Non-reactive solute diffusion in unconfined and confined specimens of a compacted soil

Waste Management 29 (2009) 404–417

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Non-reactive solute diffusion in unconfined and confined specimens of a compacted soil Catherine S. Hong a, Melanie M. Davis b,1, Charles D. Shackelford a,* a b

Department of Civil and Environmental Engineering, 1372 Campus Delivery, Colorado State University, Fort Collins, CO 80523-1372, USA Tetra Tech Inc., 3801 Automation Way, Suite 100, Fort Collins, CO 80524, USA

a r t i c l e

i n f o

Article history: Accepted 21 April 2008 Available online 16 June 2008

a b s t r a c t The effect of specimen confinement on the determination of the effective diffusion coefficients, D*, for chloride, a non-reactive (non-adsorbing) solute, diffusing in a compacted soil was evaluated. The diffusion tests were performed by placing an acetic acid/sodium acetate buffer solution containing ZnCl2 (pH  4.8) in a reservoir in contact with unconfined and confined specimens of a compacted sand–clay mixture for test durations of 7 or 14 d. The concentrations of chloride in the reservoir were measured as a function of time during the test, as well as a function of depth within the specimen at the end of the test. The resulting concentration distributions were analyzed using two models to Fick’s second law for non-reactive solute diffusion in porous media, viz., (1) an analytical model assuming the porosity distribution could be represented by a single, weighted mean porosity and (2) a commercially available model, POLLUTE, that directly accounted for the measured porosity distribution. The D* for unconfined specimens based on the analytical model tended to be overestimated by a factor ranging from 1.13 to 1.59 relative to the D* using POLLUTE, whereas the D* values based on both methods for confined specimens typically were more consistent. In addition, the D* for unconfined specimens was greater than the D* for confined specimens when soil concentrations were used for the analysis, presumably due to the higher porosity for the unconfined specimens relative to the confined specimens. Analyses based on reservoir concentrations were inconsistent and contradictory in some cases, suggesting that the D* values based on soil concentrations were more reliable. Ó 2008 Elsevier Ltd. All rights reserved.

1. Introduction Diffusion has been shown to be a significant, if not dominant, contaminant transport process in engineered waste containment barriers, including compacted clay liners (Goodall and Quigley, 1977; Crooks and Quigley, 1984; Shackelford, 1988, 1989, 1990; Toupiol et al., 2002; Willingham et al., 2004), subaqueous capping layers (Wang et al., 1991; Thoma et al., 1993), geosynthetic clay liners (Lake and Rowe, 2000a; Malusis and Shackelford, 2002, 2004), composite liners (Foose, 2002; Edil, 2003), and soil–bentonite vertical cutoff walls (Mott and Weber, 1991a,b; Devlin and Parker, 1996; Rabideau and Khandelwahl, 1998). As a result, considerable effort has been devoted to the evaluation of a variety of different methods to measure the effective diffusion coefficient, D*, of solutes diffusing in soils (e.g., Rowe et al., 1985, 1988; Cheung, 1989; Shackelford, 1991; Van Rees et al., 1991; Grathwohl, 1998; Rowe et al., 2000). In particular, the single reservoir, decreas-

* Corresponding author. Tel.: +1 970 491 50511; fax: +1 970 491 7727. E-mail addresses: [email protected] (M.M. Davis), shackel@engr. colostate.edu (C.D. Shackelford). 1 Tel.: +1 970 223 9600; fax: +1 970 223 7171. 0956-053X/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.wasman.2008.04.003

ing source concentration (SRDSC) method, which consists of placing a reservoir of a chemical solution over a column of soil so that solutes will diffuse from the reservoir into the soil, has been used extensively, especially with respect to compacted clay soils considered for use as liners in waste containment applications, such as landfills (e.g., Barone et al., 1989; Shackelford, 1989, 1991; Shackelford and Daniel, 1991a,b; Manassero and Pasqualini, 1993; Verga and Manassero, 1994; Airey and Carter, 1995; Manassero et al., 1995, 1996, 1997; Shackelford et al., 1997b; Cotten et al., 1998). For compacted clay soils, the test specimens in the SRDSC method typically are pre-saturated after compaction and before diffusion to destroy the suction in the test specimen and minimize the potential for advective mass transport of the solute from the reservoir into the soil. In such cases, unconfined test specimens typically swell at the reservoir–soil interface resulting in a nonuniform porosity distribution, with significantly higher porosities at the soil–reservoir interface (e.g., Shackelford et al., 1989; Shackelford and Daniel, 1991b; Manassero et al., 1996, 1997; Cotten et al., 1998). Because D* has been shown to correlate with the porosity (n) of the soil (or the volumetric moisture content, h, for unsaturated soils) through the tortuosity of the soil (e.g., Manheim, 1970; Lerman, 1978, 1979; Myrand et al., 1992; Parker et al., 1994;

C.S. Hong et al. / Waste Management 29 (2009) 404–417

Polak et al., 2002), the porosity distribution existing within the specimen may affect the results of SRDSC diffusion tests. Although the results of SRDSC diffusion tests performed on both unconfined and confined test specimens have been reported in some studies (e.g., Manassero et al., 1996, 1997), the focus of these studies has been on selected factors other than specimen confinement that can affect the measurement of the D*, such as the effect of nonlinear sorption on adsorbing cations and the potential influence of a concentration discontinuity existing at the reservoir–soil interface. Thus, no systematic study specifically focusing on the potential effect of the degree of confinement of the test specimens on the resulting D* values has been conducted. As a result, the primary purpose of this study was to evaluate the effect of the degree of confinement on the measured D* values of a non-reactive (nonadsorbing) solute for a compacted soil using the SRDSC method. In addition, the effects of the method of analysis of the results to determine the D* values, the duration of the tests (i.e., 7 or 14 d), and the use of reservoir or soil concentration profiles in the determination of D* also were evaluated. Although the degree of confinement of compacted clay liners in the field typically is not known a priori, and may vary depending on the nature and sequence of loading conditions, the results of this study may be useful in terms of interpreting the results of diffusion tests performed with potential compacted clay liner materials using the SRDSC method.

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Fig. 1. Compaction curve for 75% sand–25% attapulgite clay mixture.

2. Materials and methods

2.2. Liquids

2.1. Soil

Three liquids were used in this study: deionized distilled water (DDW, pH 5.8), an acetic acid/sodium acetate (HOAc/NaOAc) buffer solution (pH 4.8), and ZnCl2 dissolved in the buffer solution. The DDW was used in compacting test specimens of the sand–attapulgite clay mixture (Fig. 1). The 1.0 M HOAc/1.4 M NaOAc buffer solution was permeated through the test specimens prior to diffusion testing to: (1) saturate the tests specimens and minimize advective transport due to suction in the compacted specimens and (2) buffer the pH of the test specimens to 4.8 to control the relatively high pH (9) of the soil mixture (Shackelford et al., 1997a,b; Cotten et al., 1998). Solutions of the anhydrous ZnCl2 dissolved in the 1.0 M HOAc/1.4 M NaOAc buffer were used to evaluate the chloride migration in the diffusion tests. The measured chloride concentrations in these solutions ranged from 227 to 323 mg/L. Chloride was used in this study because chloride is generally considered a non-reactive solute with respect to adsorption by clays. A batch equilibrium adsorption test (BEAT) performed using the chemical solution and the sand–attapulgite clay mixture indicated no measurable adsorption of chloride with the soil (e.g., see Shackelford et al., 1997a,b; Cotten et al., 1998).

The soil used in this study was a mixture of 75% sand and 25% attapulgite clay (dry weight basis). Attapulgite clay is a soil comprised primarily of attapulgite clay mineral (palygorskite), and has been used in barriers for waste containment primarily because the attapulgite clay mineral is relatively inert in the presence of chemicals compared with other commonly used clay mineral soils, such as bentonite (Tobin and Wild, 1986; Ryan, 1987; Broderick and Daniel, 1990; Shackelford, 1994). Both of the constituent materials and the mixture composition have been used previously for column testing to evaluate zinc migration in unconfined specimens (Shackelford et al., 1997a), and for diffusion testing of unconfined specimens in accordance with the SRDSC method (Cotten et al., 1998). The attapulgite clay was obtained under the trade name Min-UGel FG from the Floridin Co., Quincy, FL, USA, and the sand was obtained from the Colorado Lien Co., Laporte, CO, USA, under the trade name 40-140 Silica Sand. The measured specific gravity of solids (Gs) based on ASTM D 854 for the attapulgite clay and sand were 2.56 and 2.65, respectively. The sand was comprised of 99% sand-sized particles (0.074–4.75 mm) and 1% silt-sized particles (0.002 to 0.074 mm) based on ASTM D 421 and 422, whereas the attapulgite clay was comprised of 34% silt-sized particles and 66% clay-sized particles (<0.002 mm). The measured liquid limit and plasticity index for the attapulgite clay (ASTM D 4318) were 338 and 216, respectively, and the measured cation exchange capacity (CEC) was 29.2 meq/100 g. The sand classified as poorly graded (SP) based on the Unified Soil Classification System (ASTM D 2487), whereas the attapulgite clay classified as a high plasticity clay (CH). Further properties of the constituent materials are provided by Shackelford et al. (1997a) and Cotten et al. (1998). Compaction test results (ASTM D 698) for the sand–clay mixture are shown in Fig. 1. The optimum gravimetric water content, wopt, was 23.1% and the maximum dry unit weight, cdmax, was 14.6 kN/m3 (92.9 lb/ft3) as determined using a third-order polynomial fit to the compaction test results in accordance with Howell et al. (1997).

2.3. Testing apparatus Except for allowing the possibility to confine the test specimens, the test apparatus shown schematically in Fig. 2a is the same as described by Shackelford et al. (1997a,b). The test apparatus essentially consists of a permeation/diffusion test cell located between clear acrylic influent and effluent accumulators used to store permeant liquid and to collect effluent, respectively, during the permeation stage of the test prior to diffusion testing. The diffusion test cell is shown schematically in Fig. 2b. One reservoir filling/drainage tube and the effluent collection tube were open during permeation, and closed upon commencement of the diffusion test. The length of the molds, L, in this study was 5.83 cm with a volume of 486 cm3. Therefore, the test specimen molds used in this study were approximately one-half (51.5%) of the volume

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Fig. 2. Test apparatus: (a) permeation arrangement with accumulators and (b) diffusion cell.

of a standard Proctor mold (ASTM D 698). A mold length less than the standard Proctor mold length (11.64 cm) was desired to reduce the time required for permeation prior to the diffusion test. Test specimens were confined by inserting a geosynthetic layer consisting of one 3.81-mm-thick layer of Tensar NS1305 geonet overlying one 0.89-mm-thick layer of Synthetic Industries 381 nonwoven needle-punched geotextile between the soil mold and the liquid reservoir. Thus, the combined thicknesses of the geonet and geotextile represented only 8.1% of the thickness of the com-

pacted soil specimens. A BEAT performed with the geosynthetic materials and the chemical solution indicated no measurable adsorption of chloride to the geosynthetic materials. The liquid reservoir had one sampling port and two inflow/outflow ports. The reservoir sampling ports were fitted with MininertÒ valves (VICI Precision Sampling Corp., Baton Rouge, LA) containing a septum through which a needle could be inserted for collection of a reservoir sample when the valve was open. The positions of the inflow/outflow ports allowed for mixing of the solution during reservoir filling and draining.

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2.4. Specimen preparation The sand–clay mixture specimens were mixed with DDW incrementally, as described by Shackelford et al. (1997a,b), until the water content was at least six percentage points above the optimum water content (23.1%). This relatively high initial water content was desired to ensure a high initial degree of saturation of the specimens, thereby minimizing the time required for permeation before diffusion testing. The wetted soil mixtures were placed in double ZiplockÒ freezer bags, sealed, and allowed to cure for 24 h before compaction. The wetted soil mixtures were compacted into the same stainless-steel molds as used to develop the compaction curve to prepare the test specimens. The test specimens were compacted by following ASTM D 698, except that the compaction energy was about 98% of the standard energy due to the smaller mold volume. The resulting compaction water contents and dry unit weights of the test specimens are shown in Fig. 1. 2.5. Diffusion testing procedures The compacted sand–attapulgite clay specimens were permeated prior to diffusion testing with the HOAc/NaOAc buffer solution to promote saturation of the soil specimen and to buffer the soil specimen pH to a value of 4.8 primarily to prevent precipitation of zinc (e.g., see Shackelford et al., 1997a,b; Cotten et al., 1998). Test specimens that were not confined by a geosynthetic layer swelled into the liquid reservoir during permeation. For these unconfined specimens, the swollen soil was trimmed periodically to maintain a constant soil specimen thickness equal to the length of the mold. At the end of permeation, excess pore-water pressures resulting from the applied hydraulic gradient were allowed to dissipate, the effluent collection tube at the bottom of the cell was closed, and the permeant liquid was drained from the reservoir. The weight of each test specimen was measured for determination of the initial water content in the specimen prior to diffusion testing. The diffusion tests were performed for both unconfined and confined test specimens for durations of 7 and 14 d. Each test was performed in duplicate. Thus, eight diffusion tests were performed, two tests for unconfined specimens with durations of either 7 d (UC7-1, UC7-2) or 14 d (UC14-1, UC14-2), and two tests for confined specimens with durations of either 7 d (C7-1, C7-2) or 14 d (C14-1, C14-2). Except for the confinement aspects of the confined tests as previously described, the diffusion tests followed the same procedures as detailed by Shackelford et al. (1997b) and Cotten et al. (1998) for SRDSC tests. Diffusion was initiated by introducing the ZnCl2 solution into the reservoir. The reservoir was sampled either daily (7-d tests) or every 2 days (14-d tests). The height of the reservoir liquid was measured periodically with a cathetometer (ASTM D 5084), to provide an indication of any advective transport into the specimen due to the possibility of residual suction in the soil after permeation. For all tests, the change in height of the liquid reservoir over the duration of the test accounting for reservoir sampling was negligible (<0.1%). All diffusion tests were performed at ambient laboratory temperatures (20.5 ± 2.5oC). At the end of diffusion testing, the solution was drained from the reservoir, the diffusion cell was broken down, and the soil specimen was extruded carefully from the mold using an extrusion device similar to that described by Shackelford et al. (1989). The soil specimen was sliced into 5-mm thick slices at selected intervals during the extrusion, and the weight of the each slice was measured. Spatial distributions of water content and chloride concentration within the soil specimens were based on alternate slices. The measured water contents were used to calculate the porosity

407

distributions assuming saturated soil. For determination of water content, the entire slice was weighed before being placed in an oven. For determination of the chloride concentrations, the pore fluid was squeezed from each slice using a large capacity (90 kN) load frame, and the chloride concentrations were measured using an ion selective electrode (ISE) containing an Orion chloride solid state electrode (Orion model No. 941700). 2.6. Analysis of data The diffusion test data were analyzed to determine D* values based on two approaches, viz. an analytical approach using an analytical (closed-form) model and a numerical approach using POLLUTE (Version 6, GAEA Environmental Engineering Ltd., Canada), a commercially available finite-layer contaminant migration model. Both models represented solutions to Fick’s second law for nonreactive solute diffusion in porous media for the case of decreasing source concentration and finite cell length. However, the analytical model is based on the assumption of a constant porosity distribution, whereas non-uniform porosity distributions within the soil can be taken into account with POLLUTE by separating the soil domain into a number of consecutive sub-layers each of finite thickness with different representative porosity values. The analytical approach has previously been used to analyze diffusion test data for the D* of both unconfined and confined soil specimens (e.g., Manassero et al., 1996, 1997; Shackelford et al., 1997b; Cotten et al., 1998), and POLLUTE has been used extensively to evaluate D* values from laboratory diffusion tests (e.g., Rowe et al., 1988; Barone et al., 1989; Shackelford and Daniel, 1991b; Manassero et al., 1996, 1997; Lake and Rowe, 2000a,b; Hrapovic and Rowe, 2002; Lorenzetti et al., 2005). The analytical model can be represented as follows (Crank, 1975; Shackelford, 1991; Shackelford et al., 1997b; Cotten et al., 1998): 1 X cðx P 0; tÞ a 2a ¼ þ c0 1 þ a m¼1 1 þ a þ a2 q2m   D q2 t cos½qm ð1  xLÞ  exp  2m cos ðqm Þ L

ð1Þ

where c(x, t) is the chloride concentration at any distance x and time t, co is the initial chloride concentration in the source reservoir, L is the length of the soil in the mold (Fig. 2b), and D* is the effective diffusion coefficient defined as the product of the aqueous (free-solution) diffusion coefficient (Do) and the apparent tortuosity factor (sa < 1), or D* = Dosa (Shackelford and Daniel, 1991a). The values of qm are the non-zero positive roots of the following function:

tanðqm Þ ¼ aqm

ð2Þ

where a is a constant defined as follows:

a¼

HL nL

ð3Þ

HL is the height of the liquid in the source reservoir (Fig. 2b), and n is the total porosity of the soil specimen. The value for n used in Eq. (3) was based on the weighted mean porosity, nmean (=n), which was equal to the sum of the products of the individual values of porosity for each soil slice, ni, multiplied by their respective representative thickness, DLi, and divided by the total thickness of the soil specimen, L (=RDLi), or nmean = R(niDLi)/RDLi. Eqs. (1)–(3) were programmed using the computer software, MicrosoftÒ Office Excel (Version 2003, Microsoft Corporation). The value of a (Eq. (3)) was determined using the solver in the Excel program, and the accuracy was checked by comparing the calculated a values with those tabulated by Crank (1975). The accuracy of the analytical model was checked by comparing simulation results based on a

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constant, uniform porosity distribution within the soil specimen with those generated using POLLUTE for a variety of D* values. Each model was used to determine an effective diffusion coefficient based on the reservoir concentration data, DReservoir (=D* in Eq. (1) for x = 0, t > 0), as well as an effective diffusion coefficient based on the soil concentration data, DSoil (=D* in Eq. (1) for x > 0, t = 7 or 14 d) for each test. For each set of test results, the procedure involved determining by trial and error the value for DReservoir or DSoil that matched each measured reservoir or soil concentration, respectively, and then determining the means of the D* values so determined to arrive at an overall DReservoir or DSoil value for each test. The mean DReservoir or DSoil so determined was then used with the respective model to generate a simulated concentration profile for the data set. The goodness of fit for the data set was provided by determining the coefficient of determination, r2, resulting from comparing the simulated profile with the measured data. This procedure has been used previously for the analysis for effective diffusion coefficients from the results of diffusion tests (Shackelford et al., 1989; Shackelford and Daniel, 1991b; Cotten et al., 1998). For the confined specimens, the potential effect of the geosynthetic confining layer on interpretation of the measured concentration profiles was considered (e.g., Olsen et al., 1965). However, any effect resulting from existence of the geosynthetic confining layer was expected to be minimal for two reasons. First, as previously mentioned, the chemical solution was found to be inert with respect to the geonet and geotextile used as the confining layer such that no sources or sinks for chloride within the confining layer

were expected. Second, the significantly smaller thickness and overall greater porosity of the geosynthetic confining layer relative to those for the compacted specimen suggested that diffusion of chloride through the geosynthetic confining layer would be relatively unrestricted and rapid. Nonetheless, the potential influence of the geosynthetic confining layer should be considered when interpreting the results of this study. Finally, as noted by Manassero et al. (1997), the results of diffusion tests such as conducted in this study often indicate a discontinuity in the concentration profiles at the reservoir–soil interface, whereby the concentration on the reservoir side of the reservoir– soil interface at the end of the test, or cx = 0, is greater than the concentration on the soil side of the reservoir–soil interface at the end of the test, or cx = 0+. Accordingly, they applied a correction factor, d (<1), representing the ratio of the two concentrations (i.e., d = cx = 0+/cx = 0) to the analytical model (Eqs. (1)–(3)) to force continuity in the reservoir and soil concentration profiles at the reservoir–soil interface, and reported some improvement in their assessment of the values of D* for bromide (Br–) and potassium (K+). However, Manassero et al. (1997) noted that the improvement in interpretation was primarily associated with the reactive solute (i.e., K+), as opposed to the non-reactive solute (i.e., Br–), and that the scatter in the data was still significant regardless of their revised method of analysis, such that the improvement in interpretation was not all that significant. As a result, the approach to data interpretation proposed by Manassero et al. (1997) was not undertaken in the current study.

Fig. 3. Final porosity distributions and weighted mean porosity values for unconfined (UC) and confined (C) specimens tested for 7 or 14 d.

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3. Results

3.2. Concentration profiles and effective diffusion coefficients

3.1. Porosity distributions

The measured concentration data and simulated concentration profiles for all eight diffusion tests are shown in Figs. 4–7. The resulting D* values as well as the corresponding coefficients of determination, r2, and the number of concentrations, N, upon which the r2 values were based are summarized in Table 2. Since a D* value was not determined for the initial source reservoir concentration [i.e., c(0, 0)], the number of D* values upon which DReservoir was based equals N  1, whereas the number of D* values upon which DSoil was based equals N. Some consideration of the overall quality of the data is in order prior to a discussion of the results. Measured concentrations that were excluded from consideration in the analyses based on both the analytical model and POLLUTE are denoted in Figs. 4–7 with a question mark (?), whereas measured concentrations excluded from analysis based on only the analytical model or POLLUTE are marked with a question mark subscripted with either an ‘‘A” or a ‘‘P” (i.e., ‘‘?A” or ‘‘?P”), respectively. Exclusion of these data was based on one or more of the following criteria. First, some measured concentrations apparently were outside the realm of possibility such that a D* value could not be obtained using the POLLUTE program. Second, since the apparent tortuosity factor as defined by Shackelford and Daniel (1991a), sa, must be less than unity for diffusion in porous media (i.e., sa < 1), the effective diffusion coefficient, D*, must be lower than the free-solution (aqueous) diffusion coefficient, Do, in accordance with the definition for D* (=Dosa). Thus, D* values that were obtainable but higher than the Do value for chloride of 2.03  105 cm2/s (Shackelford and Daniel, 1991a) were excluded from consideration on the basis that such D* values are physically impossible. Third, obtainable D* values that were one or more orders of magnitude lower than the mean D* value based on all the other concentrations for the data set were excluded as being unrepresentative of the data set. Except for the reservoir concentrations for specimen C7-1, the number of measured concentration data excluded from consideration based on the above criteria generally was not excessive, such that all analyses included a minimum of three concentrations. For example, N ranged from 5 to 8 based on reservoir concentrations, and from 3 to 7 based on soil concentrations. In the case of specimen C7-1, all of the DReservoir values except one based only on analysis using POLLUTE (see Fig. 6 and Table 2) were greater than the free-solution diffusion coefficient, Do, for chloride of 2.03  105 cm2/s, presumably due to error in the measured reservoir concentrations for this specimen. Based on the concentration data included in the analysis, mean D* values (i.e., either DReservoir or DSoil ) were calculated for each test. The mean D* value then was used to calculate the theoretical con-

The final porosity distributions based on the measured porosities of the soil slices at the end of diffusion testing for all test specimens are shown in Fig. 3. As expected, there is a contrast in the measured porosity distributions for unconfined versus confined specimens. The final porosity distributions for all unconfined test specimens were non-uniform with the porosity generally decreasing with increasing depth. The final porosity distributions for all confined test specimens were more uniform with depth compared to the unconfined test specimens. The difference between the porosity distributions for the unconfined and confined specimens shown in Fig. 3 represents the swelling that occurred in the unconfined test specimens during permeation relative to the confined test specimens. The porosity distributions in Fig. 3 also indicate that similar final porosity distributions existed among the four unconfined specimens as well as among the four confined specimens, suggesting that the reproducibility of the test specimens was good, and that the geosynthetic confining layer generally was effective in preventing significant swelling of the confined test specimens, although some swelling was apparent within the top 10 mm of the test specimen for test C7-1. The initial and final average properties of the test specimens are summarized in Table 1. The initial properties are based on the molding (compaction) water content and the as-compacted weight of the soil in the diffusion molds, whereas the final properties are based on values obtained from individual slices recovered at the end of the diffusion test and weighted with respect to the representatives of the slice as described by Shackelford et al. (1997a,b). The final, weighted mean porosity values given in Table 1 were used in the analyses for D* based on the analytical model (Eq. (3)). As indicated in Table 1, both unconfined and confined test specimens had similar initial (compacted) properties indicating that the specimen preparation procedure resulted in reproducible test specimens. In contrast, a comparison of the final (after testing) properties with the initial properties of the test specimens indicates a considerably greater amount of swelling associated with the unconfined test specimens relative to the confined test specimens. For example, the final mean porosity values for the unconfined test specimens ranged from 125% to 128% of the initial porosity values, whereas the final mean porosity values for the confined specimens were all within 104% of the initial porosity values. This slight increase in final porosity values for the confined specimens can be attributed to the small amount of swelling that occurred near the reservoir–soil interface (e.g., test C7-1 in Fig. 3).

Table 1 Initial and final properties of test specimens Test type

Test designation

Initial propertiesa

Final propertiesb

Ratios of properties

Water content, wi (%)

Porosity, ni

Dry unit weight, cdi (kN/m3)

Water content, wf (%)

Porosity, nf

Dry unit weight, cdf (kN/m3)

wf/wi

nf/ni

cdf/cdi

Unconfined

UC7-1 UC7-2 UC14-1 UC14-2

29.2 29.3 29.0 29.5

0.449 0.453 0.445 0.449

14.2 14.1 14.3 14.2

66.8 63.6 67.4 65.2

0.564 0.568 0.570 0.568

11.5 11.4 11.3 11.2

2.29 2.17 2.32 2.21

1.26 1.25 1.28 1.27

0.810 0.809 0.790 0.789

Confined

C7-1 C7-2 C14-1 C14-2

29.8 29.5 30.0 28.5

0.453 0.449 0.457 0.460

14.1 14.2 14.0 13.9

32.5 32.1 31.9 32.1

0.470 0.459 0.467 0.468

13.9 14.0 13.8 13.7

1.09 1.09 1.06 1.13

1.04 1.02 1.02 1.02

0.986 0.986 0.986 0.986

a b

Values based on as-compacted specimen. Values based on weighted-averages of incremental slices of specimen after testing.

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Fig. 4. Chloride diffusion test results for unconfined specimens and a 7-d test duration.

centration profiles for the soil and reservoir using either the analytical model or POLLUTE, as shown in Figs. 4–7, and r2 was determined based on the difference between the measured concentrations and the theoretical concentrations using the mean D* value. Geometric mean D* values were used instead of arithmetic mean D* values because the geometric mean D* values provided as good or better fits to the measured concentration profiles (i.e., the same or higher r2) in the majority of the analyses (i.e., 25 of the 31 analyses, or 81%). For the remaining analyses, the r2 value based on the arithmetic mean D* value was only slightly higher than that based on the geometric mean D* value (Dr2 6 0.003), such that the resulting theoretical concentration profiles based on the geometric mean D* were essentially the same as those based on the arithmetic mean D*. In all cases except for specimen C7-1, where the arithmetic mean DReservoir was the same as the geometric mean DReservoir due to the previously noted limited concentration data for this test, the geometric mean D* values were lower than the arithmetic mean D* values by a factor ranging from 0.6% (analytical-based DReservoir for specimen UC14-1) to 37.9% (POLLUTEbased DSoil for specimen C14-2). 4. Discussion 4.1. Comparison of measured D* values with the literature The D* values reported in Table 2 range from a low of 3.11  106 cm2/s (D* for C7-2 based on the analytical model using soil concentrations) to a high of 1.40  105 cm2/s (D* for C14-2

using reservoir concentrations). Shackelford and Daniel (1991a) reported apparent tortuosity factors, sa, taken from the literature for diffusion of 36Cl in confined specimens of compacted sand–bentonite mixtures as ranging from 0.04 to 0.59, which corresponds to D* values ranging from 8.12  107 to 1.20  105 cm2/s based on a Do for chloride of 2.03  105 cm2/s. Thus, the range of D* values measured in this study is somewhat higher than that reported for confined specimens of compacted sand–bentonite mixtures. The difference likely is due, in part, to the typically smaller particle sizes (smaller pores), greater surface area, and greater swelling potential associated with bentonite relative to the attapulgite clay used in this study. For unconfined specimens, Cotten et al. (1998) reported D* values for both chloride and zinc diffusing in compacted, unconfined specimens of the same sand–attalpulgite clay mixture and test procedures as evaluated in the current study, but for three testing durations (7, 14, and 21 d) and three different lengths of specimen (2.91, 5.83, and 11.60 cm). The measured D* values for chloride reported by Cotten et al. (1998) ranged from 3.4  106 to 1.2  105 cm2/s, i.e., excluding values greater than Do. Thus, the range of D* values for chloride reported in the present study compares favorably with that previously reported by Cotten et al. (1998). Finally, based on an extensive summary of the literature, Shackelford (1991) reported measured D* values for non-reactive solute species (Br–, Cl–, NO3–, and tritium) diffusing in a variety of types of saturated soils and testing conditions as ranging from 1.0  106 to 1.8  105 cm2/s. Thus, the range of D* values for chloride reported in the present study also is within the range previously reported for non-reactive solutes diffusing in a variety of saturated soils.

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411

Fig. 5. Chloride diffusion test results for unconfined specimens and a 14-d test duration.

4.2. Effect of method of analysis Values of the ratios of D* determined using the analytical model, to those determined using POLLUTE, DPOLLUTE , or for both unconfined and confined specimens are shown in Fig. 8 as a function of the concentration distribution used in the analysis (reservoir vs. soil) and the test duration (7 vs. 14 d). As indicated in Fig. 8, both individual test results and the geometric means of the individual test results are shown since the comparison involves results within the same test (i.e., within a given row in Table 2) as opposed to between different tests (i.e., between rows in Table 2). For the unconfined specimens, all D* values obtained using the analytical model were greater than those obtained using the POLLUTE model, with 1.20 6 DAnalytical =DPOLLUTE 6 1.59 based on the reservoir concentrations and 1.13 6 DAnalytical =DPOLLUTE 6 1.37 based on soil concentrations. Thus, use of the analytical model based on the simplified assumption that the non-uniform porosity distribution for the unconfined specimens could be approximated by a single, weighted mean porosity value for each specimen consistently overestimated D*, and this overestimation tended to be greater when D* was based on reservoir concentrations versus soil concentrations. For the confined specimens, significant differences between D* values determined using the analytical model versus those determined using POLLUTE were not expected, since the effect of confinement was to reduce the variation in the porosity distribution relative to that occurring for the unconfined specimens, such that the difference between the use of a single, weighted mean porosity

DAnalytical , relative DAnalytical =DPOLLUTE ,

value versus the actual porosity distribution was less that that for the unconfined specimens (see Fig. 3). In terms of the mean D* values, this expectation was generally met in that the mean DAnalytical was only slightly greater than mean DPOLLUTE , with 1.07 6 DAnalytical =DPOLLUTE 6 1.16 for all the analyses except those based on soil concentrations for a test duration of 7 d (Fig. 8), where the mean DAnalytical value was lower than the mean DPOLLUTE value by 19% (i.e., DAnalytical =DPOLLUTE = 0.81 or 81%). However, this difference in results based on soil concentrations for specimens C7-1 and C7-2 can be attributed entirely to specimen C7-2, where DAnalytical =DPOLLUTE was only 0.62 versus DAnalytical =DPOLLUTE of 1.05 for specimen C7-1. Thus, in general, less difference in the results based on the analytical model versus POLLUTE occurred for the confined specimens relative to the unconfined specimens, as expected. 4.3. Effect of concentration distribution Test results from the SRDSC diffusion tests typically have reported DReservoir greater than DSoil (Shackelford et al., 1989, 1997b; Shackelford and Daniel, 1991b). For example, Shackelford and Daniel (1991b) found that values for DReservoir =DSoil for diffusion of two anions (Br, Cl) in two unconfined, compacted clay soil specimens were in the range 1.18 6 DReservoir =DSoil 6 3.13 for seven of the eight reported test results for Cl, and 1.18 6 DReservoir =DSoil 6 1.90 for three of the five reported test results for Br. Van Rees et al. (1991) report 1.18 6 DReservoir =DSoil 6 1.36 for tests involving tritium diffusion in packed saturated littoral sediments. The somewhat improved correlation between DReservoir and DSoil for the

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Fig. 6. Chloride diffusion test results for confined specimens and a 7-d test duration.

results of Van Rees et al. (1991) relative to those of Shackelford and Daniel (1991b) may be due, in part, to the inherently improved detection sensitivity associated with measuring the activities of the radioactive tracer, tritium, as well as the difference in soil types and specimen confinement conditions. In the case of metals, the difference in DReservoir and DSoil has been attributed, in part, to the possibility of precipitation of the metals in the source reservoir (Shackelford et al., 1989; Shackelford and Daniel, 1991b). However, Shackelford et al. (1997b) found that DReservoir was still typically greater than DSoil even though the same special precautions taken in the current study were also used to control the pH and minimize precipitation of zinc. In the case of non-reactive solutes, typically anions such as chloride, no consistent explanation has been provided for the typical discrepancy between DReservoir and DSoil values previously noted. Nonetheless, the DSoil values generally are considered to be more reliable and probably more accurate than the DReservoir values (Shackelford et al., 1989). As a result of the above considerations, values of DReservoir =DSoil are shown in Fig. 9 as a function of the method of analysis (analytical model vs. POLLUTE) and test duration (7 vs. 14 d) for both unconfined and confined specimens. As indicated in Fig. 9, both individual test results and the geometric means of the individual test results are shown since the comparison involves results within the same test (i.e., within a given row in Table 2) as opposed to between different tests (i.e., between rows in Table 2). In terms of the unconfined specimens, the results of the analyses are inconsistent. For example, DReservoir is less than DSoil for test specimens UC7-1 and UC14-1 based on analyses using both the

analytical model and POLLUTE as well as for UC14-2 based on analyses using POLLUTE, whereas DReservoir is greater than DSoil for test specimens UC7-2 based on analyses using both the analytical model and POLLUTE as well as for UC7-2 based on analysis using POLLUTE. However, in terms of the confined specimens, all DReservoir values are greater than DSoil values, and in most cases significantly greater (e.g., except for specimen C14-1, 1.90 6 DReservoir =DSoil 6 4.39), regardless of method of analysis or test duration. Overall, considering both unconfined and confined test specimens, DReservoir was greater than DSoil in the majority of cases. Since no significant decrease in the reservoir liquid height was observed for the tests in this study, the relatively high DReservoir values can not be attributed to advective mass transport from the reservoir into the test specimen during diffusion testing. Also, higher DReservoir values are not likely due to precipitation of the zinc chloride in the reservoir given the special precautions taken in this study to prevent such precipitation. Regardless of the reason for the differences between DReservoir and DSoil , and despite the somewhat inconsistent results obtained for some of the analyses of the unconfined specimens, the results of this comparison suggest that DReservoir tends to be greater than DSoil , which is consistent with the results of other studies using similar materials and methods, as previously noted. 4.4. Effect of test duration Cotten et al. (1998) evaluated the effect of three test durations (7, 14, and 21 d) on values of D* for zinc and chloride diffusing in unconfined specimens of the same compacted soil as used in this study. They reported that the mean D* values from duplicate tests

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Fig. 7. Chloride diffusion test results for confined specimens and a 14-d test duration.

for both chloride and zinc tended to decrease with increasing test duration, and attributed this decrease to the possibility of concentration dependent D* values. As a result of this potential effect of test duration, values of the ratio of D* determined from the tests conducted for 14 d, D14 d , relative to D* determined from the tests conducted for 7 d, D7 d , or D14 d =D7 d , for analyses based on both the analytical model and POLLUTE are shown in Fig. 10 as a func-

tion of degree of specimen confinement (unconfined vs. confined) and as a function of the concentration distribution used in the analysis (reservoir vs. soil). As indicated in Fig. 10, only the geometric means of the duplicated tests are shown since the comparison involves results between different tests (i.e., between rows in Table 2) as opposed to within the same test (i.e., within a given row in Table 2).

Table 2 Diffusion test results for chloride Test notation

Effective diffusion coefficient, D* (106 cm2/s)a Based on reservoir concentrations Analytical

UC7-1 UC7-2 Mean UC14-1 UC14-2 Mean C7-1 C7-2 Mean C14-1 C14-2 Mean

Based on soil concentrations POLLUTE

Analytical

POLLUTE

DReservoir

r2

N

DReservoir

r2

N

DSoil

r2

N

DSoil

r2

N

4.60 9.34 6.55 3.37 9.25 5.58 – 10.2 10.2 5.59 14.0 8.85

0.871 0.856 – 0.989 0.950 – – 0.839 – 0.878 0.989 –

7 6 – 7 8 – 1 8 – 7 5 –

3.49 7.76 5.20 2.12 6.63 3.75 17.9 9.51 13.0 4.13 14.0 7.60

0.551 0.816 – 0.987 0.957 – 1.000 0.842 – 0.879 0.977 –

8 7 – 7 8 – 3 8 – 6 6 –

8.42 5.24 6.64 5.86 8.99 7.26 5.10 3.11 3.98 4.94 3.19 3.97

0.967 0.997 – 0.903 0.950 – 0.925 0.940 – 0.987 0.919 –

5 6 – 4 5 – 7 6 – 6 5 –

6.13 4.64 5.33 4.76 7.32 5.90 4.86 5.00 4.93 3.59 3.52 3.55

0.987 0.997 – 0.987 0.968 – 0.958 0.992 – 0.990 0.790 –

4 6 – 3 5 – 7 4 – 6 5 –

a 2 r = the coefficient of determination; N = the number of measured concentrations used in the analyses (Note: the number of D* values upon which DReservoir was based equals N – 1, whereas the number of D* values upon which DSoil was based equals N).

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Fig. 8. Ratio of effective diffusion coefficient based on analytical model, DAnalytical , to that based on POLLUTE, DPOLLUTE , for analyses of reservoir and soil concentrations and test durations of 7 d and 14 d.

Based on the results shown in Fig. 10, the mean D14 d values tend to be closer to mean D7 d values when the analytical model was used for the analysis versus when POLLUTE was used for the analysis. For example, based on the analytical model with soil concentrations, mean D14 d was almost identical to mean D7 d , with 1.00 6 D14 d =D7 d 6 1.09, whereas mean D14 d was somewhat lower than mean D7 d (0.85 6 D14 d =D7 d 6 0.87) when the analytical model was used with the reservoir concentrations. In contrast, mean D14 d was greater than mean D7 d based on the analysis using POLLUTE with the soil concentrations from the unconfined specimens (i.e., D14 d =D7 d = 1.11), whereas mean D14 d was substantially lower than mean D7 d (0.58 6 D14 d =D7 d 6 0.72) based on the analysis of the soil and reservoir concentrations for the confined specimens and the reservoir concentrations using POLLUTE for the unconfined specimens. Overall, mean D14 d was less than or equal to mean D7 d for all analyses involving the confined specimens. Thus, an increasing test duration tended to result in a decreasing D* value for the confined specimens, which is similar to the findings reported by Cotten et al. (1998) for tests involving unconfined specimens of the same soil and analyses based on the analytical modeling approach used herein. As noted by Cotten et al. (1998), the reasons for this trend are not certain, but could be due to concentration dependent D* values. 4.5. Effect of confinement Values of the ratio of D* determined from the tests conducted using unconfined specimens, DUnconfined , relative to D* determined from the tests conducted using confined specimens, DConfined , or DConfined =DUnconfined , for analyses based on both the analytical model and POLLUTE are shown in Fig. 11 as a function of the concentra-

Fig. 9. Ratio of effective diffusion coefficient based on reservoir concentrations, DReservoir , to that based on soil concentrations, DSoil , for analyses based on analytical model and POLLUTE and test durations of 7 d and 14 d.

Fig. 10. Ratio of effective diffusion coefficient based on 14-d test duration, D14 d , to that based on on 7-d test duration, D7 d , for analyses of reservoir and soil concentrations for unconfined and confined specimens of compacted clay soil.

tion distribution used in the analysis (reservoir vs. soil) and the test duration (7 vs. 14 d). As indicated in Fig. 11, only the geometric means of the duplicated tests are shown since the comparison involves results between different tests (i.e., between rows in Table 2) as opposed to within the same test (i.e., within a given row in Table 2). As indicated in Fig. 11, two consistent trends exist in the mean D* values determined based on confined versus unconfined specimens. First, mean DConfined is greater than mean DUnconfined when reservoir concentrations were used for the analysis, regardless of test duration or method of analysis. Second, mean DConfined is lower than mean DUnconfined when soil concentrations were used for the analysis, regardless of test duration or method of analysis. The extent to which mean DConfined is greater than mean DUnconfined when reservoir

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415

Fig. 11. Ratio of effective diffusion coefficient based on confined specimens, DConfined , to that based on unconfined specimens, DUnconfined , for analyses of reservoir and soil concentrations and test durations of 7 d and 14 d.

concentrations were used in the analysis was greater based on the analysis involving POLLUTE (i.e., 2.03 6 DConfined =DUnconfined 6 2.50) versus the analysis involving the analytical model (i.e., 1.56 6 DConfined =DUnconfined 6 1.59). With the exception of the 7-d tests involving analysis of soil concentrations using POLLUTE, where DConfined =DUnconfined = 0.93, the extent to which mean DConfined is lower than DUnconfined based on analysis using soil concentrations is relatively consistent regardless of method of analysis, with 0.55 6 DConfined =DUnconfined 6 0.60. Thus, based on the results of this study, DConfined tends to be greater than DUnconfined by a factor ranging from 1.56 to 2.50 when reservoir concentrations are used in the analysis, and the difference between DConfined and DUnconfined is greater when the non-uniform porosity distribution is taken into account in the analysis for D*, whereas DUnconfined tends to be greater than DConfined by a factor ranging from 1.08 (=1/0.93) to 1.82 (=1/0.55) when soil concentrations are used in the analysis. As previously noted, D* has been shown to correlate empirically with the porosity, n, of geologic porous media via the apparent tortuosity factor (e.g., Manheim, 1970; Lerman, 1978, 1979; Myrand et al., 1992; Parker et al., 1994; Polak et al., 2002). The general expression for this empirical correlation may be written as follows:

sa ¼

D ’ nb Do

ð4Þ

where all parameters are the same as previously defined, and values for the exponent, b, have been shown to vary between 1.3 and 5.4 depending on the type of porous medium (e.g., see Parker et al., 1994). Based on the correlation indicated by Eq. (4), values for the apparent tortuosity factor, sa, based on the geometric mean DSoil values found in this study and the previously noted aqueous diffusion coefficient, Do, for chloride of 2.03  105 cm2/s (Shackelford and Daniel, 1991a), values for the apparent tortuosity factor, sa, are plotted in Fig. 12 versus values for the arithmetic means of the weighted-mean porosities for both the unconfined and confined specimens tested in this study (see Fig. 3). Values of sa versus n reported by Parker et al. (1994) for a wide range of soil types and tracers are also shown in Fig. 12 for comparison. As indicated in Fig. 12, arithmetic mean porosities and apparent tortuosity factors, sa, based on the results of this study for DSoil generally correlate with the empirical correlation given by Eq. (4) when the exponent b varies between about 1.8 and 2.4, which is also within the range for b stated by Parker et al. (1994). In addition, because the weighted mean porosities for the unconfined specimens are greater than those for the confined specimens, sa for the unconfined specimens are generally greater than sa for the confined specimens. Thus, DSoil for the unconfined specimens is likely greater than DSoil for the confined specimens, in part, sim-

Fig. 12. Correlation between porosity of soil and apparent tortuosity factor.

ply because the porosities for the unconfined specimens were greater than those for the confined specimens. By the same rationale, the fact that DConfined is greater than  DUnconfined based on analysis of the reservoir concentrations suggests that either some factor other than specimen porosity is dominating the interpretation of the D* based on reservoir concentrations, or that the analysis for D* based on reservoir concentrations in this study is inconsistent with the analysis for D* based on soil concentrations. Regardless of the exact reason for DConfined being greater than DUnconfined based on reservoir concentrations, the results of the comparison in this study provide further evidence that D* based on soil concentrations are likely to be more reliable than D* based on reservoir concentrations, despite the relatively greater difficulty in obtaining soil concentrations versus reservoir concentrations when performing diffusion tests using the procedures in this study. 5. Conclusions For unconfined specimens with non-uniform porosity distributions, analysis of the reservoir and soil concentration profiles using an analytical model with a single, weighted mean porosity value representing the porosity distribution for each specimen consistently overestimated D* by a factor ranging from 1.13 to 1.59 (i.e., 113–159%) relative to D* based on a commercially available model, POLLUTE, that directly accounted for the non-uniform porosity distribution of the specimens. This overestimation in D* based on the analytical model tended to be greater when D* was based on reservoir concentrations versus soil concentrations. However, for confined specimens with more uniform porosity distributions, the correlation between D* based on the analytical model versus D* based on POLLUTE typically was more consistent, presumably due to the smaller difference between the weighted mean porosity used with the analytical model versus the actual porosity distribution used with POLLUTE. Evaluation of the test results based on analyses of the concentration distribution (reservoir vs. soil) and test duration (7 vs. 14 d) were somewhat inconsistent and less convincing than the evaluation of the test results based on method of analysis or degree

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of confinement. However, the use of reservoir concentrations generally resulted in higher D* values than those based on soil concentrations, and an increasing test duration tended to result in a decreasing D* value for the confined specimens. Both of these trends are consistent with those found in previous studies evaluating D* for unconfined specimens. Regardless of method of analysis, the D* based on unconfined specimens was greater than the D* based on confined specimens when soil concentrations were used in the analysis, and vice versa when reservoir concentrations were used in the analysis. The fact that D* for unconfined specimens was greater than D* for confined specimens based on soil concentration profiles is consistent with the established correlation between the porosity of the soil, n, and the apparent tortuosity factor for the diffusing solute, sa, with higher n resulting in higher sa and higher D*. However, the fact that D* for the confined specimens was greater than D* for the unconfined specimens when reservoir concentrations were used for the analyses contradicts the same rationale, suggesting that some other factor aside from specimen porosity was prevalent in the interpretation of the reservoir concentrations. Since both precipitation and advective mass transport were negligible in the tests conducted in this study, the nature of the reason that D* for the confined specimens was greater than D* for the unconfined specimens based on reservoir concentrations is unknown. Nonetheless, the results of this study provide further evidence that D* based on soil concentrations is likely to be more reliable than D* based on reservoir concentrations, despite the relatively greater difficulty in obtaining soil concentrations versus reservoir concentrations when performing diffusion tests based on the single reservoir, decreasing source concentration method.

Acknowledgments Financial support for this study was provided by the US National Science Foundation (NSF) under Grant No. MSS-9122561. This support is gratefully acknowledged. The opinions expressed in this paper are solely those of the authors and are not necessarily consistent with the policies or opinions of NSF.

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