Wenjing Sun, De’an Sun, Lei Fang, Shiqing Liu

DepartmentofCivilEngineering,ShanghaiUniversity,Shanghai200072,China

Soil-water characteristics of Gaomiaozi bentonite by vapour equilibrium technique

Wenjing Sun*, De’an Sun, Lei Fang, Shiqing Liu

DepartmentofCivilEngineering,ShanghaiUniversity,Shanghai200072,China

A R T I C L E I N F O

Articlehistory:

Received 20 September 2013

Received in revised form

27 November 2013

Accepted 12 December 2013

Gaomiaozi (GMZ) Ca-bentonite

Vapour equilibrium technique

Soil-water retention curve (SWRC)

Void ratio

Degree of saturation

Hydro-mechanical coupled parameter

SWRC at constant void ratio

Soil-water characteristics of Gaomiaozi (GMZ) Ca-bentonite at high suctions (3–287 MPa) are measured by vapour equilibrium technique. The soil-water retention curve (SWRC) of samples with the same initial compaction states is obtained in drying and wetting process. At high suctions, the hysteresis behaviour is not obvious in relationship between water content and suction, while the opposite holds between degree of saturation and suction. The suction variation can change its water retention behaviour and void ratio. Moreover, changes of void ratio can bring about changes in degree of saturation. Therefore, the total change in degree of saturation includes changes caused by suction and that by void ratio. In the space of degree of saturation and suction, the SWRC at constant void ratio shifts to the direction of higher suctions with decreasing void ratio. However, the relationship between water content and suction is less affected by changes of void ratio. The degree of saturation decreases approximately linearly with increasing void ratio at a constant suction. Moreover, the slope of the line decreases with increasing suction and they show an approximately linear relationship in semi-logarithmical scale. From this linear relationship, the variation of degree of saturation caused by the change in void ratio can be obtained. Correspondingly, SWRC at a constant void ratio can be determined from SWRC at different void ratios.

? 2013 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V. All rights reserved.

1. Introduction

The heavily compacted unsaturated Gaomiaozi (GMZ) bentonite is selected as a matrix material of buffer/backf i ll materials in deep geological disposal systems of high-level radioactive waste (HLRW) in China. GMZ bentonite can be mainly divided into Na-bentonite and Ca-bentonite. GMZ Na-bentonite, located in the underground space, is now being selected as a buffer material for HLRW disposal. Ca-bentonite is located near the ground surface with extremely plentiful reserve (Liu and Wen, 2003).

GMZ bentonite belongs to highly expansive soil, and has obvious swelling–shrinkage behaviour. Therefore, it has different soil-water characteristics from non-expansive soils or collapsible soils. Moreover, since compacted bentonite used in deep geological disposal systems has low initial water content and high initial dry density, it has a very high initial suction (Lloret and Villar, 2007). Simultaneously, at such high densities, the hydraulic conductivity of bentonite is signif i cantly low. Therefore, bentonite, as an artif i cial barrier, can eff i ciently block water intrusion from the surrounding geological medium. Moreover, because of heat from radioactive decay of nuclear wastes, the density of bentonite near the waste container will be enhanced (Villar and Lloret, 2008). Therefore, the compacted bentonite will be in high suction state for a long period of time. As a result, it is very important to study the soil-water characteristics of GMZ bentonite at high suctions.

The soil-water characteristics of different bentonites have been intensively studied, such as thermo-hydro-mechanical (THM) behaviour (Lloret and Villar, 2007) of heavily compacted “FEBEX”bentonite, water permeability, water retention and microstructure of unsaturated compacted Boom clay (Romero et al., 1999), permeability and soil-water characteristics of French FoCa7 compacted clay at 20°C, 50°C and 80°C (Imbert et al., 2005), water retention properties of MX80 bentonite by the vapour equilibrium technique at different temperatures (Tang and Cui, 2005), etc. Recently, several authors have conducted experimental and theoretical researches on soil-water characteristics of GMZ Na-bentonite. Chen et al. (2006) measured the SWRC of GMZ bentonite by osmotic technique and vapour equilibrium technique and analyzed the inf l uence of microscopic mechanisms on soil-water characteristics. Ye et al. (2009) studied the inf l uence of temperature on soil-watercharacteristics of compacted GMZ bentonite. Zhang et al. (2011) introduced the effective clay density and effective water content to modify the measured SWRCs of bentonite–sand mixtures. Meng et al. (2012) studied the SWRCs of GMZ bentonite–sand mixtures at low suctions using fi lter paper method and pressure plate method. Qin et al. (2012) investigated the temperature effect on SWRC at high suction experimentally and theoretically. However, the researches on the soil-water characteristics of bentonite are rarely reported on the inf l uence of deformation on SWRC. In fact, for highly expansive soils including bentonite, the hydraulic (e.g. degree of saturation and water content) and mechanical (e.g. deformation and strength) changes take place simultaneously when subjected to suction changes, suggesting that the total change in degree of saturation is induced by changes both in suction and void ratio (Sun and Sun, 2012). At present, formulations are developed by various authors to account for the effect of deformation on the SWRCs (e.g. Sun et al., 2007; Zhou and Kong, 2011; Ma et al., 2012).

In this paper, the soil-water characteristics of GMZ Ca-bentonite at high suctions (3–287 MPa) are measured by the vapour equilibrium technique. By analyzing the experimental data, the inf l uences of void ratio on soil-water characteristics at constant suctions and the SWRCs at different constant void ratios are obtained. After that, a transformation method from conventional SWRC with the same initial void ratio to the degree of saturation–suctionSr–scurve at constant void ratio is proposed. The research can provide parameters and experimental data to study the hydro-mechanical (HM) behaviour and establish the coupled HM elastoplastic model for highly expansive soils.

Table1Main physical parameters of GMZ Ca-bentonite.

2. Testing programme

2.1.Testingmaterials

The main mineral component of the GMZ Ca-bentonite is montmorillonite, and associated minerals are some quartz, feldspar, calcite, etc. The main physical parameters of GMZ Ca-bentonite are listed in Table 1. The free swelling ratio δefof GMZ Ca-bentonite obtained from free swelling test is 115%. According to the regulation of GB 50112-2013 (MOHURD, 2013), GMZ Ca-bentonite belongs to highly expansive soils. Deionized water is used in the tests to minimize the inf l uence of ion exchange as bentonite has a very high cation exchange capacity.

2.2.Testingmethodandprocedure

The vapour equilibrium method is employed to control the suction. Different saturated salt solutions are used to control the relative humidity (RH) of air in the closed container. According to thermodynamics, the relation between suction and RH is as follows:

wheresis the soil suction (kPa);Ris the molar gas constant, andR= 8.314462 J/(mol K);Tis the absolute temperature (K);wis the molecular mass of water vapour, andw= 18.016 g/mol; ρwis the mass density of water (kg/m3).

The RHs of corresponding saturated salt solutions adopted in the study are regulated by OIMLR 121 (OIML, 1996). The saturated salt solution and corresponding suction at 20°C are listed in Table 2. The tests were carried out in an air-conditioned room with temperature controlled at (20 ± 0.5)°C.

The soil samples were prepared by compaction to a specif i ed void ratio. After that, soil samples were placed on a rigid grid above given saturated salt solution inside a totally closed desiccator. The mass of soil samples was weighed periodically until the weight stabilized and this procedure was quick enough so that any water evaporation during the weighing process could be ignored. It was considered that the equilibrium between suction of soil samples and RH of saturated salt solution was reached if the mass change did not exceed 0.01 g within one week. The soil samples to reach equilibrium usually take about 2 months. Further details about the vapour equilibrium method can be found in Tang and Cui (2005) and Tang and Shi (2011).

After the equilibrium was reached, soil sample was taken out of desiccator and divided into two parts. One part was oven-dried in order to determine the water content at equilibrium which is the same as Tang and Cui (2005). The other part was immersed into the liquid paraff i n as shown in Fig. 1 to measure the volume of soil sample with the principle of buoyancy, but the step of volumemeasurement is different from Tang and Cui (2005). Furthermore, this method has the advantage of calculating void ratio and the degree of saturation of soil samples.

Table2Saturated salt solution and corresponding suction (temperature at 20°C).

Fig.1.Sketch of volume measurement for soil samples with irregular shapes.

Fig. 1 shows a sketch of volume measurement for soil samples with irregular shapes. In the experimental setup, a plastic container with liquid paraff i n inside was placed onto an electronic balance. An aluminium box was hung under the bracket through the fi ne wire and suspended in liquid paraff i n in the plastic container. First, the soil sample used for volume measurement was immersed into liquid paraff i n in advance for 15 min. This step is aimed to remove the bubble on the surface of soil sample with liquid paraff i n. Second, the immersed sample was taken out, wiping the excess paraff i n residue on sample’s surface with a tissue. The sample was then carefully placed into the aluminium box and immersed into liquid paraff i n. The variation of mass measured by an electronic balance was the mass of liquid paraff i n displaced by soil samples. Knowing the density of liquid paraff i n used in the experiment, the volume of measured soil sample can be obtained. After fi nishing the above steps, the water content, void ratio and degree of saturation of soil sample at equilibrium can be calculated.

Table3Test programme of soil samples No. 1 and No. 2.

3. Testing result and analysis

3.1.Soil-watercharacteristicsofGMZCa-bentoniteatthesame initialstate

Compacted soil samples No. 1 and No. 2, both 6.18 cm in diameter and 2 cm in height, were fabricated under the same conditions as mentioned in Section 2.2. The initial water content of these two samples was 21.92%, and the initial void ratio was 1.126. However, the two samples have experienced different suction paths in the tests performed. Samples No. 1 and No. 2 were fi rst saturated by vacuum-pumping method and then were divided into several equal parts separately. After that, the cutting parts of sample No. 1 were directly placed into different closed desiccators with over-saturated salt solution inside, i.e. sample No. 1 underwent the drying process. While the cutting parts of sample No. 2 were fi rstly oven-dried at 150°C for 24 h and then were placed into desiccators to carry out wetting test. The detailed test programme is listed in Table 3.

GMZ Ca-bentonite belongs to highly expansive soil, thus it has apparent swelling–shrinkage behaviour. Consequently, void ratio changes with suction during drying and wetting tests. First, by using the testing method mentioned in Section 2.2, the void ratio of each cutting part of soil samples No. 1 and No. 2 at equilibrium can be calculated. Fig. 2 shows the change in void ratio with suction of GMZ Ca-bentonite during drying and wetting. Sample No. 2 was fi rstly oven-dried to extremely high suction, and the subsequent wetting process is somewhat similar to the suction reloading process of overconsolidated sample. It can be seen that, sample No. 1 underwent drying process, and void ratio decreases with increasing suction, and sample No. 2 underwent wetting process, and void ratio increases with decreasing suction, re fl ecting the classical swelling–shrinkage behaviour of GMZ Ca-bentonite. Second, the drying process leads to a higher rate of deformation than the wetting process. Third, at same suction, void ratio in the wetting process is higher than that in the drying process. This is in part due to the reason that the sample No. 2 has experienced a stronger drying process, thus irreversible shrinkage deformation happens, and build-up of fi ssures in bentonite induces an increase in macroporosity (void ratio) (Yin et al., 2012). As a result, the internal pores of sample No. 2 are larger than those of sample No. 1 experiencing the wetting process. Note that some studies also show the same conclusion. Lin and Cerato (2013) studied the soil-water characteristics of highly expansive soil under cyclic drying and wetting in U.S. Eagle Ford. The test results also indicated that the void ratio of soil samples experiencing drying and wetting process is higher than that of sample merely subjected to drying process. The test result in Fig. 2 also provides evidence for the supposition of Alonso et al. (1999) that the build-up of aggregates can induce an increase in macroporosity during intensive drying, in other words, with intensive drying, even though the sample will shrink globally, macropore invasion may compensate for part of the shrinkage.

Fig. 3 shows SWRCs of GMZ Ca-bentonite of samples No. 1 and No. 2 with the same initial void ratio and water content in preparation. From the relationship between water content and suction shown in Fig. 3a, it can be seen that the water content in drying process is higher than that in wetting process at the same suction when the suction is less than 50 MPa. However, with increasing suction, the hysteresis is not apparent in the plane of water content versus suction relationship. This phenomenon can be explained by micropore structure of bentonite. The microscopic pores in bentonite include inter-aggregate pores and intra-aggregate pores (Romero et al., 1999). The change in water content in bentonite is mainly related to variation of water volume in the inter-aggregate and intra-aggregate pores. When suction is larger than 50 MPa, the quantity of free water existing inside the inter-aggregate pores is signif i cantly reduced. Any suction change can then only modify the absorbed water existing inside the intra-aggregate pores. Moreover, it is considered that reversible change in water content occurs in intra-aggregate pores. Therefore, hysteretic effects at higher suctions are much less pronounced. When suction is less than 50 MPa, suction change can induce signif i cant variations of free water inside inter-aggregate pores as well as absorbed waterinside intra-aggregate pores. And the difference in geometry of inter-aggregate pores leads to the hysteresis in SWRC, more readily observable. Therefore, at the same suction, water content of sample No. 1 subject to drying process is substantially higher than that of sample No. 2 subject to wetting process, when suction is less than 50 MPa. Romero et al. (1999) studied the soil-water characteristics of Boom expansive clay, and obtained that the two main mechanisms govern the storage of water inside bentonite. The hysteretic characteristics of Boom expansive clay in gravimetric water content versus suction relationship are the same with that of GMZ

Fig.2.Change in void ratio with suction during drying and wetting (e0= 1.126).

Ca-bentonite.

From the relationship between degree of saturation and suction shown in Fig. 3b, it can be observed that the degree of saturation during drying process is higher than that in wetting process at the same suction. In contrast to the water content versus suction relationship as shown in Fig. 3a, thew–srelationship shows hysteresis when suctions＜ 50 MPa but not so evident hysteresis when suctions＞ 50 MPa. Whens＞ 50 MPa, the difference in degree of saturation between drying process and wetting process is mainly caused by the change in void ratio. Whens＜ 50 MPa, the hysteresis of degree of saturation and suction relation can be attributed to the change in suction and the difference in void ratio between drying and wetting process as shown in Fig. 2.

As it is well-known, suction change can lead to changes both in void ratio and degree of saturation. Moreover, the change in void ratio can also bring about change in degree of saturation. Therefore, the total change in degree of saturation includes changes shared by suction and by void ratio, suggesting that void ratio has signif i cant inf l uence on the relationship between degree of saturation and suction. The test results of the relationship between degree of saturation and suction shown in Fig. 3b testify the conclusion that the hysteretic characteristics of SWRC, expressed bySr–srelationship, have generally to be superimposed with the aspects due to the deformability of the soil (Sun et al., 2007; Mathieu and Lyesse, 2008).

Fig.3.SWRCs of GMZ Ca-bentonite (e0= 1.126).

Fig.4.SWRCs of GMZ Ca-bentonite at different constant void ratios.

3.2.Soil-watercharacteristicsofGMZCa-bentoniteatdifferent constantvoidratios

As already mentioned, SWRC of bentonite expressed bySr–srelationship is dependent not only on the wetting or drying process, but also on the void ratio. Void ratio and degree of saturation change with suction, and change in void ratio also causes change in degree of saturation. Therefore, change in degree of saturation is separated by two parts, i.e. one is caused by suction change and the other by void ratio change. In order to establish the HM coupled elastoplastic constitutive model of unsaturated expansive soils, modelling of the SWRC needs to account for the effects of void ratio, and the SWRC at constant void ratio is usually used as the reference case to start with. Here, the soil-water characteristics of GMZ Ca-bentonite are fi rstly studied at constant void ratio.

Several tests were carried out on GMZ Ca-bentonite samples under different initial states by vapour equilibrium method. Using testing method mentioned in Section 2.2, the water content, void ratio and degree of saturation at equilibrium of cutting parts of soil samples can be calculated. The test data of drying process (or wetting process) are calculated and divided into various groups according to the void ratio at equilibrium. Each group has approximately the same void ratio at equilibrium. Subsequently, the relationship between degree of saturation and suction of each group with approximately the same void ratio at equilibrium is drawn inSr–splane as shown in Fig. 4. Test data of two groups in drying tests (e= 0.583 and 0.940) and two groups in wetting tests (e= 0.584 and 0.957) are plotted in this fi gure accordingly. It can be seen that at high suction, there is hardly any hysteresis between degree of saturation and suction at constant void ratio. In other words, at the same suction, the degree of saturation in drying process has a minor difference from that in wetting process at constant void ratio. In Figs. 3b and 4, the former shows the degree of saturation versus suction relation with void ratio changes and the latter gives the relationship between degree of saturation and suction at constant void ratio. It can be observed that the void ratio signif i cantly affects the soil-water characteristics.

Fig.5.SWRCs of samples in drying process at different void ratios.

There is hardly any hysteresis in relationship between degree of saturation and suction at constant void ratio, thus SWRCs of soil samples merely in drying process at different void ratios are presented (Fig. 5). Fig. 5a shows the relationship between water content and suction at different constant void ratios. It can be seen that void ratio has a slight inf l uence on water content versus suction relation. The same conclusion has been drawn in the study of SWRCs of FEBEX bentonite (Lloret and Villar, 2007), Boom clay (Romero et al., 1999), FoCa7 clay (Imbert et al., 2005) and GMZ Nabentonite (Zhang et al., 2011; Meng et al., 2012; Qin et al., 2012). The water mass per unit mass of solid grains in soil, no matter what shape or void ratio the soil is, is a certain value when reaching stabilized equilibrium in a humid environment except for the nearly saturated state (Romero and Vaunat, 2000).

Fig. 5b shows the relationship between degree of saturation and suction at different constant void ratios. It appears that when the void ratio decreases, the air entry value of soil sample increases and the SWRC between degree of saturation and suction shifts to the direction of higher suctions. Several studies also show the same conclusion (Sun et al., 2007; Mathieu and Lyesse, 2008; Sun and Sun, 2012), suggesting that at the same suction value, the degree of saturation of soil sample with a smaller void ratio is higher than that with a bigger void ratio. In other words, decreasing void ratio can increase water retention capacity of the sample. As to soil sample with a bigger void ratio, moisture in pores is relatively easy to be squeezed out by air. Therefore, the air entry value of sample with bigger void ratio is relatively smaller. That is, the air entry value increases with decreasing void ratio. At the same time, sample with smaller void ratio has higher density. At the same suction the moisture around soil particles increases, which improves the degree of saturation and enhances the water retention capacity of the sample.

Fig.6.Inf l uence of void ratio on water-retention in wetting process at constant suction.

3.3.Inf l uenceofvoidratioonsoil-watercharacteristicsat constantsuction

In this section, the changes in water content and degree of saturation with void ratio under constant suction are concentrated on. The in fl uence of deformation on soil-water characteristics will be analyzed, which is the basis to establish the HM coupled model of unsaturated expansive soils.

After measuring the water content and volume of cutting parts of soil samples by testing method mentioned in Section 2.2, the void ratio and degree of saturation at equilibrium are calculated. The measured and calculated test data are also divided into various groups according to the corresponding suction values of saturated salt solutions in desiccators, each group having the same suction. The relationship between water content or degree of saturation and void ratio of each group at constant suction is shown in Fig. 6.

Fig. 6 shows the in fl uence of void ratio on water-retention of samples in wetting process at different constant suctions. From relationship between water content and void ratio at different constant suctions (see Fig. 6a), it is known that water content decreases with increasing void ratio when suction is smaller, for examples= 3.3 MPa, and with the increase of suction, but basically water content does not change with void ratio. The phenomenon testifi es the former conclusion that void ratio has a minor in fl uence on water content and suction relation at high suction. The change ruleof water content with void ratio at constant suction can also be explained by the micropore structure of bentonite mentioned in Section 3.1. Two main mechanisms generally govern the storage of water inside a soil, i.e. one is mainly related to free water fl ow inside the inter-aggregate level and the other is associated with water adsorption at the intra-aggregate level. The second mechanism is virtually independent of the macroscopic structure, while the former mechanism is coupled with mechanical response of the soil such as volumetric deformation. In Fig. 6a, for water content below 15% and suction greater than 21.8 MPa, the free water presented inside the inter-aggregate pores is less, and the change in water content is mainly related to variation of absorbed water in the intra-aggregate pores. At this time, the second mechanism works, and the water content does not change with void ratio in macroscopic structure in high suction. For the water content greater than 15% and suction equal to 3.3 MPa, the moisture in soil samples includes free water existing inside the inter-aggregate pores and absorbed water existing inside the intra-aggregate pores. Because change of void ratio in macroscopic level can lead to change in free water existing inside the inter-aggregate pores, the water content can present the tendency decreasing with increasing void ratio.

Fig. 6b shows the relationship between degree of saturation and void ratio at different constant suctions. It appears that the degree of saturation increases approximately linearly with decreasing void ratio, ref l ecting that the void ratio has a signif i cant inf l uence on degree of saturation at a given suction. Moreover, the relationship between degree of saturation and void ratio can be considered to be linear and the slope of the line is theSr–ecoupled parameter λse. That is to say, λseis the slope of theSr–ecurve under constant suction larger than the air-entry value. The parameter λseref l ects the inf l uence of deformation on soil-water characteristics expressed bySr–srelationship. In other words, it ref l ects the HM coupling behaviour and belongs to the HM coupled parameter (Sun and Sun, 2012). Parameter λseis correlated to suction, and decreases gradually with increasing suction. When suction is relatively high, change in degree of saturation with void ratio tends to be stabilized, and λsealso reaches a certain value. The slope λseand suction show an approximately linear relation in semi-logarithmic coordinate,

as shown in Fig. 7. The linear relation between λseandscan be expressed with the following equation:

whereaandbare material parameters determined by plottingevs.Srfrom the results of isotropic compression tests on unsaturated expansive soils at two constant suctions respectively. For GMZ Cabentonite, we can geta= 1.49 andb= -0.19.

Fig.7.Relationship betweenSr–ecoupled parameter λseand suction.

Fig.8.SWRC at different void ratios and SWRC at constant void ratio.

3.4.DeterminationofSWRCatconstantvoidratiofrom conventionalSWRCatdifferentvoidratios

From laboratory tests such as the pressure plate method or vapour equilibrium method, we got the conventional SWRC, with void ratio changes shown in Figs. 2 and 3. However, SWRC of theSr–srelationship at constant void ratio is usually used to model hydraulic characteristics when establishing the HM coupled elastoplastic model (Sun and Sun, 2012). Therefore, it is necessary to transform the conventional SWRC with change in void ratio obtained from laboratory tests into SWRC at constant void ratio in order to determine the model parameters about hydraulic

characteristics.

Here we proposed a transformation method from conventional SWRC withechanging to theSr–scurve at constant void ratio. As mentioned above, the total change in degree of saturation dSrduring the testing is considered to be the sum of two components, one is induced by the change in suction dSr(s) and the other is caused by the change in void ratio dSr(e):

Therefore, the change inSrat constant void ratio can be determined by removing the change inSrinduced by void ratio dSr(e) from the measured total changes in degree of saturation dSr.

The relationship between degree of saturation and void ratio can be considered to be approximately linear at any particular constant suction (see Fig. 6b). Therefore, the change in degree of saturation caused by void ratio change under a constant suction dSr(e) can be obtained bySr–elinear relationship:

The relation between slope λseand suctionscan be expressed by Eq. (2). Therefore, we have

The SWRC at different void ratios and SWRC at constant void ratio are shown in Fig. 8. The test data ofSr–srelation of GMZ Ca-bentonite sample with the same initial void ratio (e0= 1.126) is measured by the vapour equilibrium method, each point having different void ratio marked by circle point “○”. Through the following three steps, theSr–scurve with void ratio of 0.6 can be obtained. First, the parameter λseat a constant suction is calculated by Eq. (2), and the change in void ratio deis determined from the real void ratio at this suction to the objective with void ratioeof 0.6. Second, the change in degree of saturation caused by void ratio change under a constant suction dSr(e) can be obtained byEq. (5). Finally, through Eq. (3), the change inSrat constant void ratio can be determined, and SWRC between degree of saturation and suction at constant void ratio can also be achieved.

In Fig. 8, the dotted line shows the fi tting result ofSr–scurve with void ratio of 0.6. The triangle points “Δ” areSr–stest results with the same void ratio of 0.603, which are obtained by the method described in Section 3.2. The test results and fi tting line show consistency, illustrating that the transformation method can obtain the SWRC at constant void ratio from conventional SWRC at different void ratios.

4. Conclusions

Soil-water characteristics of compacted GMZ Ca-bentonite at high suctions (3–287 MPa) are measured by the vapour equilibrium technique. The SWRC of samples with the same initial compaction states is obtained through drying and wetting process. By analyzing the measured and calculated test data, the relationship between water content or degree of saturation and suction at constant void ratio and the relationship between water content or degree of saturation and void ratio at constant suction are obtained. The main conclusions obtained are as follows:

(1) Void ratio changes with suction due to swelling–shrinkage behaviour of bentonite can bring about changes in the degree of saturation. The total change in the degree of saturation is induced by the change in suction and void ratio.

(2) Water content decreases with increasing void ratio at lower suctions, and suction increasing with water content basically does not change with void ratio. Void ratio has a minor inf l uence on the relationship between water content and suction at higher suctions.

(3) According to SWRC at constant void ratio, the air entry value increases and the SWRC between degree of saturation and suction with the same void ratio shifts to the direction of higher suctions with decreasing void ratio. When suction is kept unchanged, the degree of saturation decreases approximately linearly with increasing void ratio. The slope of the line decreases with increasing suction, showing an approximately linear relationship in semi-logarithmical scale.

(4) A transformation method is proposed from conventional SWRC with change in void ratio to SWRC at constant void ratio. From the linear relationship between degree of saturation and void ratio at constant suction, the variation in degree of saturation caused by the change in void ratio can be obtained. Correspondingly, SWRC at constant void ratio can be determined from conventional SWRC at different void ratios.

Conf l ict of interest

We wish to con fi rm that there are no known con fl icts of interest associated with this publication and there has been no signi fi cant fi nancial support for this work that could have in fl uenced its outcome.

Acknowledgement

The authors appreciate the fi nancial support of the National Natural Sciences Foundation of China (No. 41102163).

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Wenjing Sun is a senior engineer and supervisor of graduate students at Shanghai University. She obtained Ph.D. in structural engineering from Shanghai University in 2009 and her Ph.D. thesis was rated as “Outstanding Achievement of Graduate Student in Shanghai (Doctoral Dissertation)” in 2011. Her primary research interests relate to complex coupled process analysis, particularly to coupled hydro-mechanical (HM) behaviour and development of a coupled HM elastoplastic model for unsaturated expansive soils. She has published more than 30 papers. She is responsible for several research projects such as “Coupled hydro-mechanical behaviour of unsaturated Gaomiaozi bentonite and its elastoplastic modelling”(National Natural Science Foundation of China, No. 41102163). Moreover, she has also taken part in a number of research projects of her Ph.D. supervisor Prof. De’an Sun as primary participant. She also has registered several invention patents about test methods or apparatus of unsaturated soils and some of them have been authorized.

*Corresponding author. Tel.: +86 21 56331676.

E-mailaddress:wjsun@shu.edu.cn (W. Sun).

Peer review under responsibility of Institute of Rock and Soil Mechanics, Chinese Academy of Sciences.