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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