1 Introduction

Unsaturated soils are widespread in nature, particularly in arid and semiarid areas, where a deep ground water table exists usually. It is well known that some of the most typical geotechnical infrastructure, including earth slopes, retaining walls and pavements in arid and semiarid areas and nuclear waste disposal clay buffers, involves the use of natural or compacted expansive soils subjected to a much wider range of moderate-to-high suction values. Moreover, climate plays an important role in unsaturated ground surface soils. For example, dry season with the lower relative humidity can cause unsaturated soil surrounding dehydration to the point at which very high suction magnitudes may be encountered. Therefore, it is necessary to investigate the hydro-mechanical behavior of unsaturated soil over a wide suction range.

Expansive soils, consisting of strongly hydrophilic minerals (i.e., montmorillonite and illite), are sensitive to suction change in particular. As shown in Ng et al. [25], the climate can significantly affect the hydro-mechanical behavior of unsaturated expansive soils, which may induce severe disaster and damage to structures built on them. Therefore, the study on the influence of suction on hydro-mechanical behavior of unsaturated expansive soils over a wide suction range is essential to understand the mechanism of geotechnical hazards related to expansive soils.

It is generally recognized that suction is one of the key factors governing the behavior of unsaturated soils. The influence of suction on unsaturated soil behavior has been investigated widely via both theoretical and experimental methodologies, which has been reviewed in, for example, Gens [13, 31] and Sheng [31]. The suction can be measured or applied in different manners, such as the axis-translation technique, filter paper method and vapor equilibrium technique, while the suctions in the pressure plate apparatus and triaxial apparatus for testing unsaturated soils are usually applied using the axis-translation technique. The suitability of the axis-translation technique for imposing considerably higher values of suction during testing, however, is limited to the air-entry value (AEV) of the ceramic disk for separating air from water in soil specimens. This limitation normally constrains the testing capability of most suction-controlled pressure plate apparatus and triaxial apparatus to a suction state less than 500 or 1500 kPa. The suction range applied in most of these apparatus is from 0 to 500 kPa. Therefore, great deals of experimental studies have been conducted to investigate the hydro-mechanical behavior of unsaturated non-expansive soils [11, 19, 23, 24, 30, 36] or unsaturated expansive soils [25, 39] in a such low suction range.

The measured mechanical behavior of unsaturated soils over a wide suction range is very limited in the literature. Escario and Juca [8] performed suction-controlled direct shear tests (up to 15 MPa) on three compacted soils using a special device developed based on osmotic suction technique. Recently, Alsherif and Mccartney [2, 3] employed the vapor flow technique in triaxial cell to control the high suction in specimens to investigate the effects of elevated temperatures and high suction magnitudes on the shear strength of unsaturated silt, and Patil et al. [27] obtained experimental evidence of shear strength of compacted silty sand at a critical state from suction-controlled triaxial tests conducted in the suction range of 0.05 to 300 MPa. Gao et al. [12] performed a series of triaxial tests on a compacted clayey silt over a wide suction range by using the axis-translation technique and the vapor equilibrium technique with saturated salt solution. The above experimental studies mentioned mainly focused on non-expansive soils, and the tests on expansive soils over a wide suction range are rather limited. Blatz et al. [5] performed triaxial tests on compacted sand–bentonite that is a possible buffer material in the nuclear waste disposal repository by using saline solutions with different concentrations to induce high suction ranging from 5.0 to 42.4 MPa. Some researchers, such as Lloret et al. [20], Alonso et al. [1], Cuisinier and Masrouri [6], Nowamooz and Masrouri [26], and Zhao et al. [42] have studied the behavior of expansive bentonite–sand mixtures, or expansive bentonite–silt mixtures by modified oedometer over a wide suction range. Zhang et al. [40] investigated the hydro-mechanical behavior of expansive soil by triaxial tests in a suction range up to 38.0 MPa, but the shear strength of the expansive soil with different dry densities or at very high suction was not systematically studied.

Moreover, a number of shear strength criteria for unsaturated soils have been proposed in the literature during the past decades [10, 17, 35]. It is often recognized that most of those attempts have focused on finding a relationship between the effective stress coefficient \(\chi\) and the degree of saturation. This leads to significant overestimate of strength in high suction range, especially for fine-grained soils. In recent years, using the capillary degree of saturation to replace the effective stress coefficient \(\chi\) in the shear strength criteria of unsaturated soils can well improve the prediction in the entire suction range [18, 43], in which the pore water in soils is divided into the capillary water and adsorbed water. Whether the adsorbed soil–water retention curve (SWRC) or capillary SWRC in the entire suction range (from 0 to about 1000 MPa) can be accurately predicted or not needs to be validated by experimental data. Meanwhile, a number of coupled hydro-mechanical constitutive models for unsaturated soils [21, 22, 32, 33, 37, 38] were validated by experimental results only in a low suction range (almost below the suction of 500 kPa).

In addition, the effect of void ratio or density on shear strength of unsaturated soils is notable over a wide suction range, especially for fine-grained soils. Therefore, it is necessary to investigate the hydro-mechanical behavior of unsaturated expansive soils with different initial void ratios or densities over a wide suction range, which also can provide experimental data for validating constitutive relations used to describe the hydro-mechanical behavior of unsaturated expansive soils.

This paper presents a systematical study to investigate the effect of void ratio or dry density on the hydro-mechanical behavior of unsaturated expansive soil over a wide suction range. The suction-controlled triaxial tests are conducted on unsaturated expansive soil experiencing different suctions in a wide range of suction. To realize a wide suction range, the low suction (0–800 kPa) was imposed by the axis-translation technique (ATT) and the high suction (3.29–368 MPa) was imposed on soil specimens by the vapor equilibrium technique (VET). The experimental program in this study consists of a series of suction-controlled triaxial compression tests on soil specimens subjected to different suctions. In addition, two methods (pressure plate and vapor equilibrium methods) were employed to study the soil–water retention behavior. The detailed experimental program, test results and discussion are presented in the following sections.

2 Test apparatus and experimental techniques

2.1 Pressure plate apparatus for testing SWRC

The pressure plate apparatus used was produced by the Hong Kong GEO-Expert manufacturers. The air-entry value of the ceramic disk in the pressure plate apparatus is 1.5 MPa. The axis-translation technique (ATT) [15] was adopted to control matric suction of the soil specimen. Pore water pressure was applied through a saturated high air-entry ceramic disk sealed to the base pedestal of the apparatus, while the pore air pressure (0–1500 kPa) was applied through a coarse low air-entry disk placed on top of the soil specimen. The free air could not penetrate the saturated ceramic disk but the dissolved air is able to pass through the ceramic disk with water. The dissolved air may accumulate underneath the high air-entry ceramic disk, leading to the formation of air bubbles during a long period of testing. To correct this problem, a flushing system was employed during tests. The volume of the diffused air (i.e., air bubbles underneath the ceramic disk) is measured by the flushing system, and the measured volume is used for correcting the volume change of water (drained in/out of the specimen). The SWRCs of expansive soil in low suction range were conducted by the pressure plate apparatus.

2.2 GDS triaxial testing apparatus for unsaturated soils

All triaxial shear tests were conducted by GDS unsaturated triaxial testing apparatus, which was manufactured by the GDS Company (Hampshire, UK). The triaxial testing system consists of a triaxial cell, two independent GDS Standard Pressure Controllers (GDS SPC), a pneumatic regulator with two channels, six transducers and a computer. The GDS SPC is a hydraulic actuator for the precise regulation and measurements of fluid pressure and volume. The six transducers consist of (1) an internal load cell to measure the axial force, (2) a linear variable differential transformer (LVDT) to measure the axial displacement, (3) cell pressure transducer, (4) pore air pressure transducer, (5) pore water pressure transducer and (6) a Wet–Wet differential pressure transducer to measure the total volume change of the triaxial specimen. Water volume change of specimens is measured by a GDS SPC. A computerized control system was used to acquire the data from all of GDS units and control the stress/suction paths. The system is controlled by a closed-loop feedback scheme. The triaxial shear tests were performed by controlling axial strain.

The axis-translation technique was adopted to control matric suction in triaxial soil specimens. Pore water pressure was applied through a saturated high air-entry ceramic disk installed in the base pedestal of the triaxial apparatus, while the pore air pressure was applied through a coarse low air-entry disk placed on top of the triaxial soil specimen. The volume of the diffused air (i.e., air bubbles underneath the ceramic disk) is measured by the flushing system, and the measured volume is used for correcting the volume change of water (drained in/out of the triaxial specimen). Prior to the investigation tests, calibration tests were conducted to estimate the volume change of different components of the system (including apparent volume change of the cell due to cell pressure and loading ram displacement).

2.3 Vapor equilibrium technique

The air-entry value of the ceramic disk in GDS triaxial apparatus is 500 kPa, and thus the maximum suction of specimens applied directly in this triaxial apparatus is 500 kPa. The suction higher than 500 kPa was achieved via the vapor equilibrium technique (VET). To set suction by the VET, a common method is to place soil specimens in a sealed container with a specific relative humidity generated by saturated saline solutions [7, 29]. Details of saline solutions used in the tests are listed in Table 1, together with corresponding relative humidity and suction value, which are from Greenspan [14]. In this study, eleven saturated saline solutions (see Table 1) were used to measure the SWRC and three saturated saline solutions (i.e., K2SO4, NaCl and LiBr) were used to prepare the triaxial specimens at high suctions to study the effect of high suction on the hydro-mechanical behavior of unsaturated expansive soil. The total suctions corresponding to above the saturated saline solutions are calculated using Kelvin’s law as follows:

$$\psi = - \frac{{\rho_{\text{w}} RT}}{{\omega_{\text{v}} }}\ln ({\text{RH}})$$
(1)

where \(\psi\) is the total suction, kPa. \(\omega_{\text{v}}\) is the molecular mass of water vapor, which is assumed equal to 18.016 g/mol, and R is the universal gas constant (i.e., 8.31432 J/mol K). \(\rho_{\text{w}}\) is the density of water, T is the absolute temperature, and RH is the relative humidity, %.

Table 1 Saturated saline solution and corresponding suction (20 °C)
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3 Testing material

The soil investigated in this study is referred to as Nanyang expansive soil, which is an expansive soil according to the ‘Technical Code for Buildings in Expansive Soil Regions’ (from China National Standard). The expansive soil used in the tests was taken from Wolong, Nanyang City, Henan Province, China. The site is in the middle route of the National South-to-North Water Transfer Project, and the soil was retrieved at a depth of about 4 meters. Nanyang expansive soil has a liquid limit of 38.8% and a plasticity index of 21.6 and other physical property indexes (such as specific gravity, plastic limit, maximum dry density, optimum water content, free swelling ratio) are summarized in Table 2.

Table 2 Physical property indexes of Nanyang expansive soil
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Figure 1 shows the grading curve of the soil determined by the hydrometer analyses. It can be seen from Fig. 1 that the soil is composed of 23% clay fraction (< 2 μm) and about 77% silt fraction. Free swelling ratio \(\delta_{\text{ef}}\) (%) is defined as \(\delta_{\text{ef}} = (V_{\text{we}} - V_{0} )/V_{0} \times 100\), here \(V_{0}\) is the initial volume of oven-dried soil and \(V_{\text{we}}\) is the volume of the soil after swelling freely in distilled water, and is obtained from free swell test. X-ray diffraction analysis indicated that the predominant minerals of the soil were 62% quartz, 12% albite, 10% microcline, 9.9% illite and 5.8% montmorillonite, with a small percentage of kaolinite (0.3%).

Fig. 1
figure 1

Grading curve of Nanyang expansive soil

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4 Specimen preparation and testing program

A series of soil–water retention tests and triaxial shear tests were conducted to investigate the hydro-mechanical behavior of unsaturated expansive soils with different initial dry densities over a wide suction range.

4.1 Soil–water retention tests

To study the water retention behavior of expansive soil in the entire suction range, two suction control or measurement methods are used: the pressure plate method for low suction range of 0–1.5 MPa, and the vapor equilibrium technique (VET) for high suction range of 3.29–368 MPa.

  • For the pressure plate method, the specimens (diameter = 50 mm, height = 20 mm) were prepared by static compaction at the initial water content of about 21.5%. The specimen after static compaction is shown in Fig. 2a. The compacted specimens with three dry densities of about 1.25, 1.35 and 1.50 Mg/m3 were saturated before the tests.

    Fig. 2
    figure 2

    Specimen for soil–water retention and triaxial test

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  • For the vapor equilibrium technique, the specimens were prepared and saturated by the same method for the pressure plate tests and the size and initial dry density of the specimens are also similar to those for the pressure plate tests. After saturated, the compacted specimens were cut into eight parts with the almost same size. In this way, not only the consistency of the sample was maintained, but also the time for the suction equilibrium was shortened. The small pieces then were put into desiccators containing different saturated saline solutions at the bottom and rigid grids were used to support the soil pieces above the solutions.

4.2 Triaxial shear tests

To investigate the influences of suction levels on hydro-mechanical behavior of unsaturated soil, a series of triaxial shear tests on compacted unsaturated Nanyang expansive soil was conducted using the suction-controlled triaxial apparatus. All of the compacted triaxial specimens were prepared by static compaction at the initial water content of about 21.5%. After the static compaction, the dry density is about 1.25, 1.35 and 1.50 Mg/m3, respectively. To produce uniform specimens, soil powder with the initial water content was compacted in five layers. The height and diameter of specimens were about 76 mm and 38 mm, respectively. The triaxial specimen after compaction is as shown in Fig. 2b. The average initial suction of specimens after compaction was about 200 kPa measured by the axis-translation technique in GDS triaxial apparatus.

Table 3 gives a summary of the initial states of all specimens for triaxial tests and stress/suction paths in details. It can be seen from Table 3 that the maximum suctions for specimens of tests CL1 ~ 4 are smaller than 1500 kPa, which were achieved by using the axis-translation technique and the maximum suctions for specimens of tests CH1 ~ 3 were greater than 1500 kPa, which were achieved by using the vapor equilibrium method produced from different saturated saline solutions.

Table 3 Water content, degree of saturation and void ratio of triaxial specimens at molding state and before triaxial shearing, and stress/suction path
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The stress/suction paths in space of deviator stress (q), net confining stress (\(\sigma_{3n}\)) and suction (s) for triaxial tests are shown in Fig. 3. Point A in Fig. 3a and point A1 in Fig. 3b stand for the initial state of the specimens (after compaction). Triaxial shear tests for twenty-one compacted specimens were all under the same net confining stress of 100 kPa. Triaxial shear tests on specimens for tests CL1 ~ 4 and CH1 ~ 3 were completed under different suctions of 0, 0.2, 0.4, 0.8, 3.29, 38.0 and 368 MPa, respectively, which were used to study the effect of suction level on the hydro-mechanical behavior of unsaturated expansive soil.

Fig. 3
figure 3

Stress and suction paths for triaxial tests

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In this study, the suction equilibrium was assumed to be attained when the changing rate of water volume is less than 0.1 cm3 per day and the change in the specimen volume is less than 0.1 cm3 per day. The shear rate should be sufficiently slow to avoid non-uniformity in the pore water pressure distribution within the soil specimen [16]. For all triaxial tests, the shear rate (i.e., axial displacement rate) was set to 0.00192 mm/min while the net confining stress and suction were kept constant. The observation during testing confirmed that the shear rate we selected was slow enough to avoid generating the excess pore water pressure in the specimens.

5 Test results and discussion

5.1 Effect of dry density on water retention behavior

Figure 4 shows the measured SWRCs over a wide suction range, which is described by the changes in gravimetric water content, degree of saturation and void ratio with suction for compacted Nanyang expansive soil with the initial molding dry densities of about 1.25, 1.35 and 1.50 Mg/m3 by using both the ATT and VET methods at zero net stress. Figure 4a represents the relationship between gravitational water content and suction, Fig. 4b represents the relationship between degree of saturation and suction, and Fig. 4c represents the relationship between void ratio and suction. It can be seen that the SWRCs in terms of water content are independent of the initial dry density when the suction is larger than about 250 kPa, as shown in Fig. 4a. We can conclude that the void ratio or dry density does not have an effect on the SWRC at high suctions in terms of gravimetric water content. Romero et al. [28] and Gao et al. [12] also obtained the similar experimental results for silty clay and clayey silt. When the SWRCs were expressed by the relation between the suction and degree of saturation in Fig. 4b, the SWRC with large initial dry density is higher than that with smaller one, but when the suction is larger than about 100 MP, the SWRCs in terms of degree of saturation are independent of the initial dry density. This result corroborates the trend drawn by other authors ([4, 28, 41], etc.). Moreover, the SWRC depends on several factors such as the soil type, mineralogical composition, soil structure and stress state. For the same type of soil, the effect of stress state on the SWRC can be attributed to the effect of the void ratio change [34].

Fig. 4
figure 4

Hydro-mechanical response of compacted Nanyang expansive soil measured by combining two different methods

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When the suction reaches 368 MPa, the gravitational water content of the specimen is only 0.33%, which is approximately the completed dried state of soils. The residual threshold for Nanyang expansive soil is not explicit and no residual region can be observed from the measured SWRCs. Test results, shown in Fig. 4c, indicate that the void ratio keeps decreasing along with increasing the suction in the entire suction range for Nanyang expansive soil, and the curve with large initial dry density is always lower than that with smaller one over an entire suction range. For expansive soils at low water content, the solid matrix may change somewhat during a drying process. Here, for simplicity, the same assumption was adopted as traditional soil mechanics, i.e., the volume of soil particles remains unchanged for calculating the void ratio.

The renowned mathematical equation developed by Fredlund and Xing [9] was adopted to fit the drying SWRC in the entire suction range measured by the pressure plate method and vapor equilibrium technique, as shown in Fig. 4b. The SWRC equation proposed by Fredlund and Xing [9] can be expressed as follows.

$$S_{\text{r}} = \dfrac{C(s)}{{\left\{ {\ln [2.71828 + \left( {\dfrac{s}{a}} \right)^{n} ]} \right\}^{m} }}$$
(2)

where

$$C(s) = 1 - \frac{{\ln \left( {1 + \dfrac{s}{{s_{\text{re}} }}} \right)}}{{\ln \left( {1 + \dfrac{{10^{6} }}{{s_{\text{re}} }}} \right)}}$$
(3)

sre is the residual suction; a, n and m are three fitting parameters. The parameters for fitting the SWRC in Fig. 4b are as follows: sre = 100,000 kPa; the fitting parameters a, n and m for specimens with the initial dry densities of about 1.25, 1.35 and 1.50 Mg/m3 are 37.661, 0.679, 1.024; 107.832, 0.686, 0.995; and 345.680, 0.614, 1.254; respectively.

5.2 Effect of dry density on hydro-mechanical behavior

5.2.1 Effect of dry density on stress–strain behavior

Figures 5 and 6 depict the deviator stress versus strain and volumetric strain versus axial strain curves obtained from triaxial shear tests on compacted expansive soil specimens with the initial dry densities of 1.25, 1.35 and 1.50 Mg/m3 under the net confining pressure of 100 kPa over a wide suction range. In the cases, a negative sign in the volumetric strain represents dilative volume change, whereas a positive sign indicates shear-contraction behavior. The soil behavior with respect to different dry densities over a wide suction range is summarized as follows:

Fig. 5
figure 5

Deviator stress versus axial strain relation from triaxial shear tests at different suctions

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Fig. 6
figure 6

Volumetric strain versus axial strain relation from triaxial shear tests at different suctions

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  1. 1.

    Triaxial test results indicate that the specimen with higher suction shows the higher peak shear strength and the smaller contraction (i.e., higher dilation). For the low suction range (i.e., suctions of 0, 200, 400 and 800 kPa), all the deviator stress versus strain curves (in Fig. 5) show a strain-hardening behavior with the shear contraction except dry density of 1.5 Mg/m3 at suction of 800 kPa. The stress versus strain curve increases with increasing the imposed suction. For the high suction range (i.e., suction of 3.29 MPa), the deviator stress versus strain curves with the initial dry densities of 1.25, 1.35 and 1.50 Mg/m3 show a strain-hardening–softening behavior with the shear contraction and dilation. At very high suction (i.e., suctions of 38.0 and 368 MPa), the expansive soil becomes very stiff with high peak strength and strong shear dilation, together with a sharp strain softening after peak at relatively small strain. Therefore, the features of stress–strain curves, such as the peak strength, softening and shear dilation, are changing along with the suction levels. The main reason is that the void ratio of the expansive soil decreases with increasing the applied suction, as shown in Fig. 4c and Table 3. In these figures, the change from the strain-hardening type to strain-softening type, due to the introduction of the suction in all unsaturated specimens, is readily manifested. They also corroborate the fact that the magnitude of strain softening is more pronounced with increasing the suction. That is, the soil tends to fail at lower axial strain and takes less axial strain to reach the failure with increasing the suction. It can also be noticed that all the specimens were sheared until they softened back to the residual states, at which they are expected to exhibit only shear deformations without further change in strength or volume.

  2. 2.

    For the same imposed suction, the shear strength increases with increasing the initial dry density. For the same initial dry density, the shear strength increases with increasing the imposed suction in the entire suction range, while it changes obviously in high suction range. Finally, we can conclude that the effect of void ratio or dry density on shear strength of unsaturated expansive soils is notable over a wide suction range.

Figure 7 depicts the deviator stress versus axial strain relation of compacted Nanyang expansive soil with different dry densities for the same suctions. For the low suction range (i.e., suctions of 0, 200, 400 and 800 kPa), the deviator stress versus strain curves of expansive soil specimens with dry densities of 1.25, 1.35 and 1.5 Mg/m3 (Fig. 7a–d) shows a strain-hardening behavior while specimen with dry density of 1.5 Mg/m3 shows a strain-hardening–softening behavior at suction of 800 kPa. For high suction (suctions of 3.29, 38.0 and 368 MPa), the deviator stress versus strain curves with the initial dry densities of 1.25, 1.35 and 1.5 Mg/m3 show a strain–hardening–softening behavior (Fig. 7e–g). Therefore, it can be concluded that the strain–hardening–softening response depends on dry density and suction level and occurs when the suction exceeds a certain value, which decreases with increasing the initial dry density.

Fig. 7
figure 7

Deviator stress versus axial strain relation of compacted Nanyang expansive soil with different dry densities under different constant suctions

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Figure 8 shows the deviator stresses at failure and residual of compacted Nanyang expansive specimens with different initial void ratios over a wide suction range, which is extracted from Fig. 5. In this paper, the failure point was determined as follows: (1) if the stress–strain curve has a peak, the peak is chosen as the failure point; and (2) if the stress–strain curve has no peak, the point at the axial strain of 15% is chosen as the failure point. In addition, zero suction (test CL1) was plotted at 1 kPa for the horizontal axial being logarithmic plot.

Fig. 8
figure 8

Deviator stress at failure and residual over a wide suction range

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It can be seen that the deviator stresses at failure and residual increase with increasing the suction. For the same imposed suction, the deviator stresses at failure and residual increase with increasing the initial dry density. When the imposed suction is higher than a specific suction value, the deviator stress at failure presents a larger change compared with that at residual. We can conclude that the effect of the initial dry density on shear strength of unsaturated expansive soils is notable over a wide suction range.

Moreover, different types of soils may present different strength behavior over a wide suction range. Patil et al. [27] also showed similar behavior of compacted silty sand. Gao et al. [12] reported that the failure deviator stress of compacted clayey silt shows little change or a decrease trend, when the imposed suction is higher than a specific suction value. Therefore, further studies are needed to find the change law in shear strength for different types of soils over a wide suction range.

5.2.2 Relationship between strain softening and sliding surface development

Figure 9 shows the photos of the specimens with initial dry density of 1.35 Mg/m3 after triaxial shear tests under different suctions of 0.80, 3.29 and 38.0 MPa. No obvious shear surface appeared for the specimen with the suction of 0.80 kPa, while the shear surface appeared at suction 3.29 MPa, but the shear surface did not fully develop. At the suction of 38.0 MPa, the specimen was sheared divided into two parts, and the sliding surface fully developed. About the stress strain relation, the specimen with the suction of 0.80 MPa shows a strain-hardening behavior. Under suction of 3.29 MPa, the specimen shows a strain–hardening–softening behavior, but there was no sharp peak. The stress–strain curve of the specimen with suction of 38.0 MPa shows a sharp strain softening after peak at relatively small strain. From what has been discussed above, three different failure states correspond to three different types of stress–strain curve. Therefore, we can conclude that the strain softening of the specimen is related to the sliding surface. Patil et al. [27] also showed similar phenomenon after the triaxial shear tests on compacted silty sand.

Fig. 9
figure 9

Specimens after triaxial shear tests at different suctions (ρd0 = 1.35 g/cm3)

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Elastic and plastic strains appear in the process of shearing, so the axial strain of the specimen is mainly composed of elastic and plastic strains, which cause the strain-hardening behavior. During increasing the axial strain, the sliding surface gradually formed. After the formation of sliding surface, the axial strain of the specimen was composed of elastic strain, plastic strain and the sliding part. As the specimen slides along the sliding surface, the elastic strain and plastic strain increment of the specimen gradually decrease, the axial stress gradually decreases (such as the specimen with initial dry density of 1.35 Mg/m3 under the suction of 3.29 MPa), and thus the strain softening occurs. When the sliding surface fully develops and forms, the axial stress of the specimen is mainly controlled by the sliding friction of the sliding surface, such as the flat section of the stress–strain curve of the specimen with suction of 38.0 and 368 MPa after the peak.

5.2.3 Effect of dry density on volumetric strain over a wide suction range

It can be seen from Fig. 6 that volumetric strain of the specimen gradually decreases with increasing suction at the shearing (except for the suction of 0 kPa), i.e., the specimen volume changed gradually from the shear contraction to shear dilation. It can also be seen from Fig. 6 that when the axial strain is equal to about 1.5% to 2.0%, the peak of stress–strain curve and maximum volume contraction strain occurred simultaneously for specimens with suctions of 38.0 MPa and 368 MPa. The specimens with initial dry densities of 1.25 and 1.35 Mg/m3 did not show shear dilation until the suction of 38.0 MPa, while the specimens with initial dry density of 1.5 Mg/m3 shows a slight shear dilation at the suction of 0.8 MPa. It can be observed that the specimen presents shear dilation behavior when the suction exceeds a certain suction value, and the higher the initial dry density, the smaller the suction value.

The volumetric strain of specimens with initial dry densities of 1.25 and 1.35 Mg/m3 during triaxial shearing under suction of 0 kPa is less than that under suction of 0.2 MPa, but volumetric strain of specimen with initial dry density of 1.50 Mg/m3 during triaxial shearing under suction of 0 kPa is larger than that under suction of 0.2 MPa. The reason can be considered as follows: the specimens with initial dry densities of 1.25 and 1.35 Mg/m3 are loose, and thus the collapse appeared in wetting from initial suction about 200 kPa to zero suction. That is, the void ratios of specimens with suction of 0 kPa before shearing is smaller than that under the suction of 200 kPa. However, the specimen with initial dry density of 1.5 Mg/m3 is dense, there is no collapse happened in wetting, and thus the void ratio with suction of 0 kPa before shearing is larger than that under suction of 200 kPa. The void ratios of all specimens before shearing are shown in Table 3.

Figure 10 shows the relationship between axial strain or volumetric strain at the failure and the suction during triaxial shearing. As shown in Fig. 10a, the axial strain at the failure decreases with increasing the suction under the net confining pressure of 100 kPa, and the axial strains at failure are almost the same when the suction is larger than or equal to 38.0 MPa. As shown in Fig. 10b, for the specimen with the initial dry density of 1.50 Mg/m3, volumetric strain at the failure increases first and then decreases with increasing the suction under the same net confining pressure. For specimens with the initial dry densities of 1.25 and 1.35 Mg/m3, the change trend is the same as that with 1.5 Mg/m3 except zero suction, under which collapse occurred before triaxial shear, and the specimen became dense. When the suction is less than 38.0 MPa, volumetric strain at failure will gradually decrease with increasing the initial dry density. When the suction is greater than or equal to 38.0 MPa, volumetric strain at failure keeps almost the same with increasing the suction.

Fig. 10
figure 10

Change in axial and volumetric strains at failure of specimens with different suctions

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5.2.4 Hydraulic responses during triaxial shearing

Figure 11 shows the variation in gravimetric water content of specimens during triaxial shearing over a wide suction range. The gravimetric water content of three specimens decreases with increasing the axial strain under constant suctions in a low suction range (i.e., suctions of 0, 200, 400 and 800 kPa). For the high suction range, the gravimetric water content of all specimens remained unchanged during shearing, as shown in Fig. 11. This is because the specimens in high suction range were triaxially sheared with constant water content.

Fig. 11
figure 11

Variation in water content with shearing at different suctions

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6 Conclusions

A series of water retention tests and suction-controlled triaxial shear tests were conducted on Nanyang expansive soil with different initial dry densities over a wide suction range. The test results obtained from compacted specimens were discussed by highlighting the effects of suction level and dry density on the hydro-mechanical behavior. The following conclusions can be drawn:

  1. 1.

    Water retention test results on the expansive soil show that the void ratio keeps decreasing along with increasing the suction in a wide suction range from 0 to 368 MPa. The SWRCs in terms of gravimetric water content versus suction relationship are independent of the dry density or void ratio when suction is larger than 250 kPa. Therefore, the tests on specimens with constant water content can be considered as that at constant suction when the suction is higher than 250 kPa.

  2. 2.

    Results of triaxial shear tests on Nanyang expansive soil at different suctions show different stress–strain relationships and strength characteristics under the same net confining pressure. For compacted expansive soil with the same dry density, the higher the suction, the higher the stress–strain curve, strength and volume contraction. The expansive soil with extremely high suction shows distinct peak strength, strain-softening and dilative behavior. For the same imposed suction, the shear strength increases with increasing the initial dry density, and the effect of the dry density on shear strength of unsaturated compacted expansive soil is notable over a wide suction range.

But different types of soils may present a different shear strength behavior over a wide suction range, and further studies are needed to find the change law in shear strength for different types of soils over a wide suction range. The triaxial shear tests were performed under net confining pressure of 100 kPa in this paper, and the different net confining pressures may affect the hydro-mechanical behavior, which deserves further studies.