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
-------
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
-------
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
-------
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
BULK RATE
POSTAGE & FEES PAII
EPA
PERMIT No G-35
Official Business
Penalty for Private Use $300
EPA/600/S2-87/049
QQ01961 MWER
LIBRARY REGION V
US EPA
IJ?ff.DEARBORN ST
vHICAGQ
60604
* U.S. GOVERNMENT PRINTING OFFICE: 1988—548-013/870;
------- |