United States
Environmental Protection
Agency
Hazardous Waste Engineering
Research Laboratory
Cincinnati OH 45268
Research and Development
EPA/600/S2-88/045 Sept. 1988
Project Summary
Determination of Effective
Porosity of Soil Materials
Robert Horton, Michael L. Thompson, and John F. McBride
Hazardous waste disposal landfills
require liners constructed of
compacted soil material to help
prevent the migration of hazardous
wastes. The performance of a
compacted soil liner is partly a
function of the porosity. Porosity is
Important because the transport of
materials through the liner will occur
via the pore space. The main
purpose of this project is to study
the pore spaces of compacted
materials and to estimate the
effective porosity, which is the
portion of the pore space where the
most rapid transport of leachate
occurs.
The pore space of three soil
materials with a range in clay
content, till, loess, and paleosol, is
studied by using mercury intrusion
porosimetry, water desorption, and
image analysis. These analyses
provide cumulative porosity curves
from which the pore size distribution
of a soil sample may be estimated.
Theory is developed to estimate
the effective porosity of a compacted
soil material based upon a model of
Its pore size distribution and pore
continuity. The effective porosities of
the compacted till, loess, and
paleosol materials are estimated to
be 0.04, 0.08, and 0.09, respectively.
These values are 10 to 20% of the
total porosities.
Comparisons between measured
and predicted CI" travel times
through compacted soil samples are
made to verify the estimated
effective porosities. The estimated
effective porosities are reasonable
because predicted first breakthrough
times of CI are similar to the
measured first breakthrough times in
compacted till, loess, and paleosol
materials. For the three soil materials
used in this study, predicted first
breakthrough times are 5 to 10 times
earlier when effective porosity is
used in calculations based on the
Darcy equation compared with
calculations that utilize total porosity.
This suggests that effective porosity
should be consideed when
estimating the lifetimes of landfill
liners.
This Project Summary was devel-
oped by EPA's Hazardous Waste
Engineering Research Laboratory,
Cincinnati, OH, to announce key
findings of the research project that is
fully documented in a separate report
of the same title (see Project Report
ordering information at back).
Introduction
Compacted clay is frequently used to
line hazardous waste disposal landfills.
The purpose of the compacted clay liner
is to restrict the movement of hazardous
liquid materials out of the landfill.
Currently, saturated hydraulic con-
ductivity (usually referred to as soil
permeability in the Environmental
Protection Agency's design standards) is
the most common measurement used to
estimate the ability of liner material to
contain wastes. Soil saturated hydraulic
conductivity, K (L3/L2/T), is defined for
Darcy's equation:
K = J/l
[1]
where J is the fluid flux density (L3/L2/T)
and I is the hydraulic gradient (L/L). Soil
saturated hydraulic conductivity has
dimensions of volume per unit area of
liner per unit time, and thus, it is a bulk
parameter related to the areal average
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fluid flow in the liner. Saturated hydraulic
conductivity is often used to make
prelimnary estimates of solute transit
times, but knowledge of average fluid
flow alone is not adequate for accurate
prediction of pollutant breakthrough of
travel time. Nonuniform flow velocities
through a cross-sectional area should
be accounted for because faster-than-
average fluid flow may be responsible for
the first appearance of the pollutant
below the liner.
Effective porosity, E, has been de-
scribed as that portion of the total liner
porosity that contributes significantly to
fluid flow. Effective porosities are less
than total porosities because some of the
pore space is discontinuous (dead end)
and some of the pore space is so narrow
that fluids in these spaces are essentially
immobile. This project develops a new
technique based upon Darcy's equation
for estimating effective porosity and
solute travel time. Because the fluid flux
density through a clay liner can be
determined by using Darcy's equation,
the mean effective fluid velocity, Vg,
can be described by:
VE = KI/E
[2]
With a constant hydraulic gradient and
the liner K and E both known, the
average pollutant travel distance per unit
time can be estimated. Thus, the time of
first breakthrough, T, of a noninteracting
pollutant can be predicted by the equa-
tion:
T = EL/KI
[3]
where L is the liner thickness (m).
The Environmental Protection Agency,
requires that a disposal unit liner prevent
migration during the active life of a unit.
The active life of a unit containing
noninteracting pollutants can be
estimated by using Equation (3).
Knowledge of the liner permeability alone
is not sufficient information to accurately
estimate the length of time of liner
effectiveness. When a disposal unit is
constructed with known liner thickness,
L, and designed for a known hydraulic
gradient, I, measurement of both
permeability and effective porosity are
required to estimate the active life of the
unit with Equation (3). Although methods
to estimate permeability of compacted
clay materials have received much
attention in the literature, determination
of effective porosity has received little
attention.
This project develops a method for
estimating the effective porosity of
compacted clay materials. This method
is based upon the soil pore size
distribution. The estimates of effective
porosity are used in Equation (3) to
predict the travel time of a noninteracting
solute through samples of compacted
materials.
Materials and Methods
We collected subsurface samples from
three soils developed in major Iowa soil
parent mateials: till (21% clay), loess
(35% clay), and paleosol (44% clay). The
clay fraction of each material was
dominated by smectite, with small
amounts of clay mica and kaolinite.
The pore size distribution of samples
of each compacted subsoil material was
determined by mercury porosimetry.
Samples were freeze-dried before
mercury was intruded in four steps.
Standard soil-water characteristic data
were obtained by determining soil water
contents of samples at 0.05, 0.1, 0.2, and
1.5 MPa matric tensions. These
pressures correspond to equivalent pore
radii of 3, 1.5, 0.75, and 1 iim, re-
spectively, and were chosen to measure
pores in size ranges roughly comparable
to those measured by the mercury
porosimeter. In addition, soil porosity
was studied by image analysis methods.
Permeability of compacted soil
materials was measured using fixed-
wall permeameters. Three replicates of
each subsoil material were ocmpacted at
moisture contents ~1 to 2% above
optimum, determined from the
moisture-density relations. De-aired,
saturated CaSO4 solution (adjusted to
0.06% formaldehyde to control microbial
growth) was introduced at 6.9 kPa
pressure at the bottom of the
permeameter to slowly saturate the
compacted sample. The source of the
pressure was compressed air. The air
was separated from the saturated CaSO4
solution by a rubber membrane within
the solution container to help prevent the
desaturation of the soil material. After
saturating the material, the CaS04
solution was introduced at the top of the
permeameter at hydraulic gradients of
~170 to 270, and the rate of solution
movement through the sample was
measured over time.
Solute breakthrough measurements
were made for compacted soil samples.
The breakthrough measurements were
made on the same soil samples used to
determine permeability. A de-aired,
0.05 N CaC\z solution with 0.016% Acid
Fuchsin (red dye), and 0.06% formal-
dehyde was used as the tracer solutio
The tracer solution was exchanged f<
the saturated CaS04 solution an
allowed to leach through the compacte
soil sample under the same hydraul
gradient used in the permeability tes
The leachate was collected in equa
volume increments with a fractio
collector and was analyzed for chlorid
concentration with an automatic titrator.
Theoretical
Theory based upon water flow throug
interconnected cylindrical pores wa
used to describe pore water velocit
distributions within samples undergoin
solute breakthrough measurements. Th
theory estimates sample effectiv
porosity from total porosity, 0S, and
pore size distribution parameter, i
Effective porosity is defined here as thi
portion of the soil pore space that allow
liquid to travel at velocities greater tha
the overall mean liquid velocity.
Figure 1 shows a relationship betwee
the effective porosity, E, and the soil por
size distribution parameter, n, for seven
values of total porosity, 8S. This figur
summarizes the theoretical relationshi
developed by this project.
Once E is determined for a soil mate
rial, the time of first chemical break
through can be estimated using Equatio
(3).
.75
.12
.09
.06
.03
.00
1.0 1.5 2.0 2.5 3.0 3.5
n
Figure 1. Influence of n on effective
porosity (E) at various values of
6,.
Results and Conclusions
Mercury intrusion porosimetry was th<
method that best measured the fulles
range of pore sizes of the compactei
samples. Results from mercur
porosimetry measurements are pre
sented in Table 1. Values of tota
porosity, 9S, ranged from 0.28 to 0.40
while the pore size distriubtioi
parameter, n, ranged from 1.5 to 2.1. Thi
smaller the value of n, the wider thi
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jistribution of pores within a sample.
"hus, the loess samples were most
jniform in pore size.
'able 1. Total porosity, BSi and pore size
distribution parameters for the
three soil materials
So/7 Material
es
till
loess
paleosol
0.28
0.40
0.40
1.52
2.11
1.98
Table 2 presents measured values of
sermeability and times of first chloride
Breakthrough (relative effluent con-
;entration equal to 0.01), estimated
effective porosities, and predicted times
Df first breakthrough of noninteracting
pollutants for compacted till, loess, and
Daleosol samples. Each compacted soil
material had permeability less than the
EPA-maximum value of 1 x 10~9
7i3/m2/s for hazardous waste disposal
liners. The estimated effective porosities
were between 10 and 20% of the total
porosities of the compacted samples.
The predicted breakthrough time was
calculated based on the mean
permeability. The measured chloride
breakthrough time was adjusted to
correspond to the breakthrough time of a
permeameter with the mean perme-
ability.
The predicted noninteracting pollutant
breakthrough times agreed well with the
measured chloride breakthrough times.
Predicted breakthrough values were
about equal to measured values for
loess. Predicted breakthrough was earlier
than measured for till and later than
measured for paleosol. For one replicate
of till and one replicate of paleosol, the
measured and predicted breakthrough
times were nearly equal. Because the
clay fractions of the compacted samples
had a net negative charge and chloride is
an anion, it is reasonable to assume that
chloride could move through the samples
somewhat faster than a true non-
interacting pollutant (i.e., tritiated water).
Till soil material had less clay than the
other materials, and thus anion exclusion
would be expected to be less.
The theory presented provides the
basis for estimating effective porosity of
compacted clay liners. To predict the
travel time of noninteracting substances
through a clay liner, the hydraulic
gradient, liner permeability, liner
thickness, and effective porosity are
required. As an example of how the
theory can be used, we will now make
such a prediction for a hypothetical liner
constructed of till soil material. The
information that we assume is: liner
thickness = 1 meter, hydraulic gradient
= 1.33, liner permeability = 10~9
m3/m2/s.
If we follow only the Darcy equation,
Equation (1), fluid flux density is 1.33 x
10"9 m3/m2/s. However, the fluid flux
density does not represent the fluid
velocity within the liner. We know that a
portion of the total porosity is responsible
for conducting fluid at velocities higher
than the average velocity and the
remaining portion of the porosity
conducts fluids at velocities lower than
the average velocity. What is important in
Table 2. Permeabilities, measured time of first chloride breakthrough, estimated effective porosities, and
pfredicted noninteracting pollutant breakthrough times for the compacted soil materials (peameters
were 11.64 cm long)
Soil Material
Till
Rep 1
Rep 2
Rep 3
Mean
Loess
Rep 1
Rep 2
Rep 3
Mean
Permeability
(m3/m2/s
5.47 x /0~"
6.58 X10'11
1.22 x Iff10
8.08 x 70""
2.84 x 10~10
2.67 x 10~10
2.61 X JO"'0
2.71 x 10~10
Breakthrough Time Estimated Effective Breakthrough Time
(d) Porosity (d)
3.0 0.04 2.6
4.2
4.6
3.9
1.7 0.08 1.6
1.2
1.5
1.5
Paleosol
Rep 1
Rep 2
Rep 3
Mean
3.38 x 10'
2.17 x 10
.-10
1.11 x 10
,-10
1.21 x 10'
,-10
4.8
4.4
3.9
4.4
0.09
5.1
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pollutant transport is the portion of
porosity that conducts fluid at higher-
than-average velocities. To determine
the average effective fluid velocity, we
must first estimate the effective porosity.
Effective porosity is determined based
on theory previously presented. From
mercury porosimetry data for the till
materials the n-parameter is 1.5 and 9S
is 0.28 (Table 1). By using Figure 1,
effective porosity is estimated to be 0.04.
Based upon Equation (3) the travel time
for noninteracting solutes through a till
clay liner in this example is predicted to
be 0.95 years. Therefore, under these
conditions, we predict that after about
one year, noninteracting pollutants will
reach the bottom of the clay liner.
Although the concentration of the
noninteracting pollutant may be low
because of dilution and lateral mixing by
diffusion, the initial fraction is predicted
to appear after one year. In this example,
if the product of liner permeability and
hydraulic gradient (i.e., fluid flux density,
J) is mistakenly used as the fluid
velocity, the pollutant travel time is
calculated to be 23.8 years. If the fluid
velocity is mistakenly assumed to be
equal in all soil pores, the noninteracting
pollutant travel time is calculated as 6.7
years. Thus, travel time for non-
interacting pollutants is significantly
overestimated if effective porosity is not
taken into account. The active lifetime of
hazardous waste disposal units may be
overestimated if liner effective porosity is
not properly estimated and used in the
prediction of pore-fluid velocity.
Robert Horton, Michael L Thompson, and John F. McBride are with Iowa Statt
University, Ames, IA 50011.
Walter E. Gnibe, Jr., is the EPA Project Officer (see below).
The complete report, entitled "Determination of Effective Porosity of So/
Materials," (Order No. PB 88-242 391/AS; Cost: $19.95, subject to change,
will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA22161
Telephone: 703-487-4650
The EPA Project 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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POSTAGE & FEES PAID
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Penalty for Private Use $300
EPA/600/S2-88/045
0001961 HWER
REGION V
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