Introduction

In the Chinese Loess Plateau, there are plenty of loess landslides causing great loss of lives and properties every year. Many triggering factors of these landslides have been recognized, and rainfall is the most common one. To understand the impact of rainfall on the potential stability of the loess landslide masses, a lot of investigations have been undertaken in the last several decades (e.g., Dijkstra et al. 1994, 2014; Derbyshire 2001; Collins and Znidarcic 2004; Tu et al. 2009). Gvirtzman et al. (2008) and Xu et al. (2011) considered that the soil hydrology characteristics might be responsible for slope destabilization with the process of rainfall infiltrating into loess through the slope surface. It has also been reported that the earthquake-induced landslides in the mountainous loess region of northwest China have caused catastrophes (Derbyshire et al. 2001; Wang et al. 2014). As pointed out by Zhang and Wang (2007), the saturated loess specimens would generate high pore water pressure due to the collapse of soil structure when subjected to cyclic loading, which could cause dramatic loss of shear strength and produce the high mobility of loess landslides.

Although much work have been carried out to examine the properties of saturated loess under different mechanical conditions (i.e., static or dynamic loading) for better understanding the mechanisms of the loess landslides triggered by rainfall or earthquake, it is worth noting that some loess landslides have occurred in urban areas without the above-mentioned triggering factors (i.e., rainfall or earthquake). For example, on May 16, 2009, a landslide struck the Jiuzhoutai District of Lanzhou City, Gansu Province, China. It was reported that this landslide caused seven causalities and one injury (Mu et al. 2010). Dijkstra et al. (2014) reported that this landslide might have been triggered by gradually building up of the groundwater levels; however, this hypothesis was not supported by any field evidence. Generally, these slopes have loess that is primarily unsaturated and weekly cemented, and the catastrophic loess flowslides also can occur under relatively dense, or even unsaturated condition (Hungr et al. 2014). Although the previous works (Griffiths and Lu 2005; Sorbino and Nicotera 2013) considered the influence of soil suction on the slope stability, the hydro-mechanical properties of unsaturated soils have rarely been examined to provide the evidence for unsaturated loess landslide events.

Specifically, to address the fundamental concern, as pointed out by Fredlund and Rahardjo (1993) and Lu and Likos (2004), the SWCC plays a crucial role in understanding and modeling the characteristics of shear strength, permeability and volume change for unsaturated soils. Additionally, some empirical equations have been proposed to describe the SWCC (van Genuchten 1980; Fredlund and Xing 1994). One of the crucial questions is which one is better to describe the SWCC for loess among the existing equations, and it is also expected that a better understanding of the SWCC could be made thorough model analysis considering the influences of soil properties. In addition, we normally can use the effective stress to interpret the shear strength properties for saturated soils, while the effective stress of unsaturated soils has been a major long-standing challenge for unsaturated soils research since the 1930s. Although some stress state variables have been proposed to interpret elastoplasticity, critical state, and coupled yield limits for unsaturated soils (Fredlund and Morgenstern 1977; Alonso et al. 1990; Wheeler and Sivakumar 1995), these theories have limitations in the applications to a wide range of matric suction and unsaturated soil parameters (Gens et al. 2006; Nuth and Laloui 2008). Recently, the concept of suction stress has been proposed by Lu and Likos (2006) to further understand the effective stress of unsaturated soil, which considered the local inter-particle forces generated within a matrix of unsaturated particles owning to the combined influences of negative pore water pressure and surface tension. The suction stress has an inherent relationship with the matric suction or effective degree of saturation, and this relationship is termed as the suction stress characteristic curve (SSCC). The conceptualized SSCC also can expand the form of effective stress principles (Lu et al. 2010). Similar to the SWCC, the soil properties have significant influences on the SSCC. Song et al. (2012) examined the SSCC for sand and silt, and the influence of the relative densities on SSCC for sand had also been investigated based on the SWCC tests (Song 2014). By conducting a series of triaxial shear strength tests and pressure plate extractor tests for several residual soils, the instinct relationship between SSCC and SWCC had been investigated and discussed by Oh et al. (2012). It had shown that the SSCC could be uniquely linked to the SWCC. Moreover, to further examine the validity of the SSCC, Oh et al. (2013) provided an alternative way to obtain the SSCC by carrying out triaxial K 0 consolidation tests for decomposed granitic soils; it was found that the SSCC could be used to describe the consolidation and shear strength properties of unsaturated soils.

Definitely, it is also worth mentioning that the fundamental concern of loess mentioned above has been rarely examined. Therefore, in order to provide more evidence for better understanding the unsaturated loess landslide events, we used a loess soil taken from the main scarp of a loess landslide (Fig. 1b), and conducted a series of SWCC tests by using the conventional pressure plate extractor. Based on the test results, we evaluated two SWCC equations for unsaturated loess and estimated the SWCC variables. In addition, we also calculated the SSCC based on the concept proposed by Lu and Likos (2006) by using the SWCC models. Finally, the influence of soil properties (i.e., initial dry density and water content) on the SWCCs and SSCCs for compacted loess specimens were examined and discussed.

Fig. 1
figure 1

Location of the loess sample tested in this study

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SWCC and SSCC

SWCC variables and equations

The definitions of SWCC variables are illustrated in Fig. 2. These variables such as air-entry value (AEV), rate of desorption (S 1) and residual water content (θ r) are commonly used to study the SWCC and other relative properties such as shear strength and permeability (Fredlund et al. 1994, 1996; Vanapalli et al. 1999). The AEV is related to the largest pores in soils, and S 1 represents the desorption rate of water in soils. As pointed out by some researchers (van Genuchten 1980; Fredlund and Xing 1994; Vanapalli et al. 1999), the definition of θ r is still vague and open to interpretation, and an empirical procedure for its quantitative determination would be useful. Detailed discussion of the determination of the residual state of an unsaturated soil–water system is beyond the scope of this study. Therefore, in this work, we adopted the method proposed by Zhai and Rahardjo (2012) to estimate these variables.

Fig. 2
figure 2

Definitions of soil–water characteristic curve variables (After Zhai and Rahardjo 2012)

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By now, plenty of empirical models or equations have been proposed by researchers to describe the SWCC for unsaturated soils (van Genuchten 1980; Fredlund and Xing 1994). However, as pointed out by Leong and Rahardjo (1997), the specific form of SWCC was found to be restricted to the particular mathematical properties of SWCC equations, and was determined by soil textures. Some SWCC equations were better for sand or clay, while some SWCC equations had limitations in the applications to the high range of matric suction. In this research, we compare two common models to evaluate which one is better for loess soil. One proposed by van Genuchten (1980), and the other proposed by Fredlund and Xing (1994). Hereinafter we call the two SWCC equations as the V-G model and F-X equation, respectively. The V-G model has widespread usage with a simple mathematical formula for different soil types, while the F-X equation can provide a good fit for a variety of soils with a wide range of matric suction (i.e., 0 to 106 kPa; Gallage and Uchimura 2010). The V-G model and F-X equation are shown in Eqs. (1) and (2), respectively.

$$ S_{e} = \frac{{\theta - \theta_{r} }}{{\theta_{s} - \theta_{r} }} = \left[ {\frac{1}{{1 + (\alpha \psi )^{n} }}} \right]^{m} $$
(1)

where S e is the effective degree of saturation, θ is the volumetric water content, θ s is the saturated volumetric water content, θ r is the residual volumetric water content, α is the parameter related to the AEV, n is the parameter related to the slope of the SWCC, and m is the parameter related to the residual volumetric water content.

$$ \theta = \left[ {1 - \frac{{\ln (1 + \psi /c_{r} )}}{{\ln (1 + 10^{6} /c_{r} )}}} \right] \cdot \frac{{\theta_{s} }}{{\left\{ {\ln [e^{1} + (\frac{\psi }{a})^{b} } \right\}^{c} }} $$
(2)

where θ is the volumetric water content; ψ is the matric suction (kPa); c r is the constant related to the soil suction corresponding to the residual water content; θ s is the saturated volumetric water content; e is natural number (2.718); a is related to the AEV value (kPa); b is fitting parameter that controls the slope at the inflection point in the SWCC; c is fitting parameter that is related to the residual volumetric water content.

SSCC

The concept of the SSCC was proposed by Lu and Likos (2006) to express the influence of the degree of saturation on the effective stress of unsaturated soil. Considering the particle scale forces and physicochemical stress in a matrix of unsaturated particles, a closed-form equation for calculating the suction stress has been established. The macroscopic of suction stress is a tension force that tends to draw the soil particles toward one another (Lu et al. 2010). Originally, the suction stress can be expressed as the functions of matric suction and effective degree of saturation [as shown in Eq. (3)]. In addition, we can derive the matric suction as the function of effective degree of saturation (the definition of SWCC), vice versa. Therefore, we can express the suction stress only as a function of matric suction or effective degree of saturation. In Eq. (4), we use the V-G model [Eq. (1)] to express the relationship between suction stress and matric suction, and estimate the suction stress for loess soil.

$$ \sigma^{s} = - (u_{a} - u_{w} ) \cdot S_{e} = - (u_{a} - u_{w} ) \cdot \frac{{\theta - \theta_{r} }}{{\theta_{s} - \theta_{r} }} $$
(3)

in which σ s is the suction stress defined as a function of matric suction and effective degree of saturation; S e is the effective degree of saturation and has the same definition as Eq. (2).

$$ \sigma^{s} = - (u_{a} - u_{w} )\left\{ {\frac{1}{{1 + [\alpha (u_{a} - u_{w} )]^{n} }}} \right\}^{m} $$
(4)

in which u a and u w are the pore air pressure and pore water pressure, respectively; the other parameters have the same definition as Eq. (1).

Soil samples and testing producers

Soil samples

In order to investigate the influence of initial dry density and water content on the SWCC and suction stress of loess, the loess samples were taken from the main scarp of a landslide in Jiuzhoutai District of Lanzhou City, Gansu Province, China (see Fig. 1), and used in this study. This landslide attacked the Jiuzhoutai District of Lanzhou City, caused seven casualties and one injury, and occurred without any obvious triggering factors (i.e., rainfall or earthquake). The landslide was 160 m in length, 50 m in width, had an average depth of 4 m, and an estimated volume of 20,000 m3, approximately. The displaced loess layer reached the national road and destroyed several houses, and the travel angle was close to 30° (Mu et al. 2010). The specific gravity of the soil was 2.71, and the particle size distribution is shown in Fig. 3. The percentages of sand, silt, and clay were 0.9, 91.9, and 7.2 %, respectively. Some basic geotechnical properties of loess soil are summarized in Table 1.

Fig. 3
figure 3

Particle size distribution of tested loess

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Table 1 Basic properties of loess soil
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The soil was air-dried and pulverized using a rubber mallet and passed through a 2-mm sieve. A prescribed amount of distilled water was sprayed on the air-dried soil in several layers and then was thoroughly hand-mixed. To prevent the formation of soil–water clods, we passed the mixed soil again through a 2-mm sieve following the suggestion presented in Vanapalli et al. (1999). Finally, the mixed soil was placed in plastic bags and kept in a humidity-controlled room for at least 48 h.

All samples for this study were statically compacted in a cube mould with an edge of 70.7 mm, and then a specimen 61.8 mm in diameter and 20 mm in height was cut from the cube sample. After that, the specimens were placed in a sealed chamber to pump the vacuum for 2 h and then distilled water was slowly injected into the chamber. We calculated the degrees of saturation by measuring the weight of samples after pumping to ensure that the degree of saturation was greater than 95 % for all samples. These saturated specimens were then used to measure the SWCC.

Testing program

The SWCCs of loess samples were experimentally examined by using a conventional 15 bar pressure plate extractor. Seven compacted soil specimens with different initial water contents and dry densities were prepared and tested (as summarized in Table 2). Four loess specimens were compacted at the same initial water contents but different dry densities [i.e., T01(D)–T04(D)]. The other three loess specimens had the same dry density with different initial water contents [i.e., T05(W)–T07(W)].

Table 2 Testing program for determining soil–water characteristics
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In the pressure plate extractor, the prepared specimens were placed on a high air-entry ceramic disk in a sealed air pressure chamber. The saturated ceramic disk is designed to control the matric suction of specimens. The air pressure was applied to increase the matric suction in a series of steps for the drying path. As the matric suction increased, the water in specimens would be expelled until the equilibrium condition was reached. The equilibrium condition for each matric suction was deemed to be reached when there was no water outflow at the bottom of the high air-entry ceramic disk. Normally, it took 4–7 days to achieve equilibrium under a given level of matric suction. After reaching equilibrium, the volumetric water contents (or degrees of saturation) at various levels of matric suction were measured.

Results

We firstly evaluated the two models (V-G model and F-X equation) through a least square optimization method and nonlinear curve-fitting algorithms for loess soil. Selected results are shown in Fig. 4. The test results reveal that the V-G model and F-X equation have almost the same good performance in describing the SWCC of unsaturated loess. The SWCC variables (i.e., AEV, S 1 and θ r) were determined based on the quantificational method proposed by Zhai and Rahardjo (2012), and the results are shown in Table 3.

Fig. 4
figure 4

Typical result for a loess specimen compacted with dry density = 1.60 g/cm3 and initial water content = 17.85 %

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Table 3 Results of SWCC fitting parameters and variables
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Influence of initial dry density on SWCC and SSCC

The SWCCs of loess specimens compacted at the same initial water content but different dry densities [T01(D) toT04(D)] are presented in Fig. 5a. The different compaction efforts were used to obtain different initial dry density during the preparation of specimens, which can have some significant effects on the SWCC. As can be seen from Fig. 5a, with increasing the matric suction, the volumetric water content in soil specimens nonlinearly decrease. Based on the capillary model, the AEV is related to the maximum pore radius in the soil (Fredlund and Xing 1994), the total amount of pore voids of soils will vary due to the change of dry density, and the pore size distribution will be different. Ng and Pang (2000) investigated the SWCC of a volcanic soil compacted at different dry density. The AEV was estimated by using the “judging-by-eye” method, and a very small increase in the estimated AEV was presented (i.e., changing between 4 kPa and 5 kPa) due to a small increase in dry density (i.e., only 4 % increase in dry density). The same results had been reported for clay (Tinjum et al. 1997; Birle et al. 2008) and sand (Gallage and Uchimura 2010) and there was about a 5-kPa variation for clay and about a 3-kPa variation for Edosaki sand. By studying the experimental data and analysis results of loess, there are also about 2-kPa variations for each loess specimen. It is more reasonable to infer that the effect of dry density on AEV values might be negligible due to the test conditions and data accuracy. However, it has more profound influence on the rate of desorption and residual conditions. As depicted in Fig. 5a and Table 3, the rate of desorption decreases as the dry density increases, which indicates that a higher dry density will have higher residual volumetric water content at the same level of matric suction.

Fig. 5
figure 5

Soil–water characteristics (a) and suction stress characteristics (b) for loess specimens compacted at different dry densities. T01(D) = 1.40 g/cm3, T02(D) = 1.50 g/cm3, T03(D) = 1.60 g/cm3, T04(D) = 1.66 g/cm3, respectively. I intersection point

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Based on the method proposed by Lu and Likos (2006), the SSCCs of different dry densities deduced from SWCC data are illustrated in Fig. 5b, in terms of matric suction and effective degree of saturation. As shown in the figure, the suction stress for different dry densities present different behaviors. When the matric suction is lower than the AEV, there is an approximate linear increase relationship between suction stress and matric suction. The magnitude of suction stress is equal to the matric suction at high degree of saturation. When the matric suction is greater than the AEV of each specimen, the suction stress exhibits different behaviors, depending on the dry density. For lower dry density specimen [i.e., T01(D)], the suction stress has slightly nonlinear decrease as matric suction increased. While for specimen with greater dry density [i.e., T04(D)], the suction stress has obvious nonlinear increase as matric suction increased. However, the magnitude of suction stress is lower than the matric suction. Therefore, the effective stress of unsaturated loess will exhibit a nonlinear relationship with regards to the matric suction. On the other hand, as depicted in Fig. 5b, the suction stress of specimen with greater density is larger than the lower dry density at the same matric suction, which indicate that the shear strength of higher dry density will be higher than the lower one.

Influence of initial water content on SWCC and SSCC

As pointed out Vanapalli et al. (1999) and Birle et al. (2008), the initial water content had a significant influence on the inherent structures (i.e., aggregation), which could affect the ability of water flow in soil skeleton. We examined the influence of initial water content on the SWCC of loess using the compacted specimens with the same initial dry density but different initial water contents. Figure 6a shows the SWCCs with the relationship between matric suction and effective degree of saturation for specimens T05(D)–T07(D) and T02(D), respectively. The fitting parameters of SWCC equations and the variables (AEV, S 1, θ r) are shown in the Table 3. As the four soil specimens have the same initial dry density, it is reasonable to suppose that the total amount of voids will be the same according to Mitchell and Soga (2005). However, as pointed out by Vanapalli et al. (1999), the initial water content would affect the pore-size distributions, and the high water content could result in more aggregates in soil matrix. Therefore, for the tested loess, the specimen compacted at higher water content [i.e., T07(D)] will have relatively large pores among the aggregations of soil, which can result in lower AEV. On the contrary, the specimen compacted at lower water content [i.e., T05(D)] will have relatively small pores among the clods of soil, which can generate higher AEV. Although the total amount of voids may be the same, the pore-size distribution will be different due to the influence of initial water content. We assume that the total amount of voids equal to the sum of large and small pores in the soil specimens. And the specimen with relatively large pores [i.e., T07(D)] will have smaller pores, which can lead to lower rate of desorption (Fig. 6a and Tabel 3).

Fig. 6
figure 6

Soil–water characteristics (a) and suction stress characteristics (b) for loess specimens compacted at different initial water contents. T05(W) = 6.64 %, T06(W) = 13.06 %, T02(D) = 17.85 % and T07(W) = 20.20 %. I intersection point

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Figure 6b illustrates the SSCCs of loess specimens compacted to the same dry density but different initial water content. Although these specimens received the same compaction efforts, the amount of initial water content in the voids of the specimens can affect the inter-particle forces. As presented in Fig. 6b, the suction stress is almost equal to the matric suction under a high degree of saturation (i.e., the matric suction is lower than the AEV of the specimen). In this stage, the voids of specimens are nearly fully filled with water, and the capillary attraction between particles is almost zero. As de-saturation occurred, the SSCCs of specimens show different behaviors. The suction stress of specimens compacted under higher initial water contents [i.e., T06(D) and T07(D)] increase with matric suction, while there are slight decreases for lower initial water contents [(i.e., T02(D) and T05(D)]. The suction stress between particles is controlled by the water content when the macro-pores are effectively empty during the de-saturation process (Baker and Frydman 2009). For specimen T07(D) compacted at a high initial water content, it is more easily to maintain high water content at the same matric suction level due to the formation of aggregates which can lead to a non-uniform pore-size distribution.

Relationship between SWCC and SSCC

Two distinct types of SSCCs were mathematically confirmed by Lu et al. (2010), and the intrinsic relationship between the SWCC and SSCC for residual soils had also been validated by Oh et al. (2012) based on the triaxial and pressure plate extractor test results. It has been clarified that the suction stress data can be obtained from the triaxial tests and deduced from the SWCC data by using Eq. (1). The differences are only with several tens of kPa to predict the suction stress according to triaxial test data or SWCC data (Lu et al. 2010; Oh et al. 2012). In order to evaluate the SSCC rules for loess soil, and better understand the influence of initial dry density and water content in the soil–water system, we calculated the suction stress for loess based on the SWCC data. The relationship between SWCCs and SSCCs for different initial dry densities and water contents are presented in Figs. 7 and 8, respectively. As shown, the patterns of SSCC vary with the change of initial dry density and water content. For lower initial dry density or water content, suction stress is zero at a saturated condition and small value of effective degree of saturation, and can reach a minimum value at a certain effective degree of saturation. Although this “down and up” characteristic of suction stress is well known for sand-sized granular media (Lu et al. 2007; Song 2014), our data showed that this characteristic also could be followed in the loess specimens under lower initial water content or dry density condition. With an increase of initial dry density or water content, the pattern of suction stress shows monotonic characteristics as the effective degree of saturation decreases. The minimum suction stress for higher initial dry density or water content loess specimens [T04(D) or T07(W)] will be several hundreds of kPa. Although the mechanisms for suction stress and shear strength for unsaturated soils are poorly understood, our results provided more experimental evidences on the nonlinear characteristic of shear strength for unsaturated loess soils considering the influence of initial water content and dry density.

Fig. 7
figure 7

Relationship between the SWCC and SSCC for loess specimens compacted with different initial dry densities. a ρ d = 1.40 g/cm3; b ρ d = 1.50 g/cm3; c ρ d = 1.60 g/cm3; d ρ d = 1.66 g/cm3

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Fig. 8
figure 8

Relationship between the SWCC and SSCC for loess specimens compacted with different initial water contents. a w = 6.64 %; b w = 13.06 %; c w = 17.85 %; d w = 20.20 %

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Discussion

Intersection of SWCC

The results of initial dry density and water content on SWCC for loess soil are shown in Figs. 5a and 6a, respectively. It is noted that the volumetric water content reached the same magnitude at a certain level of matric suction for all the tests (hereinafter term this point as intersection, point “I”, as shown in Figs. 5a and 6a). For the intersection point, the magnitude of matric suction is about 37 kPa in Fig. 5a and 30 kPa in Fig. 6a; the volumetric water contents are about 0.275 in Fig. 5a and 0.311 in Fig. 6a, approximately. Before the point, the phenomena show that lower initial dry density or water content specimens [i.e., T01(D) or T05(W)] will have higher volumetric water contents at the same level of matric suction. While after the point, the higher initial dry density or water content specimens [i.e., T04(D) or T07(W)] can maintain higher volumetric water content.

Of particular interest here is to better understand the possible mechanism of the intersections as they are a direct reflection of the influence of the initial dry density and water content for unsaturated loess. Fredlund and Xing (1994) and Vogel and Roth (2001) examined and concluded that the pore characteristics (i.e., pore size, pore volume and pore amount, etc.) in unsaturated soils had great influence on the SWCC, and the capillary tube model had been used to understand the possible mechanism of pore characteristics on the flow of water in unsaturated soils. Therefore, we assume that the uniform pore size distribution could be formed for the loess specimens compacted at the same initial water content with different densities, and the initial dry density just had a significant influence on the amount of total pores, which directly influenced the SWCC. This hypothesis suggests that there would be a critical volumetric water content at a certain magnitude of matric suction for the loess specimens with different initial dry densities, as shown in Fig. 5a. Moreover, as pointed out by Mitchell and Soga (2005), the initial water content has an important role in forming and controlling the macro-structure and micro-structure in soils. Vanapalli et al. (1999) also reported that macro-structures could influence the soil–water characteristic behaviors within lower water content, particularly in the low range of matric suction, and micro-structures would affect the soil–water characteristic behaviors within high water content for the fine-grained soils. From this point of view, we infer that the pore size would be different due to the influence of initial water content, and the transition of pore structure would occur and induce a critical condition for loess specimens, in which the volumetric water content could be the same under certain magnitudes of matric suction (as shown in Fig. 6a).

Theoretical and practical implications

In general, the main causes of landslides in most unsaturated slopes are often initiated by the process of infiltration or rising pore water pressures (Schnellmann et al. 2010; Lourenço et al. 2015). These unsaturated slopes have soils that have different water contents from the ground surface (dry condition) to a considerable depth (saturated), and the pore water pressure in this unsaturated zone is generally negative with respect to atmospheric pressure. The presence and magnitude of suction pressure have been found to be important to the stability of such kind of slopes (Sorbino and Nicotera 2013). Infiltration of rainfall leads to a reduction in soil matric suction, or the rising of the water table results in an increase in pore water pressure (e.g., from negative to positive at the potential shear surface). This, in turn, results in a decrease in shear resistance on the potential failure surface to a point where equilibrium can no longer be sustained in the slope and then failures can occur (Fredlund and Rahardjo 1993). Therefore, studies of SWCCs can assist in the understanding of pore water pressure distributions in the slope and thus play an important role in understanding the possible mechanism for the formation of landslides. However, the different parts of slopes will show different dry densities or water contents; therefore, the influence of these basic properties on the flow of water in soils could play a critical role in affecting the slope behaviors, especially under the unsaturated condition. Our experimentally derived results can basically provide more evidence for better understanding the hydro-mechanical properties, and also for analyzing and modeling the unsaturated loess slopes with considering the influence of dry density and water content. Furthermore, as shown in Figs. 5b and 6b, the magnitude of suction stress for loess specimens can range from several tens or hundreds of kilopascals. A practical implication of these results is evidenced by loess cutting slopes. The existing of suction stress in these slopes could enable stability even though the slopes were cut to several ten to hundred meters in a near-vertical direction under a dry environment.

Summary and conclusions

To investigate the basic properties of unsaturated loess in northwest China, a series of tests was conducted to examine the influences of initial dry density and water content on the SWCC for a loess soil. Based on the test results, two SWCC models [i.e., Fredlund and Xing Eq. (1994), and van Genuchten model (1980)] were evaluated and the fitting parameters were obtained by the least square optimization method using nonlinear fitting algorithms. The SWCC variables were estimated using the method proposed by Zhai and Haradjo (2012). These fitting parameters and SWCC variables were also used to calculate the SSCC based on the method proposed by Lu and Likos (2006). An attempt has been firstly made to investigate the influence of initial water content and dry density on suction stress for loess soil. Some conclusions can be drawn as follow.

  1. 1.

    The test results reveal that the Fredlund and Xing Eq. (1994) and van Genuchten model (1980) have approximately the same performance, and both models can be used to describe the SWCC of unsaturated loess.

  2. 2.

    With increasing the initial dry density, the residual water content increases and rate of desorption decreases. Meanwhile, the initial dry density has negligible influence on the air-entry value with a slightly increase as the dry density is increased. With increasing the remolding water content, the air-entry value and rate of desorption decrease, and the level of residual matric suction increases.

  3. 3.

    It has been observed that different soil–water characteristic behaviors can be shown before and after an intersection for loess soil. The initial dry density may cause a uniform pore size distribution and different amounts of total pores, while the initial water will give rise to different pore sizes. In either condition, a critical volumetric water content may exist.

  4. 4.

    Suction stress exhibits different behaviors for loess samples. The magnitude of suction stress has an approximately linear relationship with matric suction in the high degree of saturation range (i.e., matric suction is lower than air-entry value). When the matric suction exceeded the air-entry value, the SSCCs exhibit a nonlinear relationship with matric suction, depending on the initial conditions (dry density and water content) of soil specimens. For certain magnitudes of matric suction, the suction stress increases as dry density and initial water content increase.