Coupled hydro-mechanical analysis of expansive soils: Parametric identification and calibration

Ahishek Rwt, Linzhi Lng, Wieke Bille, Anne-Ctherine Dieudonne,Frederi Collin

a Department of Foundation Engineering, Soil and Rock Mechanics, Ruhr-Universität Bochum, Universitätsstraße 150, 44780, Bochum, Germany

b Faculty of Civil Engineering and Geosciences, Delft University of Technology, Building 23, 2628 CN Delft, the Netherlands

c ArGEnCo, University of Liege, 4000 Liege, Belgium

Abstract A methodology for identifying and calibrating the material parameters for a coupled hydro-mechanical problem is presented in this paper.For validation purpose,a laboratory-based water infiltration test was numerically simulated using finite element method(FEM).The test was conducted using a self-designed column-type experimental device, which mimicked the wetting process of a candidate backfill material in a nuclear waste repository. The real-time measurements of key state variables (e.g. water content,relative humidity, temperature, and total stresses) were performed with the monitoring sensors along the height of cylindrical soil sample. For numerical simulation, the modified Barcelona Basic Model(BBM) along with soil-water retention model for compacted bentonite was used. It shows that the identified model parameters successfully captured the moisture migration process under an applied hydraulic gradient in a bentonite-based compacted soil sample. A comparison between the measured and predicted values of total stresses both in axial and lateral directions along with other state variables revealed that heterogeneous moisture content was distributed along the hydration-path, resulting in non-uniform stress-deformation characteristics of soil.

2020 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords:Compacted bentonite Backfill material Deep geological repository Constitutive modeling Hydro-mechanical coupling Water infiltration test

1. Introduction

A compacted bentonite-sand mixture(50%:50% by dry mass) is generally proposed as a backfill material in the deep geological repositories in Germany for the final disposal of long-lived radioactive waste (e.g. Jobmann et al., 2015; Jobmann et al., 2017;Rothfuchs et al., 2005). The primary function of a backfill material is to limit advective water flow towards the waste canisters via available constructional gaps.The presence of bentonite in backfill materials fills such gaps when it comes in contact with water.Once these gaps are completely sealed with the bentonite, the material imposes swelling pressure on the roof and wall of disposal tunnel as a result of progressive hydration. Hence, the rate of saturation and the resulting swelling pressure are coupled with each other and it is a crucial coupling problem from the design point of view.Additionally, the mathematical formulation to reproduce this hydro-mechanical coupling is one of the major issues in the constitutive modeling for predicting the long-term behavior of backfill material. For this, several field and laboratory-based experimental and numerical investigations have been performed(e.g. Alonso et al., 2005; Martin and Barcala, 2005; Villar et al.,2005; Gens et al., 2009; Saba et al., 2014; Villar et al., 2014;Tripathy et al., 2015).

The Barcelona Basic Model (BBM) proposed by Alonso et al.(1990) is one of the most popular elastoplastic models. The model is an extension of the modified Cam-Clay model (MCCM)(Roscoe and Burland,1968) for an unsaturated state. The model is suitable for predicting the mechanical behavior of collapsible soils and low to moderate expansive soils. Several modifications have been suggested in the original formulation of the BBM (e.g.Delahaye and Alonso,2002;Vaunat and Gens,2005;Sánchez et al.,2012;Sun and Sun,2012;Zandarin et al.,2013;Gatabin et al.,2016)to reproduce the swelling potential of compacted bentonite-based materials. In general, the coupling between hydraulic and mechanical processes is introduced by incorporating the soil-water retention model, which features the relationship between the soil suction and degree of saturation in the mechanical constitutive model (Sheng and Zhou, 2011).

In the last decade, several soil-water retention models have been proposed(e.g.Gallipoli et al.,2003;Sun et al.,2007;Nuth and Laloui,2008;Tarantino,2009;Ma sín,2010;Gallipoli,2012),which correlate the air entry/air expulsion suction with the initial void ratio/dry density of soil samples.Based on the clay microstructural features in the compacted state, the double-structure water retention models have also been formulated (Romero and Vaunat,2000; Della et al., 2015). Recently, Dieudonne et al. (2017) proposed a model to account for different water retention mechanisms in each structural level of a compacted bentonite.One of the major challenges when simulating coupled hydro-mechanical problems is the large number of model parameters. As a result, the model calibration and the parametric identification are not straightforward(Wheeler et al.,2002;Gallipoli et al.,2010;D’Onza et al.,2012;Gallipoli and D’Onza, 2013).

This paper presents a methodology for identifying and calibrating the material parameters for a fully coupled hydromechanical analysis using the modified BBM along with the soilwater retention model proposed by Dieudonne et al. (2017). For validating the identified model parameters, a laboratory-based water infiltration test was simulated using the finite element method (FEM) code LAGAMINE (Collin et al., 2002). The test was performed with a self-designed column-type experimental device,which facilitated the simultaneous measurements of water content,relative humidity, and the total stresses both in axial and lateral directions at various pre-selected locations during the hydration.The measured and predicted values of water content, relative humidity,axial and lateral stresses were compared,revealing that the identified model parameters successfully captured the moisture migration process in the compacted soil sample. The test results highlighted the key features of hydration-induced processes in unsaturated compacted expansive soils. The impact of moisture migration under an applied hydraulic gradient on the soil stiffness was found to be quite significant.

2. Materials

The Calcigel bentonite and medium sand(DIN18123,2010)were used in this study. Table 1 summarizes the relevant geotechnical properties of the tested materials. The Calcigel bentonite contains 60%e70% montmorillonite and has the cation exchange capacity(CEC) of 740 mmol/kg with 67% of Ca2þas a predominant exchangeable cation.For preparing a mixture of bentonite and sand(50%:50% by mass) with 9% initial moisture content, the required volume of distilled water was added to the oven-dried sand beforemixing the Calcigel powder having 6%moisture content.The moist mixture was stored in sealed plastic bags for a period of 28 d.

Table 1Soil properties used in this context.

3. Methods

3.1. Column-type experimental device

A column-type experimental device was designed for investigating the coupled hydro-mechanical behavior of soils under an applied hydraulic gradient (Rawat et al., 2019). Fig. 1 shows the details of the designed experimental device.The technical details of the device can be found in Rawat et al. (2019). The monitoring instruments facilitate transient measurements of stresses both in axial and lateral directions along with the simultaneous measurements of temperature, water content and relative humidity at various pre-selected locations.

3.2. Preparation of soil sample

A cylindrical soil sample (diameter150 mm, and height300 mm) was assembled using three identical precompacted blocks (diameter150 mm, and height100 mm) of Calcigel bentonite-sand mixture having 9%moisture content.These blocks were prepared using uniaxial static compaction method by compacting the mixture into three layers.Each layer was subjected to vertical stress of 30 MPa in a specially designed cylindrical compaction mold (diameter150 mm, and height150 mm). It has a detachable base plate and a removable collar of 50 mm (in height). Once the compaction process was completed, the compacted block was removed from the mold.Further technical details concerning the compaction process in conjunction with the installation procedure of various monitoring sensors are provided in Rawat et al. (2019).

3.3. Water infiltration test

A test was performed by hydrating the soil sample from the bottom-end under a hydration pressure of 15 kPa in a controlled laboratory environment;the air outlet at top plug was kept open to evacuate the pore-air during saturation process. Effect of groundwater geochemistry on the clayewater interaction was not considered in this study,thus the distilled water was used to mimic the water ingress from the host rock. Monitoring sensors along with data logger continuously monitored relative humidity, temperature,water content,and total stresses both in axial and lateral directions.The test was performed for a period of 349 d.The postexperimental measurements (i.e. soil total suction and water content)were performed by collecting the soil samples from different locations along the height during dismantling of test set-up.

3.4. Numerical simulation

The water infiltration/wetting test was numerically analyzed using the FEM code LAGAMINE (Collin et al., 2002). The modified BBM(Alonso et al.,1990)along with the soil-water retention model proposed by Dieudonne et al.(2017)was used for this purpose.The proposed water retention model can consider different water retention mechanisms in each structural level, i.e. adsorption in intra-aggregate pores at microstructural level and capillarity in inter-aggregate pores at macrostructural level. The model was formulated in terms of water ratio (ew), which is expressed as the sum of contributions from the water stored in micropores (ewm)and the water in macropores (ewM). The water stored in intraaggregate pores is based on the Dubinin’s adsorption theory(Dubinin and Radushkevich,1947), which is expressed as

Fig.1. Details of the self-designed column-type experimental set-up: (a) and (b) Vertical and horizontal sectional views, and (c) A photograph of the device (Rawat et al., 2019).

where Uwmis the volume of water adsorbed in the micropores at relative pressureand temperatureT;Umis the total volume of the micropores; R is the universal gas constant (8.314 J/mol$K);nadsis the material parameter;Dis the similarity constant;andE0is the characteristic energy of adsorption for a reference vapor for whichD1.

Eq.(1)can be expressed in terms of water ratio by dividing both sides by volume of solid particles Usas

whereemis the microstructural void ratio.

Kelvin’s equation (Edlefsen and Anderson, 1943) relates the relative vapor pressure in the soil pore volume with the soil total suction:

whereRHis the relative humidity,Mwis the molecular mass of water (0.018 kg/mol),wis the density of water, andsis soil total suction.

By rearranging the constant parameters, the microstructural water retention domain can be expresses as

whereCadsis the material parameter. The parameternadscontrols the curvature of the water retention curve at the high suction values andCadsis related to the original Dubinin’s equation(Eq.(1))throughDE0.

The microstructural void ratio (em) in the bentonite-based materials evolves during the hydration process. Dieudonne et al.(2017) adopted the microstructural evolution model (Eq. (5)) proposed by Della Vecchia et al. (2015) for calculating the structural changes of the material along with the water retention curve:

whereem0is the microstructural void ratio for the dry material atew0;and0and1are the material parameters that quantify the swelling potential of the bentonite aggregates.In Eq. (5), it should be noted that for high dry density and high water content, it may lead to values ofemhigher than the total void ratioe.In this case,it is assumed that the microstructure is completely developed and then we haveeme.

The water stored in inter-aggregate pores (ewM) is caused by capillarity:

wherenandmare fitting parameters.

In order to feature the effect of macrostructural void ratio (eM)on the air-entry suction value, the parameter a is introduced:

whereAis a parameter controlling the dependency of air-entry suction on the macrostructural void ratio(eM).

The Kozney-Carman (KC) equation (Kozeny, 1927; Carman,1938) along with the Mualem-van Genuchten equation (van Genuchten,1980) provides a good estimate of deformation/stressdependent hydraulic conductivity in unsaturated state during the transient hydration process. The original Kozeny-Carman formulation (Kozeny, 1927; Carman, 1938) did not consider the dual porosity domains in compacted bentonite. Thus the equation is modified to incorporate the effect of change in the macrostructural void ratio (eM) on the saturated hydraulic conductivity of soil:

whereKis the intrinsic permeability (m2) for the compacted soil sample having macroscopic void ratioeM;K0is the intrinsic permeability(m2)for the reference macroscopic void ratioeM0;andMandNare the fitting parameters.

4. Parametric identification and calibration

The procedure for identifying and calibrating the model parameters for a coupled hydro-mechanical analysis is presented herein. The model parameters can be grouped into three categories: (i) parameters related to the mechanical behavior of soil(BBM parameters), (ii) parameters related to the soil-water retention behavior (Dieudonne water retention model), and (iii) parameters related to the hydraulic behavior (saturated and unsaturated hydraulic conductivities).

4.1. Identification and calibration of BBM parameters

Suction-controlled oedometer tests were performed for identifying the BBM parameters. Tests were conducted using the highpressure oedometer device. The bentonite-sand mixture (50%:50%by mass) having 9% initial water content was compacted directly inside the oedometer ring (diameter50 mm, and height15 mm) using uniaxial static compaction method. The achieved initial dry density was 1.8 Mg/m3similar to the compacted blocks in the water infiltration test.A total of four tests were performed (see Fig. 2). In the first test, the as-compacted sample(initial suction of 26.9 MPa)was subjected to one-dimensional(1D)compression-rebound stage.The other three tests were performed in two stages, i.e. suction-equilibrium stage and 1D compressionrebound stage. The vapor equilibrium technique (VET) was used to apply the desired suction level (i.e. 3.39 MPa or 10 MPa) in suction-equilibrium stage under 50 kPa vertical stress.As reduction in the soil total suction resulted in soil volumetric deformation,the change of the soil samples’ height was continuously monitored during suction-equilibrium stage. Once the targeted suction-level was attained, the second stage, i.e.1D compression-rebound, was initiated. For the test on saturated sample, the distilled water was supplied from the bottom-end under 50 kPa surcharge load prior to initiation of the second stage.

Fig. 2. Stress paths for suction-controlled oedometer tests.

The original BBM (Alonso et al.,1990) was an extension of the MCCM by introducing the concept of hardening plasticity. Soil suction was considered as a hardening parameter signifying that the yield surface corresponding to MCCM expands with an increase in soil suction.The rate of expansion is represented by another yield surface known as the loading-collapse(LC)curve,which changes its position when the sample undergoes plastic deformation,whereas any combination of the net mean stress and soil suction (ps)inside the elastic domain does not affect its position. Hence, it is essential that the sample should remain in the elastic domain during the suction-equilibrium stage. In this regard, the applied surcharge pressure should be kept lower than the expected swelling pressure of the compacted soil sample under constant volume condition,in order to ensure that the soil stress state(p;q;s)is within the elastic domain.In the present study,the sample was subjected to 50 kPa surcharge pressure and allowed to attain equilibrium with the applied suction level(i.e.3.39 MPa or 10 MPa)underK0condition. The suction-controlled oedometer test results are shown in Fig. 3, along with the preconsolidation stress for saturated soil sample.It should be noted that the slope of unloading path for sample at 10 MPa suction applied is not shown in Fig.3 due to the power failure during the test.

In the parametric analysis, three parameters ((0),andr),which control the slope of normal compression lines at different suction levels were identified first. The results of oedometer test indicated that the collapse potential decreased with an increase in vertical net mean stress. On the other hand, Alonso et al. (1990)assumed that the slope of normal compression line would decrease when increasing the soil suction, based on the experimental results from García-Tornel(1988)on compacted low plastic kaolin and Maswoswe (1985) on compacted sandy clay. To overcome this problem that the collapse potential decreased with an increase in net stress, Wheeler et al. (2002) proposed a procedure for selecting suitable values of the model parametersrandpc(reference stress). Following the procedure proposed by Wheeler et al. (2002),Fig.4a shows the predicted variation of(s)with soil suction.

Fig.3. Identification of the BBM parameters from suction-controlled oedometer tests.

In the second step, the model parameters related to the elastic behavior of soil (kandks) were identified. Fig. 4b presents the predicted variation ofkwith soil suction and the experimental values.It should be noted here that the fitting parameters in Fig.4b were strongly affected by the elastic stiffness of soil in saturated condition (s0). For the slope of reversible wetting-drying line(ks), the experimental data during suction-equilibrium stage (soil suction vs. specific volume) were used. Fig.4c shows the variation ofkswith soil suction less than 50 kPa surcharge pressure. In the last step,the parameterpcwas selected to match the experimental data on preconsolidation stress values at different suction levels.Fig. 4d shows the LC curve for the compacted bentonite-sand mixture with the fitting parameters. Table 2 summarizes the BBM parameters for the Calcigel bentonite-sand mixture (50%:50% by mass).

4.2. Identification and calibration of soil-water retention model parameters

There are eight model parameters in formulation of doublestructure water retention model proposed by Dieudonne et al.(2017), i.e.

Table 2BBM parameters for compacted bentonite-sand mixture(50%:50% by dry mass).

(1)em0,0and1signify the evolution of the microstructural void ratio(em) with the water ratio(ew);

(2)Cadsandnadscontrol the water retention response of the intra-aggregate pores; and

Fig.4. Identification of the BBM parameters:(a)Slope of suction-dependent normal compression lines,(b)Applied net stress vs.specific volume at different applied suction levels,(c) Applied suction vs. specific volume at different applied net mean stresses; and (d) Loading-collapse curve.

(3)A,nandmgovern the water retention behavior of the interaggregate retention region.

The model parameters(em0,0and1)should be estimated first,independently of other parameters. It requires the pore size distribution (PSD) data of the compacted mixture of Calcigel bentonite-sand (50%:50% by mass) at different water ratios (em0).Additionally, the identification ofem0requires the PSD data of the oven-dried sample, i.e. water void ratioew0. Agus (2005) obtained the PSD data from mercury intrusion porosimetry (MIP)tests on the samples having an identical water ratio (i.e.ew0.245). The MIP tests were conducted for the as-compacted,oven-dried and swollen samples. To quantify the microstructural and macrostructural void ratios from the PSD data, the delimiting pore sizes were identified by drawing tangents on the cumulative intrusion curves for as-compacted (0.05 mm), swollen (0.02 mm)and oven-dried (0.02 mm) samples,as shown in Fig. 5.

The MIP test data for the as-compacted samples revealed that the intra-aggregate or micropore volume was 59%, while the interaggregate pore volume was 41% of the total pore volume. For the oven-dried samples, the intra-aggregate and inter-aggregate pore volumes were 55%and 45%of the total pore volume,respectively.For the swollen samples, the intra-aggregate and inter-aggregate pore volumes were 57% and 43% of the total pore volume, respectively.Based on the above MIP test data,the corresponding microstructural and macrostructural void ratio were obtained for as-compacted samples (em0.3 andeM0.21 forew0.245), oven-dried samples (em00.25 andeM0.2 forew0) and swollen samples(em00.45 andeM0.35 forew0.8).Fig.6 shows the evolution of microstructural void ratio with water ratio, and the obtained data were fitted with the model proposed by Della Vecchia et al.(2015).

It is clear that the model parametersCadsandnadscontrol the soil-water retention behavior of intra-aggregate or micropores.The identification of these parameters requires sorption/wetting tests under constant volume condition on the compacted samples having different initial dry densities. In the present study, the compacted samples(initial dry density of 1.8 Mg/m3)were subjected to wetting under a constant volume condition, while the data for samples of 2 Mg/m3were collected from Agus (2005). The soilwater retention behavior at higher suction level was governed by the intra-aggregate or micropores and did not depend on the sample initial state.The parameterCadscontrolled the slope of soilwater retention curve at higher suction value and varied in 0.018e 0.0018 MPa1(Dieudonne et al., 2017). The parameternadscontrolled the curvature of water retention curve in the high suction range and could be treated as a fitting parameter.

Fig.5. Determination of micropores and macropores from the PSD data from Agus(2005).

Fig. 6. Evolution of microstructural void ratio with water void ratio for compacted Calcigel bentonite-sand mixture (50%:50% by mass) from Agus (2005).

The macrostructural water retention model parametersA,nandmwere identified using the sorption/wetting tests data for soil samples having different initial dry densities (i.e. 1.8 Mg/m3and 2 Mg/m3). The macroscopic parameter (A) captured the dependency of air-entry (or air-occlusion) suction on the initial void ratio.The parametersnandmcontrolled the drying-wetting rate of materials in low suction range. Fig. 7 shows the calibration of Dieudonne water retention model and the van Genuchten model against the experimental data.

4.3. Identification and calibration of hydraulic parameters

The parametric identification for Kozeny-Carman (Carman,1938; Kozeny, 1927) formulation (Eq. (9)) requires the intrinsic permeability values of saturated soil samples having different initial porosities. The intrinsic permeability (m2) of material is related to the saturated hydraulic conductivity (m/s) of material.

whereKis the intrinsic permeability(m2)of material with porosity,K0is the intrinsic permeability (m2) of material with reference porosity0, andmandnare the fitting parameters. The saturated permeability can be written as

Fig. 7. Calibration of soil water retention model against the experimental data on Calcigel bentonite-sand mixture (50%:50% by mass) at two different dry densities(wetting path under confined condition).

wherekfis the saturated permeability (m/s),Kfis intrinsic permeability (m2),fis the density of fluid (kg/m3),gis the gravitational acceleration(m/s2),and mfis the dynamic viscosity of fluid(Pa s).

The saturated hydraulic conductivity values at different initial dry densities of the Calcigel bentonite-sand mixture (50%:50% by mass)were collected from the literature (Agus, 2005; Long, 2014). For an initial dry density of 1.8 Mg/m3,the saturated hydraulic conductivity of the compacted mixture was determined by the oedometer test.The collected and measured saturated permeability data with the Kozeny-Carman model parameters for the investigated material are shown in Fig.8.For the relative permeability in unsaturated state,a closed-form equation proposed by van Genuchten(1980)was used.The parameterwas calibrated by best fitting the response of three relative humidity sensors located at 50 mm,150 mm and 250 mm from the bottom-end.Table 3 summarizes the water retention model and the hydraulic parameters.

5. Numerical analysis of water infiltration test

Fig. 8. Sample initial porosity vs. intrinsic permeability: Experimental data and predicted values using Kozeny-Carman formulation.

Table 3Model parameters for hydraulic behavior of compacted bentonite-sand mixture(50%:50% by mass).

The model geometry along with the initial boundary conditions used in the numerical simulation is shown in Fig. 9. The model dimensions were determined according to the sample size in the water infiltration test (75 mm alongX-axis and 300 mm alongY-axis). The initial stress in the material was assumed to be atmospheric(0.1 MPa and isotropic).The temperature in this study was kept constant at 20C.The initial total suction of the material was assigned to 26.9 MPa. For initiating the hydration, the liquid pressure at the bottom nodes was changed by a hydration pressure of 15 kPa.

6. Results and discussion

6.1. Rate of saturation during hydration phase

Fig. 10a,b shows a comparison between the predicted vs.observed relative humidity and water content evolution along the hydration path with the measured post-experimental values. It shows that the distance to the hydration-end significantly affected the rate of saturation. As a result, the water content increased rapidly at section X1. The predicted values showed a good agreement with the measured ones; however, the predicted values of water content were slightly higher than the measured ones at farther sections (i.e. X2 and X3).

Fig.11 compares the predicted, calculated and measured infiltrated water volumes during the hydration process.The calculated values were deduced from the measurements of transient water content. The predicted values show a good agreement with the measured and calculated ones. A decrease in the flow rate with elapsed time was observed,which signified the effect of soil suction gradient on the rate of saturation.

6.2. Development of stresses due to wetting process

The clayewater interaction in terms of either sorption(wetting)or desorption (drying) of bentonite results in volumetric deformation (swelling or shrinkage, respectively). The sorption or wetting of compacted bentonite under confined conditions generates swelling pressure,which acts against the confinement. During the water infiltration test,the swelling pressure was measured both in axial and lateral directions.The predicted values obtained from the numerical analysis were compared with the measured ones(Fig.12 in axial direction and Fig.13 in lateral direction).

Fig. 12 presents the predicted and measured axial total stress values at the top- and bottom-end of a cylindrical soil sample. In the water infiltration test, the hydration was initiated from the bottom-end, and the top load cell measured the swelling pressure exerted from the bottom elements due to wetting. For frictionless cell boundaries between the soil sample and test cell,the measured axial stresses at two extreme ends should be the same in case of hydration under a confined condition. On the other hand, the measured axial stress values at the top- and bottom-end were dissimilar.This dissimilarity in the measured axial stresses may be due to some reasons, such as (i) dissimilar compressibility characteristics along the hydration-path due to the non-homogeneous moisture distribution, (ii) presence of construction joints meant for installing the pressure transducers,(iii)side frictional resistance between the sample and the PVDF (Polyvinylidene fluoride) rings,and (iv) composite nature of the sample due to the presence of sensors that created complex stress-deformation characteristics of the system. These features were not considered explicitly during the simulation. A decent agreement was observed between the predicted and measured axial total stress data at the bottom-end;however, the predicted values were slightly higher than the measured ones.

In the numerical analysis of water infiltration test under a confined condition,the elastic strain according to the BBM is given:

Fig. 9. Finite element simulation of water infiltration test: Features of numerical analysis.

Fig.10. Rate of saturation during transient hydration process: Measured vs.predicted values of (a) Relative humidity, and (b) Water content evolution.

For hydration under confined conditions, we have

Fig.11. Comparison between measured and predicted values:Infiltrated water volume over elapsed time.

Fig. 12. Development of swelling pressure in axial direction due to wetting under confined conditions: Measured vs. predicted values.

Fig. 13. Development of swelling pressure in lateral direction due to wetting under confined conditions: Measured vs. predicted values. (a) At section X1 (50 mm from bottom-end);(b)At section X2(150 mm from bottom-end);(c)At section X3(250 mm from bottom-end).

By integrating Eq. (15), the increase in mean stresspwith suctionswithin the elastic domain can be expressed as

wherep0ands0are the initial mean net stress and soil suction,respectively.

Eqs. (15) and (16) reveal that the incremental change in mean stress in the elastic domain depends on the ratio of elastic stiffness(ks=k),incremental change in suction(ds)and the soil stress state(p;s). Fig. 13 presents a comparison between the predicted and measured values of lateral total stress along the height of soil sample. With initiation of hydration, the measured total stress at the section X1 increased quickly and reached 2.18 MPa within 45 d.With further hydration, the measured values at the section X1 showed some oscillations before reaching a value of 2.13 MPa in 349 d. The model predictions showed a good agreement with the measured data at section X1; however, the predicted values disagree with the measured data at sections X2 and X3.In general,the stress-deformation characteristics of a compacted bentonitebased soil sample during hydration from one end involves various complex processes, which includes swelling of soil layers,hydration-induced heterogeneity along the height of soil sample,and interaction between different soil layers. Also,the presence of technical gaps and non-uniform soil stiffness in axial and lateral directions are responsible for a different axial and lateral swelling pressure response.

7. Concluding remarks

The present study investigated the coupled hydro-mechanical behavior of a compacted bentonite-sand mixture (50%:50% by mass). A water infiltration test was conducted to mimic the transient hydration process of a candidate backfill material in nuclear waste repository. The test was conducted using a column-type experimental device. Later, the water infiltration test was numerically simulated using FEM.In the numerical analysis, the modified BBM along with the double-structure water retention model was used. For identifying the model parameters, a methodology was proposed using conventional laboratory-based experiments on the elementary soil samples. To validate the identified model parameters, the predicted values from the numerical analysis were compared with the measured ones. The experimental results revealed the moisture migration along the height of unsaturated soil sample under an applied hydraulic gradient. The doublestructure water retention model proposed by Dieudonne et al.(2017) successfully captured the moisture migration process in the compacted soil sample.

The axial and lateral total stress measurements during the water infiltration highlighted the consequences of a heterogeneous moisture distribution in compacted bentonite-based materials. A comparative analysis of the measured and predicted total stress values along the height of soil sample signified the role of interfacial friction between the soil sample and cell-wall and anisotropic swelling behavior, which provided the key inputs to improve the existing constitutive models for a coupled hydro-mechanical analysis.

Declaration of Competing Interest

The authors wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.

Acknowledgments

The authors are grateful to the German Research Foundation(DFG) for the financial support (Grant No.SCHA 675/17-1).