are more appropriate for envelopes.

     As water approaches a subsurface drain, che flow velocity  increases
as a result of convergence towards  the  perforations or joints in the pipe.
This increase in velocity is accompanied by an increase in  hydraulic gradi-
ent.  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 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  entrace  resistance which can
cause the water  level to rise  above the drain.

     Although  filter and envelopes  have different  distinct  functions,
it  is possible  to  meet  the  requirements of  both  a  filter  and an envelope
                                                                      . JRB Associates —

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by using well graded sands and gravels.   The  specifications  for granular
filters, however, are more rigid than 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 (SCS,  1971).

2.3.2  Design of Sand and Gravel Filters

     Detailed design procedures are available for both gravel and sand
envelopes.  SCS (1971) 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 evelope.  The separate SCS design criteria will be considered below
for the following reasons:

     o  Site specific condtions 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 co use a fabric filter with a gravel envelope.

     The approach recommended by SCS is first to determine whether the
drainage system needs a  filter and second to determine the need  for an
envelope.  Generally, this sequence is performed because a well graded
filter can also  function as an envelope.

     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:

        50percent grain  size of  the filter _ .„  to 55
        50 percent grain  size of the base
                                      _^_____—._________^_— JRB Associates __
                                       24

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         15  percent  grain size  oE  the  filter _  11  ro  40
         15  percent  grain size  of  the  base

 Multiplying the  50  percent  grain  size of  the base material  by 12 and 58
 gives  the  limits the  50 percent grain size of  the filter should fall within.
 Multiplying the  15  percent  grain  size of  the base material  by 12 and 40
 gives  the  limits the  15 percent grain size of  the filter should fall within.

     All of the  filter material should pass the 1.5  inch sieve, 90 percent
 of  the material  should pass the 0.75-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 Prain size =
         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 on-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).
 2.3.3  Design of Sand and Gravel Envelopes

      The  first requirement of sar.d and gravel envelopes is that the en-
 velope 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.
__„,_._^— JRB Associates __
                                       25

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     The optimum thickness of envelope materials has been a subject of
considerable debate.  Theoretically, by increasing the diameter of the
pipe, the 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. 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:

        P85 (85% pore size of the filter fabric)	 <
        D85 (85% grain size of the subgrade material)

     or PB85 < 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, 1981).
                                      _________________________—. JRB Associates -_
                                       26

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                         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.   This site is
presented in Figure 3-1.  Table 3-1 presents some of the typical ranges
of values that may be encountered at a site. 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 drawndown  to drain
         level
     o  Groundwater system is at equilibrium  (steady state)  conditions
     o  Groundwater pressures in the underlying aquifer do  not  affect
        groundwater movement  into the bottom of the  pit
                                     _^______________^—. JRB Associates —
                                      27

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KJ
00
                             Landfill Material
           Recompacted
              Clay
Original Water
    Table
           PVC Pipe
              in  pea  gravel
                                          Base  Grade
                                              1%
                                                                         Final  Clay Cover
                                                            Clay (10 5<:K2slO~7)
                                                                                                                 V    	
   3)
   00
      1"=250*  horizontal
      l"=25'  vertical
                                                            Dolomite
                                       Figure 3-1.  Hypothetical Zone of Saturation  Landfill

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                 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 space


Hydraulic Data

   o  Depth to water  table

   o  Permeability of:
         Clay  till
         Refuse
         Compacted  clay

   o  Drain diameters

   o  Gradient  of  base
20 to 30 feet average up to
60 feet

3 to 5 feet
5 feet average


20 to 30 feet minimum usually
greater than 50 feet

200 to 400 feet
 10  feet average


 10"5  to 10 "7  cm/sec
 10"2  to 10"5  on/sec
 >  10~7cm/sec

 A  to  6  inches

 1  % average
                                                                    , JRB Associates —
                                     29

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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 assumption are invalid.

3.2  SENSITIVITY ANALYSIS

     Sensitivity analyses were performed on the drain equations for:

     o  Drains on impermeable barriers
     o  Drains on sloping impermeable barriers
     o  Drains above impermeable 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 Impermeable Barriers

     The equations for drains placed on an impermeable barrier is (Equation
1, Chapter 2):
        L =
                                                                           (2)

When using this equation, a barrier is usually considered impermeable
if the barrier material has a permeability (K_) less than 0.1 of the over-
lying material (K ) such that K,/K2 is less than or equal to 0.1. This
situation typically occurs in landfills that have recompacted clay bases.

     Table 3-2 presents the results obtained when equation 2 is solved
for drain spacing (L) using various values of flow rates (q), head mainte-
nance levels (h), and hydraulic conductivities (K ) of the landfill materi-
al.  A log-log plot of drain length versus flow rate for four hydraulic
conductivities (holding the head level constant at one meter) is shown
in Figure 3-2.  Table 3-2 and Figure 3-2 show how the proper drain spacing
                                     ______________-—— JRB Associates _
                                      30

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                      TABLE 3-2.  DRAIN LENGTH SPACING (m) FOR DRAINS ON AN IMPERMEABLE BARRIER

q
(./day)


0.5
0.01
O.OOS

0.001
0 0005

0.0001

0 00(105



.


h-2
B|


k-l(,
i) h-0.5(.)
K(»/sic)
io"2 10° io'* io"s
	 i
157 [ 50 '6 5
353 1 III 35 II
1 	 .
49> 157 | SO 16
I
1115 353 ! Ill 35
I. 	 ,
1577 499 157 ! 50
1
3527 1115 353 j III
1 	
4989 1577 499 157
Isobar equal to
io"2 io"3 io"* io"5

1 105
L
235 '
333 |
L
744
1052

2352
—
3328
122 (eters

33
74
105

235 j
333 1
L.
744

1052
|400 ft

II
23
33

74
105
_ _
235

333
,,

3
7
II

23
33
-|
1 '*

1 105
•ainui
,0"' ,B"3
1
1 52 17
j 118 37
166 | 52
1
,0"*

s
12
17

371 1 118 37
L--,
525 166

1174 371

1661 525
L for theoretical
1 52
1
1 118
1 	
166
lite
io"s

2
4
5

12
17

37
-1
1 52
L_

,o"2

26
59
83
	
186
263

588

831

,o"3

8
19
26
-\
1 59
1
1 83
1
1 186
1 	
263

10"* ID"* IO"2 IO"1 10"* IO"5

3 1
6 2
8 3

19 6

13 4 1 > 1
29 9 3 1
42 13 4 1

93 29 9 3
26 8 131 42 13 4
"- ~l
59 19 294 1 93 29 9
-j I
I 83 26 416 J 131 42 13
1 	 1 	 	

DO
00

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                                MO. 3-iOR-L:i5 DIETiUtw fiRAI'H
                                          LOGARITHMIC
                                       n nvrirs x s cvni.rn
[II, ,, ,,, tl Cl_,-r-._,l»AT,,JI
     IXAUF IN i' '. .\
10001
                                         3  4  567891
                                                                 3  4  S  6 7 8 9 1
                                                                                          3   4  S 6 7 891
                                                                                                              2    3  4 5678
                    0.00005  0.0001      0.0005     .001            0.005    0.01

                                                              (q(m/day)

                         Figure 3-2.   Drain Length versus Flow Rates for  Head Levels  Equal to 1-meter

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(L) is directly related to head maintenance levels (h), inversely related
to the square root of the leachate generation rate (q), and directly related
to the square root of the landfill permeability (K ).

     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 hardest
to determine with precision.  Head maintenance levels are usually pre-
determined and therefore are not sensitive even though they potentially
can have the greatest affect on drain spacing.

     One apsect of the equation for drains on impermeable barriers that
is not readily apparent is  that this equation can also be used for determining
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 precision, which  is not the case with most landfill materials.
Table 3-2 can be used to demonstrate the use of the drain equation for
blanket design.  For example, if the leachate generation rate, q, is de-
termined to be 0.001 m/day, the landfill material has a hydraulic conductivi-
ty, K  of 10~  cm/sec, and  the maximum head  levels are chosen to be 4
meters, the drain spacing required would be  23 meters.  By installing
a drainage blanket with a depth of 0.5 meter (i.e., also maximum height
                                                _2
of head levels) and hydraulic conductivity of 10   cm/sec the drain spacing
can be increased to 93 meters.  Installing a drainage  blanket not only
allows for spacing drains further apart but  also reduces the head pressures
on the confining layer or compacted base.  Reducing  these head  levels
minimizes the possibility for contaminant  release from the landfill especially
if the landfill is above  the water table.

     Table 3-2 also shows the combination  of flow rates, hydraulic conduc-
tivities, and head maintenance  levels  that yield drain spacings  that are
equal to or less than the maximum spacing  used in the  theoretical site
(i.e., 400 ft).  Generally, when  flow  rates  are  large  and hydraulic conduc-
tivities are  low, the theoretical upper limit of ^00-feet on drain spacing
                                     ^^________^_^— JRB Associates _
                                      33

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is coo 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
            = (c°-5/2h)[(tan2a/c) + 1 - ( tano/c) (tan2a+c)0- 5]
by:
                                                                            (6
where:
                c =
As discussed in the previous section, the underlying drain material is
typically considered impermeable if  its permeability  is 0.1 of the permea
bility of the overlying material.  This situation is typical of landfills
that have compacted clay bases.

     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, a, and directly related
to c = q/K..  Generally, the greatest decrease in h/L occurs when the
barrier angle, a, increases from zero to five degrees (i.e., 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 affect 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
                                     __^_________^——— JRB Associates —
                                      34

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                             TABLE 3-3  VALUES OF h/L  FOR VARIOUS C=q/K, AND ANGLES a
c=q/K1
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
30

00
S
in

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    0.02 •
Figure 3-3.  Plot of h/L versus  I=tar. a for
             drain and  sloping imnervious layers
             (Moore, 1980)
                                                     . JRB Associates __
                       36

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Table 3-4 presents the results of this analysis, and Figure 3-4 shows
a plot of drain length versus c = q/!^ for barrier angles of 0 ,  1  and
5°.  This data shows that if h is held constant, barrier angle,a, 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 permea-
bilities).

     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 KI for the permeability
of the drain blanket.  For example, a landfill without a drainage blanket
has the following parameters: q = 0.0005 m/day, Kj = 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 KI = 0.864
m/day (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 subtantial 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.

3.2.3  Drains Above an Impervious Barrier

     The governing equation for a drain system above an impervious barrier
 is:
        L =  [(8K2dh-t-4K1h2)/q]°'5
                                                                            (3)
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.
                                      ___^__—_——. JRB Associates _
                                      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
                               ^_^__.^^_________^— JRB Associates _
                                38

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                 n-itiF i :v. oirrrnrN i:r»Ar»H r

                       i nt: API 11 iMtr:

                     < f • ' •! i -• •• • c> ni r •-.
                                                                                               3	4  5  67891
                                                                                                 ~"
5.787(10
5.787(10  3)
5.787(10  2)
5.787(10~1)
                                                                                                     5.787
                                           c=q/K
                                                 I
                                                                       o   , o
      Figure 3-4.  Drain Length  (L)  versus c=q/K1  for a equal to fl  ,  1  ,  and  5  .

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     Solutions to che equation are shown in Table 3-5 for a head level
(h) of two meters, a permeability (K ) of the landfill material of 0.00864
                c                   •*•
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 (K2).  These
presentations show that when the permeabilities of the overlying (Kj)
and the underlying (K,) material are the same, the drain spacing (L) in-
creases.  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 (Kj) is an order
of magnitude (0.1) less than the overlying material (Kj), 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 impact the results of the drain
spacing equation.  Consequently, the "rule of thumb"  for designing drains
is that if  the underlying layer has a permeability of 0.1 of 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
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 istropic,
(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 situations,  the Wong (1977) model  can be used
to predict  releases.
                                     ____^^_^______— JRB Associates _
                                      40

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TABLE 3-5  DRAIN SPACING (m)  FOR DRAINS ABOVE  AN  IMPERMEABLE
           BARRIER (h=2m,  1^=0.00864 m/day  (10-5cm/sec) , D=30.4m)
q
(m/day)
0.05
0.01
0.005
0.001
0.0005
0.0001
0.00005

ID'5
2
5
7
19
31
114
212

io-6
2
4
5
12
18
43
64
K2 (cm/ sec)
io-7
2
4
5
12
17
37
52

Impermeable
2
4
5
12
17
37
52
                             ________________________ JRB Associates __

                             41

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                       itif r/nrN t;i.*Ai'n I-AIII--
                      I [ 11 : A M ( » M M 11 :
                        I • . '. I . I -I I •.
                                                                                             3  4967891
0.0005 0.0001
0.0005  0.001
0.005     0.01
0.05
             Figure 3-5.   Drain Snaring  (I.)  versus Inflow  rates (n) where
                           li=2 meters and K  = ]0~^ cm/sec.

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3.3.1  Parameter Estimation

     In order Co ucilize the drain spacing equations, the input parameters
must be known with some accuracy.  The two parameters that are the hardest
to obtain accurate estimates of are leachate generation rates, q, and
hydraulic conductivities, K.  Head maintenance levels, h, and barrier
slope angles.o, 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, unseasonally 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 tend to create discrete cells.  Waste mixtures
tend to cause the landfill to be very heterogeneous and anisotropoic making
estimations of permeabilities difficult.  Here as before, the hydraulic
conductivity selected should be the lowest conductivity for the waste
materials.  The problems associated with daily cover can be minimized
if the cover is removed each day, allowing old and new fill materials
to be hydrologically connected.

     The use of drainage blankets in a landfill effectively eliminates
the problem associated with determining conductivities.  Hydraulic conduc-
tivities for the drainage blanket can be determined easily in the lab
and most blanket materials are 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
                                      ^__—— JRB Associates _
                                       43

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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.

3.3.2  Landfill Size

     The limits of depth, width, and length of a landfill in the zone
of saturation appeared to be of concern when landfills are designed.
Technically a landfill is not depth limited in a zone of saturation setting
because theory shows that the lower the base grade of the fill the higher
the hydraulic gradients will be into the site.  These higher gradients
will result in larger quantities of groundwater that must be removed from
the site.  Problems can arise, however, if the base grades are extended
deep enough to cause quick conditions  in the base or if the base intercepts
an aquifer that has a lower head level than the overlying aquifer.  If
quick conditions occur, extensive dewatering may be necessary to maintain
a stable base.  If the base extends into an underlying aquifer with a
lower head level, contamination of the aquifer is likely when the pit
is filled.  The areal extent of the landfill is generally not considered
limiting if the drainage system is functioning properly.

3.3.3  Example Problem

     An example of the use of the drain equations for the hypotetical
site developed in Section 3.2   is present 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 0.01 of the fill material.  Solving
equation 6 for drain spacing  (L):

         = (c°'5/2h)[(tan2a/c)  + 1 -  (tana/c)(tan2a+c)0-5]
                                      ___^- JRB Associates —
                                      44

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             TABLE 3-6  EXAMPLE DATA SET
 Parameter
                                        Value
Cell Dimensions

 o Width
 o Length
 o Depth
Clay Thickness Below Base


Hydraulic Conductivities

 o Fill (K.)
 o Clay

   - compacted or natural


Base Grade


Water Table  (b.l.s.)


Head Maintenance Levels
1000 ft (304m)
1000 ft (304m)
  30 ft (9.1m)
  50 ft (15.2m)




10"5 cm/sec (0.00864 m/day)

10~7 cm/sec (0.0000864 m/day)




1% (0.6 degrees)


10 ft  (3.0m)


10 ft  (3.0m)
Inflow  (q) From  Percolation   10 in/yr (0.0007 m/day)
                                                     . JRB Associates —
                        45

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where:
                c = q/K1
                  = 0.0007(m/day)/0.00864(m/day)
                  = 0.08102

     1/L = (0.08102°'5/2(3.0))[(can20.6/0.08102)+l-(tan 0.6/0.08102)
           (tan20.6+0.008l02)°<5]
     1/L = (0.04744)[(0.00135)+1-(0.12926)(0.28483)]
     1/L = 0.0458
     1/L = 21.85m(71.89 ft)

The value obtained for drain spacing using these parameters is significantly
less than the currently specified allowable upper  limit (i.e., 200  to
400 ft).  This solution would not be considered conservative  for an actual
site if (1) conductivities of the fill were not a  uniform 10~  cm/sec,
(2) inflow rates were higher than expected such as when the site is not
capped, and (3) materials with high water content  are  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:
where q,  inflow,  is 0.0007 m/day and A, area,  is  22m  x  30'rr  (drain  spacing
times length)

        Q =  (0.0007 m/day)(22m)(304m)
           =  4.7  m3/day  (0.002  ft3/sec)

Using Figure  2-5  for plastic  pipes with a  roughness coefficient  of  n  =
0.013 and a design velocity of  1.4 ft/sec,  a  4-inch drian  pipe  should
                                                                     . JRB Associates..
                                       46

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be sufficient to handle the discharge.  Total discharge from the main
header pipe is:
        QT = qA
           = (0.0007 m/day)(304m)(304m)
           = 64.7 m/day (0.03 ft3/sec or 1241 gal/day)

Using Figure 2-5 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 zone of saturation
landfill design criteria for 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 conditons

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
     o  Compliance with specified design criteria for slopes, and drain
        blanket thickness and gradation
                                      _^^——— JRB Associates __
                                      47

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     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 weakeness
and cracks throughout the layer which can easily transmit leachate out
of the cell.  Construction inspections can be used to 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 would 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 would ensure proper construction.
Inspections should also be performed during the placement of drain blanket
to ensure adequate blanket thickness and proper gradiation 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
                                     _^— JRB Associates _
                                      48

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for adequate access to the drain system components both for inspections
and cleanings.  Regular maintenance inspections should be 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.A.3  Future Operating Conditions

     Landfill designs should anticipate and account for the type of waste
disposal operations planned.  As mentioned previously, 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 should be adjusted accordingly.

     For zone of saturation landfills the total quantity of water that
must be extracted can vary widely.  Waters can be derived from percolating
rainfall, groundwater intrusion, and from sludges or liquids brought into
the site.  Underestimating the amount of water that must be removed will
result in rising interval head levels and the eventual release of generated
leachate.  Therefore, care must be exercised to ensure that design water
removal capacities realistically represent the eventual landfill operations.
                                                                     .JRB Associates —
                                      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 ircompressibility and laminar
Darcian flow.  Consideration of site conditions at each of the three
landfills being studied 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




YTILL
C 4

\
n
V


K=s1 x 10"^ cm sec"
' *
o n '
S
DRAINS

-1

0 C



v
1



1
_ jL




1« 70 -80 FEE1
~KH«1x10~3emsec~l

 Kv«2x10~7emsec~1
    DOLOMITE,
                                               h*50-75FEET
/   /
                            /
/   /    /    /          t
/    /   /     /    /    /
      /   /   /    /    /-
                                                        20 40  60 FEET
                                                                           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.
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:

   R^ =V	  where L = length of landfill
                     W = width of landfill
    Values of L and W were chosen equal to 300 ft. so that Ry = 169 ft.
   R  = CahY	~  where C = a constant ranging from l.S to 3
    o        in
                        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  = 19 feet.
                                  o
    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 factor used is ylty/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.  This convention
has been attempted in these sketches, but some variances were allowed to
arrive at reasonable figures without an undue expenditure of time.
    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 = ffK(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
                        rw= effective radius of "well" = 169 feet
                        K = hydraulic conductivity in ft-sec~  =
                            3.3 x 10~7
              _2
    = 1.4 x 10   cfs (about 6 gpm)
    However, this formula assumes that the radius of the well is small
(not the case here) so that inflow through the landfill floor has been
underestimated.  This may be estimated by:
    Q = K iA      where K  = vertical hydraulic conductivity
                           = 6.6 x 10~9 ft sec -1
                        i  = hydraulic gradient = 10
                                                     2
                        A  = surface area = 90,000 ft
      = 5.9 x 10~  cfs (about 2.7 gpm)
                                      53

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                                 LANDFILL CELL
                        300 FEET •
                                               AQUIFER ACTS AS LINE SOURCE
                                              ' OF SEEPAGE BEYOND THESE LINES
FIGURE 4-2. INFLOW WITH TYPICAL LANDFILL CELL (PLAN VIEW)
                          54

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These values are for a 10 - foot head difference and would be reduced by
about half if the head difference were reduced to 5 feet.
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 leackage 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
                                      55

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       A)  LEACHATE LEVEL AT (H-h)





                           t
      (I)  LEACHATE LEVEL AT (H-1)
      C)  LEACHATE LEVEL AT (H-Jh)
                                                SCALE:
                                                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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         TWO CORNER DRAINS
      B)  THREE DRAINS
        r
~i
       C) SIX DRAINS
                               \J-\.
FIGURE 4-5.  FLOW NETS WITH DIFFERENT NUMBERS OF DRAINS
                         58

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maintenance level is set at the base of the fill, the amount of inflow in
relation to excavation depth varies as follows:

          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—the release rate models and
the solute transport models.  Typically estimates of leachate quantity
and quality released from a site are obtained from a release rate model
and 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 indepth 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 this source term can a solute transport model be performed.
This section briefly describes the theory behind release rate models and
present 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 cocentra-
tions 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.

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
                                                                       lpn Associates —
                                       60

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chat 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 instrusion.  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's work for applicacion to other cypes of wasce
disposal sices.  Basically, water balances numerically partition the amount
of fluid moving inco, around, and through che cap of a land disposal facility
utilizing che equation:

Perc   =  P - RO - ST - ET

where:

Perc   =  percolation race; che portion of precipitation which infilcrates
          che surface and is noc caken up by plants or evaporaced
    P  =  precipitation race
   RO  =  surface wacer runoff; che portion of the precipitation which
          does noc infilcraCe inCo  che ground buc instead moves overland
          away from Che site
   ST  =  change  in soil moisture storage
   ET  =  Actual evapocranspiration; the combined amount of wacer recurned
          Co  che acmosphere chrough direct evaporacion from surfaces and
          vegetative transpiration.

     Values for the parameters needed for such an analysis can be found
in a variety  of sources or estimated using a variety of  techniques.  Pre-
cipitation values for a given locacion are available from a number  of
sources including che Nacional Weacher Service.  Runoff  is very sice specific
and difficult co measure.  Most release rate models use  one of the  following
methods Co estimate runoff:
                                     _„._^______^___^^^-_^ JRB Associates _
                                      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


Evapotranspiration



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 flucuations

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
                                                                  .JRB Associates—.
                                    62

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     o  Rational Formula—utilizes empirical runoff coefficients based
        on vegetative type, soil type, and slope

     o  SCS Curve Numbers—utilizes empirical coefficients which relate
        runoff to soil type, land use, management practices, and daily
        rainfall

     o  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.  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 tempera-
ture, 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 flexi-
bility.  Some methods allow multiple clay-synthetic liners, others only
clay liners, while still another can only be applied to open sites without
covers.  Cover vegetation, slope, countour, and soil properties can also
be set 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:
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     o  Approximate methods (utilizing correction factors)  derived from
        the Boussinesq equation for lateral saturated flow

     o  Empirical methods development by Moore (i960) 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.

     o  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:

     o  Darcy's Law for saturated conditions which relate 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

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

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

     o  Darcy's Law with provisions  to  arbritrarily  increase  liner  permea-
        bility  assuming  that  certain  events occur (e.g., burrowing  animals
        or equipment breech of  the  liner)
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     o  Prediction of unsaturated flow driven by capillary forces utilizing
        the Greem-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 fails completely (i.e., after 20 years the
        model treats the faciity 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
percolating into 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 1007. of the maximum potential amount, 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.
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5.1.1.2  Leachate Constituent Concentrations

     For a release rate model to be useful, not only must the quantity
of leachate produced be estimated but also the quality (i.e., leachate
constituent concentrations).  The quantitative simulation of the processes
and interactions occurring within a landfill to produce leachate would
be very complex, and therefore most available models do not attempt to
simulate all these processes.  Table 5-2 lists some of the factors affecting
leachace constituent concentrations that would have to be considered.

     Because of the complex interdependent interactions occurring within
a disposal site and the lack of knowledge needed to characterize the interac-
tions, 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:

     o  Constituents are at the saturation solubility concentration levels
        in leachate

     o  Constituents exist at equilibrium concentrations between the aqueous
        and sorbed phases

     o  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.
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       TABLE 5-2  FACTORS AFFECTING LEACHATE CONSTITUENT CONCENTRATIONS
   Major Components
Waste Composition
Physicochemical
Properties
Contact Time
Chemical Reactions
and Interactions
Chemical Reactions
and Interactions
(continued)
 Facility  Age
   Primary Factors
                                                           Secondary Factors
Volume
Constituents
Constituent
Concentrations

Solubility


Mobility


Persistence
                          Volatilization
Phase/State

Conditions of Waste
Environment
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

1'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; complexation
state; concentration and type of
reducing agents: pH: temperature

Solar radiation; transmissivity ot
water; presence of sensitizens and
quenchers

Microbial peculation; soil moisture
content; temoerature; pH, oxvgen
concentration, redox potential
                                                    oh:  temoerature;  removal  of most
                                                    soluble  constituents
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                TABLE 5-3  FACTORS AFFECTING LEACHATE RELEASE
  Major Components
   Primary Factors
                                                           Secondarv  Factors
Synthetic Liners
Physical Factors
                          Chemical Factors
Clay Liners
                          Leachate Collection
                          Phvsicochemical Factors
                          Chemical Factors
                          Physical Factors
                          Biological Factors
                          Leachate 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 imorooer
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-
bilitv: nature soil chemistry; pH,
temperature

Efficiency, maintenance; design

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

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

Internal loading stresses; dehydration;
hvdrogeology; weathering; erosion:
bathtub effect; aging; impingment
rate; hvdraulic head: structural and
design considerations (e.g., proper
siting and design to handle
differential suosidence

Microoial population; burrowing
animals: deep  root growth, human
activities

Efficiency; maintenance; design
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     Prediction of leachace releases involves the estimation of leachate
quantity escaping from the site over time, which is combined with constitu-
ent 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

DRAINMOD/DRAINFIL (Skaggs, 1982)

     DRAINMOD (1980) is a compouter 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 infilatration 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 approxi-
mate 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 depth,  surface
compaction, vegetation, depth of root zone,  hydraulic conductivity  (saturated
and unsaturated), and  pressure head.  Most of the data are  readily available,
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chough some difficulty in obtaining reliable unsaturated hydrualic conduc-
tivity and pressure head data may exist.  In addition, to simplify calcu-
lations the models assume:

     o  One-dimensional, saturated flow in the bottom liner

     o  Infiltration rates for uniform deep soils with constant initial
        water content are expressed in terms of cumulative infiltration
        alone, regardless of the rate of application

     o  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 constitutent concen-
trations, 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
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of water that will move through various landfill covers.  This model can
simulate daily, monthly, and annual values for runoff, percolation, tempera-
ture,  soil-water chatacteristics,  and 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 chracteristics 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
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released co 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:

     o  Horizontal flow through sand and gravel drain layers
     o  Vertical flow through low permeability clay liners
     o  Efficiencies of liner-drain layer systems
     o  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:

     o  Liquid routing diagram for the site
     o  Water balance for the site
     o  Slopes in the routing system
     o  Hydraulic conductivities
     o  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:

     o  Surface water runon has been intercepted and directed away from
        the site so that only the rainfall impinging directly on the landfill
        need be accounted for

     o  Proper precautions have been taken to prevent erosion of the cover
        soils which would degrade cover performance
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     o  Synchecic liners have been installed properly to ensure their
        integrity for design life.

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 i960.  The fund will provide for liability claims resulting
from failure of RCRA permitted sites after proper closure.  The analytical
approach involves:

     o  Assisting failure probabilities to facilities
     o  Determining environmental exposure
     o  Assessing damage potential
     o  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 configu-
rations.  The  components of the model consists of:

     o  Users  supplied inputs which characterize the site design and oper-
        ation, and identify the wastes placed within the  fill

     o  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

     o  A data base of climate, soils, and the geology of various regions
        of the U.S.
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     o  A base line analysis with which to set starting site conditions

     o  Water movement simulation which uses Monte Carlo simulation techniques
        to generate values for seepage velocity, effective porosity, disper-
        sion, 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.

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 (Pope-Reid Associates, 1982)

     The Leachate Travel Time Model (currently under development by Pope-Reid
Associates) combines several analytic 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
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Che 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 form landfills and surface
impoundments which will be incorporated into EPA's RCRA Risk/Cost Policy
Model Project (ICF Incorporated, Clement Associates, Inc., and SCS Engineers,
Inc., 1982).  The approach assumes that:

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

     o  Clay liners retain their integrity for longer than 100 years

     o  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

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

     o  Synergistic effects do not occur.

     The time required for leakage to appear beneath the bottom of a clay
liner is given by:

        t = Ttd2/4D
where:
        t = time to first appearance of leakage (sec)
        d = thickness of clay liner (cm)
                                                2
        D = linearized diffusivity constant, (cm /sec) asssumed to be
              5   2
            10  cm /sec.
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     The volume of leachate release over time is given by:

         q = Ks(dh/d)A(At)
where:

         q = volume of leachace released over time
        Ks = saturated permeability coefficient
         ,— = hydraulic gradient
        dz
         A = Area at base of faciity
        At = length of time over which leachate releases.

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 overtime in one- two-, or three-dimensions.
A brief discussion of the principles used in transport modeling and descrip-
tions of several transport models are contained in the following sections.

5.2.1  Fundamentals

     The transport models presented in this section are  all consider mathe-
matical models, rather than rating or ranking type models (e.g., 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
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equations, allowing solutions to be obtained by analytical methods (i.e.,
function of real variables).  Numerical models, on the other hand, approxi-
mate 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 con-
ditions.  The physical and chemical characteristics considered by chese
models include:

     o  Boundary Conditions—hydraulic head distributions, recharge and
        discharge points, locations and types of boundaries

     o  Material Constants—hydraulic conductivity, porosity, transmissivity,
        extent of hydrogeologic units

     o  Attenuation Mechanisms—adsorption-desorption, ion exchange, cotn-
        plexing, nuclear decay, ion filtration, gas generation, precipi-
        tation-dissolution, biodegradation, chemical degradation

     o  Hydrodynamic Dispersion—diffusion and dispersion (transversee
        and  longitudinal)

     o  Waste Constituent Concentration—initial and background concentra-
        tions, 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 is:
                3h      e 3h
                        * — +  w
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            Mass Transport
              Equations
             Mass  Balance
             for Chemical
               Species
                                 Transport
                                 Equation
Groundwater Flow
   Equations
     Water
   Momentum
    Balance
Figure 5-1.   Major Components  of Groundwater Transport Equation
             (after Mercer  and Faust,  1981)
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where:
     h = hydraulic head
     K = hydraulic conductivity
     S = storage coefficient
     W = volume flux per unit area (e.g., pumping or injection wells,
         infiltration, leakage)
     x = distance
     t = time
The Darcy equation is generally represented as:
     Vi°

where:

     V ° groundwater velocity
     n = porosity
     K • hydraulic conductivity


     The mass transport side of the model, which describes the concentration
of a chemical species in a flow pattern in general form is:


     3C      3 ,_      3C ,     3   .   .     C'W
     31  = 3x7 (DiJ  '  3ir} '  3T7  (CVi)  *  ~n— *  R

where :
     C1 = concentration of solute in the source or sink fluid
     C  = chemical species concentration
     D  • dispersion tensor (i.e., hydrodynamic dispersion)
     V  » ground water 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 eicher
type of model, a sensitivity analysis of model results can  be  performed
by varying the input  characteristics singularly or  in  combination.   One
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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 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 wich 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.
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     The numerical methods most commonly used co simulate groundwater
transport problems can be divided into four groups:  finite difference
(FD); finite element (FE); method of characteristics (MOC); and discrete
parcel random-walk (DPRW).  In each method, the governing equations (e.g.,
groundwater flow eauations) are solved by subdividing the entire problem
domain using a grid system of polygons.  Every block has assigned hydro-
geology properties (e.g., transmissivity) associated with it that define
the aquifer.  Accompanying each grid as 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 trans-
formed to integral form (functionals) and minimized to solve the dependant
variables.  The algebraic equations for each node point, derived by the
FD or FE methods, are then combined to 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 numeri-
cal 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 (MOC) 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 MOC 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 recal-
culated using summed particle concentrations at the new  locations.  The
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random-walk method varies from the MOC mechod 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 MOC method
is reportedly 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
from the other models, therefore, selection of a model should be based
on making the best use of available data given the desired output.

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 simulations.  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.
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PESTAN (Enfield. 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.

PLUME (Wagner, 1982)

     PLUME is a steady state analytical model developed at Oklahoma State
University to model contaminant transport in the saturated zone.  The
model 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 adsoption and degradation were ignored.

Leachate Plume Migration Prediction (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
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(i.e., radioaccive 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.

Cleary 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 constitu-
ents (i.e., without degradation).  The ten available models are:

     o  1-dimensional, mass transport; 1st type boundary conditions
     o  1-dimensional, mass transport; 3rd type boundary conditions

     o  2-dimensional, mass transport; strip boundary, finite width
     o  2-dimensional, mass transport; strip boundary, infinite width
     o  2-dimensional, mass transport; Gaussian source, infinite width
     o  3-dimensional, mass transport; patch source, finite dimensions
     o  3-dimensional, mass transport; 5 area Gaussian source
     o  2-dimensional, groundwater flow; infinite dimensions, recharge
        boundary
     o  2-dimensional, groundwater flow; finite dimensions, recharge boundary
     o  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 analytical transient, one-, two-, or three-dimensional computer
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model for escimating waste transport in both the unsaturated and saturated
zones.  The model is flexible, providing 450 options: 288 for the 3-dimension-
al case; 72 for the 2-dimensional case in the x-z plane; 72 for the 2-di-
mensional case in the x-y plane; and 18 for the 1-dimensional case in
the longitudinal direction.  AT123D models all of the following options:

     o  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)

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

     o  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)

     o  Modeling of radioactive wastes, chemicals, and head levels.

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., i960)

     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
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to encounced in groundwater.  The procedure developed involves two pares,
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 this study indicate that the
procedure 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.

5.2.2.2  Numerical Models

     The nine numerical models characterized in this section generally
address the following characteristics:

     o  Coupled saturated/unsaturated zones
     o  Primary porosity
     o  Heterogeneous, anisotropic aquifers
     o  Miscible constituents
     o  Dispersion
     o  Attenuation/degradation

     This group of models represents the most flexible approach to modeling
a wide range of hydrogeologic conditions and contaminant types because
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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-membered 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 Un-
saturated Flow) model for the unsaturated zone.  A computer package facili-
tates interpretation of results by providing graphic data displays. The
model has been used at the Hanford, Washington, site to predict tritium
concentrations.

CFEST/UNSAT1D (Battelle, 1982)

     CFEST (Coupled Fluid Energy and Solute Transport) predicts fluid
 pressure, temperature, and contaminant concentrations in saturated ground-
water 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 pharma-
ceutical chemical waste (organics).  Model documentation  is in preparation.
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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-un-
sacurated 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 (Yen, 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-unsaturaced 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.
Additionally, FEMWASTE 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,
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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, 1974)

     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 transmis-
sivity, 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).

SWIFF (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 analyt-
ically 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.
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Solute Transport/Groundwater Flow (Colder Associates, 1982)

     This model simulates che 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-unsacurated
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.

5.3  MODEL LIMITATIONS

     The following issues provide a context for the considering the limi-
tations inherent in the application of models  to evaluate or predict ground-
water problems:

     o  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.

     o  Models  should be verified against actual field observations to
        determine  how closely they simulate real world situations; verifica-
        tion should be performed  in the  actual hydrogeologic system to
        which the  model is going  to be applied.
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     o  Model accuracy may vary dramatically when models are applied to
        situations for which they have not been verified.

     o  Models presently do not simulate all the processes that control
        contaminant movement; the equations that describe attenuation
        and dispersion are especially weak

     o  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, and the model reliabiity becomes a function
        fo data accuracy, i.e., "garbage in-garbage out"

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

     Because of the complexity and limitations of models, assertions deter-
mined through the use of models should not be interpreted as actual values
but only as estimates.
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                              6.0   RECOMMENDATIONS

      Zone  of  saturation  landfills  are  by  nature  very  susceptible  to  contami-
 nant  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:

      o  Determine as  accurately as possible the  variables 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

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

      o  Design the landfill base  so that  it slopes toward the drains thus
         allowing for lower head maintenance levels and  quicker  leachate
         removal

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

      o  Select the proper drain  equation  for system design and  allow for
         a margin of error in the  results  obtained (i.e., design con-
         servatively)

      o  Design filters and evelopes for drain pipes that prevent  silting
         and allow for free flow of liquids

      o  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

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

     o  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

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

     o  Design leachate collection systems so that routine maintenance
        and inspections can be performed to adequately maintain flows

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

     o  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  incor-
porating the above recommendations into the original  landfill design  can
substantially reduce  the chances of  leachae  release.  However, unless
the designs are incorporated properly during construction, the system
will fail to meet its  intended purpose.
                                                                        IDP Associates.

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                               7.0.   BIBLIOGRAPHY

 7.1  BACKGROUND

 Fenn, D.G.  et al.  1975.   Use of  the  water  balance method  for predicting leachate
 generation  from solid waste disposal sites.  U.S.E.P.A.,  SW-168.

 Fungord,  A.A.  1971.   Pollution  of subsurface  water  by  sanitary  landfills.
 U.S.E.P.A.  Solid Waste Management Series,  SW-12.  Volume  1.  132  p.

 Fungord,  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.  35.   93 p.

 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 p.

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

 Hughes, G.M. et al.  1971.  Hydrogeology of solid waste disposal sites in
 NE Illinois, USGS SW-12d.

 LeRoux, E.F.  1957.  Geology and ground water resources of  Outagamie County.
 USGS Water Supply Paper 1421.

 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.

 Roudkivi, A.J. and R.A. Callander.   Analysis  of groundwacer flow.   John
 Wiley and Sons, N.Y.  214  p.

 Sherrill, M.G.  1978.  Geology  and  ground water in  Door  County,  Wisconsin,
 with emphasis on contamination  potential  in the Silurian Dolomite.  Geo-
 logical Survey Water  Supply  paper 2047.

 Soil Conservation Service.   1980.   Soil Survey of Winnebago County,
 Wisconsin,  U.S. Department  of Agriculture.

 Young, H.L.  and Balten, W.G.  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 p.


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7.2  DRAINS

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

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

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

Konet, 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, WI.

Moore, C.A. 1980.  Landfill and Surface Impoundment Performance Evaluation.
SW-869.  US Environmental Protection Agency, Office of Water and Waste Manage-
ment, 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.
684 p.

Sichardt, W. and W. Kyrieleis. 1940.  Grundwasserabenkungen bei Fundierungs-
arbeiten.   Berlin, Germany.

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

Van Schlifgaarde,  J.  1974.  Drainage  for Agriculture.  American Society of
Agronomy  17, Madison, Wisconsin.

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 Pine Drain-Design.
American  Society of  Agricultural Engineers.  Chicago,  Illinois, December  8-11.
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7.3.   MODELS

7.3.1.  Release Rate Models

All,  E.M., C.A. Moore, and I.L. Lee.  1982.  Statistical Analysis of Uncertain-
     ties 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, Cincinnaci, OH.  pp. 174-178.

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  Hexachloro-
      cyclopentadiene.  Proceedings  of  the  Eighth  Annual  Symposium.   Land  Dis-
      posal 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  Confernece Proceedings.

Dragun, James  and Charles  S.  Helling,  1982.   Soil and Clay Catalyzed Reaction:
      1.  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,  (unpblished
      paper)

Fenn,D.G.,  K.J.  Hanley,  and T.V.  Degeare.  1975.   Use  of che 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.
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Freeze, R.A. and J.A. Cherry.  1979.  Groundwacer.  Prentice-Hall,  Inc.,  Engle-
     wood Cliffs, N.J.

Fuller, W.H.  1982.  Methods for Conducting Soil Column Tests to Predict  Pollu-
     tion 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.  Laboatory
     and Field Studies of Factors in Predicting Site Specific Composition
     of Hazardous Waste Leachate.  Proceedings of the Eighth Annual Research
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Gibson, A.C., and P.G. Malone.  1982.  Verification of the U.S. EPA HSSWDS
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Giroud, J.P. and J.S. Goldstein.  1982.  Geomembrane Liner  Design.  Waste
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Glaubbinger, R.S., P.M. Kohn and R. Ramirez.   1979.  Love Canal Aftermath:
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Guerero, P. November  1982.   Personal Communication.

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Haxo,  H.E.  et al, September  1980.   Lining  of Waste  Impoundment  and Disposal
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Haxo,  H.E., Jr.   1981.  Testing  Materials  for  Use  in  the  Lining of Waste  Dis-
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Haxo,  H.E.   1982.   Effects on  Liner  Materials  of  Long-Term  Exposure  in Waste
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Huck,  P.J.   1982.   Assessment  of Time  Domain Reflectrometry and Acoustic  Emis-
     sion Monitoring;  Leak  Detection Systems  for  Landfill Liners.   Proceedings
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Hughes,  J.   1975.   Use of  Bentonite  as  a  Soil  Sealant  for Leachate Control
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Hung, Cheng Y., 1982.  A Model to Simulate Infiltration of Rainwater Through
     the Cover of a Radioactive Waste Trench Under Saturated and Unsatureated
     Conditions.  Draft submitted to AGU for the publication, "Role of the
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ICF Incorporated, Clement Associates, Inc., and SCS Engineers, Inc., 1982.
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JRB Associates, Inc.  1982.  Techniques for Evaluating Environmental Processes
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Kinman, Riley N., Janec I. Rickabaugh, James J. Walsh, and W. Gregory Vogt,
     1982.  Leachate from Co-Disposal of Municipal and Hazardous Waste in
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Krisel, W.J., Jr.  Editor.   1980.  CREAMS, a Field Scale Model for  Chemical
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Lentz, J.J.   1981.   Apportionment of Net  Recharge  in Landfill Covering Layer
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Lytnan, W.J.,  W.F. Reehl, and D.H. Rosenblatt, 1982.  Handbook of  Chemical
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Mingelgren, U. ec al., 1977.  A Possible Model for che Surface-induced Hydro-
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Mill, T.  1980.  Data Needed to Predict the Environmental Fate of Organic
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Montague, P.  1982.  Hazardous Waste Landfills:  Some Lessons from New Jersey.
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Moore, C.A.  September 1980.  Landfill and Surface Impoundment Performance
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Moore, C.A., and M. Roulier.  1982.  Evaluating Landfill Containment Capability.
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Moore, C.A., and E.M. All.  1982.   Permeability of Cracked Clay  Liners.  Pro-
     ceedings of the  Eighth Annual  Research  Symposium.  Land  Disposal  of Hazard-
     ous Wastes.  EPA-600/9-82-002; U.S. Environmental Protection Agency,
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Perrier, E.R., and  A.C. Gibson.  September  1980.  Hydrologic  Simulation  on
     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 Techni-
     ques  for Location Liner  Leaks.   Proceedings  of  the  Eighth  Annual  Research
     Symposium.  Land Disposal of Hazardous  Waste.   EPA-600/9-82-002;  U.S.
     Environmental  Protection Agency,   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  Eighth Annual  Research Symposium:
     Land  Disposal  of Hazardous  Wastes.   EPA-600/9-82-002;  U.S.  Environmental
     Protection  Agency, Cincinnati, OH.   pp. 360-371.

Pope-Reid  Associates, Inc.   1982.   Hazardous Waste  Landfill  Design,  Cost and
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Pricket"-,  T.A.   July  1982.   Personal  Communication.

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

Shuckrow,  Alan  J.  and Andrew P.  Pajak,  1982.  Studies on Leachate and Ground-
     water Treatment  at  Three Problem Sites.  Proceedings of che Eighth Annual
      Research Symposium:   Land Disposal of Hazardous Waste.  EPA-600/9-82-002;
      U.S.  Environmental  Protection Agency. Cincinnati,  OH.  pp.346-359.
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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 Protec-
     tion Agency, Cincinnati, OH.  pp. 224-238.

Silka, L.R., and T.L. Swearingen.  1978.  A Manual for Evaluating Contamination
     Potential of Surface Impoundments.  EPA 570/9-78-003; U.S. Environmental
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Skaggs, R.W.  1980.  Combination Surface-Subsurface Drainage System for Humid
     Regions.  Journal of the Irrigation and Drainage Division, ASCE, Vol.
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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 Caro-
     lina 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
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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.

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 Construc-
     tion for Pollution Migration Control.  EPA Contract No. 68-01-3113.

Stokes, W.L. and D.J. Vames.  1955.  Glossary of Selected Geologic Terms.
     Peerless Printing Co.  Denver, CO.

Thornthwaite, C.W., and J.R. Mather, 1955.  The Water Balance.  Centerton,
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Thornthwaite, C.W. and J.R. Mather, 1957.  Instructions and Tables for Computing
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Tolman, A.L., A.P. Ballescero, Jr., W.H. Beck, Jr., and G.H. Emrich.  1978.
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U.S. Evironmental Protection Agency, 1981.  Land Disposal of Hazardous Waste:
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U.S. Environmental Protection Agency.  June 1982.  Post-Closure Liability
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U.S. Evironmental Protection Agency, 1982.  Hazardous Waste Management System;
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Waller, Muriel Jennings and J.L. Davis, 1982.  Assessment of Techniques to
     Detect Liner Failings.  Proceedings  of the Eighth  Annual  Research Sympo-
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Weber, W.J., 1972.  PhyBiochemical Processes  for Water  Quality Control.  As
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Wong, J., 1977.  The Design of a System for Collecting  Leachate  from  a Lined
     Landfill Site.  Water Resources Research, v.  13, No.  2, p 404-410.  As
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 7.3.2.  Transport Models

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 Bachmat, Y., J. Bredehoeft, B. Andrews, D. Holtz and  S.  Sebastian.  1980.
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 Battelle; Pacific Northwest Laboratories.  1982.  Personal communication.


 Bibby, R.  1981.  Mass transport of solutes  in dual-porosity media.   Water
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 Bonazountas, M. and J. Wagner.  1981.  "SESOIL" A seasonal soil  compartment
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 Chang, S.,  K. Barrett, S.  Haus and  A. Plate.  1981.   Site ranking model  for
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Charbeneau, R.J.   1981.  Groundwater contamination  transport  with  adsorption
and ion exchange chemistry:  method of characteristics  for  case  without
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Chou, S.J., B.W. Fischer and R.A. Griffin.   1981.   Aqueous  chemistry  and
adsorbtion of hexachlorocyclopentadiene by  earth materials.   In  Proceedings
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and  numerical models  of  groundwater  flow.   Part 1.   Mathematical development.
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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:  Hazardous Waste.
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Duffy, J.J., E.  Peake and M.F.  Hohtadi.   1980.   Oil spills  on land as
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Enfield, C.G., R.F. Carsel,  S.Z.  Cohen,  T.  Phan  and D.M.  Walters.   1982.
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(unpublished paper).


Falco, J.W., L.A. Mulkey, R.R.  Swank,  R.E.  Lipcsei  and S.W.  Brown.   A
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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  sices.
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Fuller, W.H.  1982.  Methods  for  conducting soil  column tests  to predict
pollutant migration.   In Proceedings of  the Eighth  Annual Research  Symposium
on Land Disposal:  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, US EPA,
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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
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Gorelick, S.M. and I. Remson.  1982.  Optimal dynamic management of
groundwater pollutant sources.  Water Resources Research 18(1):71-76.


Grisak, G.E. and J.F. Pickens.  1980.  Solute transport through fractured
media.  1. The effect of matrix diffusion.  Water Resources Research
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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 Resources Division.  Denver CO.
USGS/WRI-77-49.


Haque, R.  1980.  Dynamic exposure and hazard  assessment of  toxic chemicals.
Ann Arbor  Science Publishers, Inc.  496 p.


Haxo, H.  Jr.,  S. Dakessian,  M. Fong, and  R. White.   1980.   Lining  of waste
impoundment and  disposal  facilities.  US  EPA, MERL,  Cincinnati, OH.


Intercom? 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.


JRB  Associates,  Inc.  1980.   Methodology  for  rating the hazard potential of
waste disposal sites.   JRB Associates,  Inc.,  McLean, VA.


Jury, W.A.  1982.   Simulation of solute transport using a transfer function
model.   Water Resources Research 18(2):363-368.


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.
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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.


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, TN.


LeGrand, H.E.  1980.  A standardized system for evaluating waste-disposal
sites.  National Water Well Association.  42 p.


LeGrand, H.E.  1964.  System for evaluation of contamination  potential of some
waste disposal sites.  Journal of  the American Water Works Association
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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.H. Faust.  1981.  Ground-water modeling.   National Water
Well Association.  60 p.


Moore, C.A.  1980.  Landfill and surface  impoundment performance  evaluation
manual.  US 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.
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Perrier, E.R. and A.C. Gibson.  1980.  Hydrologic simulation on solid waste
disposal sites (HSSWDS).  US EPA, MERL, ORD.  SW-868.  Ill p.


Pettyjohn, W.A., T.A. Priekett, D.C. Kent and H.E. LeGrand.  1981.  Prediction
of leachate plume migration.  In Proceedings of  the  Seventh Annual Research
Symposium on Land Disposal:  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  17(6):1701-1711.


Pickens, J.F. 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).


Pope-Reid Associates, Inc.  1982.  Technical review of groundwater models.
Office of Solid Waste, US EPA, Washington, D.C.  28 p.


Prickett, T.A.  1981.  Mathematical modeling techniques for groundwater
management.  In Proceeding and Recommendations of the Workshop on Groundwater
Problems in the Ohio River Basin, Cincinnati, Ohio.   April 28-29, 1981.
p. 97-104.


Prickett, T.A., T.G. Naymik and C.G. Lonnquist.  1981.  A "Random Walk"  solute
transport model for selected groundwater quality evaluations. Illinois State
Water Survey, Bulletin 65.


Rao, P.V., K.M. Portier and P.S.C. Rao.  1981.   A stochastic approach  for
describing connective-dispersive solute transport in  saturated porous media.
Water Resources Research  17(4):963-968.


Ross, B. and C.M. Koplik.  1978.  A statistical  approach to modeling transport
of pollutants in groundwater.  Journal of the International Association  for
Mathematical Geology 10(6):657-672.


Sagar, B. and A. Runcal.  1982.  Permeability of fractured rock:  effect of
fracture size and data uncertainties.  .Water Resources Research 18(2):266-274.


Science Applications, Inc.  1981.  System analysis of shallow land burial.
Science Applications, Inc., McLean, VA.  NUREG-CR-1963.
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 Schnoor,  J.L.   1981.   Assessment of the exposure, fate and persistence of
 toxic organic  chemicals to aquatic ecosystems in stream and lake environments.
 Lecture notes  for water quality assessment of toxic and conventional
 pollutants in  lakes and streams sponsored by US  EPA (R&O).  Arlington, VA.


 SCS Engineers,  Inc.  1982.  Release rate model.  Currently under development
 for EPA.


 Siefken,  O.L.  and R.J. Stanner.  1982.  NRC-funded studies on waste disposal
 in partially saturated media.   AGU Spring Meeting, 4 June 82.


 Silka, L.R.  and T.L.  Swearingen.  1978.  A manual for evaluating contamination
 potential of surface  impoundments.  US EPA, Groundwater Protection Branch.
 EPA 570/9-78-003.  73 p.


 Smith, L. and  F.W. Schwartz.  1980.  Mass transport.  1.  A stochastic
 analysis of macroscopic dispersion.  Water Resources Research 16(2):303-313.


 Smith, L. and  F. W. Schwartz.   1981.  Mass transport.  2.  Analysis of
 uncertainty in prediction.  Water Resources Research 17(2):351-369.


 Smith, L. and  F.W. Schwartz.  1981.  Mass transport.  3.  Role of  hydraulic
 conductivity data in  prediction.  Water Resources Research 17(5):1463-1479.


 Sykes, J.F., S. Soyupak and G.J. Farquhar.  1982.  Modeling of leachate
 organic migration and attenuation in groundwater below sanitary  landfills.
 Water Resources Research 18(1):135-145.


 Tang, D.H.,  E.G. Frind and E.A. Sudicky.  1981.  Contaminant transport in
 fractured porous media .'analytical solution for a single fracture.  Water
 Resources Research 17(3):555-564.


 Tang, D.H.,  F.W. Schwartz and L. Smith.  1982.   Stochastic modeling of mass
 transport in a random velocity field.  Water Resources Research  18(2):231-244.


 US EPA.  1982.   Post-closure liability trust fund model development.  Personal
 communication.


 Van Genuchten,  M.T.,  G.F. Finder and W.P. Saukin.   1977.  Modeling of leachate
 and soil interactions in an aquifer.  Proceedings of the  Third Annual
 Municipal Solid Waste Research Symposium on Management of Gas and  Leachate  in
 Landfills.  EPA-600/9-77-026.  p. 95-103.

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Wescon, R.F.  1978.  Pollution prediction techniques - a state-of-the-art
assessment.  US EPA, Office of Solid Waste.   EPA-513/684-8491.


Wilson, J.L. and L.W. Gelhan.  1981.  Analysis of longitudinal dispersion  in
unsaturated flow.   1.  The analytical method.  Water Resources Research
17(1):122-130.


Wilson, J.T., C.G.  Enfield, W.J.  Eunlap, R.L. Cosby,  D.A.  Foster  and  L.B.
Baskin.  1982.  Transport and  fate of selected organic pollutants  in'a sandy
soil.  US  EPA.  RSKERL.  Ada, Oklahoma,  (unpublished report).


Wyrick, G.G. and J.W. Borchers.   1982.  Hydrologic effects  of  stress-relief
fracturing  in an Appalachian Valley.  USGS  Hater Supply Paper  2177.


Yen, G.T.   1981.  AT123D:Analytical transient one-, two- and three-dimensional
simulation  of waste  transport  in  the aquifer  system.  Oak  Ridge National
Laboratory, Environmental Sciences  Division.  Publication  No.  1439.
ORNL-5601.  83 p.


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 Sciences  Division.  Publication  No.  1462,  ORNL-5601.
137 p.


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 Sciences  Division,  Publication No. 1370, ORNL-5567.
153 p.
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7.4   Flow Nets
Bennett, Robert R., 1962, Flow Net Analysis, in. Ferris, J.G., Knowles, D.B.,
Brown, R.M., and Stallman, R.W., 1962. Theory of Aquifer Tests:  U.S.
Geological Survey Water Supply Paper 1536-E, pp. 139-144.

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

Cedergren, Harry R., 1977, Seepage, Drainage, and Flow Nets  (Second Edition):
John Wiley and Sons, New York. 534 p.

Freeze, R.A., and Cherry, J.A., 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 Kaufman, R.I., 1962, Dewatering, JJL Leonards, G.A.  (ed.),
1962, Foundation Engineering:  McGraw-Hill, New York, pp. 241-350.

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