Applied Clay Science xxx (2013) xxx–xxx

CLAY-02720; No of Pages 8

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Applied Clay Science

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Research paper

An alternative approach for the use of DDL theory to estimate the swelling pressureof bentonites

Tom Schanz ⁎, Muhammad Ibrar Khan 1, Yasir Al-Badran 1

Laboratory of Foundation Engineering, Soil and Rock Mechanics, Ruhr-Universität Bochum, Building IA 4/126, Universitätsstrasse 150, D-44780 Bochum, Germany

⁎ Corresponding author. Tel.: +49 234 32 26135; fax: +E-mail addresses: tom.schanz@rub.de (T. Schanz),

abrar_fifa@hotmail.com (M.I. Khan), yasir.al-badranyasiralbadran@gmail.com (Y. Al-Badran).

1 Tel.: +49 234 32 26078.

0169-1317/$ – see front matter © 2013 Elsevier B.V. All rihttp://dx.doi.org/10.1016/j.clay.2013.07.018

Please cite this article as: Schanz, T., et al., Anplied Clay Science (2013), http://dx.doi.org/

a b s t r a c t

a r t i c l e i n f o

Article history:Received 10 May 2012Received in revised form 17 July 2013Accepted 19 July 2013Available online xxxx

Keywords:BentonitesSwelling pressureDiffuse double layerVoid ratio

An approach to estimate the swelling pressure of compacted bentonite (Bent) using Gouy–Chapman diffusedouble layer theory is presented. Several laboratory swelling pressure tests on compacted Bent (MX80 andCalcigel) under constant volume conditionswere performed and comparedwith the calculated swelling pressureusing the original theory. The study revealed that at low dry density the as prepared total void ratios are less thantheoretical void ratios using diffuse double layer theory, however, reverse behavior has been noticed for highcompaction dry densities. Based on the experimental results of Bent with different valences, the relationshipbetween the theoretical void ratio from diffuse double layer theory and as prepared total void ratio weredetermined. New equations were derived on the basis of diffuse double layer theory and experimental swellingpressure data. Themethod categorizes the different Bents into two groups depending upon theweighted averagevalency. A good agreement was observed in all the cases between experimental and estimated swelling pressureusing derived equations. The applicability of the proposedmethod was investigated by comparing the estimatedswelling pressure results with the additional reported in literature laboratory results on swelling pressure ofcompacted Bent.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

The safe disposal of high-level radioactive nuclear waste generatedfrom nuclear power plants is a great concern in many countries todaybecause of their long-term detrimental impact on humans if releasedinto the environment. Several methods for isolating this waste fromthe environment have been proposed by many countries. Of thesemethods, the geologic disposal of nuclear waste at depths of 300 to1000 m is the most viable method for many countries (Atomic Energyof Canada Limited, 1994; Japan Nuclear Cycle Development Institute,1999 Swedish Nuclear Fuel and Waste Management, 1992).

For the buffer and backfill materials it is required to have very lowhydraulic conductivity, long-term stability, high radionuclide adsorp-tion capacity, and high heat transfer capacity for very long periods(N10,000 years) (Brookins, 1984). Compacted Bent has attractedconsiderable attention as a candidate for buffer and backfill materialon account of its high swelling capacity, low hydraulic conductivity,and high radionuclide adsorption capacity (Ito, 2006; Martin et al.,2000; Sato and Suzuki, 2003; Stewart et al., 2003; Tripathy et al.,2004; Villar et al., 2005).

49 234 32 14236.muhammad.khan@rub.de,@rub.de,

ghts reserved.

alternative approach for the10.1016/j.clay.2013.07.018

Laboratory swelling pressure tests on compacted Bent have beencarried out by many researchers (Baille et al., 2010; ENRESA, 2000;Komine and Ogata, 1996; Schanz and Tripathy, 2009; Tripathy et al.,2004). Agus and Schanz (2005a) investigated the rate of swellingpressure of compacted Bent using plot of time versus pressure dividedby maximum pressure (or swelling pressure). It was found thatthe rate of swelling pressure development is a function of initial totalsuction of the specimen. The evolution of swelling pressure with timeduring the saturation process has been shown to be influenced by theinitial water content and dry density of clays (Baille et al., 2010;Schanz & Tripathy, 2009). Schanz and Tripathy (2009) measured theswelling pressures of compacted divalent rich Bent specimensemploying constant volume for a range of dry density from 1.10 to1.73 Mg/m3. They stated that during the saturation process, therates of expansion of the interlayer and interparticle pores, andthe contraction of the larger voids, influence the overall swellingpressure development in compacted Bent. Baille et al. (2010) inves-tigated the swelling behavior of Ca-Bent with an initial watercontent of 9.0%. They reported that initial compaction conditions af-fected the swelling pressure of the Bent. At the same water content,the swelling pressure increased with an increase in the dry density,whereas, at the same dry density, the swelling pressure was foundto decrease with an increase in the water content.

This paper presents the laboratory investigation of two Bents (MX80andCalcigel). The experimental swellingpressures of the Bents are com-pared with the swelling pressures obtained from the Gouy–Chapman

use of DDL theory to estimate the swelling pressure of bentonites, Ap-

2 T. Schanz et al. / Applied Clay Science xxx (2013) xxx–xxx

diffuse double layer theory. Modified equations for the determinationof swelling pressure are suggested. The suitability of the proposedequations was verified with additionally reported in the literatureexperimental swelling pressures of other Bents that have also beenproposed for use as barrier materials.

2. Theoretical background

Bents are clays that are composed of montmorillonite (Mt) withparticles commonly arranged in stacks of several 2:1 unit layers. Mt inBent expands by absorbing water. The Mt is consisting of an octahedralsheet sandwiched between two silica sheets. The octahedral sheet iscomposed of magnesium or aluminum coordinated octahedrallywith oxygen atom or hydroxyl group. The silica tetrahedron is inter-connected in a silica sheet structure. Three of the four oxygen atomsin each tetrahedron are shared to form a hexagon. Interlayer waterand exchangeable cations exist between the Mt layers. If the pressurerequired to keep the clay water system at the required equilibriumis less than the swelling pressure, volume expansion occurs, if thepressure is more than the swelling pressure, volume compressionoccurs (Bergaya et al., 2006; Grim, 1968).

In a clay water system, the adsorbed cations near the surface of theclay particles produce a much higher concentration as compared withthe ion concentration in solution away from the surfaces. Because ofthe difference in ion concentration in solution near the surfaces andaway from the surfaces of the clay particles, the cations near the surfacesof the particles try to diffuse away to equalize the concentrationthroughout. Their tendency to do so, however, is opposed by the nega-tive electric field originating in the particle surfaces. The tendency of theions to diffuse away and the opposing electrostatic attraction lead to iondistribution adjacent to a clay particle in suspension. The charged claysurface and the distributed charge in the adjacent phase are togethertermed the diffuse double layer (Bolt, 1956; Mitchell, 1993; Tripathyet al., 2004; Van, Olpen, 1963).

The Gouy–Chapman diffuse double layer theory (Chapman, 1913;Gouy, 1910) has been the most widely used approach to relate basicparticle water cation interaction (Mesri and Olson, 1971; Sridharanand Jayadeva, 1982). According to this theory, the interaction forcebetween two double layers depends on the ion concentration at themidplane between two adjacent parallel clay layers and is given bythe osmotic pressure in that plane (Bolt, 1956). Therefore, for anygiven separation distance between two clay layers the osmotic pressurecan be determined from the theory by knowing the concentration of theions in the central plane between the layers. According to Bolt (1956),the swelling pressure is the difference between the osmotic pressurein the central plane between clay layers and the osmotic pressure inthe equilibrium solution.

Many researchers have attempted to use the Gouy–Chapman diffusedouble layer theory for determining the swelling pressure of clays.Earlier studies have pointed out somedifferences between experimentaldata and relationships derived theoretically from the diffuse doublelayer theory (Low, 1980; Pusch and Yong, 2003; Sridharan andChoudhury, 2002; Tripathy et al., 2004; Yong and Mohamed, 1992;Yong et al., 1984). The difference between the theoretical and exper-imental results was attributed to many factors (Bolt, 1956; Mitchell,1993; Schanz and Tripathy, 2009; Sridharan, and Jayadeva, 1982):(i) poorly developed or partially developed diffuse double layer,(ii) deviation of soil structure and fabric from the parallel plateconcept, (iii) surface hydration forces at close particle distances,(iv) non-uniform size of clay plates, (v) existence of electricalattractive forces, (vi) presence of multivalent cations, (vii) effect ofion size, (viii) anion adsorption, and (ix) particle size. One of thesefactors or a combination of several of these factors may contributeto the difference between the theoretical and experimental resultsdepending on the initial stress state of clay.

Please cite this article as: Schanz, T., et al., An alternative approach for theplied Clay Science (2013), http://dx.doi.org/10.1016/j.clay.2013.07.018

Various approaches have been proposed in the past for deter-mining the swelling pressure of clays. Low and Margheim (1979)and Low (1980) suggested an empirical exponential relationshipbetween dry density and swelling pressure for Na+-Mt. Madsenand Müller-Vonmoos (1985) reported a good agreement betweenthe theoretical and experimental swelling pressures of an overconsolidated Jurassic opalinum shale. Gens and Alonso (1992)stated that the advantage of using the diffuse double layer theoryis that various parameters responsible for swelling of clays can bevaried as and when required. An attempt was made by Komineand Ogata (1996) to use the theory for determining the swellingstrain and swelling pressure of a highly compacted Bent. New equa-tions were suggested based on the equations for single clay layer.Sridharan and Choudhury (2002) proposed a swelling pressureequation for Na+-Mt while analyzing the compression data of slur-ried samples of Na+-Mt, reported by Bolt (1956), Mesri and Olson(1971) and Low (1980).

Tripathy et al. (2004) reported on swelling pressures of compactedBent. They summarized previous work, which suggested that at lowdry densities, theoretical predictions overestimate swelling pressurescompared with experimental measurements. At high dry densities theopposite was observed to be the case. Their work consisted of makingcorrections to the relationship between a midplane potential functionand nondimensional distance function relationship applying theoryfor interacting particle. The corrections involved back calculating themidplane potential function from the experimentally measured values,calculating the error between the original midplane potential functionand nondimensional distance function, followed by subtracting theerror from the original theoretical prediction to gain new functions.The calibration process resulted in good predictions for those materialsover various ranges of average valences. For verification, the correctedequations were used to calculate swelling pressures for additionalmaterials using their average valence. The three equations were validon average valence ranges of 1.14–1.50, 1.66–1.73 and 1.97.

Schanz and Tripathy (2009) reported swelling pressure of severalcompacted Bents experimentally. A comparison of experimental resultsand theoretical swelling pressures from the diffuse double layer theorywas carried out in the context clay water cation system and the range ofapplicability of the diffuse double layer theory to divalent rich Mt. Theswelling pressures were determined using the modified diffuse doublelayer equations proposed by Tripathy et al. (2004) for mixed valentBents and compared with the experimental results.

2.1. Diffuse double layer

Based on the diffuse double layer theory for interacting particles,five important equations were used to establish swelling pressureversus void ratio relationships for clays (Sridharan and Jayadeva,1982; Tripathy et al., 2004):

p ¼ 2n0kT coshu−1ð Þ ð1Þ

− dydξ

� �x¼0

¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 coshz−2 coshuð Þ

q¼ B

S

� � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

2ε0Dn0kT

� �s; x ¼ 0; y ¼ z

ð2ÞZuz

1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 coshy−2 coshuð Þ

p dy ¼Zd0

dξ ¼ −Kd ð3Þ

K ¼ 2n0e02v2

ε0DkT

!1=2

ð4Þ

ed ¼ GρwSd� 106 ð5Þ

use of DDL theory to estimate the swelling pressure of bentonites, Ap-

3T. Schanz et al. / Applied Clay Science xxx (2013) xxx–xxx

where p is the swelling pressure in (N/m2), n0 is the ionic concentra-tion of the bulk fluid in (ions/m3), u is the nondimensional midplanepotential, k is the Boltzmann's constant (1.38 × 10−23 J/K), T is theabsolute temperature in Kelvin, ξ is the distance function, y is thenondimensional potential at a distance x from the clay surface, z isthe nondimensional potential function at the surface (x = 0), B isthe CEC (meq/100 g), S is the specific surface area (m2/g), ε0 is thepermittivity of vacuum (8.8542 × 10−12 C2 J−1 m−1), D is thedielectric constant of bulk fluid (80.4 for water), K (1/m) is thediffuse double layer parameter, e′ is the elementary electric charge(1.602 × 10−19 C), v is the valency of exchangeable cations, ed isthe void ratio of the clay specimen following the concept given byDDL theory, G is the specific gravity of soil solids, d is half thedistance between clay layers in meters, and ρw is the unit weightof water.

For any given pore fluid medium, determination of the swellingpressure using Eq. (1) requires the nondimensional midplane potentialfunction, u. A relationship between u and the nondimensional distancefunction, Kd, must be established to determine u for any given value ofKd and vice versa. For the given properties of the Bent (i.e., G, S, B, v)and for given values of swelling pressures, the u values were calculatedfromEq. (1). The corresponding values of zwere calculated fromEq. (2).Knowing z and u for any given swelling pressure, Eq. (3) was used tocalculate Kd and K from Eq. (4). Knowing the values of Kd and K, thedistance between clay layers, d was calculated, after getting d values,void ratios, ed, were calculated using Eq. (5). The dry density can bedetermined from the basic volume mass relationship by knowing thespecific gravity and the initial void ratio of the specimen.

3. Materials and testing procedure

3.1. Materials and methods

Two Bents were used in this study; Ca2+-Bent (name Calcigel)— a German Bent and MX80 an American Bent. The Bents havebeen proposed to be used as barrier and backfilling materials inhigh-level radioactive waste disposal facilities in Germany andUSA respectively (Komine and Ogata, 1996; Schanz and Tripathy,2009). Table 1 shows the origin and percentage of Mt in the Bent.Table 1 additionally summarizes physico-chemical characteriza-tion of the Bent. The percentage of Mt for Calcigel Bent and MX80Bent were found to be about 60% and 75% respectively. For CalcigelBent was found the exchangeable cation amount in the Mt fractionto contain about 94% of bivalent exchangeable cations (Ca2+ andMg2+) whereas, in case of MX80 Bent, 72% of monovalent

Table 1Physico-chemical characterization of the clays studied and used for verification of swelling pre

Properties Bentonites

This study

MX80 Calcige

Specific gravity, G 2.80 2.72Liquid limit, (%) 490 110Specific surface area, (m2/g) 711 525Total cation exchange capacity (meq/100 g) 91 57Weighted average valency 1.27 1.95Montmorillonite (%) 75b 60c

Dry density used (Mg/m3) 1.4, 1.6, 1.8 1.4, 1.6Initial water content (%) 10.5 9.0Plastic limit, (%) 48 39Basic exchangeable cation Na+, K+, Ca2+, Mg2+ (meq/100 g) 64, 2, 19, 6 2, 1, 35

a Data from Bucher and Müller-Vonmoos (1989) for MX80, Komine et al. (2009) for Volcla(2009) for Calcigel, ENRESA (2000) for Febex.

b Data from Baille et al. (2010).c Data from Tripathy et al. (2004).

Please cite this article as: Schanz, T., et al., An alternative approach for theplied Clay Science (2013), http://dx.doi.org/10.1016/j.clay.2013.07.018

exchangeable cations (Na+ and K+) and 27% contains bivalentcations (Ca2+ and Mg2+).

The specific surface areas of the Bent were measured following eth-ylene glycol monoethyl ether (EGME) method (Cerato and Lutenegger,2002). The CEC of the Bent was determined by silver thiourea method(Pleysier and Juo, 1980). As shown in Table 1, MX80 Bent containsmore monovalent cations than bivalent, whereas Calcigel Bent containsmore divalent cations thanmonovalent cations. Therefore, for the pres-ent study, the valencies of Bent were computed fromweighted averageof the valencies of the cations present in the Bent. The hygroscopicwater contents of Calcigel Bent and MX80 Bent at laboratory environ-ment were found to be 9.0% and 10.5% respectively.

The testing device used in the experimental program consists of anewly developed high pressure constant volume cell for measuringswelling pressures of compacted Bent specimen (Fig. 1). The bottompart of the constant volume cell contains inlet and outlet lines for satu-rating the Bent specimens during swelling pressure test. The top part ofthe device contains inlet and outlet lines for de-airing and saturating thespecimens from top. A thick stainless-steel base at the bottom houses astainless-steel porous plate and a bottom water chamber. The bottompart of the device holds a thick-walled specimen ring of height 20 mmand diameter 50 mm that in turn accommodates a compacted Bentspecimen. The top part of the device carries a piston which is in turn isattached with a load cell. The top and the bottom parts of the deviceare connected with the help of heavy screws. When distilled water issupplied to the compacted Bent specimens, development of the swell-ing pressure can be recorded using the load cell. The maximum loadingcapacity of the load cell is 45 MPa.

Prior to testing for Bent specimens, the pressure–expansion charac-teristic of the new constant volume cell was studied. The change in cellvolume due to any appliedwater pressurewas determined byfilling thecell with distilled water in the presence of a dummy metal sample.Hydraulic pressure was applied step-wise up to a pressure of 10 MPausing the volume pressure controller (VPC) and the correspondingimmediate volume change was recorded. Based on the pressure–expansion characteristics of the cell, the dry density of thecompacted specimens was corrected at the end of the each test.

3.2. Test procedure

Swelling pressures of compacted Bent specimens were measuredunder isochoric condition using the high pressure constant volumecell (Fig. 1). Filter papers were used at the top and bottom of the speci-mens to prevent direct contact of the specimens with the porous plateand to avoid chocking of the porous plate. The specimen rings werelubricated prior to the specimen preparation to minimize the side

ssure equations.

From literaturea

l MX80 Volclay MX80 Bent S-2 Calcigel Febex

2.76 2.84 2.88 2.78 2.80 2.70411 565 437 105 178 102562 560 615 615 650 72574 105 135 97 74 1111.14 1.43 1.49 1.66 1.90 1.73

75 69 76 92 80 92, 1.8

, 19

y, Komine et al. (2009) for MX80, ENRESA (2000) for bentonite S-2, Schanz and Tripathy

use of DDL theory to estimate the swelling pressure of bentonites, Ap-

Fig. 1. RUB High pressure constant volume cell: left – schematic sketch; right – photo.

4 T. Schanz et al. / Applied Clay Science xxx (2013) xxx–xxx

friction. During the swelling pressure tests, distilled water was suppliedinitially via the bottom inlet of the cell. After about 4–5 days of hydra-tion period, a burette was connected to the top inlet of the cell to supplywater from top. The procedure adopted enabled releasing air from theinitially unsaturated Bent specimens during the hydration process andalso was found to reduce the swelling pressure equilibration time.

The full saturation of any tested specimens was confirmed based onthe time-swelling pressure response. The time needed for the full satu-ration was found to be dependent on the dry density of the specimenand generally varied between 3 and 4 weeks. The final water contentsof compacted specimens testedweremeasured by oven dryingmethod.The calculated degree of saturations of the specimens based on thecorrected volumes (i.e., based on expansion of the cell) and the mea-sured water contents clearly indicated that the specimens were fullysaturated after the swelling pressure tests. The corrected dry densitieswere obtained for both Bents after cell expansion was applied.

4. Experimental and theoretical swelling pressure

Fig. 2 shows the u–Kd relationships for MX80 and Calcigel Bentsrespectively, the n0 (ionic concentration of bulk fluid) value con-sidered in this study is 10−4 M, which refers to distilled water.Sridharan and Jayadeva (1982) noted that for the range of n0 values(i.e., 10−3 M, 10−4 M, and 10−5 M), the u versus log (Kd) relation-ship is almost unique for homoionic clays for (dy/dξ)x = 0 N 100.To establish the theoretical u–Kd relationships for MX80 andCalcigel Bents, the following procedure was adopted: (i) for known

Fig. 2. Theoretical u–Kd relationship of MX80 (v

Please cite this article as: Schanz, T., et al., An alternative approach for theplied Clay Science (2013), http://dx.doi.org/10.1016/j.clay.2013.07.018

swelling pressure values, u values were computed using Eq. (1);(ii) actual B and S values were considered for computing (dy/dξ)x = 0

values and then z values using Eq. (2); and (iii) the corresponding Kdvalues were computed by numerical integration using Eq. (3). Theu versus Kd values were plotted for each of the Bent (Fig. 2). From theplots, the best-fit equations were obtained for each of the Bent usinga least-squares method and the equations are also shown in thegraphs. These equations are then used to determine the u values forthe computed Kd values and can be stated as:

u ¼ 3:86−1:392 ln Kdð Þ for MX80 ð6Þ

u ¼ 3:56−1:434 ln Kdð Þ for Calcigel : ð7Þ

Fig. 3 shows the experimental swelling pressure results for thecorresponding dry densities of the Bent considered in the study. Theequilibrium swelling pressure values were considered for comparingwith the theoretical swelling pressure dry density relationship for theBent. The theoretical swelling pressure dry density relationship wasdetermined using Eqs. (1) to (5). Moreover, Eq. (6) for MX80 andEq. (7) for Calcigel Bent were used to determine u–Kd relationship.The parameters considered for determining the theoretical swellingpressure dry density relationship are shown in Table 1.

As can be seen in Fig. 3 that there is a good agreement betweenthe experimental and theoretical swelling pressures at low drydensities (i.e., below 1.4 Mg/m3), whereas at higher dry densities,

= 1.27) and Calcigel bentonite (v = 1.95).

use of DDL theory to estimate the swelling pressure of bentonites, Ap-

Fig. 3. Comparison of experimental and theoretical swelling pressures from original DDL theory of MX80 and Calcigel bentonite.

5T. Schanz et al. / Applied Clay Science xxx (2013) xxx–xxx

the experimental swelling pressures are found to be greater thanthat predicted from the diffuse double layer theory.

The disagreement between the theoretical and experimental swell-ing pressure results can be attributed due to the several factors thatarise while applying the diffuse double layer theory to compacted Bentsystems (Schanz and Tripathy, 2009) which include nonparallel layerconcept, nonuniform size of clay layers and additional repulsive forces.Diffuse double layer theory assumes an ideal fabric system i.e., the par-allel layers between the clays and uniform size of clay layers (Nagarajand Jayadeva, 1981). Additional repulsive forces can be contributedto the difference between the theory and experimental results, especiallyin case of high density state (Tripathy et al., 2004). Yong and Mohamed(1992) stated that the repulsive forces arising due to interaction of claylayers at close particle spacing are primarily due to the hydration ofions. For dry densities of the clay greater than 1.4 Mg/m3, the swellingpressures developed can be primarily attributed due to the hydrationforces that are much greater than that predicted from the diffuse doublelayer theory. Pusch and Yong (2003) stated that the hydration forcesreside in the inner Helmholtz planewhere the ions are at their anhydrousstate. Pashley (1981) and Israelachvili (1982) have also mentioned thatadditional repulsive forces could be present when the d spacing becomesless. Hence the theoretical predictions by original DDL theory need somemodification which has been attempted in the following section.

5. Proposed equations for void ratio

An attempt was made to account for the difference between theexperimental and theoretical swelling pressures with increasing drydensity of the Bent. For the known experimental swelling pressurevalues, the void ratio, ed, was calculated using diffuse double layertheory. The steps to calculate the void ratio, ed, from diffuse doublelayer have been discussed in Section 4. The relationship between thetotal void ratio, eT, and void ratio, ed, from diffuse double layer wasestablished. Fig. 4 shows the relationship between total void ratio, eT,and void ratio, ed, calculated from diffuse double layer theory. As canbe seen in Figs. 6 and 7, in case of MX80 Bent, for high total void ratioor for low dry density, the void ratio, ed, calculated using diffuse doublelayer theory is greater than total void ratio, eT. Similarly, in case ofCalcigel Bent, the same trend has been observed. The resulting equa-tions from the best-fit lines in Fig. 4 relate total void ratio to the voidratio calculated from diffuse double layer. The new equations for thevoid ratios are also shown in Fig. 4 and are given as follow:

ed ¼ 0:896eT2:09 for MX80 ð8Þ

ed ¼ 0:832eT2:87 for Calcigel : ð9Þ

For the knownmodified void ratios i.e., ed shown in Eqs. (8) and (9)for MX80 and Calcigel Bent respectively, the new d spacing (i.e., half

Please cite this article as: Schanz, T., et al., An alternative approach for theplied Clay Science (2013), http://dx.doi.org/10.1016/j.clay.2013.07.018

distance between parallel clay layers) is calculated using Eq. (5). KnowingK values from Eq. (4), the new Kd values can be found.

As shown in Fig. 2, the established u–Kd relationship was used tocalculate the u values by knowing the new Kd values from the relation-ship between total void ratio, eT, and void ratio fromdiffuse double layertheory, ed (Fig. 4). Hence, Eqs. (6) and (7) can be directly used to calcu-late the u values. Substituting the u values of Eqs. (6) and (7) in Eq. (1),the equations for swelling pressure are obtained as:

p ¼ 2n0kT cosh 3:86−1:392 ln Kdð Þð Þ−1ð Þ v ¼ 1:01–1:50ð Þ ð10Þ

p ¼ 2n0kT cosh 3:56−1:434 ln Kdð Þð Þ−1ð Þ v ¼ 1:51–2:0ð Þ ð11Þ

or, by using Eq. (5) with newmodified void ratio from Eqs. (8) and (9),d values can be obtained, and Eqs. (10) and (11) can be written as:

p ¼ 2n0kT cosh 3:86−1:392 lnK � 0:896eT

2:09

GρwS� 106

! !−1

!

� v ¼ 1:01–1:50ð Þ ð10aÞ

p ¼ 2n0kT cosh 3:56−1:434lnK � 0:832eT

2:87

GρwS� 106

! !−1

!

� v ¼ 1:51–2:0ð Þ: ð11aÞ

Eqs. (10a) and (11a) relate the swelling pressure to the void ratio forthe given clay fluid system. The clay is represented by its specificsurface, S and its specific gravity, G. The pore fluid properties are givenby K (Eq. (4)) and the concentration of ions, n0 in the bulk fluid.

The experimental swelling pressures and those calculated fromEqs. (10) and (11) for MX80 and Calcigel Bents respectively areshown in Fig. 5. As expected, thedry density–swellingpressure relation-ships obtained from these two equations are in very good agreementwith the experimental data for the two Bents.

6. Verification of the new swelling pressure equations

The new swelling pressure equations (i.e., Eqs. (10) and (11)) arefor two different types of Bents having different valencies of exchange-able cations and different mineralogical properties. The investigationwas extended to use the equations for additional Bents that were alsoproposed for use as barrier materials. Experimental swelling pressureresults for MX80 (Bucher and Müller-Vonmoos, 1989), Volclay(Komine et al., 2009), MX80 (Komine et al., 2009), Bent S-2 (ENRESA,2000), Calcigel Bent (Schanz and Tripathy, 2009) and Febex Bent(ENRESA, 2000) were chosen for this verification. Table 1 shows theproperties of all the Bents used here in this research.

The swelling pressures for these Bents were calculated usingEqs. (10)–(11) for different dry densities. The calculated swelling

use of DDL theory to estimate the swelling pressure of bentonites, Ap-

Fig. 4. Relationship between the total void ratios, eT and void ratio from diffuse double layer, ed for MX80 and Calcigel bentonite.

6 T. Schanz et al. / Applied Clay Science xxx (2013) xxx–xxx

pressure from these equations was matched with the reported exper-imental swelling pressures of these Bents. It was observed, however,that Eq. (10) is applicable to MX80, Volclay and MX80 Bents (Komineet al., 2009), whereas Eq. (11) is suitable for Calcigel, Bent S-2and Febex Bent, which confirms the suggested grouping of averageweighted valency of exchangeable cations. Therefore, Eq. (10) provedto be used for the Bent having a cation valency from 1.01 to 1.50, andEq. (11) for Bent with a cation valency from 1.51 up to 2.0. The exper-imental and calculated swelling pressures of the Bent are plotted inFig. 6. The agreement between the proposed equations and the exper-imental results is good in all cases. Fig. 7 shows the experimental andcalculated swelling pressures of the eight Bents considered in thisstudy. The agreement between the experimental and calculated swell-ing pressures using suggested equations (Eqs. (10) and (11)) is verygood for all the Bents studied.

7. Discussion

In the current research, the separation distance versus swellingpressure from the DDL theory has been considered for calculating theswelling pressure of Bent. The DDL theory does not take into accountthe ion sizes and treats the ions as point charges. Therefore, additionaleffects due to hydration energy are not accommodated in theory. Thecalculation is based on the concentration of the ions in the mid-planebetween two parallel clay layers. Correcting the void ratio, as has beendone in this research, takes into account three possible effects one

Fig. 5. Comparison of experimental swelling pressure and swelling pressure fr

Please cite this article as: Schanz, T., et al., An alternative approach for theplied Clay Science (2013), http://dx.doi.org/10.1016/j.clay.2013.07.018

would assume to occur at close layers spacing, such as (i) the van derWaals attractive pressure (which exceeds the osmotic repulsive pressureat close spacing and one then requires to add the additional pressuresdue to hydration effect), (ii) hydration effect (hydrated size of cationand the energy of repulsion; which possibly can be added by consideringthe Stern theory), and (iii) the fabric effect which may be dissimilar tothe assumed fabric in the DDL theory (this aspects is conjectural whenthe dry density of Bent is a variable and its influence on the anisotropyis significant).

A review of the literature pertaining towater layers on the surfaces ofthe clay layers and the corresponding water contents of the compactedBent corresponding to a range of dry density considered in this studyclearly indicated that the saturation water contents of the Bent underisochoric condition were greater than the water content correspondingto 4-layers of water. Therefore, instead of considering three possible ef-fects independently (attraction, additional repulsion, and fabric) alongwith the DDL repulsion, it was possible to obtain semi-empirically theswelling pressure response of the Bent just by treating the ions as pointcharges (following the DDL theory) and further correcting their voidratio.

8. Conclusion

Swelling pressure of two Bents that are proposed for use as thebarrier material with a range of dry density between 1.10–1.80 Mg/m3

was experimentally determined and compared with the calculated

om suggested in this research equation for MX80 and Calcigel bentonite.

use of DDL theory to estimate the swelling pressure of bentonites, Ap-

Fig. 6. Comparison of experimental swelling pressure and swelling pressure from sug-gested in this research equation for bentonites (Theory = original DDL theory).

7T. Schanz et al. / Applied Clay Science xxx (2013) xxx–xxx

swelling pressure using Gouy–Chapman diffuse double layer theory.Based on the given swelling pressure versus dry density data of thetwo Bents, relationships between the nondimensional midplane poten-tial function, u, and the distance function, Kd, were established. Thestudy showed that for the compacted Bent the as prepared total voidratios, eT at low dry densities are higher than theoretical void ratiosusing diffuse double layer theory, however, reverse behavior has beennoticed for high dry densities. The relationship between the theoreticalvoid ratio from diffuse double layer theory and as prepared total voidratio was established and new modified void ratio is suggested.

Fig. 7. Comparison of experimental and calculated swelling pressures from suggested inthis research equations.

Please cite this article as: Schanz, T., et al., An alternative approach for theplied Clay Science (2013), http://dx.doi.org/10.1016/j.clay.2013.07.018

Two new equations that have theoretical support were proposedand the equations were verified with six other reported Bents fromliterature that have been also proposed for use as barrier materials inhigh-level radioactive storage units. The agreement between the calcu-lated swelling pressure using the suggested equations and the reportedexperimental data was very good. The use of the modified equations isbased on weighted average valency of the cations in the Bent, sincethe valency of the exchangeable cations present in clays has a significantinfluence on the swelling pressure.

Acknowledgment

The financial assistance provided by Bundesministerium für Bildungund Forschung (BMBF), Germany through research grant 02E10437 forthis research work is gratefully acknowledged. The first author thanksHanna Viefhaus for preparation of the manuscript and discussion.

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