United States
                    Environmental Protection
                    Agency
Hazardous Waste Engineering
Research Laboratory
Cincinnati OH 45268
                    Research and Development
EPA/600/S2-87/049  Mar. 1988
AEPA         Project Summary
                    Verification  of the Lateral
                    Drainage Component of the
                    HELP  Model  Using  Physical
                    Models
                    P. R. Schroeder and R. L. Peyton
                     The study described was conducted
                    to verify the Hydrologic Evaluation of
                    Landfill Performance (HELP) computer
                    model using existing field data from a
                    total of 20 landfill cells at 7 sites in
                    the United States. Simulations using
                    the HELP model were run to compare
                    the predicted water balance with the
                    measured water balance. Comparisons
                    were made for runoff, evapotranspira-
                    tion, lateral  drainage to collection
                    systems and percolation through liners.
                    The report also presents a sensitivity
                    analysis of the  HELP model input
                    parameters.
                     This Project Summary was devel-
                    oped by EPA's Hazardous Waste Engi-
                    neering Research Laboratory, Cincin-
                    nati, OH, to announce key findings of
                    the research project that is fully doc-
                    umented in a separate report of the
                    same title (see Project Report ordering
                    information at back}.

                    Purpose  and Scope
                     This  study was conducted to test and
                    verify the liquid management technology
                    for lateral subsurface drainage in covers
                    and  leachate  collection systems. The
                    specific objective was to verify the lateral
                    drainage component of the Hydrologic
                    Evaluation of Landfill Performance
                    (HELP) Model and other regulatory and
                    technical  guidance, provisions and
                    procedures developed by the U.S. Envi-
                    ronmental Protection Agency (USEPA).
                     The HELP model is a computer model
                    that generates water budgets for a
                    landfill by performing a daily sequential
                    simulation  of water  movement  into,
                    through and out of the landfill. The model
                    produces estimates of depths of satura-
                    tion and volumes of runoff, evapotrans-
piration, lateral drainage, and percola-
tion. Lateral drainage is computed in the
model as a function of the average depth
of saturation above the liner, the slope
of the surface of the liner, the length to
the drainage collector, and the hydraulic
conductivity of the lateral drainage layer.
Therefore, to accomplish the objective of
this study, the lateral drainage rate was
measured  as a function of the hydraulic
conductivity, slope, length and depth of
saturation of the lateral drainage layer
in large-scale physical  models. The
measured  average depths of saturation,
drainage rates and drainage times in the
physical models were then  compared
with HELP model predictions and numer-
ical solutions of the Boussinesq equa-
tion,  which applies Darcy's  law to
unsteady, unconfined flow through
porous media.
  Two large-scale physical models of
landfill liner/drain systems were con-
structed and filled with a 3-foot (ft) sand
drain layer overlying a 1 -ft clay liner. A
2-inch (in.) layer of gravel was placed
under the  liner to collect seepage from
the clay. The models were instrumented
to measure the water table  profile,
subsurface lateral drainage rate, water
application, runoff and  percolation
through the liner. Evapotranspiration and
other water losses were estimated from
the water budget for each  test. The
models have adjustable slope,  ranging
from 2 to 10 percent in this study; and
different lengths, one being 26.5 ft and
the other being 53.5 ft.
  Several  drainage tests were  run on
each  configuration  of the  models by
applying water as rainfall to the surface
of the sand layer, and  then measuring
the water table along the length of the

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models and the lateral drainage rate as
a function of time. Lateral drainage rates
and water table profiles were measured
during periods of increasing, decreasing
and steady-state drainage rates. In these
drainage tests, two  drainage  lengths
were compared—25.4 ft  and 52.4 ft.
Three slopes were examined—approxi-
mately 2, 5 and 10 percent. Sands of two
hydraulic conductivities were used—4 x
10~3 centimeter/second (cm/sec) (fine
sand) and 2.2 x  10~1 cm/sec (coarse
sand) as measured in soil testing  per-
meameters.  Four rainfall  events were
examined—a 1-hour (hr) rainfall at 0.50
inches/hour  (in./hr),  a 2-hr rainfall at
1.50 in/hr, a 6-hr rainfall at 0.50 in./hr
and 24-hr rainfall at 0.125 in./hr. Also,
water was applied to the sand for a long
period of time (generally more than 36
hr) at a rainfall intensity  which would
maintain the average depth of saturation
in the sand at 12 in. In addition to these
drainage tests, the sand was saturated,
predominantly from the bottom  up for
several test conditions, and then allowed
to drain.  In total,  more than sixty tests
were performed.
  A complete block experimental design
was  used to examine  the effects of
drainage length, slope, hydraulic conduc-
tivity, depth of saturation, rainfall inten-
sity and rainfall duration on the lateral
subsurface drainage  rates. The  block
design was selected because it provided
the most data with the least time and
expense for construction and  model
preparation.  Several slopes and rainfall
events could  be examined quickly since
very little time was required for changing
these test conditions.  Also the time
requirements and costs for running an
additional test with a  different slope or
rainfall were less than 10 percent of the
requirements for preparing the model for
a different  sand. Additional  rainfall
events were  examined in lieu of repli-
cates since the lateral drainage rate as
computed by the  HELP model  does not
directly  consider the  effects of rainfall
intensity  or duration.  Also,  since  a
complete  block design  was  used, the
effect of a change in a  variable is directly
examined under multiple test conditions,
reducing the need for  replicates.

Results of Drainage Tests
  A comparison of profile shapes for the
depth of saturation along  the length of
the drainage layer indicates significant
differences   between   the   rising
saturated-depth profile  (during  filling)
and  the  falling saturated-depth profile
(during draining) for the same average
depth of saturation (y). The profiles are
steeper near the drain when filling than
when draining. The difference is greater
for higher infiltration rates. Steady-state
profiles are very similar to the profiles
for draining.
  The drainage rate for a given average
depth of saturation was greater during
the filling  portion of each  experiment
than during the draining portion. This is
consistent with  the  saturated-depth
profiles which show steeper hydraulic
gradients  near the drain for filling
conditions. Plots of drainage rates as a
function of average depth of saturation
also show that drainage continues after
y has essentially reached zero. This is
presumed to be drainage capillary water,
commonly called  delayed yield.  An
estimate of this capillary water volume
when y had just drained to 0 in.  based
on an analysis of the experimental data
is about 0.1 in. (cubic inches per square
inch) for the fine  sand and 0.3 in. for
the coarse sand.
  The drainage results indicated that the
drainable porosity of the sands decreased
with  increasing  depths of saturation
above  the clay liner.  In  addition,  the
drainable porosity at  all  depths was
considerably  smaller  than the  value
estimated from soil moisture data and
other soil  properties collected on  the
sands.  Low  drainable porosity  values
were obtained in part due to the delayed
yield and capillary effects that  results
from the high drainage rate. However,
the presence and vertical distribution of
entrapped  air  appear to  be  primarily
responsible for the low drainable poros-
ities and the change in drainable porosity
with height, although  no measurments
of entrapped air were collected.
   All parameters required to compute the
drainage  rate by the HELP  equation
except  the hydraulic conductivity were
measured for each drainage test. Due to
variable air entrapment and differences
in placement, compaction and prepara-
tion of the sand  drainage  media,  the
hydraulic conductivity measured  in a
permeameter in the soils testing labor-
atory differed significantly from  the
actual test values calculated from data
on drainage rates and depths of satura-
tion from the physical models. As des-
cribed in the documentation report for
the HELP  model, the lateral drainage
equation was developed to approximate
numerical solutions of the  Boussinesq
equation for one-dimensional, unsteady,
unconfined flow through porous media.
Therefore,   the   actual   hydraulic
conductivity for the drainage tests was
estimated by adjusting  its value while I
solving the Boussinesq equation until the
results matched the measured drainage
rates and saturated depths. The hydraulic
conductivity estimates  are summarized
in Appendix A. Determining the hydraulic
conductivity in this manner provided the
best estimate obtainable  for each test
since the  Boussinesq  solution  is  the
commonly accepted representation  of
the actual drainage process. Compari-
sons were made for both steady-state
drainage during rainfall and unsteady
drainage following cessation of rainfall.
  The computed hydraulic conductivity
values differed  significantly from  the
measured values. For steady-state drain-
age  from the fine  sand, the average
computed  value  was  only 8 percent
greater than the measured value, while
for unsteady drainage  the  average
computed value was about 150 percent
greater. For steady-state and unsteady
drainage  from the  coarse sand,  the
average  computed  value  was  respec-
tively 92 and 84 percent  less than the
measured value.  For both  sands,  the
average computed hydraulic conductivity
for unsteady drainage was twice as large
as the computed hydraulic conductivity
for steady-state drainage.
  In analyzing the computed hydraulic
conductivity values,  it was apparent that
hydraulic  conductivity  decreased  with
increasing y. This is consistent with the
earlier hypothesis that the volume of
entrapped air increased with increasing
distance  above the  clay liner. A larger.
volume  of  entrapped  air  decreases
drainable  porosity and cross-sectional
flow-through area,  thereby decreasing
hydraulic conductivity.
  The computed hydraulic conductivity
values varied considerably between tests
on the same sand, even  in the same
model without disturbing the placement
of the sand between tests. Considerable
variability occurred between tests having
exactly the same configuration of sand,
slope, length,  and depth of saturation,
where only the rainfall  intensity and
duration differed. This variance was
examined using an unequal three-way
analysis  of variance (ANOVA)  test to
determine  whether  the  computed
hydrualic conductivity was a function of
another variable besides average satu-
rated depth.
  The test variables used in the ANOVAs
included type of sand, average saturated
depth, slope,  drainage length,  rainfall
duration and rainfall intensity. No effects
of rainfall  duration and intensity could
be discerned by inspection; therefore, the

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initial ANOVAs were run using depth,
slope and length as the variables for data
sets containing  hydraulic conductivity
estimates  for one type of sand. These
ANOVAs indicated that the computed
hydraulic conductivity estimates for both
sands varied as a function of average
saturated  depth  and slope.  Additional
ANOVAs indicated that drainage length,
rainfall  intensity and duration did not
significantly contribute to the variance in
the computed hydraulic conductivity as
a  function  of  slope. Therefore,  the
variability  due to slope probably arises
from  inaccuracies in the  manner in
which the effects of slope are modeled
by the Boussinesq equation.

Verification of the HELP Model
  The drainage rates computed by the
HELP model was  compared  with  the
results of  the drainage tests in several
manners. The hydraulic conductivity that
was needed to yield  the measured
drainage rate for  the  same  drainage
length,  slope, and  average saturated
depth existing in the drainage test was
computed  for several times during each
test. This  hyudraulic  conductivity value
was compared with the value measured
in the soils testing laboratory and the
value estimated  using the Boussinesq
equation. If the HELP equation accurately
predicted  the  results of  the drainage
tests, the  hydraulic conductivity value
would agree  with the measured or
estimated  hydraulic conductivity value
for the sand. If the hydraulic conductivity
value was  greater than  the value
obtained for the sand, the HELP equation
underpredicted the lateral drainage rate.
Another method of comparison was to
examine the effects of changing a single
variable on the lateral  drainage  rate
measured  in the drainage tests and
predicted  by  the HELP  equation.  The
effects of drainage length, slope, average
depth of saturation, and the head  con-
tributed by the slope of the liner were
compared in this manner.
  The hydraulic conductivity of the sand
at various depths of saturation  was
estimated for each test using the Bous-
sinesq  solution of  Darcy's  law  for
unsteady,  unconfined flow through
porous  media and the HELP  lateral
drainage  equation.  These  hydraulic
conductivity values were compared to
determine  the agreement between  the
HELP model and the Boussinesq solu-
tion. For steady-state drainage, the HELP
model estimates of the hydraulic conduc-
tivity were 44 percent greater than the
Boussinesq solution estimates. This
result means that the  HELP model
underestimated the steady-state lateral
drainage rate  predicted by the Bous-
sinesq solution by 30 percent. The HELP
estimates were 31  percent greater than
the laboratory measurements for the fine
sand  and 88  percent less than the
laboratory measurements for the coarse
sand. For unsteady drainage, the HELP
model estimates were only 13 percent
greater  than the  Boussinesq  solution
estimates which would underpredict the
lateral drainage rate by 11  percent. The
closeness of the  estimates  was not
unexpected since the HELP lateral
drainage equation  was developed  from
numerical solutions of the Boussinesq
equation for saturated unconfined lateral
flow  through  porous  media under
unsteady drainage conditions.  The
underprediction of the cumulative lateral
drainage volume would be expected to
be very  small since the removal rate of
water from the drain layer by all other
means is much smaller than the lateral
drainage rate.  Consequently, the effect
of differences in the predicted and actual
drainage times are  small.
  The differences  between the labora-
tory measurement of the hydraulic
conductivity and  either  of  the  two
estimates computed from drainage data
were  much larger  than the differences
between the estimates. The HELP model
and Boussinesq equation predicted very
similar drainage rates at 2-percent slope
but the  HELP model predicted lower
drainage  rates  at 10-percent slope.
Unlike the laboratory measurements, the
hydraulic conductivity in the  drainage
tests varied  as a function  of the depth
of saturation apparently due to entrap-
ment of air in the sand. This phenomenon
makes it very difficult to model the lateral
drainage process  and produce good
agreement between the predicted and
actual results for drainage rate and depth
of saturation as a function of time.
  An  analysis was performed  to deter-
mine  how well the lateral  drainage
equation in the HELP model accounts for
the effects of drainage length,  slope of
the liner, average depth of saturation and
head above the drain contributed by the
liner in  the estimation of the  drainage
rate. The  drainage equation  overesti-
mates the decrease in  drainage  rate
resulting from an  increase in length
given  the same  sand, slope,  depth of
saturation and head from the liner. Using
the drainage rate for a drainage length
of 25.4 ft to predict the rate for a length
of 52.4  ft, the HELP model underpre-
dicted the rate by 18 percent. The HELP
equation overestimated the increase in
drainage rate by 30 percent that resulted
from an increase in slope from 2 percent
to 10 percent. Similarly, the  HELP
equation overestimated the increase in
drainage rate by 20 percent that resulted
from increasing the height (head) of the
crest  of the liner from 15.3 to 30.5  in.
above the drain. The effects of  changes
in the average  saturated depth on the
drainage rate  predicted  by  the  HELP
equation agreed very well with the actual
results.
  Since the HELP lateral drainage equa-
tion was developed  to approximate
numerical  solutions  of the   one-
dimensional Boussinesq equation for
unsteady, unconfined, saturated flow
through porous media,  it cannot  be
expected to perform any better  than the
Boussinesq equation. Therefore,  it was
necessary to compare the Boussinesq
solutions  to the laboratory measure-
ments in order to form a basis for judging
the significance  of the differences
between the HELP equation predictions
and the laboratory measurements, and
between the HELP equation  and the
Boussinesq solution.
  To  summarize, the Boussinesq solu-
tion after  calibration still produced
results significantly different from those
measured in the  drainage tests. The
results  obtained with  the HELP  model
were generally as good or better than the
Boussinesq solution. The HELP equation
performed better on tests conducted with
2-percent slope and  the Boussinesq
solution performed somewhat better on
tests conducted at 10-percent slope. The
differences between predictions by the
two methods for a given set of conditions
were  small in comparison to the range
of actual results. Similarly, the differen-
ces between the  predictions  and the
actual results were much larger than the
differences between the HELP equation
and the Boussinesq equation.

Conclusions and
Recommendations
  The following conclusions and recom-
mendations are made. Lateral drainage
in landfill liner/drain  systems is quite
variable, probably due to air entrapment.
The hydraulic conductivity measurement
made in the laboratory is quite  different
than the in-place value. Consequently,
the estimation of the lateral drainage rate
is prone to considerable error despite
having  a  good  equation or solution
method for the  estimation. Neither the
HELP  model nor the Boussinesq solution
agreed  completely with  the  drainage

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  results. Nevertheless, the prediction of
  the cumulative volume of lateral drain-
  age is likely to be quite good since the
  depth of saturation will be overpredicted
  if the drainage rate is underpredicted and
  vice versa, thereby adjusting the drain-
  age rate.  However, the predicted depth
  of saturation will be quite different from
  the measured value.
    Improvements should  be made  to
  improve the predictions of drainage rates
  resulting  from  changes in slope and
  drainage  length. The drainage equation
  should be modified to  increase its
  applicability to  slopes as large as 30
  percent and drainage lengths as large as
  2000 ft.
    Evaluation of the effects  of drainage
  length, slope of the liner, depth  of
  saturation and head above the drain on
  the drainage rate predicted by  the1
  Boussinesq solution  should be  per-
  formed to determine whether the effects
  observed  with the HELP drainage equa-
  tion  are  unique or derived from  the
  Boussinesq equation. Similarly, an
  additional data  set of drainage results
  should be collected to determine whether
  the effects are unique to  this data set.
  Additional data  should be collected for
  longer drainage lengths and  greater
  slopes and from actual  landfill/liner
  systems.
         P. R. Schroeder and R. L  Peyton are with  U.S. Army Engineer Waterways
           Experiment Station. Vicksburg, MS 39180.
         Robert Landroth is the EPA Project Officer (see below).
         The complete report, entitled "Verification of the Lateral Drainage Component
           of the HELP Model Using Physical Models." (Order No. PB 87-227 104/
           AS; Cost: $18.95, subject to change) will be available only from:
                National Technical Information Service
                5285 Port Royal Road
                Springfield. VA  22161
                Telephone: 703-487-4650
         The EPA Officer can be contacted at:
                Hazardous Waste Engineering Research Laboratory
                U.S. Environmental Protection Agency
                Cincinnati, OH 45268
United States
Environmental Protection
Agency
Center for Environmental Research
Information
Cincinnati OH 45268
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EPA/600/S2-87/049
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