Evaluation of hydro-mechano-chemical behaviour of bentonite-sand mixtures

Wnjing Sun, Chng Liu, Diansn Yang, Dan Sun

a Department of Civil and Energy Engineering, College of Environmental Science and Engineering, Donghua University, Shanghai, 201620, China

b Institute for the Conservation of Cultural Heritage, Shanghai University, Shanghai, 200444, China

c State Key Laboratory of Geomechanics and Geotechnical Engineering,Institute of Rock and Soil Mechanics,Chinese Academy of Sciences, Wuhan,430071,China

d Shanghai Construction Group Co., Ltd., Shanghai, 200080, China

e Department of Civil Engineering, School of Mechanics and Engineering Science, Shanghai University, Shanghai, 200444, China

Keywords:Bentonite-sand mixture Hydro-mechano-chemical (HMC) behaviour Salt solution True effective stress

ABSTRACT Bentonite-sand mixtures are widely used in engineering barrier of deep geological disposal of high-level radioactive nuclear waste and anti-seepage barrier of civil geotechnical engineering.Under the action of groundwater solution infiltration and external stress,the hydro-mechanical(HM)behaviour of bentonitesand mixtures,i.e.the swelling characteristics and permeability,will change.Once the anti-seepage and filtration effect is weakened or lost,the pollutants will spread to the biosphere.Therefore,it is necessary to study the swelling characteristics and permeability of bentonite-sand mixtures under coupled mechanochemical(MC)effect and to establish corresponding prediction model.For this reason,swelling tests under salt solution with different concentrations are conducted on pure bentonite and its mixtures with 30%,70%and 90% sand contents, the compression tests are carried out on saturated samples, and the saturated permeability coefficient k of the sample under each load is calculated by Terzaghi’s one-dimensional consolidation theory.The concepts of true effective stress pe, montmorillonite void ratio em and critical sand content αs are introduced to determine the em-pe relationship and finally the k-em relationship of bentonite-sand mixtures.It is found that when the sand content α ≤αs, the em-pe relationship of the mixture is linear and independent of the salt solution concentration, and when α > αs, the em-pe relationship of bentonite-sand mixture is bi-linear with the true effective deviatoric stress pesα as the intersection.In addition,the em-k relationship also shows the linear trend when α ≤αs,and the slope of the line increases with the increase of the salt solution concentration.When α > αs, the k-em relationship will deviate from the linear relationship.Moreover,the larger the sand content is,the farther the deviation is.On the basis of summing the regularity,a model for predicting the HM behaviour of bentonite-sand mixture under the coupled MC effect is proposed.By comparing the swelling and permeability test results with model prediction results of different types of bentonite and its sand mixtures, the predictive model is verified.The study on the HM behaviour of bentonite-sand mixtures under salt solution infiltration and the model establishment can provide experimental and theoretical basis for the design and construction of anti-seepage engineering by bentonite-sand mixtures.

1.Introduction

Bentonite is an ideal material in the artificial engineering barrier for deep geological disposal of high-level radioactive nuclear waste(HLW), landfills and cultural relic protection, due to its high expansibility,low permeability and excellent adsorption capacity(Ye et al., 2010; Shackelford et al., 2010).As the engineering barrier in HLW repository,different countries suggested different mixing ratios between bentonite and sand for buffer/backfill materials,considering the anti-seepage performance,storage capacity and economic benefits.For example,Sweden adopted pure bentonite(SKB,2010);China adopted pure Gaomiaozi bentonite(Wang,2010;Wang et al.,2018);Canada recommended 50%bentonite and 50%sand as buffer/backfill material(AECL,1994);Czech Republic used mixture of Rokle calciumbased bentonite,sand and graphite with a dry mass ratio of 85:10:5(Pacovsky et al., 2007); and Japan planned to use mixture of 70%bentonite and 30%sand as the buffer material and 30%bentonite and 70%sand as the backfill material(JNC,1999).In anti-seepage barriers in geotechnical engineering structures, such as landfills, the horizontalimperviouslayerisusuallycomposedofpurebentoniteandthe vertical cutoff wall adopts bentonite enhanced materials(Evans et al.,2008;Fan et al.,2014),about 4%-12%bentonite content,which can meet the US Environmental Protection Agency(EPA)regulations on the permeability(Alawaji,1999).

vCompared to pure bentonite,bentonite-sand mixtures have the higher strength and thermal conductivity.However, the mixture shows the lower swelling characteristics, which affects its sealing performance(Mollins et al.,1996;Karnland et al.,2008).At the same time, the swelling characteristics and permeability of the mixture will be influenced by the other factors,such as temperature(Shirazi et al.,2010;Cui et al.,2018),sand grain size(Sivapullaiah et al.,2000;Shirazi et al.,2010;Monkul and Yamamuro,2011;Cabalar and Hasan,2013;Srikanth and Mishra,2016;Wang et al.,2021),and the salt in groundwater (Komine et al., 2009; Sun et al.,2015a).It is indicated that the salt content in the groundwater near the coastal nuclear waste repository and landfill site is higher(Komine et al.,2009;Fan et al.,2014).Moreover,the groundwater in inland regions is also very salty due to transpiration.China’s nuclear waste geological repository is located in Beishan, Gansu Province (Wang, 2010; Wang et al.,2018), where the groundwater salt concentration is relatively high(Sun et al.,2015a).

Under external stress and the infiltration of groundwater, the hydro-mechanical (HM)behaviour, i.e.the swelling characteristics and permeability of bentonite-sand mixture,will change,which are the important basis for evaluating the long-term anti-seepage performance of engineering barriers.Once its anti-seepage and filtration capacity is weakened or lost,the pollutants will accelerate the spread to the biosphere.Therefore, it is necessary to study the swelling characteristics and saturated permeability of bentonitesand mixture under coupled mechano-chemical(MC)effect.

In addition, due to extremely low permeability of bentonite, it takes a long time to determine the swelling characteristics and permeability of bentonite-sand mixture through experiments,and many factors such as mixing ratio, salt type and concentration of groundwater must be considered.Therefore, in order to meet the needs the requirements of design and evaluation of impervious barrier for bentonite-sand mixtures,it is urgent to propose a model for predicting the HM behaviour of bentonite-sand mixtures under coupled MC effect.

At present, many scholars have studied the swelling characteristics and permeability of different types of bentonite and its sand mixtures, for example, FEBEX bentonite (Villar and Lloret, 2008),Kunigel V1sodium bentonite (Komine and Ogata, 1994; Komine,2004; Sun et al., 2009), Calcigel calcium bentonite (Agus and Schanz, 2008), MX80 bentonite (Wang et al., 2012), and Gaomiaozi sodium bentonite (Ye et al., 2010; Sun et al., 2013).The above swelling and permeability experiments were carried out with distilled or deionized water to avoid ion exchange between the solution and bentonite.However, when infiltrated by salt solution, the physico-chemical properties of bentonite are different with those under distilled or deionized water, leading to the changes in swelling and anti-seepage capacities (Zhang et al.,2012a; Zhu et al., 2013).The weakening effect of chemical composition in solution on swelling potential of bentonite is related to the chemical environment of the solution, the properties of bentonite, the external stress conditions, etc.(Alawaji, 1999;Castellanos et al., 2008; Herbert et al., 2008; Komine et al., 2009).Moreover,the main factors affecting the permeability coefficient of bentonite include the aggregate size,the montmorillonite content,the adsorption layer thickness, the hydration conditions, the void ratio, the type and concentration of the solution, the dielectric dispersion of soils, etc.(Petrov et al., 1997; Thevanayagam and Nesarajah,1998; Komine et al., 2009).

In terms of swelling prediction model, the montmorillonite swelling volumetric strain(Komine and Ogata,2004),the montmorillonite void ratio (Sun et al.,2009; 2015b, 2017), and the effective clay density(Zhang et al.,2012b)were adopted in the swelling prediction of bentonite-sand mixtures.The above prediction methods did not consider the effect of salt solution on swelling.Sun et al.(2015a) proposed swelling prediction model of bentonite saturated by different total dissolved solid(TDS)solutions using the montmorillonite void ratio.In terms of permeability prediction model,S?llfors and ?berg-H?gsta(2002)and Komine(2008)predicted the permeability of bentonite-sand mixture with different sand contents,without considering the effect of salt solution.Katsumi et al.(2008)established the relationship between the free expansion rate and the saturated permeability coefficient of pure bentonite at lower dry density saturated under salt solutions with different concentrations and types.Tripathi(2013)predicted the permeability coefficients of different types of bentonite and its sand mixtures under the action of salt solution.A model proposed by Guimaraes et al.(2013) can simulate the saturated permeability of bentonite under different MC loading paths, based on the existing double-layer structure model,and considering the effects of ion content and cation exchange on the microstructure of expansive soils.

The above models predicted the swelling characteristics and permeability respectively.However,the permeability of bentoniteinclusive mixture is connected with its swelling characteristics,i.e.the saturated permeability coefficient is related to the soil deformation, which is caused by the external stress.Therefore, the relationship among external stress, deformation and permeability coefficient is closely related.A model should be established to predict the swelling and saturated permeability of bentonite-sand mixture under pure water or salt solution infiltration.

Therefore, we need to establish a model on the basis of the swelling and permeability characteristics of bentonite-sand mixtures with different sand contents under the action of salt solution,which can comprehensively reflect the hydro-mechano-chemical(HMC) behaviour of bentonite-sand mixtures.

In this paper, the swelling tests on pure bentonite and its sand mixtures with 30%,70%and 90%sand contents under salt solutions with different concentrations are conducted,and then the compression tests on saturated samples are carried out.The saturated permeability coefficient k at each load is calculated by Terzaghi’s onedimensional(1D)consolidation theory.Then,the em-perelationship and the em-k relationship of bentonite-sand mixtures are determined by introducing the concepts of true effective stress pe, montmorillonite void ratio emand critical sand content αs,and the deformation characteristics and saturated permeability of bentonite-sand mixtures under salt solution infiltration are obtained.Finally,a model for predicting the HM behaviour of bentonite-sand mixtures under coupled MC effect is proposed and verified.Through the model,once given the values of the external stress and the salt solution concentration, the deformation and saturated permeability coefficient of bentonite-sand mixtures can be deduced.Meanwhile, the type of bentonite and the sand content can also be determined according to the environmental salt concentration,the vertical stress and the antiseepage requirements allowed by local regulations.

2.Tests and results

2.1.Materials and testing method

Sodium modified calcium bentonite in geosynthetic clay liner(GCL) bentonite and Fujian standard sand were used for tests.Table 1 shows the main mineral compositions of bentonite, determined by X-ray diffraction analyses.The main mineral component of the bentonite is montmorillonite with content of 45.8%, and associated minerals are some clinoptilolite,feldspar,calcite,quartz,etc.The geotechnical properties of GCL bentonite and Fujian standard sand are presented in Table 2.

Table 1Mineral composition of GCL bentonite.

Table 2Geotechnical properties of GCL bentonite and Fujian standard sand.

Table 3Plans for swelling and compression test.

Bentonite and sand were mixed by weight ratio of 10:90,30:70,70:30 and 100:0,respectively.As previously mentioned,bentonitesand mixture with different sand contents is used as buffer/backfill material or anti-seepage barrier in practical engineering.Therefore,bentonite-sand mixtures with 10% (Alawaji, 1999), 30% and 70%(JNC, 1999) bentonite content and pure bentonite (Wang, 2010)were selected.The ratio range is wide coverage to determine the HMC behaviour of bentonite-sand mixtures.

The compressed samples with the dry density of 1.5 g/cm3and the initial water content of 15% were prepared.The test apparatus and the prepared samples are presented in Fig.1,whereFig.1a shows the photo of oedometer;Fig.1b shows the sampling device,i.e.the mixed soil specimens are placed in a sampler and compacted with a jack to prepare compacted samples with a diameter of 6.18 cm and a height of 2 cm;and Fig.1c shows the four representative samples of bentonite-sand mixtures with sand content α of 0%, 30%, 70% and 90% in sequence.NaCl solution with different concentrations was prepared at 0 mol/L, 0.1 mol/L, 0.5 mol/L and 1 mol/L, using NaCl(analytical reagent)and deionized water in the tests.

In engineering practice,the swelling of bentonite-sand mixtures can be considered as a 1D expansion or swell under constant stress.Gens and Alonso (1992) put forward three common swelling test methods: constant volume loading, loading after wetting, and swelling under load.Among them, the second swelling test method-loading after wetting was adopted more often (Komine et al., 2009; Sun et al., 2009, 2015a; Shirazi et al., 2010; Ye et al.,2014).Moreover, the second method can not only obtain the swelling characteristics, but also determine the permeability according to the indirect method derived from consolidation theory.Therefore,the second swelling test method was used.

First,under the vertical stress of 25 kPa,the swelling deformation tests on the mixtures saturated by the NaCl solutions with different concentrations were carried out.After the completion of swelling deformation test,a series of compression tests on saturated samples was conducted in accordance with ASTM D2435/D2435M-11(1995).From the above tests, the swelling deformation under constant vertical stress and compression curves of bentonite-sand mixtures with different sand contents can be obtained.

Sun et al.(2015b)presented that there is a state curve between the final void ratio and the vertical stress after full saturation for bentonite-sand mixtures with a specified sand content,and verified by different types of bentonite that the final saturated state of bentonite-sand mixture all fell on the final saturated log10e-log10σvrelationship under any vertical pressure.Therefore,no matter how large the stress is,or in other words,if the stress changes,not under 25 kPa,the final e-σvrelationship after full wetting will still fall on the specific state curve.

Fig.1.Test apparatus and prepared samples: (a) Oedometer; (b) Sampling device; and (c) Bentonite-sand mixed samples with α = 0%, 30%, 70% and 90%.

Because of the low permeability of bentonite, it is difficult to measure the saturated permeability coefficient by conventional variable head permeability test method.Therefore, the saturated permeability coefficient was calculated using the indirect method derived from Terzaghi’s 1D consolidation theory.Shirazi et al.(2010)performed a series of laboratory experiment on saturated bentonitesand mixture prepared by distilled water, to investigate the permeability coefficient using direct permeability test by falling head method and indirect test methods derived from the consolidation theory.Sun et al.(2014)conducted a series of compression tests on saturated bentonite prepared by deionized water, and obtained the calculated saturated permeability coefficient using the indirect method derived from Terzaghi’s 1D consolidation theory.

In this indirect method, the time, t90, corresponding to 90%primary consolidation, was firstly estimated from the timedeformation curve from square root of time method (ASTM D2435/D2435M-11,1995), i.e.the deformation readings, d, versus the square root of time(normally in minutes)for each increment of load.Then,the vertical consolidation coefficient cvunder each load was calculated through the formula:cv=0.848/t90,where cvis the vertical consolidation coefficient (cm2/s),is the average drainage path length and equal to half the average of initial height and final height at one vertical stress (cm).Finally, the saturated permeability coefficient can be calculated according to Terzaghi’s 1D consolidation theory, i.e.k = cvmvγw, where k is the permeability coefficient (cm/s); mvis the coefficient of volume compressibility (m2/kN); γwis the unit weight of water, and γw= 9.8 kN/m3.Subsequently, the permeability characteristics of saturated bentonite-sand mixture can be obtained.

Table 3 shows the test plans, including sand content α, salt solution concentration m,samples’initial state(initial dry density ρd0,water content w0and void ratio e0),final void ratio ef,vertical stress σvduring water uptake,and loading paths in the compression tests.

2.2.Test results

2.2.1.Deformation of bentonite-sand mixtures infiltrated by salt solution

Fig.2 shows the swelling deformation of pure bentonite and bentonite-sand mixtures with 30%, 70% and 90% sand contentsinfiltrated by salt solution with different concentrations under constant stress of 25 kPa, and the compression curve (e-log10σv)of the samples after fully saturated.It can be seen that the swelling of bentonite-sand mixtures decreases with the increase of sand content and with the increase of salt solution concentration: the void ratio of pure bentonite and bentonite-sand mixture with 30% sand content increases after fully saturated by salt solution, and the increase of void ratio decreases gradually with the increase of solution concentration; when the sand content is 70% and 90%, the swelling of mixture does not even occur due to wetting under vertical stress of 25 kPa, and the e-log10σvcurves of the mixture infiltrated by salt solution with different concentrations basically coincide, indicating that when the sand content is large, the solution concentration has no obvious effect on the deformation of bentonite-sand mixtures.The compression data of bentonite-sand mixtures after full swelling are shown in Table 4.

Table 4Compression data of bentonite-sand mixtures after full swelling.

Fig.2.Swelling and compression test results of bentonite-sand mixture infiltrated by salt solution: (a) α = 0%, (b) α = 30%, (c) α = 70%, and (d) α = 90%.Exp stands for the experiment.

Sun et al.(2009)observed that the log10em-log10σvrelationship of bentonite-sand mixtures saturated by distilled water presented a unique linear relationship when the sand content is less than the critical sand content.The montmorillonite void ratio emis the ratio of the liquid volume Vwat full saturation to montmorillonite volume Vm, which characterizes the liquid mass absorbed by montmorillonite per unit volume after fully saturated.The critical sand content αsis defined as the sand content that a sand skeleton will not be formed in the bentonite-sand mixture under any external stress.The montmorillonite void ratio emand critical sand content αsare expressed as follows (Sun et al., 2017):

where e is the void ratio at full saturation;β is the montmorillonite content in bentonite;ρ,ρm,ρnmand ρsare the densities of mixtures,montmorillonite,non-montmorillonite and sand,respectively;and esmaxis the maximum sand void ratio,and can be obtained through the maximum void ratio test.

When considering the effect of salt solution on HM behaviour of bentonite, the concept of true effective stress in Rao et al.(2017) is adopted.The stress on bentonite under salt solution infiltration is called the true effective stress pe, and can be expressed as

where uwis the pore water pressure, and it equals 0 for the saturated sample in the steady state;pπ is the osmotic stress, which is significantly dependent on the equilibrium solution’s concentration and the surface fixed charge density (Wei, 2014; Xu et al.,2014).

Fig.3 shows the log10em-log10perelationship of bentonite-sand mixtures with different sand contents saturated by salt solutions with different concentrations.It can be seen from Fig.3 that the deformation data of pure bentonite and the mixtures with 30%sand content are normalized with respect to sand content and salt solution concentration using log10em-log10peplot, and presents a linear relationship.The deformation data of the bentonite-sand mixture with 70% or 90% sand content can also be normalized with respect to salt solution concentration.In addition, for the bentonite-sand mixture with 70% or 90% sand content, when the true effective stress is greater than a certain value,the relationshipbetween the montmorillonite void ratio and true effective stress deviates from the above-mentioned log10em-log10pelinear relationship.The deviation is mainly due to the formation of sand skeleton.The critical content αsis used to judge when the sand skeleton is formed (Sun et al., 2009).The above conclusions are similar to those obtained by Sun et al.(2015b, 2017).The crucial distinction is that the x-coordinate is the true effective stress instead of the effective stress.

Fig.3.log10em-log10pe relationship of bentonite-sand mixtures with different sand contents saturated by salt solution with different concentrations.

Fig.4.log10k-log10e relationship of bentonite-sand mixtures: (a) m = 0 mol/L, (b) m = 0.1 mol/L, (c) m = 0.5 mol/L, and (d) m = 1 mol/L.

2.2.2.Permeability of bentonite-sand mixtures saturated by salt solution

Fig.4 shows the log10k-log10e relationship of bentonite-sand mixtures with different sand contents after saturated by deionized water or salt solution with different concentrations(m = 0 mol/L, 0.1 mol/L, 0.5 mol/L and 1 mol/L).The data of permeability coefficient of the mixture calculated by indirect method derived from consolidation theory are shown in Table 5.It can be seen that k increases approximately linearly with the increase of e for the mixture with a constant sand content;when the void ratio is the same,the higher the sand content is,the greater the permeability coefficient is.Shirazi et al.(2010) investigated the permeability coefficient using direct and indirect test methods derived from consolidation theory.Sun et al.(2014) conducted a series of compression tests on saturated bentonite prepared by deionized water, and obtained the calculated permeability coefficient.The relationship between permeability coefficient and void ratio obtained by Shirazi et al.(2010) and Sun et al.(2014) shows consistency with the log10k-log10e relationship in Fig.4a.

Table 5Permeability coefficient calculated by indirect method derived from consolidation theory.

Fig.5 presents the log10k-log10emrelationship of bentonite-sand mixtures.It is observed that for pure bentonite and bentonite-sand mixture with 30%sand content infiltrated by the salt solution with the same concentration, emis linearly correlated with k in the double logarithmic coordinates.The deviation occurs when the sand content is 70%and is more obvious at sand content of 90%.

Four groups of the log10k-log10emrelationship of bentonite-sand mixtures saturated by salt solutions with different concentrations are shown in Fig.5.The log10k-log10emrelationship of pure bentonite and bentonite-sand mixtures with 30% sand content is linear in Fig.5.The critical sand content for the studied bentonitesand mixture is 46.6% according to Eq.(2).It can be observed that the log10k-log10emdata of mixtures with α > αs, such as 70% and 90%, deviated from the linear relationship of pure bentonite and 30% sand content, and for this kind of bentonite with the montmorillonite content of 45.8%,the k-emrelationship of mixtures with 70% or 90% sand content (α > αs) is not closely tied with the salt solution concentration.

Four groups in Fig.5 are organized in one log10k-log10emdiagram, as shown in Fig.6.It can be observed that the k-emrelationship of mixtures with 70% or 90% sand content (α > αs) is not closely tied with the salt solution concentration.

For pure bentonite and bentonite-sand mixture with 30% sand content, due to the sand content is less than αs, the em-k relationship is obviously affected by the salt solution concentration, as shown in Fig.7.It can be observed that in the double logarithmic coordinates, the k-emrelationship for bentonite-sand mixtures saturated with sand content less than αsby salt solutions of same concentrations is linear, and with increase in the salt solution concentration, the slope of em-k linear relationship of saturated samples with sand content less than αsincreases gradually,and the permeability coefficient of bentonite-sand mixture also increases.The reason for this phenomenon is that under the action of salt solution, the thickness of double-electric layer of bentonite decreases (Rao and Mathew, 1995), and the double-electric layer thickness decreases with the increase of salt solutionconcentration,the colloid structure of bentonite collapses,the flow channel among soil particles increases,and finally the permeability of bentonite-sand mixtures increases.

2.3.Test results of deformation and permeability in the literature

2.3.1.Deformation

Karnland et al.(2008)studied the swelling deformation of pure MX80 bentonite and its mixture with 30% sand content saturated by salt solution with different concentrations.The deformation data are reorganized by the montmorillonite void ratio emand true effective stress pe, as shown in Fig.8.It can be observed that the relationship between emand peof bentonite-sand mixtures with α = 0% and 30%, less than αs= 49.3%, is linear in the double logarithmic coordinates.

Mollins et al.(1996) and Studds et al.(1998) carried out the swelling deformation tests on Wyoming bentonite-sand mixtures with different sand contents infiltrated by distilled water and salt solutions with different concentrations, respectively.The deformation data of Mollins et al.(1996) and Studds et al.(1998) are reorganized by emand perelationship,as shown in Fig.9.The em-perelationship of pure Wyoming bentonite shows the linearcorrelation, and the deviation occurs when the sand contents are 80%,90%and 95%.From Fig.9b,it can also be found that the effect of salt solution concentration on the swelling deformation of the mixtures with different sand contents can be negligible.

Fig.5.log10k-log10em relationship of bentonite-sand mixtures saturated by salt solutions with different concentrations:(a)m=0 mol/L,(b)m=0.1 mol/L,(c)m=0.5 mol/L,and(d)m = 1 mol/L.

Fig.6.log10k-log10em relationship of bentonite-sand mixtures.

Fig.7.log10k-log10em relationship of bentonite-sand mixtures(α ≤αs)saturated by salt solution with different concentrations.

Fig.8.log10em-log10pe relationship of MX80 bentonite-sand mixtures with α ≤αs infiltrated by salt solution.

2.3.2.Permeability

Ye et al.(2014)measured the saturated permeability coefficient of pure GMZ01 bentonite infiltrated by salt solution with different concentrations.Fig.10 shows the log10k-log10emrelationship.It can be seen that the log10k-log10emrelationship of GMZ01 bentonite infiltrated by salt solution with different concentrations is linear,and the slope of the log10k-log10emrelation line increases with increasing salt solution concentration.Moreover,the log10k-log10emrelation lines of GMZ01 bentonite infiltrated by salt solution with different concentrations intersect at the same point.

Studds et al.(1998) conducted the permeability tests for pure Wyoming bentonite and its mixture with the sand contents of 80%and 90% infiltrated by distilled water and 0.1 mol/L salt solution.Fig.11 shows the log10k-log10emrelationship.It can be observed that the log10k-log10emrelationship of pure bentonite infiltrated by distilled water or 0.1 mol/L salt solution is linear.The latter has a higher slope than the former, and the two lines intersect at one point,which is consistent with the rules shown in Fig.10.When the sand content is 80%or 90%,the log10k-log10emrelationship deviates from the log10k-log10emline of pure bentonite,and the greater the sand content is, the more obvious the deviation is.Moreover, the log10k-log10emrelationship after the deviation presents the roughly bi-linear relation.At the first stage, the slope of log10k-log10emrelation line increases with increasing sand content.At the second stage,the slope of log10k-log10emrelation line is almost the same as that of pure bentonite infiltrated by the salt solution with the same concentration.The log10k-log10emrelation lines of the mixtures with 80% or 90% sand content infiltrated by salt solution with different concentrations do not coincide with each other, which is different with the log10k-log10emrelationship of the mixtures with α>αs,as shown in Fig.6.The reason may be related to the higher montmorillonite content of Wyoming bentonite of about 80%.

Fig.9.log10em-log10pe relationship of Wyoming bentonite-sand mixtures infiltrated by distilled water or salt solution: (a) Data from Mollins et al.(1996), and (b) Data from Studds et al.(1998).

Fig.10.log10k-log10em relationship of GMZ01 bentonite saturated by salt solution with different concentrations.

Fig.11.log10k-log10em relationship of Wyoming bentonite and its sand mixture(α > αs).

To sum up,the log10em-log10peand log10k-log10emrelationships can reflect the deformation and permeability respectively of different types of bentonite and its sand mixture infiltrated by the salt solution with different concentrations.Therefore,according to above experimental rules, the model for predicting the HM behaviour of bentonite-sand mixtures under coupled MC effect can be established.

3.HM behaviour prediction model of bentonite-sand mixture under salt solution infiltration

3.1.Swelling prediction model

Based on the above swelling characteristics analysis,it is known that the em-perelationship of bentonite-sand mixtures saturated by salt solution can be normalized with respect to salt solution concentration.Therefore, the swelling prediction model of bentonitesand mixture in a full range of sand content under the salt solution infiltration is shown in Fig.12, in which pemis defined as the true effective stress borne by montmorillonite alone.

Fig.12.Deformation prediction model of bentonite-sand mixtures under salt solution infiltration (α2 > α1 > αs): (a) log10em-log10pe, and (b) pem-pe.

It displays similar to the swelling prediction model of bentonitesand mixture infiltrated by distilled water(Sun et al.,2015b,2017),with the main difference of abscissa of the true effective stress instead of the effective stress,considering the effect of salt solution concentration.Specifically, in the swelling prediction model of bentonite-sand mixture infiltrated by salt solution,when the sand content α is less than or equal to the critical sand content αs, the sand skeleton will not be formed,and the unique linear relationship of em-pewith the slope of b0in a double logarithmic em-pecoordinates will be consistently satisfied, which can be expressed as follows:

where a0and b0are the material parameters varying with types of bentonite,and can be determined by the two swelling tests on pure bentonite samples under any vertical stress.

Moreover, a sand skeleton will not form at this time, and therefore the true effective vertical stress is borne by montmorillonite alone, i.e.pem= pe, and the stress distribution ratio λ = 1;when peis larger than the true effective deviatoric stress pesα,pemisassumed to increase linearly with peand the slope is λ,as shown in Fig.12b.

When α is greater than αs, taking the mixture with a sand content α=α1as an example,the em-perelation of bentonite-sand mixture deviates from the unique linear em-perelationship, and presents a bi-linear relation with pesα as the intersection.The phenomena of deviation shown in Fig.12a can be attributed to the formation of a sand skeleton in bentonite-sand mixtures.

According to the test results,a sand skeleton will form when the void ratio of sand in the mixture is equal to the maximum sand void ratio esmax(Sun et al., 2009).Meanwhile, sand particles just make contact in mixtures when the vertical true effective stress equals pesα,and at this time the montmorillonite void ratio equals emsα,as shown in Fig.12a.Moreover, emsα and pesα were satisfied with the linear em-perelationship, as shown in Eq.(4), and therefore, the true effective deviatoric stress pesα can be expressed as follows:

where pais the atmospheric pressure of 100 kPa.

When the true effective stress is less than or equal to the true effective deviatoric stress, i.e.pe≤pesα, the sand skeleton is not formed, and the em-pelinear relationship (i.e.Eq.(4)) is still satisfied; when pe> pesα, the sand skeleton is formed, and the em-perelationship begins to deviate from the em-perelation line, and shows another linear relationship with the slope of bα.Meanwhile,the point(pesα,emsα)is the end of the deviated em-perelation line,as shown in Fig.12.Therefore, the linear em-perelationship when pe> pesα can be expressed as follows:

where emsα is the montmorillonite void ratio corresponding to pesα,and the point (pesα, emsα) is the intersection where em-perelationship begins to deviate from the em-perelation line;bαis the slope of em-peline after deviation, related to the sand content α and montmorillonite content β in bentonite.

The deformation data of bentonite-sand mixtures are normalized with respect to salt solution, consequently the em-perelation after the deviation can be obtained by the method in Sun et al.(2017), i.e.after determining the stress distribution ratio λ between bentonite and sand skeleton, the true effective stress borne by bentonite can be determined.Afterwards, according to the rule for the montmorillonite void ratio and the true effective stress borne by montmorillonite is satisfied with the unique linear relationship, the montmorillonite void ratio corresponding to true effective stress can be obtained.

Once the em-perelationship is determined, the relationship between the final void ratio and the vertical stress(ef-pe)after full wetting for mixtures with a specified sand content can be obtained.According to the ef-perelationship, the deformation after full wetting (swelling or collapse) under any true effective vertical stress can be judged for mixtures at any initial state.In practical engineering, bentonite-sand mixture is also in a constant volume state, i.e.the void ratio keeps almost unchanged as the initial void ratio e0(Sun and Sun, 2016).From the ef-perelationship, the swelling pressure psof mixture can be obtained.When the mixture undergoes a vertical stress greater than ps, the mixture is compressed;and when the mixture undergoes a vertical stress smaller than ps, the mixture swells.The final state will reach the ef-σvrelationship determined from the predicted em-σvrelationship.

Fig.13.Permeability prediction model due to salt solution concentration variation of bentonite-sand mixture with α ≤αs.

3.2.Permeability prediction model

Based on the permeability obtained from the k-emrelationship,the permeability prediction model of bentonite-sand mixtures with different sand contents under infiltration of salt solution with different concentrations is established.The relationship between montmorillonite void ratio and saturated permeability coefficient of bentonite-sand mixtures can be divided into two parts.

3.2.1.Permeability prediction model due to salt solution variation of bentonite-sand mixtures with α ≤αs

Fig.13 shows the sketch of permeability prediction model due to salt solution concentration variation of bentonite-sand mixtures with α ≤αs.Tripathi (2013) studied the permeability of bentonite under infiltration of salt solution with different concentrations and showed that the permeability coefficient of pure bentonite reached a minimum in a dense condition.The k-emrelationship of bentonite-sand mixtures with α ≤αsobtained in this study, as shown in Fig.7, also indicates that the k-emrelation lines of bentonite-sand mixtures with α ≤αsintersect to a point.The same trend of k-emrelationship can also be observed for pure GMZ01 bentonite in Ye et al.(2014),as shown in Fig.10.All of the above can prove that there is a critical point P (emf, kf) in the log10k-log10emdiagram, as shown in Fig.13, where emfand kfare the montmorillonite void ratio and saturated permeability coefficient at critical point P, respectively.The values of emfand kfof different types of bentonite and its sand mixture are related to the montmorillonite content in bentonite,and can be obtained through the permeability tests on two groups of sand-bentonite mixtures with different void ratios.When emis greater than emf, the slope of the k-emrelation line increases with increasing salt solution concentration.Therefore,the relationship between emand k of bentonite-sand mixtures with α ≤αsis expressed as follows:

where ηmis the slope of the k-emrelation line of saturated bentonite-sand mixture with α ≤αssaturated by salt solutions with different concentrations.When the salt solution concentration is 0,we have ηm= η0.The slope ηmis related to the montmorillonite content β and salt solution concentration m, and can be expressed as Eq.(8) through summarizing the permeability test data ofdifferent types of bentonite and its sand mixture infiltrated by salt solution with different concentrations(Mollins et al.,1996;Studds et al.,1998; Karnland et al., 2008; Ye et al., 2014).

Fig.14.log10k-log10pe relationship for bentonite-sand mixtures with α ≤αs saturated by salt solution.

When α ≤αs,the sand skeleton will not be formed,and unique em-perelation line expressed in Eq.(4) keeps satisfied.Combined with Eq.(7), the relationship between saturation permeability coefficient and true effective stress(k-pe)of bentonite-sand mixtures with α ≤αscan be established, as shown in Fig.14, and the relationship between k and peis expressed as follows:

where pefis the true effective stress corresponding to the critical point P.Through Eq.(9), the saturated permeability coefficient of bentonite-sand mixture with α ≤αsunder different true effective stresses and salt solution concentrations can be calculated once given the salt solution concentration, sand content, montmorillonite content, and values of a0and b0.

3.2.2.Permeability prediction model due to sand content variation of bentonite-sand mixtures saturated by salt solution with constant concentration

Fig.15 shows the sketch of permeability prediction model due to sand content variation of bentonite-sand mixtures saturated by salt solution with constant concentration.

When α ≤αs, the em-k relation keeps satisfying the linear relationship, with the slope of constant ηm, and obeys the expression of Eq.(7).

When α > αs, the k-emrelation deviates from the linear relationship,and the starting deviation point is M(em0,k0),where em0is the montmorillonite void ratio when the true effective stress peis 1 kPa in deformation model, and k0is the permeability coefficient when pe=1 kPa in the k-perelationship of bentonite-sand mixtures with α ≤αssaturated by salt solution.

Fig.15.Permeability prediction model of bentonite-sand mixtures saturated by salt solution (m is kept constant and α changes).

When α > αs, the k-emrelation is approximately bi-linear.For example, the dash lines for mixture with sand content of α1intersect at Point N1and the dot dash lines for mixture with sand content of α2intersect at Point N2, as shown in Fig.15, where the abscissa values of Points N1and N2represents the montmorillonite void ratio emsα of the deviation point in the deformation prediction model where the em-perelationship begins to deviate from the emperelation line,as shown in Fig.12.It can be seen from Eqs.(4)and(5) that emsα is related to the montmorillonite content and sand content but is uncorrelated to the salt solution concentration.Moreover, the higher the sand content, the greater the emsα.

At the right side of the intersection point N1or N2,i.e.em>emsα,the slope of the k-emrelation line is ηmα,which is related to the sand content, the montmorillonite content of bentonite, and the salt solution concentration.At this part,the void ratio of the mixture is relatively large, and the pores are not filled with saturated bentonite.Therefore, the permeability of the mixtures is closely related to the sand content.The slope ηmαincreases with increasing sand content.For example,due to α1<α2,the former slope is less than the latter.In addition,the salt solution concentration also has an impact on the saturated permeability of bentonite-sand mixtures.The swelling potential of bentonite decreases with increasing salt solution concentration(Ma et al.,2016),causing the increase of permeability coefficient of bentonite-sand mixtures.Therefore,for mixture with the same sand content, the higher the salt solution concentration, the greater the slope ηmα.

At the left side of the intersection N1or N2, i.e.em< emsα, the slope of the em-k relation line is supposed to equal the slope ηmof the em-k relation line of the mixture with α ≤αs, because in this part, the mixture is in the relatively dense state and the saturated bentonite can be completely filled with sand pores (Sun et al.,2017).Therefore, the variation of permeability of mixture with α > αsin this part is almost the same as that of the mixture with α ≤αs.

Therefore, the k-emrelationship of mixture with α > αscan be expressed as follows:

In Eq.(10),ηmαis the slope of k-emrelation line in the range of α>αsand em≥emsα.Fig.16 shows the sketch of ηmα-α relationship.When α ≤αs, sand skeleton is not formed, and the slope of k-emrelation line of mixture is constant,i.e.ηm.When α is close to 100%,k equals the permeability coefficient of sand,and ηmαis supposed tobe close to infinity.When αs≤α<100%,the relationship between ηmαand α is assumed as the downward convex parabolic relation.The reason for this assumption is that when the sand content increases gradually, the impact of bentonite on permeability of mixture decreases,while the sand does the opposite.Therefore,the slope ηmαof the k-emrelation line changes slowly with the increase of the sand content at the beginning and varies rapidly.In addition,according to the published permeability data of bentonite-sand mixture (Mollins et al.,1996; Studds et al.,1998), the relationship between ηmαand α of different types of bentonite and its sand mixture can be summarized as follows:

Fig.16.Sketch of ηmα-α relationship.

To sum up, the sketch of permeability prediction model for bentonite-sand mixtures due to salt solution concentration and sand content variation is shown in Fig.17.The dash line represents the case that the bentonite-sand mixture infiltrated by the salt solution with concentration of mi,and the solid line is the case that the salt solution concentration is mj,which is higher than mi.When α ≤αs,the k-emrelation line of mixtures saturated by salt solution with different concentrations intersects at the critical point P (emf,kf) and the slope increases with increasing salt solution concentration.When α>αsand the salt solution concentration is mi,the kemrelationship deviates from the line at point Mi, and point Ni(emsα, kmsαi) is the intersection point of bi-linear relationship.Similarly,for the case of mjconcentration(the solid lines),point Nj(emsα, kmsαj) is the intersection point of bi-linear relationship.

Fig.17.Sketch of permeability prediction model for bentonite-sand mixtures due to salt solution concentration and sand content variation.

According to the permeability prediction model, the saturated permeability coefficient of bentonite-sand mixtures under external stress and saturated by the salt solution with different concentrations can be calculated, given the basic parameters of bentonitesand mixtures, such as a0, b0, sand content α, montmorillonite content β, and salt solution concentration m.

4.Model verification

The prediction model is adopted to predict the deformation and saturated permeability coefficient of different types of bentonitesand mixtures saturated by salt solution with different concentrations.The parameters required in the prediction are listed in Table 6.

Table 6Parameters of deformation and permeability prediction model for four types of bentonite and its sand mixture.

4.1.Deformation prediction for bentonite-sand mixtures with different sand contents saturated by salt solution

The deformation prediction model was adopted to predict the deformation of Wyoming bentonite-sand mixture due to saturation.The predicted results are in good agreement with the deformation results of the mixtures saturated by salt solution with different concentrations in Studds et al.(1998) and by distilled water in Mollins et al.(1996), as shown in Fig.18.

The model is also used to predict the deformation of bentonite and its sand mixture used in this study, and the predicted results are also consistent with the test results in Section 2.3 of bentonitesand mixtures with different sand contents saturated by the salt solution with different concentrations, as shown in Fig.19.Therefore, the deformation prediction model can be adopted to predict the deformation of different types of bentonite and its sand mixture saturated by salt solution.

Fig.18.Deformation prediction of Wyoming bentonite-sand mixtures.

Fig.19.Deformation prediction of GCL bentonite-sand mixtures used in the study.

Fig.20.Permeability prediction of GCL bentonite-sand mixtures with α ≤αs used in this study: (a) k-em, and (b) k-pe.Pre stand for prediction.

4.2.Permeability prediction model of bentonite-sand mixtures

Fig.21.Permeability prediction of Wyoming pure bentonite saturated by salt solution with different concentrations: (a) k-em, and (b) k-pe.

The permeability prediction model is adopted to predict the saturated permeability coefficient of bentonite-sand mixtures with α ≤αssaturated by salt solution with different concentrations.The predicted results are in good agreement with the measured permeability results in terms of k-emand k-perelationships of different types of bentonite and its sand mixture with α ≤αs,such as GCL bentonite and its sand mixture in this study, as shown in Fig.20, Wyoming bentonite (Studds et al.,1998) in Fig.21, GMZ01 pure bentonite(Ye et al.,2014)in Fig.22,and MX80 pure bentonite(Karnland et al., 2008) in Fig.23.

From Figs.20-23, it can be concluded that the permeability prediction model can be used to predict the saturated permeability coefficient of different types of bentonite and its sand mixture with α ≤αs.Moreover, the predicted k-perelationship is more convenient for practical application.

The k-emrelationship of bentonite-sand mixtures with α > αssaturated by the salt solution with different concentrations is predicted using the permeability prediction model, such as Wyoming bentonite and its mixture in Studds et al.(1998), as shown in Fig.24, and GCL bentonite and its mixture used in the study, as shown in Fig.25.It can be seen that the permeability prediction results are basically consistent with experimental results.

From Figs.20-25, it can be concluded that the permeability prediction model can be used to predict the saturated permeability coefficient of different types of bentonite and its sand mixture at a full range of sand content saturated by salt solutions with different concentrations.

To sum up, the proposed swelling and permeability prediction model can comprehensively reflect the HMC behaviour of bentonite-sand mixtures, i.e.it can predict not only the swellingcharacteristics including swelling deformation (swelling or collapse)and swelling pressure,but also the saturated permeability of bentonite-sand mixture at a full range of sand content under the salt solution infiltration with different concentrations.

Fig.22.Permeability prediction of pure GMZ01 bentonite saturated by salt solution with different concentrations: (a) k-em, and (b) k-pe.

Meanwhile,the type of bentonite,the initial dry density and the optimum bentonite-sand mixing ratio can also be determined according to the proposed model once given the environmental groundwater salt concentration, the vertical pressure, the maximum allowable swelling pressure, and the anti-seepage requirements allowed by local regulations.To be specific, it is different in permeability coefficient required by the impermeable isolation layer of landfill and the buffer/backfill barrier of HLW repository.In the deep geological disposal, the allowable swelling pressure of bentonite-sand mixture ought to be confined considering the integrity of surrounding rock barrier.Moreover, the determination of the bentonite type and the optimum bentonitesand mixing ratio is mutually influenced, and should consider the engineering properties and economic requirements.

5.Conclusions

The deformation and saturated permeability behaviour of GCL bentonite-sand mixture under the salt solution infiltration were obtained through the swelling and compression tests.A model for predicting the HM behaviour of bentonite-sand mixtures under the coupled MC effect was proposed subsequently.The following conclusions were drawn:

Fig.23.Permeability prediction of pure MX80 bentonite and its mixture with 30%sand content: (a) k-em, and (b) k-pe.

(1) The em-perelationship of bentonite-sand mixtures with α ≤αssaturated by salt solution can be normalized with respect to salt solution and sand content, and presents a linear relationship.When α > αs, the em-perelationshipdeviates from the em-perelation line at the true effective deviatoric stress.

Fig.24.Permeability prediction of Wyoming bentonite-sand mixtures.

Fig.25.Permeability prediction of GCL bentonite-sand mixtures.

(2) When α ≤αs, the k-emrelation line of bentonite-sand mixtures saturated by salt solutions with different concentrations intersects at a critical point, and the slope of k-emline increases with the increase in salt solution concentration.When α > αs, the k-emrelationship deviates from the k-emline; moreover, the larger the sand content, the farther the deviation.After the deviation, the k-emrelationship is approximately bi-linear, and the intersection is consistent with the deviation point in the em-perelationship.

(3) The proposed model can uniformly predict the swelling(including swelling deformation and swelling pressure) and saturated permeability coefficients of different types of bentonite and its sand mixture at a full range of sand content under the salt solution infiltration with different concentrations.Meanwhile,according to the swelling and anti-seepage requirements of the project, the appropriate initial state indices of bentonite-sand mixtures can be quantitatively determined through the model.The proposed model provides the theoretical support for the design and construction of the anti-seepage engineering of bentonite-sand mixtures.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors are grateful to the National Natural Science Foundation of China (Grant No.41977214), the National Key R&D Program of China(Grant No.2019YFC1520500)and the Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences (Grant No.Z013008) for the financial supports.