Persistence of Semipermeable Membrane Behavior for a Geosynthetic Clay Liner 1
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3
4
5
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A. Meier , K. Sample-Lord , D. Castelbaum , S. Kallase , B. Moran , T. Ray , and C. Shackelford
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Graduate Research Assistant, Department of Civil and Environmental Engineering, Colorado State University, Fort Collins, Colorado, USA, 80523-1372; PH +1 612 817 0262; email:
[email protected] 2 Graduate Research Assistant, Department of Civil and Environmental Engineering, Colorado State University, Fort Collins, Colorado, USA, 80523-1372; PH +1 781 724 3996; email:
[email protected] 3 Graduate Research Assistant, Department of Civil and Environmental Engineering, Colorado State University, Fort Collins, Colorado, USA, 80523-1372; PH +1 970 221 2068; email:
[email protected] 4 Undergraduate Research Assistant, Department of Civil and Environmental Engineering, Colorado State University, Fort Collins, Colorado, USA, 80523-1372; email:
[email protected] 5 Undergraduate Research Assistant, Department of Civil and Environmental Engineering, Colorado State University, Fort Collins, Colorado, USA, 80523-1372; email:
[email protected] 6 Undergraduate Research Assistant, Department of Civil and Environmental Engineering, Colorado State University, Fort Collins, Colorado, USA, 80523-1372; email:
[email protected] 7 Professor, Department of Civil and Environmental Engineering, Colorado State University, Fort Collins, Colorado, USA, 805231372; PH +1 970 491 5051; email:
[email protected]
ABSTRACT Geosynthetic clay liners (GCLs) consist of sodium bentonite (Na-bentonite) sandwiched between two geotextiles. Na-bentonite is preferred for GCLs due to the high swell and low hydraulic conductivity of the bentonite. Bentonites also may exhibit semipermeable membrane behavior, or the ability to restrict the migration of solutes through the clay. In previous studies, membrane behavior of GCLs has been evaluated primarily on the basis of exposure to relatively low salt concentrations (≤ 54 mM) of simple monovalent salts, such as potassium chloride (KCl), with increasing salt concentrations corresponding to decreasing membrane behavior. The objective of this study was to evaluate the persistence of membrane behavior for a GCL specimen exposed to salt solutions containing increasingly higher concentrations of KCl until any observed membrane behavior was completely destroyed. The results indicate that membrane behavior persisted until the specimen was exposed to a KCl concentration of 400 mM, which is well beyond the salt concentrations used in any previous study evaluating the membrane behavior of GCLs. In addition, the results clearly show that the relationship between the membrane efficiency coefficient () and the logarithm of the salt concentration becomes nonlinear with increasing salt concentration, a trend that previously has been hypothesized to exist on the basis of limited experimental data. Thus, the results of this study represent the first evaluation of the persistence of membrane behavior of a GCL exposed to simple monovalent salt solutions. Keywords: Bentonite, Clay barriers, Chemico-osmosis, Geosynthetic clay liner, Membrane, Solute restriction 1
INTRODUCTION
Membrane behavior in clay barriers refers to the ability of the clay to selectively restrict the passage of dissolved chemical species (solutes). Restriction of inorganic ions is attributed to electrostatic repulsion of the ions due to interaction of the electric fields associated with the diffuse double layers (DDLs) of adjacent clay particles (Fritz 1986). This interaction occurs when the clay particles are sufficiently close (i.e., pore sizes are sufficiently small) as to cause overlapping of the electric fields. Generally, this requirement is achieved only in clays such as sodium bentonite (Na-bentonite) that contain highly active clay minerals, such as the smectites (e.g., montmorillonite). If a clay exhibits membrane behavior, chemico-osmosis may occur, whereby liquid flows from lower solute concentration (higher water activity) to higher solute concentration (Shackelford et al. 2003). In geoenvironmental containment applications utilizing bentonite-based barriers, such as geosynthetic clay liners (GCLs), compacted clay liners (CCLs), and soil-bentonite (SB) cutoff walls, where the primary objective is chemical containment, the existence of membrane behavior represents a potentially significant beneficial aspect of such barriers that heretofore has not been considered in the design of such barriers. However, there are some applications, such as the use of GCLs and highly compacted bentonite buffers for containment of low-level and high-level radioactive wastes, respectively, where quantification of such membrane behavior plays an important role in predicting the
long-term performance (e.g., 1,000 to 10,000 years) of such barriers (e.g., Bonaparte et al. 2008, Gens 2013). Thus, prudence dictates continued evaluation of the fundamental aspects of membrane behavior in such clay barriers. Membrane behavior is quantified in terms of a membrane efficiency coefficient, , with values ranging from 0 to 1 representing membrane efficiencies ranging from 0 % to 100 %, respectively. An value of zero represents the case where membrane behavior does not exist (e.g., sand), whereas an value of unity (100 %) represents the ideal case of complete solute restriction. Typically, the values of for naturally occurring clays that exhibit membrane behavior are between these two limiting cases (i.e., 0 < < 1), due to the variation in pore sizes that exist in naturally occurring clays resulting in only some of the pores being restrictive. In this case, the clays are referred to as semipermeable or imperfect membranes. Previous studies have shown that the membrane efficiency of clay membranes is a function of the average salt concentration in the pore water and the type of solute species (e.g., monovalent or multivalent ion). In laboratory tests where salt solutions are circulated at the specimen boundaries to induce membrane behavior, the average concentration across the specimen, Cave, is defined as follows: Cave = (Co + CL)/2
(1)
where Co and CL are the upper and lower boundary salt concentrations, respectively. As shown in Figure 1, for a given type of salt (e.g., KCl vs. NaCl) and specimen porosity (n), the value of decreases as Cave increases. This trend results because, as the concentration of the salts in the pore water increases, the thickness of the diffuse double layers and electric fields controlling ion restriction decreases, resulting in progressively larger pores and correspondingly lesser solute restriction (Fritz 1986, Shackelford 2011).
M e m b ra n e E ffic ie n c y C o e ffic ie n t,
1
C lo se d : K C l (M a lusis & S h a ckelfo rd 2 0 0 2a ) O p e n: N aC l (K e m p e r & R ollin s 1 96 6 )
0 .9
I = -0 .5 2 6
n = 0 .7 4
0 .8
n = 0 .8 6
2
(r = 0 .9 7 0 )
n = 0 .8 0
0 .7
I = -0 .4 6 5
n = 0 .8 4
2
0 .6
n = 0 .9 1
(r = 0 .9 9 7 ) I = -0 .4 9 2
0 .5
2
(r = 0 .9 9 6 )
0 .4
T h re sho ld co nc e n tra tio n = C @
0 .3 I = -0 .3 9 5
ave
2
(r = 0 .9 7 8 )
0 .2
= 0
I = -0 .4 5 5
0 .1
2
(r = 0 .9 6 3 )
0 1
10
1 00
A v e ra g e S a lt C o n ce n tra tio n , C
1 00 0 ave
(m M )
Figure 1. Membrane efficiency versus average salt concentration for sodium bentonite specimens at different porosities (n). [Note: I = membrane index representing the semi-log linear slope of the observed trend]. Previous studies have suggested that the relationship between and Cave in clays is approximately semi-log linear, with the slope of the trend represented by the membrane index, I (Shackelford et al. 2003, Shackelford 2013), where: I = /log(Cave)
(2)
This semi-log linear relationship between and Cave has been extrapolated to identify the value of the threshold salt concentration (Cave,) for various clays, representing the average concentration at which membrane behavior is destroyed ( = 0) (Shackelford et al. 2003). However, previous experimental membrane behavior studies utilizing monovalent salt solutions have not included concentrations high enough to determine the actual value of Cave, Kang and Shackelford (2010) predicted threshold concentrations for GCLs (via extrapolation of the semi-log linear relationship described previously) ranging from 37 mM to 99 mM for KCl. However, based on the data shown in Figure 1, as Cave approaches Cave, the relationship between and Cave may actually become non semi-log linear. Therefore, the purpose of this study was to evaluate the persistence of membrane behavior in a GCL subjected to increasingly higher concentrations of a simple monovalent salt, KCl, until the observed membrane behavior of the GCL was completely destroyed, thereby providing for an evaluation of the actual nature of the trend in versus Cave at high concentrations and any resulting difference in the measured value of Cave, versus Cave, calculated based on the value I.
2 2.1
MATERIALS AND METHODS Membrane test apparatus
The closed-system test method with a rigid-wall cell (see Malusis et al. 2001) was used to evaluate the persistence of semipermeable membrane behavior in the GCL. In a closed-system apparatus, volume change and liquid flux across the specimen cannot occur such that chemico-osmosis is prevented. Thus, if the clay behaves as a semipermeable membrane, the restriction of chemicoosmosis results in the development of a chemico-osmotic pressure difference across the specimen (P) to counteract the tendency for chemico-osmosis. Differential pressure transducers (Omega Engineering Inc., Model PX26, Stamford, CT) were used to measure P for each concentration stage. To maintain a controlled concentration gradient across the specimen, ports in the top and bottom of the cell allow for continuous circulation of separate electrolyte (salt) solutions through porous plastic disks at the boundaries of the specimen. Circulation of the electrolyte solutions is controlled by a dual-carriage flow pump (Harvard Apparatus, Model 944, Holliston, MA) with stainless steel syringes that advance at a constant rate. All plumbing connected to the rigid-wall cell was stainless steel to minimize volume change in the system. Further details of the testing apparatus can be found in Malusis et al. (2001). 2.2
Specimen preparation ®
The GCL evaluated in this study was Bentomat (Colloid Environmental Technologies Company (CETCO), Hoffman Estates, Illinois, USA), which has been evaluated in several previous membrane behavior studies (Malusis and Shackelford 2002a,b, Kang and Shackelford 2009, 2010, 2011). The mineralogy, cation exchange capacity (CEC), and index properties of the bentonite in the GCL were reported by Malusis and Shackelford (2002a). The mineralogy includes 71 % smectite (montmorillonite), 15 % quartz, 7 % mixed layer illite/smectite minerals, and 7 % other minerals. The CEC was 47.7 meq/100 g, with 53 % of the exchange complex comprised of exchangeable sodium. The liquid limit (LL) and plastic limit (PL) measured in accordance with ASTM D4318, were 478 % and 39 %, respectively. Based on the Unified Soil Classification System (USCS, ASTM D2487), the soil classified as a high plasticity clay (CH). Further details on the chemical and physical properties of the bentonite in the GCL can be found in Malusis and Shackelford (2002a). A 90-mm-diameter specimen was extracted from the GCL roll. The edges of the cut specimen were slightly hydrated with de-ionized water (DIW) to minimize the loss of bentonite granules. The specimen had a dry thickness of 8 mm and a porosity, n, of 0.79. After the initial dimensions were measured, the specimen was placed on the base pedestal in the rigid-wall cell. The top piston was placed on top of the GCL and locked in place to prevent increases in thickness due to swelling. Previous studies have permeated specimens for up to several months prior to testing to remove excess soluble salts and enhance membrane behavior (Shackelford 2013). In this study, flushing and determination of hydraulic conductivity were achieved via permeation with DIW under a constant head difference, followed by constant flow conditions using the flow pump. Constant-head permeation and constant-flow permeation were performed for 60 days and 14 days, respectively. The specimen was permeated from the bottom upward. The electrical conductivity (EC) of the outflow decreased during
permeation from 229 mS/m to 30 mS/m, indicating effective flushing of soluble salts from the pores of the specimen. As a comparison with long-term permeation methods used previously, Kang and Shackelford (2010) reported EC values of flushed specimens ranging from 27 mS/m to 72 mS/m. 2.3
Membrane testing procedure
Prior to the first stage of membrane testing, DIW was circulated at both specimen boundaries to establish a baseline, steady-state value of ΔP, or ΔPDIW. Conceptually, ΔPDIW should be zero, since the concentration gradient across the specimen is zero, such that there is no tendency for chemicoosmotic pressures to develop. However, a non-zero ΔPDIW typically is observed, due to slight differences in the hydraulic resistance of the top and bottom porous disks (e.g., Malusis et al. 2001, Malusis and Shackelford 2002a). During the membrane test stages, circulation of DIW at the bottom boundary of the specimen was continued whereas a KCl solution was circulated at the top boundary to establish and maintain a concentration difference across the specimen (C). The salt type and concentration range of the solutions were chosen based on previous membrane testing, to allow for comparison of the results. The solution concentrations were confirmed using inductively coupled plasma atomic emission spectroscopy (ICP-AES) and ion chromatography (IC). During membrane testing, P was measured at 15-minute intervals and recorded with LabView (Version 12.0.1f2, National Instruments Corporation, Austin, TX). Each concentration stage was performed for a minimum of three weeks, until steady values were achieved for both the measured ΔP and the EC of the outflows at the boundaries. Upon achieving a steady state, the KCl concentration was increased in 15 mM increments at lower concentrations (20 mM, 35 mM and 50 mM), and then doubled at higher concentrations (100 mM, 200 mM, 400 mM) in an effort to thoroughly attack the membrane behavior of the GCL specimen and better define the actual trend of versus Cave at high values of Cave and, therefore, low values of . To quantify the threshold concentration, the concentrations of the multistage test were increased until the value of ΔP decreased to the value of ΔPDIW. The measured P was considered steady when the values for the last four data points were all within ±5 % of the geometric mean of the same values. Upon completion of this criterion, the resulting geometric average was taken as the final steady-state P for the concentration stage, ΔPss. The effective differential pressure (ΔPe), defined as the difference between ΔPss and ΔPDIW (i.e., ΔPe = ΔPss – ΔPDIW), was used to calculate the resulting value of (Groenevelt and Elrick 1976, Malusis et al. 2001), as follows: = Pe/
(3)
where Δ is the theoretical, maximum chemico-osmotic pressure difference across an ideal membrane (i.e., = 1.0). The value for Δ is calculated based on the van’t Hoff expression as follows (Barbour and Fredlund 1989): = RTC
(4)
where is the number of ions per molecule of salt (e.g., = 2 for KCl), R is the universal gas constant -1 -1 (8.314 J mol K ), T is the absolute temperature (K), and ΔC represents the difference between the electrolyte concentrations at the top and bottom boundary. 3 3.1
RESULTS AND DISCUSSION Electrical conductivity
The stainless-steel syringes were refilled with fresh KCl solution and DIW every two days. During this refilling period, the collected outflows from the top and bottom boundaries of the specimen were emptied into 50-mL vials for measurement of EC and pH. The EC of the outflow solution from the bottom boundary of the specimen, ECbot, can be used to approximate the KCl concentration and, thus, + the flux of K and Cl across the specimen (Malusis and Shackelford 2002a, Malusis et al. 2013, 2014). Based on Fick’s first law for diffusion, an increase in the concentration gradient across the
specimen, iC (= C/L, where L = the specimen thickness) should result in a directly related increase in the solute mass flux through the specimen as reflected by an increase in ECbot. As shown in Figure 2, as the concentration of the KCl source solution increased (i.e., as the applied C increased), ECbot also increased.
-5
0
T im e , t (w k) 10 15
5
20
25
E le ctrica l C o nd u ctiv ity o f O u tflow , E C (m S /m )
10 0 00
T op , E C 1000
to p
B ottom , E C
k -tes ting
bo t
1 00 B a se lin e E C
10
100m M D IW
20m M
1 -42 -2 8 -1 4
0
14
28
35m M
42
56
70
84
200m M
400m M
50m M
9 8 1 1 2 1 26 1 4 0 1 54 1 6 8 18 2 1 9 6
T im e , t (d )
Figure 2. Electrical conductivity (EC) measurements of the outflows from the top and bottom specimen boundaries versus time for each KCl concentration stage. The value of ECbot typically increased at a higher rate than the increase in the concentration of the source KCl solution. For example, when the KCl concentration increased from 20 mM to 35 mM (75 % increase), ECbot increased from 51 mS/m to 97 mS/m (90 % increase). A 100% increase in the KCl solution, from 50 mM to 100 mM, resulted in a 117% increase in ECbot. This trend can be attributed to + decreased solute restriction (decreased ) and increased diffusion of K and Cl resulting from increasingly greater double layer suppression with increasing Cave. 3.2
Chemico-osmotic pressure difference
As shown in Figure 3, the value of P generally decreased as KCl concentration increased, representing decreasing with increasing Cave (see Figure 4). The values for ΔPss were 16.1 kPa, 15.4 kPa, 15.3 kPa, 13.9 kPa, 11.2 kPa, and 0.88 kPa for source KCl concentrations, Co (=C), of 20 mM, 35 mM, 50 mM, 100 mM, 200 mM, and 400 mM, respectively. The final stage (400 mM KCl) resulted in ΔPss approaching the value of ΔPDIW, indicating a Pe of approximately zero.
4
8
12
T im e , t (w k ) 16
20
24
28
25 3
20 1 6 .1 kP a
1 5 .4 kP a
1 5 .3 kP a
15
1 3 .9 kP a
2 1 1 .2 kP a
P
10
D IW
= 6.1 kP a
1 5
100m M 20m M
35m M
2 0 0m M
4 0 0m M
50m M
0
0 0
14
28
42
56
70
84
P res su re D iffe re n ce , - P (ps i)
P re ss ure D iffe re n c e, - P (k P a )
0
9 8 1 1 2 1 2 6 14 0 1 54 1 6 8 1 8 2 19 6 T im e , t (d )
Figure 3. Temporal behavior of measured chemico-osmotic pressure difference for each KCl concentration stage.
Note that the first data point for P for each new KCl concentration stage reflected the final ΔPss value of the previous stage, due to the delayed increase in concentration at the top boundary (as indicated in Figure 2 by the delayed increase in ECtop at the beginning of each stage). Also, as shown in Figure 3, the measured ΔP in each stage starts lower than ΔPss, and then gradually increases to the steady ΔPss value as the concentration throughout the pressure system approaches equilibrium. 3.3
Membrane efficiency and threshold concentration
M e m b ra n e E fficien cy C o e fficie n t,
The membrane efficiency results shown in Figure 4 support the hypothesis that the initially linear trend between and the logarithm of Cave at lower values of Cave eventually becomes non-linear as Cave increases, such that approaches zero. This non-linear trend in the -versus-log Cave relationship with increasing Cave reflects the persistence in the developed chemico-osmotic pressure differences shown in Figure 3 at the higher values of Cave. The resulting observed persistence in membrane behavior is consistent with limited experimental data reported by Sherwood and Craster (2000), who tested 120 m-thick specimens of a mixture of montmorillonite and glass beads subjected to 0.5 M and 3.0 M concentrations of NaCl or KCl.
0 .12 = 0 .2 5 7 -0 .1 5 8 *log (C
0 .10
2
a ve
)
(r = 0 .97 2 ) 0 .08 0 .06 42 m M
0 .04
200 m M
0 .02 0 .00 1
10
1 00
A ve ra g e K C l c on c e ntra tion , C
1000 ave
(m M )
Figure 4. Plot of membrane efficiency, , versus average specimen concentration, Cave, demonstrating underestimation of threshold concentration using semi-log linear extrapolation. As shown in Figure 4, a semi-log linear extrapolation of the lower concentration data leads to an estimated threshold concentration of 42 mM KCl, consistent with previously estimated values in the literature. For example, Malusis and Shackelford (2002a) tested specimens up to source KCl concentrations of 47 mM, and reported a threshold concentration of 48 mM for the same GCL product (n = 0.74). The data shown in Figure 4 indicate that semi-log linear extrapolation significantly underestimates the threshold concentration, with the actual threshold concentration occurring between 100 mM and 200 mM. This threshold concentration is up to four times higher than that previously estimated for the same GCL, indicating greater significance and persistence of membrane behavior at higher salt concentrations. In the field, maximum contaminant level (MCL) values for inorganic contaminants in contact with -8 -6 GCLs commonly range from 1 x 10 M to 2 x 10 M (Shackelford et al. 2003). The observation of the -1 -1 persistence of membrane behavior for KCl source concentrations between 2 x 10 M and 4 x 10 M -1 -1 (Cave of 1 x 10 M and 2 x 10 M) indicates membrane behavior remains relevant when in contact with such solutions up to seven orders of magnitude above the MCL, covering a broad range of possible geoenvironmental containment applications (Shackelford et al. 2003). A comparison of the results from two previous studies involving the same GCL product, a similar closed-system testing apparatus, and KCl as the salt is shown in Figure 5. The porosities of the GCL specimens are indicated in the legend. A slightly, semi-log nonlinear trend at higher Cave values can
be interpreted from the data in many of the previous studies. The data from this study were in close agreement with the data reported by Kang and Shackelford (2011) for a GCL specimen with a similar porosity (0.79 ≤ n ≤ 0.81).
M e m b ra ne E fficie ncy C o efficien t,
1 T ria ng les : F le xible -w all c ell (o the rw ise R ig id-w all ce ll) D a sh ed Lin e s: M a lus is & S h a cke lford (2 00 2a ) S o lid L ine s: K an g & S h ac k elford (20 11 )
0 .9 0 .8 0 .7
T his stu dy, n = 0.79 n = 0 .8 6 n = 0 .7 4 n = 0 .7 9 - 0 .8 1 n = 0 .7 9 - 0 .8 0 n = 0 .7 6 - 0 .7 7 n = 0 .6 6 - 0 .7 1 n = 0.7 4 n = 0 .7 8 - 0 .8 0 n = 0 .8 6
0 .6 0 .5 0 .4 0 .3 0 .2 0 .1 0 1
10
1 00
A verag e K C l C on c e ntratio n , C
10 0 0 a ve
(m M )
Figure 5. Membrane efficiency, , versus average KCl concentration for GCL specimens at different porosities (n). 4
CONCLUSIONS
The test program used in this study, which included longer testing durations and higher KCl source concentrations than previous studies, provided further insight into the persistence of semipermeable membrane behavior at higher source concentrations. The threshold concentration of 42 mM KCl estimated via semi-log linear extrapolation of the -versus-log Cave data is shown to under estimate the true threshold concentration of ~ 200 mM measured at higher concentrations, due to the persistence of membrane behavior with increasing values of Cave and the resulting nonlinear trend in -versus-log Cave at increasing higher values of Cave. The results of the study indicate membrane behavior may persist when in contact with solutions of inorganic contaminants at concentrations that are significantly higher (e.g., by as much as seven orders of magnitude) than the MCL, covering a broad range of clay barrier applications where membrane behavior may affect contaminant migration rates. 5
ACKNOWLEDGEMENTS
This study was supported by the U.S. Department of Energy, under Cooperative Agreement Number DE-FC01-06EW07053 entitled, “The Consortium for Risk Evaluation with Stakeholder Participation III” awarded to Vanderbilt University. The opinions, findings, conclusions, or recommendations expressed herein are those of the authors and do not necessarily represent the views of the Department of Energy or Vanderbilt University. REFERENCES Barbour, S., and Fredlund, D. 1989. Mechanisms of osmotic flow and volume change in clay soils. Canadian Geotechnical Journal, 26(4):551–562. Bonaparte, R., Beech, J., Griffin, L., Phillips, D., Kumthekar, U., and Reising, J. 2008. Design, construction, and performance of low-level radioactive waste disposal facility. Proceedings of 6 th International Conference on Case Histories in Geotechnical Engineering, August 11-16, 2008, Arlington, Virginia, USA. Evans, J., Shackelford, C., Yeo, S., and Henning, J. 2008. Membrane behavior of soil–bentonite slurry-trench cutoff walls. Soil
and Sediment Contamination, 17(4): 316–322. Fritz, S. 1986. Ideality of clay membranes in osmotic processes: A review. Clays and Clay Minerals, 34: 214-223. Gens, A. 2013. Coupled modelling of barriers for radioactive waste disposal. Proceedings of Coupled Phenomena in Environmental Geotechnics, M. Manassero, A. Dominijanni, S. Foti, and G. Musso, Eds., July 1-3, 2013, Torino, Italy, CRC Press/Balkema, Taylor & Francis Group, London, 21-34.. Groenevelt, P.. and Elrick, D. 1976. Coupling phenomena in saturated homo-ionic montmorillonite: II. Theoretical. Soil Science Society of America Journal, 40: 820-823. Kang, J., and Shackelford, C. 2009. Clay membrane testing using a flexible-wall cell under closed-system boundary conditions. Applied Clay Science, 44(1-2): 43-58. Kang, J., and Shackelford, C. 2010. Membrane behavior of compacted clay liners. Journal of Geotechnical and Geoenvironmental Engineering, 136(10): 1368-1382. Kang, J., and Shackelford, C. 2011. Consolidation enhanced membrane behavior of a geosynthetic clay liner. Geotextiles and Geomembranes, 29(6): 544-556. Kemper, W., and Rollins, J. 1966. Osmotic efficiency coefficients across compacted clays. Soil Science Society of America, Proceedings, 30(5): 529-534. Malusis, M., and Shackelford, C. 2002a. Chemico-osmotic efficiency of a geosynthetic clay liner. Journal of Geotechnical and Geoenvironmental Engineering, 128(2): 97-106. Malusis, M., and Shackelford, C. 2002b. Coupling effects during steady-state solute diffusion through a semipermeable clay membrane. Environmental Science and Technology, 36(6): 1312-1319. Malusis, M., Shackelford, C., and Olsen, H. 2001. A laboratory apparatus to measure chemico-osmotic efficiency coefficients for clay soils. Geotechnical Testing Journal, 24(3): 229-242. Malusis, M., Kang, J., and Shackelford, C. 2013. Influence of membrane behavior on solute diffusion through GCLs. Proceedings of Coupled Phenomena in Environmental Geotechnics, M. Manassero, A. Dominijanni, S. Foti, and G. Musso, Eds., July 1-3, 2013, Torino, Italy, CRC Press/Balkema, Taylor & Francis Group, London, 267-274. Malusis, M., Kang, J., and Shackelford, C. 2014. Restricted salt diffusion in a geosynthetic clay liner. Environmental Geotechnics, http://dx.doi.org/10.1680/envgeo.13.00080. Manassero, M. and Dominijanni, A. 2003. Modelling the osmosis effect on solute migration through porous media. Géotechnique, 53(5): 481-492. Shackelford, C. 2011. Membrane behavior in geosynthetic clay liners. Proceedings of Geo-Frontiers 2011, Dallas, TX, March 13-16, 2011, (CD-ROM) ASCE, Reston, Virginia, USA, 1961-1970. Shackelford, C. 2013. Membrane behavior in engineered bentonite-based containment barriers: State of the art. Coupled Phenomena in Environmental Geotechnics (CPEG 2013), M. Manassero, A. Dominijanni, S. Foti, and G. Musso, Eds., CRC Press/Balkema, Taylor & Francis Group, London, 45-60. Shackelford, C., Malusis, M., and Olsen, H. 2003. Clay membrane behavior for geoenvironmental containment. Soil and Rock America Conference 2003, P.J. Culligan, H.H. Einstein, and A.J. Whittle, Eds., Verlag Glückauf GMBH, Essen, Germany, Vol. 1, 767-774. Sherwood, J., and Craster, B. 2000. Transport of water and ions through a clay membrane. Journal of Colloid and Interface Science, 230(2): 349-358.
