Study on the Unified Mechanical Properties of Ili Undisturbed Loess under the Influence of Soluble Salt

Abstract

Through three stress path tests of unsaturated Ili undisturbed loess, the effect of soluble salt content on the deformation of net mean stress, suction, and deviated stress were investigated. The mechanical properties of the normalized compression curve, soil water characteristic curve and critical state line were revealed. The test results indicate that: in the isotropic compression test, the normal compression curves controlling different suctions can be characterized by using the initial void ratio and the yield net mean stress, and can be described as a two-parameter exponential function. In the triaxial shrinkage test, the soil water characteristic curves controlling vary net mean stresses are dimensionless by using saturated moisture and air entry value, and the normalization formula can be characterized by a single parameter exponential function. In the consolidation shear test, the corresponding effective net mean stress is calculated by suction and saturation. The critical state lines under the unsaturated condition controlling vary suctions can be described as the critical state line under the saturated condition on the plane of effective net mean stress and deviator stress. When the effective net mean stress is constant, the critical state lines under the unsaturated condition can be characterized by the degree of gas saturation and the ratio of unsaturated void ratio to saturated void ratio. The research will offer reference pointing at the regulation and utilization of water and salt in the loess region of Central Asia, so as to better guarantee the sustainable development of saline-alkali land project construction.

1. Introduction

Central Asia is one of the core areas of the Belt and Road, which is located in the transition region with different climate systems, including the Asian monsoon [1,2], the mid latitude westerly wind [3], and the Arctic polar front [4]. Central Asia is also a sensitive area of global climate change. The Ili Basin in China is located in a meso-cenozoic fault basin sandwiched by the Tianshan orogenic belt, which belongs to this sensitive area. Ili Basin is bounded by the north and south Tianshan mountains and presents a trumpet shape opening to the west, which is subjected to westerly winds all year round, and its annual average temperature is 2.6~10.4 °C. The precipitation distribution is uneven due to the influence of local topography, which is concentrated in the east of this area. The research results show that loess is mainly distributed in temperate semi-arid grassland; this is because the vegetation can intercept the dust in the deposition process and moderate precipitation promotes silty sand deposition [5,6,7]. Therefore, extensive loess deposits exist in the Ili Basin [8], which are distributed on the windward slopes of mountains on both sides of the valley in terms of distribution characteristics mostly [9]. According to the analysis of material composition, grain size composition, quartz surface morphology, and geochemistry [10,11], it has been shown that Ili loess has typical aeolian sedimentary characteristics, which belongs to the typical loess in the westerly region.

In addition, the physical and mechanical properties of Ili loess in the west wind area with high soluble salt are very different from those in the monsoon area. The results show that the soluble salt content of Ili loess in the west wind region is as high as 1.92%, and the maximum self-weight collapsibility measured by in-situ immersion tests is 3.52 m [12]. The results show that the global saline alkali land area has reached 9.5 × 10⁸ hm², and the annual growth rate is 1–1.5 million hm² [13]. Research shows that more than half of the arable land might be salinized by 2050 [14]. Saline alkali land accounts for 8.16% of cultivated land in the Ili prefecture of China [15]. The special Ili loess with characteristics of saline soil needs to be studied in a special and systematic way.

In the last few years, studies on Ili loess are largely concentrated on the aspects of distribution characteristics, ages, dust sources, chemical weathering, particle size, magnetism, and mineralogy [8,16,17,18,19]. Viles and Goudie [20] show that the component of the site’s groundwater has a significant impact on the physical and mechanical characteristics of saline soil. Some scholars have explained that the influence mechanism of salt on the soil is more complex from the perspective of comparing the time variation coefficient of salt and water. Yang [21] pointed out that the unreasonable utilization of farmland in the drought areas is the main reason for accelerating salinization. Due to the migration of water and salt, the salinity distribution in practical engineering is quite different, which causes enormous harm to large-scale water diversion projects, such as canals and slopes etc. [22,23,24,25,26,27]. At present, there are many studies on the loess in the monsoon area in the reports [28,29,30,31], and the research on Ili loess mainly focuses on the mechanical properties under cycling test conditions of dry–wet [32,33] and freeze–thaw [34,35], respectively. However, there are few studies on the mechanical properties of Ili loess under the change of soluble salt content. Therefore, studying the influence of soluble salt on engineering properties of Ili loess will provide insights for the regulation and utilization of water and salt and show benefits for the sustainable development of the engineering constructions in saline areas.

This paper targets the Ili loess in China to explore the effect of soluble salt content on the compression, soil–water, and critical state characteristics. Moreover, a normalization analysis is carried out to obtain the hydraulic and mechanical characteristics of Ili loess considering the influence of soluble salt content. This has important theoretical and application significances in the field of unsaturated loess and special soil, and can also promote the sustainable development of Central Asia and the construction of Belt and Road.

2. Material and Test Method

2.1. Physical Properties and Sample Preparation

The undisturbed loess taken from the Tekes River in Zhaosu, Ili, Xinjiang, China, with a depth of 18.5–22 m was used, which is classified as the Late Pleistocene (Q₃) loess. The basic physical properties of Ili loess measured according to the test method standard [36] are displayed in

Table 1. Basic physical properties of Ili loess.

Dry Density ρd (g·cm−3)	Initial Water Content w0 (%)	Liquid Limit wl (%)	Plastic Limit wp (%)		Plasticity Index Ip (%)	Specific Gravity Gs	Particle Content (%)			Soil Classification
							Sand 2–0.075	Silt 0.075–0.005	Clay <0.005
1.32–1.41	6.18–6.73	29.2	19.0		10.2	2.72	0.6	76.4	23.0	CL
Depth of soil layer (m)	Ion content (%)								Soluble salt content θ (%)
	HCO3−	Cl−	SO42−	Ca2+	Na+	Mg2+	K+	CO32−
18.5–19	0.0287	0.0206	0.1228	0.0098	0.1645	0.0073	0	0	0.354
21.5–22	0.0186	0.0354	0.1616	0.0725	0.2338	0.0529	0	0	0.575

.

According to Table 1, Ili loess is classified as low liquid limit clay (CL). For the soil samples with depths of 18.5–19 m and 21.5–22 m, the initial total soluble salt content is 0.354% and 0.575%, and the ion content ratio of HCO₃⁻:Cl⁻:SO₄²⁻:Ca²⁺:Na⁺:Mg²⁺ is 1:0.7:4.3:0.3:5.7:0.3 and 1:1.9:8.7:3.9:12.6:2.8, respectively. The standard triaxial cylindrical samples (3.91 cm diameter, 8 cm height) were extracted from the undisturbed soil blocks. Then, the water film transfer method was used to prepare the undisturbed soil samples under varying water contents and soluble salt contents, the details of which can be found elsewhere [37].

2.2. Test Method

The test equipment is FSY30 stress–strain controlled unsaturated soil triaxial apparatus [38]. The apparatus is mainly composed of a testing machine, body transformer, pressure chamber, and acquisition system. The pressure chamber is composed of double plexiglass inner and outer pressure chambers. The advantage is that the value of inner and outer pressure chambers is equal after pressurization, which reduces the shape change of the inner pressure chamber brought on by loading, so as to improve the accuracy of volume variable measurement. The bottom of the pressure chamber is a clay plate with an air intake value of 5 Bar. The main principle of saturated clay plate is to use kaolin fired into a clay plate to generate uniform small pores and produce surface tension after saturation to achieve the effect of water and gas separation. There are three kinds of stress path triaxial tests experimented for unsaturated undisturbed loess, namely, the isotropic compression test under constant suction, the triaxial contraction test under constant net mean stress, and the shear test after consolidation under constant net confining pressure and suction. The test method and loading scheme for specific soluble salt content are shown in

Table 2. The specific test operation taking one salt sample as an example.

Test Name	State of Stress	Loading Steps (kPa)
Isotropic compression test	Initial suction	5/50/100/150
	Net mean stress	5→400 (graded loading: ① p < 100 kPa, 20 kPa/level; ② p ≥ 100 kPa, 50 kPa/level)
Triaxial shrinkage test	Initial suction	5
	Net mean stress	100
	Suction	5→150 (graded loading: 25 kPa/level)
Consolidation shear test	Suction	5/50/100/150
	Net confining pressure	100/200/300

.

All samples before the test should be fully saturated to the clay plate at the bottom of the instrument, and the suction balance stage should be carried out immediately after the sample installation, to ensure the smooth development of the test process and the effectiveness and accuracy of the data. Each stress path test included five sets of tests with soluble salt content formulated at 0.5%, 0.8%, 1.4%, 2%, and 2.6%, respectively. The drainage valve needs to be open at all times during the test so that the suction loading can be achieved by adjusting the pore air pressure. After applying each load condition, once the volume variation of the collected data is below 0.006 cm³ and the water discharge is less than 0.012 cm³ within two consecutive hours, the sample under this load is considered to have reached a stable state. The specific test process is as follows.

In the isotropic compression test controlling suction, for a certain soluble salt content, four tests were conducted controlling the suction of 5 kPa (i.e., saturated sample), 50 kPa, 100 kPa, and 150 kPa. The specific test operation takes the saturated sample as an example, as shown in Table 2. After the net mean stress was ratcheted up 5 kPa and kept constant, then the suction was ratcheted up 5 kPa. After the sample was stabilized under this load and slowly loaded, the net mean stress was increased step by step to 400 kPa during the invariable suction of 5 kPa.

In the triaxial shrinkage test controlling for net mean stress, for a definite soluble salt content, the tests were all accomplished with a controlling net mean stress of 100 kPa. The specific test operation takes one salt sample as an example, as shown in Table 2. After the suction was regulated to 5 kPa and kept invariant, then the net mean stress was increased up to 100 kPa. After the sample was stabilized under this load, the suction was slowly loaded step by step to 150 kPa during a constant net mean stress of 100 kPa.

In the shear test, after consolidation controlling net confining pressure and suction, twelve tests in total were put up for a given soluble salt content. Orthogonal test conditions were obtained for four suctions with 5 kPa, 50 kPa, 100 kPa, and 150 kPa, and three net confining pressures with 100 kPa, 200 kPa, and 300 kPa. The specific test operation takes one salt sample as an example, as shown in Table 2. In the first period (i.e., consolidation period), when the sample was loaded to the target values of suction and net confining pressure, the consolidation test began. The second period (i.e., shear period) came after the sample was consolidated and stabilized. After the target shear rate was set, the drainage shear test was started, and the shear stage was considered to be over until 15% of the axial strain of the sample was reached.

After each test, the drying method was used to measure the final water content of the sample. According to the measured initial and final moisture content, the acquired value of water discharge was corrected. The comparison shows that the difference between the two was small, but the corrected value of water discharge was still adopted in the paper.

3. Test Results and Normalized Analysis

3.1. Normal Compression Curve

In the isotropic compression test controlling suction, the relationships of void ratio (e) and net mean stress (p) under various suctions are displayed in Figure 1a and the soluble salt content of 1.4% is taken as an example. As can be seen from Figure 1a, two straight lines were drawn according to the test points of the same sample. The intersection represents the yield stress point, and the corresponding net mean stress is the structural yield net mean stress (p_c). For a certain soluble salt content, the e-lg(p) curves are different for different suctions, the structural yield net mean stress (p_c) is larger due to the stronger structure under the larger suction. When the stress is larger than p_c, the slope of the e-lg(p) curve is greater, due to the damaged soil structure and reorganized skeleton particles. The reduction rate of the void ratio then increases on account of a faster reorganization under a larger suction.

In this research, the influence of suction on the e-lg(p) relationship was normalized by using parameters reflecting the basic physical and structural properties, such as initial void ratio (e₀) and structural yield net mean stress (p_c). Shao et al. [39] used the ratio of void ratio to initial void ratio (e/e₀) and the logarithm of the ratio of vertical loading to structural yield net mean stress (p_h/p_c) to normalize the e-p_h curves with different water contents under confined compression conditions. The mathematical equations for compression deformation before and after yielding were then established. But it is complicated to express the compression characteristic in polynomial form before yielding. Subsequently, Wang et al. [40] unified the compression curves before and after yielding as follows:

$$\frac{e}{e_0}=A\exp \left(-\alpha {\left(\frac{p_h}{p_c}\right)}^{\beta }\right),$$

(1)

where e₀ is the initial void ratio and e is the void ratio for stabilization under the loading; p_h and p_c are the vertical load and the structural yield net mean stress, respectively; A is the factor associated with the compression period, α and β are the loess parameters greater than 0. Equation (1) effectively simplifies the normalized compression equation, but the different parameters bounded by the value of (p_h/p_c) are required to describe the compression curves before and after yielding. Another scholar [41] adopted one curve in the e/e₀-lg(p_h/p_c) plane to normalize the compacted loess, and the corresponding equation is as follows:

$$\frac{e}{e_0}=\frac{1}{1+a{\left(\frac{p_h}{p_c{}_{}}\right)}^b},$$

(2)

where a and b are soil parameters.

The above Equations (1) and (2) are established on the basis of the confined compression condition. Whether it is applicable to the results of the isotropic compression test needs further verification. Thus, the relationship of e/e₀ and p/p_c is proposed in this paper:

$$\frac{e}{e_0}=m\exp \left(-n\left(\frac{p}{p_c}\right)\right),$$

(3)

where m and n are soil parameters.

Figure 1b shows the fitting curves of e/e₀ and lg(p/p_c) under different suctions. For a determinate soluble salt content, the samples under various suctions exhibit a consistent relationship, indicating that a better normalization by e/e₀-lg(p/p_c) was obtained. Equations (1)–(3) were then used to fit the results of the isotropic compression test under different conditions (see Figure 1b). Here, the vertical load (p_h) is replaced by the net mean stress (p), and the fitting parameters of the normalization equation of normal compression lines (NCLs) are shown in

Table 3. Fitting parameters of normalization equation of normal compression lines.

Fitting Equation		Equation (1) [40]						Equation (2) [41]		Equation (3)
		p/pc ≤ 1			p/pc > 1
	Parameters	A	α	β	A	α	β	a	b	m	n
Soluble salt content θ (%)	0.5	0.29	−1.22	−0.01	0.16	−1.80	−0.11	0.08	0.88	0.97	0.05
	0.8	0.17	−1.72	−0.01	0.29	−1.18	−0.17	0.09	0.91	0.98	0.06
	1.4	0.10	−2.23	−0.02	0.58	−0.44	−0.53	0.23	0.95	0.99	0.10
	2	0.10	−2.20	−0.01	0.46	−0.69	−0.33	0.11	1.12	1.01	0.11
	2.6	0.10	−2.21	−0.01	0.64	−0.35	−0.56	0.10	0.92	0.99	0.08
	R2	0.69–0.90			0.78–0.94			0.90–0.96		0.85–0.96

.

From Figure 1b and Table 3, it is thus clear that the values of α and β are less than 0 by using Equation (1), which does not meet the aforementioned definition. Both a and b have higher discreteness when the soluble salt content is 1.4% when using the Equation (2). The correlation coefficients (R²) of fitting by Equation (3) are all above 0.85, and the parameter m with different soluble salt contents varies slightly, so the mean value (m = 1) is desirable. That is, Equation (3) can be simplified to a single-parameter equation including only the parameter n. Figure 2 shows the relationship between n and soluble salt content. It can be seen that, as the soluble salt content grows, n first amplifies to reach the peak, and afterwards reduces again. By substituting its equation into Equation (3), the equation of the normalized compression curve considering soluble salt content can be obtained as follows:

$$\frac{e}{e_0}=\exp \left\{\left(0.04{\theta }^2-0.13\theta +0.01\right)\left(\frac{p}{p_c}\right)\right\},$$

(4)

where θ is the soluble salt content (%).

3.2. Soil Water Characteristic Curve (SWCC)

The relationship between suction and degree of saturation or volume moisture content is used to describe the soil water characteristics. When the volume of the sample is not convenient to measure, it is simpler to directly use the water content. However, the soil water characteristics of samples under different stress conditions are different. The SWCCs under the same net confining pressure and different levels of shear stress are well normalized, which can be expressed as follows:

$$\frac{w}{w_s}={\left[1+{\left(j\frac{s}{s_c}\right)}^k\right]}^{-\left(1-\frac{1}{k}\right)},$$

(5)

where w and w_s are the water content in the given and saturated conditions, respectively; s is the suction, and s_c is the air entry value; j and k are the soil parameters.

Figure 3a shows the curves of w-lg(s) under different net mean stresses [38,39,40,41,42]. The above method is utilized to normalize the w-s curves under different net mean stresses. Figure 3b shows the curves of w/w_s-lg(s/s_c) under different net mean stresses. It can be apparent that the stress points with vary net mean stresses are all distributed in a narrow range in the plane of w/w_s-lg(s/s_c). The fitting result with high suction uses Equation (5). The dotted curve in Figure 3b is not appropriate; therefore, a better exponential equation is proposed to directly describe the relationship of w/w_s-lg(s/s_c) under different net mean stresses, which can be expressed as:

$$\frac{w}{w_s}=x\exp \left(-y\frac{s}{s_c}\right),$$

(6)

where x and y are soil parameters.

It is proven that the fitting of Equation (6) is reasonably improved (the solid curve in Figure 3b), and is able to normalize the SWCCs under different net mean stresses in the whole suction range. It is worth noting that the parameters x and y obtained by Equation (6) are independent of the net mean stress. Thus, Equation (6) is used in this paper to fit the SWCCs of different soluble salt contents under three kinds of test methods, and the corresponding parameters obtained are shown in

Table 4. Fitting parameters of normalization equation of SWCCs under three kinds of test methods.

Test Method	Triaxial Apparatus Method		Centrifuge Method [37]		Filter Paper Method [37]
Soluble Salt Content θ (%)	x	y	x	y	x	y
0.5	1.083	−0.559	0.662	−0.042	2.088	−0.025
0.8	1.148	−1.058	0.685	−0.042	1.988	−0.012
1.4	1.241	−0.999	0.707	−0.058	2.02	−0.013
2	1.144	−0.713	0.705	−0.065	2.038	−0.009
2.6	1.065	−0.502	0.717	−0.046	1.996	−0.005
R2	0.79–0.97		0.66–0.73		0.74–0.84

.

It can be seen that the correlation coefficient (R²) for the test results of the triaxial apparatus method is larger in comparison with that of the other two methods, which indicates a better applicability. The parameter x is slightly affected by the soluble salt content, and thus its mean value of 1.14 was taken. The parameter y is approximately linearly correlated with the soluble salt content (see Figure 2), and the normalized soil water characteristic equation considering soluble salt content can be obtained by substituting its expression into Equation (6) as follows:

$$\frac{w}{w_s}=1.14\exp \left[-\left(0.33\theta -1.37\right)\frac{s}{s_c}\right],$$

(7)

where θ is the soluble salt content (%).

3.3. Critical State Line of the p-q Plane

The experimental outcomes show that the stress–strain relationship of the samples are all stiffening under different conditions. The stress corresponds to 15% of the axial strain of the sample as do the failure stresses during shear (q_f and p_f). Figure 4a shows the shear failure stresses (p_f, q_f) under different suctions on the plane of net mean stress–deviator stress (p-q). It can be seen from Figure 4a, for a specific suction, that the points of shear failure stresses fall on a straight string, which is called the critical state line (CSL) of the p-q plane. The deviator stress (q) improves with the rising of the net mean stress (p) linearly for different suctions. The CSLs under different suctions are approximately parallel, but the CSL gradually shifts to the lower left as the suction decreases, implying that the failure stresses during shear (q_f and p_f) are smaller in the case of the lower suction, and vice versa.

Under the condition of triaxial shear, the equation of the effective net mean stress p′ is determined as follows:

$$p\prime =p+S_{r}s,$$

(8)

where S_r and s are, respectively, the degree of saturation and suction during shear failure. On the plane of effective net mean stress–deviator stress (p′-q), the CSLs with the same soluble salt content under different suctions were normalized, as shown in Figure 4b. For a specific soluble salt content, the stress points of unsaturated undisturbed Ili loess under different suctions are distributed in a narrow area in the p-q′ plane, which can approximately be represented by the saturated CSL in the p-q′ plane:

$$q=Mp\prime +c\prime ,$$

(9)

where M and c′ are the slope of the saturated CSL and effective cohesion in the p-q plane. This indicates that the strength characteristics of saturated and unsaturated soils follow a consistent rule, which is in line with references [41,43,44]. Thus, Equation (9) is able to characterize the shear strength characteristics of unsaturated soil only by determining the parameters M and c’ of saturated soil, which solves the complex problems of determination for the shear strength of unsaturated soil and adsorption cohesion in the p-q plane, and effectively simplifies the shear strength theory of unsaturated soil.

Figure 5 presents the relationships between slope (M) and intercept (c′) of the saturated CSL with the soluble salt content. It is apparent that the slope (M) decreases linearly and the effective cohesion (c′) first expands to a maximum value, then gradually reduces in the wake of the increase of soluble salt content. Substituting the equations of M and c′ into Equation (9), the normalized CSL considering the influence of soluble salt content is as follows:

$$q=\left(1-0.02\theta \right)p\prime +\left(-9.97{\theta }^2+32.77\theta -10.72\right),$$

(10)

where θ is the soluble salt content (%).

3.4. Critical State Line in e-p Plane

Figure 6a shows the CSLs on the plane of void ratio and net mean stress (e-p) with diverse suctions, when the soluble salt content is 2%. For a specific soluble salt content and suction, the void ratio (e) declines approximately linearly along with the growth of the net mean stress (p). The unsaturated CSL shifts upward as the increase of suction, and its slope is larger than that of the saturated samples, which is consistent with the undisturbed loess under a constant water content test condition [41]. Figure 6b shows the relationship between the specific value of the unsaturated and saturated void ratio (e/e_s) and the degree of gas saturation (1−S_r) under different suctions; the corresponding soluble salt content is 0.8%. For a specific soluble salt content, the test points gradually move to the upper right with the increase of suction, indicating that both the (1−S_r) and e/e_s increase as the suction increases. This is because the greater suction causes the larger value of (1−S_r) due to the lower water content, and greater suction causes a larger value of e/e_s because of the stronger structure. In addition, the test points under different suctions are uniformly distributed in a narrow band and can be approximately normalized as a single-valued nonlinear function, which is the relationship between the specific value of unsaturated and saturated void ratio (e/e_s) and the gas saturation (1−S_r).

Gallipoli et al. [45] claimed that the specific value of unsaturated and saturated void ratio (e/e_s) under the condition of the constant effective net mean stress (p′) is the function of cementation coefficient (ξ), which can be expressed as follows:

$$\left\{\begin{array}{c}\frac{e}{e_s}=1-g[1-\exp (h\xi )]\\ \xi =f(s)(1-S_r)\end{array}\right.,$$

(11)

where g and h are soil parameters; for the saturated soil, 1−S_r = 0, e/e_s = 1. ξ is a dimensionless quantity reflecting the cementation of shrinkage membrane at the contact point of soil particles, which is mainly determined by the number of volume shrinkage membranes and the cohesive force within a single shrinkage membrane caused by suction. The above two aspects are expressed by the degree of gas saturation (1−S_r) and the ratio of the normal binding force between unsaturated soil and saturated soil (f(s)). As the suction varies from 0 to infinity, the corresponding f(s) changes monotonically from 1 to 1.5. The cementation coefficient ξ = 1−S_r when f(s) = 1, thus Equation (11) is simplified as follows:

$$\frac{e}{e_s}=1-g\{1-\exp [h(1-S_r)]\}.$$

(12)

In this paper, the following equation is proposed to characterize the specific value of unsaturated and saturated void ratio (e/e_s) and the gas saturation (1−S_r):

$$\frac{e}{e_s}=\exp [d(1-S_r)].$$

(13)

In Equation (13), d represents the soil parameters, and the boundary conditions are satisfied: 1−S_r = 0 and e/e_s = 1.

The soil parameter d is obtained by fitting the test points for different soluble salt contents. Figure 7 represents the relation between the soil parameter d and the soluble salt content. It is apparent that the soil parameter d first falls off and then enlarges along with the growth of the soluble salt content. By substituting the equation of d expressed by soluble salt content into Equation (13), the equation between the specific value of unsaturated and saturated void ratio (e/e_s) and the gas saturation (1−S_r) for unsaturated undisturbed Ili loess considering the soluble salt content were obtained:

$$\frac{e}{e_s}=\exp [(0.11{\theta }^2-0.32\theta +0.57)(1-S_r)],$$

(14)

where θ is the soluble salt content (%).

4. Conclusions

In this paper, the compression curve (e-p), soil–water characteristic curve (SWCC), and critical state lines (i.e., CSLs in the plane of p-q and e-p) are normalized, and the normalization equations considering the influence of soluble salt content are obtained. The research provides a probable reference value for the sustainable development of extensive channel projects similar to those in the special area of Central Asia. The main conclusions are summarized as:

1)

The compression curves (e-p) with diverse suctions under the condition of the isotropic compression test can be normalized by the ratios of e/e₀ and p/p_c. Similarly, the SWCCs with diverse net mean stresses under the condition of the triaxial shrinkage test can be uniformly described as the ratios of w/w_s and s/s_c. The normalized e/e₀-lg(p/p_c) and w/w_s-lg(s/s_c) curves can both be approximately expressed by an exponential equation.

2)

In the consolidation shear test, for a specific soluble salt content, the unsaturated CSLs under different suctions in the p-q plane can be normalized by the saturated CSL in the p-q’ plane, and the unsaturated CSLs under different suctions in the e-p plane can be normalized by the specific value of unsaturated and saturated void ratio (e/e_s) and the gas saturation (1−S_r) under the same effective net mean stress.