Dynamic Behavior of Remolded Saline Soil Under Dual Symmetric Factors: Cyclic Loading and Freeze–Thaw Cycles

Abstract

The growing urgency for transportation network development in seasonally frozen regions brings attention to two critical symmetrical factors: cyclic loading and freeze–thaw cycles. In saline soil areas, these symmetrical mechanical and environmental processes, along with varying salt content, significantly affect soil mechanical properties, posing considerable challenges for engineering design. In this study, the dynamic triaxial tests were conducted on a type of carbonate saline soil considering four factors, including moisture content, salt content, freeze–thaw cycle and confining pressure, and the variations in dynamic parameters, including dynamic strength and dynamic elastic modulus, with the above four factors were studied, and the influential mechanisms of four factors were fully discussed. The results demonstrated that the variations in dynamic strength (τ_d) versus vibration cycles (N_F) were better fitted by logarithmic functions than by a linear one. An increase in moisture content, salt content, and freeze–thaw cycle all reduced the τ_d and dynamic elastic modulus (E_d); in addition, the E_d decreased significantly when the dynamic axial strain was less than 0.2%, and then stabilized with further increases in dynamic axial strain. The dynamic parameters of saline soil became nearly constant after undergoing five freeze–thaw cycles, and increased significantly with increasing confining pressure. Moreover, the relationship between the maximum dynamic elastic modulus (E_dmax) and the four factors could be described by power functions. These findings could provide certain references for addressing the combined effects of symmetrical cyclic loading and freeze–thaw cycles in subgrade design for saline soil regions.

1. Introduction

Symmetry, appearing in numerous applications and products [1], is defined as a balanced and proportional correspondence of form or configuration across a dividing line or plane, often resulting in invariance under specific transformations. This fundamental concept extends beyond geometry into the realm of engineering, where repetitive and opposing actions can be perceived as symmetrical in their application and effect. Globally, with the vigorous development of transportation networks and water conservancy projects, numerous linear infrastructure engineering projects, including highways and railways, are required to traverse cold regions. The dynamic mechanical parameters could provide more valuable data for calculation than static and quasistatic parameters. The dynamic behavior of subgrade soils in seasonally frozen regions is predominantly governed by two such critical symmetrical factors: cyclic loading, which applies rhythmic and reversing mechanical stresses, and freeze–thaw cycles, which subject the soil to periodic and opposing temperature variations [2]. The symmetrical nature of these mechanical and environmental processes, characterized by their repetitive, predictable, and often mirroring patterns, is paramount in understanding the resultant dynamic behavior and deterioration patterns of soil.

The effects of passing traffic [3,4] and machine vibration [5] are both common factors that influence the dynamic characteristics of soil, including dynamic strength, elastic modulus, shear modulus, damping ratio and so on. In addition, considering that soil is a type of porous elastoplastic material that will damage progressively before reaching a failure state, it is necessary to investigate the response of soil to dynamic loadings to understand the variation trend and determine appropriate values before commencing construction. Previous studies have revealed that the dynamic characteristics were affected by many internal and external factors, such as compaction degree [6], moisture content [7,8], consolidation ratio [9], confining pressure [10,11], loading frequencies [3,4,7], strain rates [12,13,14], strain ranges [15,16], initial consolidation state [17], dynamic stress amplitude [11], dynamic strain amplitude [18], etc. Most of the studies mentioned above have focused on the dynamic shear modulus and damping ratio. However, very few have investigated the dynamic strength [7] and elastic modulus [19], although they also play important roles in soil dynamics [19].

Moreover, for seasonally frozen regions, such as the western Jilin Province in China, the freeze–thaw cycles could lead to considerable deterioration in soil structure [20] as well as mechanical behaviors [21]. The essential effect of the freeze–thaw cycle is the physical changes in the state of pore solution. The frost heaving of pore water and expansion of soluble salt during freezing can enlarge the volume of pores and disintegrate larger aggregates into smaller ones and thus alter the frictional behavior among particles. During the thawing process, the ice crystals melt and redissolve salt crystals, and then the pore solution redistributes in the soil body and alters the cohesion and viscous resistance, which also has obvious effects on the soil strength. Accordingly, freeze–thaw cycles represent a crucial external factor in the discussion on the dynamic characteristics of seasonally frozen soil, and this factor can induce changes in moduli and damping ratios of soil [3,5,11].

With the rapid development of highway and railway construction in western Jilin Province, China, which helps broaden the transportation network in this region, the subgrade will be built on the widespread seasonally frozen saline soil. Saline soil is a type of special soil with more than 0.3% soluble salt content [22,23]. The effects of salt content, namely the salt skeleton support and cementation, on the static mechanical behavior of saline soils have been explored by numerous researchers, and the type and amount of soluble salt have significant impacts on the strength [24,25]. In addition, the freeze–thaw process also interferes with the salt crystallization or dissolution, thus influencing the soil strength [26,27]. Due to the complexity of how soluble salts affect soil physical properties [28], the understanding of their impact on the strength of various soil types remains limited. Consequently, corresponding works should be urgently supplemented to provide references for the needs of different research fields.

As the other two basic factors in the study of dynamic characteristics of soil, the moisture content greatly influences on consistency state of soil, and the confining pressure can be used to test the ability of resistance to deformation. In addition, there remain inconsistent standpoints about the effects of confining pressure on the mechanical properties of soil. For instance, Simonsen and Isacsson [29] concluded that the confining pressure had a weak influences on static elastic modulus of soil, whereas researchers such as Ling, et al. [19] and Zhu, et al. [7] found a close relationship between confining pressure and soil modulus through dynamic tests; hence, it is meaningful to clarify their relationship by conducting dynamic mechanical tests for a newly studied saline soil.

Because of the scale and complexity of dynamic experiments, however, the studies on the dynamic characteristics of subgrade soil are less frequently conducted [30]. It is necessary to study the dynamic characteristics of saline soil under the dual symmetric factors: cyclic loading and freeze–thaw cycles. In current research, in order to prioritize the simulation of complex environmental conditions, based on the control variate method, the respective effects of moisture content, salt content, freeze–thaw cycle and confining pressure on the principal dynamic characteristics including dynamic strength, backbone curves, and dynamic elastic modulus (including the maximum dynamic elastic modulus) of a remolded carbonate saline soil were studied, and some meaningful conclusions were drawn, which could be applied to provide empirical references for the construction activities related to saline soils in seasonally frozen regions.

2. Materials

2.1. Geological Setting for Salinization

The western Jilin Province, in Northeast China, is located in one of three major sodic saline–alkaline soils distribution regions around the world [31]. Geologically situated in the central depression of the Songliao fault depression belt, the region experienced significant tectonic activity during the late Yanshan Movement. This period saw the uplift of surrounding mountains and the subsidence of the Songliao Basin, forming a faulted lake basin where intense weathering produced abundant weathered clasts and soluble salts, providing a rich source for salinization. Subsequent crustal uplift and the shrinkage of lakes during the late Pleistocene further concentrated these salts, shaping the region’s geochemical environment [32].

This region exhibits a dry, semi-arid monsoon climate. Overall, the annual evaporation far exceeds the annual rainfall [33], leading to salts being brought to the surface through capillary action during the summer and autumn months (Figure 1a). Meanwhile, the annual temperature variation surpasses 40 °C with remarkable symmetry [2] (Figure 1b). The freezing period typically extends from late November to April of the following year, with the coldest phase occurring between November and January, characterized by an average minimum environmental temperature of approximately −20 °C. Complete thawing takes place from April to May, during which the average maximum environmental temperature reaches around 20 °C.

Based on long-term observations by our research group and other studies, the corresponding freezing depth is approximately 180 cm [32,33]. Prolonged freeze–thaw cycles promote the formation of unfrozen water films around soil particles. In winter, driven by thermal and hydraulic gradients, unfrozen water moves toward the freezing front, and certain soluble salts are transported upward concurrently. During the spring thaw, as melting progresses downward from the surface, the rapid evaporation of meltwater retains salts, thereby exacerbating soil salinization.

2.2. Study Area and Soil Properties

The saline soil samples for tests were collected at a representative site in Zhenlai City. (Figure 2a–c). Carbonate saline soil is the major type [34,35], and it exhibits visible structural features [36], which may be caused by periodical freeze–thaw together with wetting–drying cycles. Based on previous field studies [22], it was observed that saline soil collected at a depth of 40 cm elevated levels of soluble salts, accompanied by dynamic migration patterns. The accumulation of soluble salts near the 40 cm depth is primarily influenced by cyclical processes of rainwater leaching and evaporation, leading to pronounced salt enrichment in this layer. This specific stratum is considered representative of the region’s predominant physicochemical characteristics of saline soils, hence its selection for experimental analysis. Consequently, a sampling depth of 40 cm below the ground surface was selected for this study (Figure 2d). The soil samples were collected in spring, when the combined effects of intense evaporation during summer and autumn, coupled with unfrozen water migration during the freezing period, result in a higher degree of salt accumulation.

Some basic physical properties of the sampled saline soil are listed in

Table 1. List of elementary physical properties of natural saline soil.

Soil Type	Plastic Limit (%)	Liquid Limit (%)	Plasticity Index	Optimum Moisture Content (%)	Maximum Dry Density (g/cm3)
CL	18.5	32.4	13.9	20.0	1.74
Clay fraction (<0.005 mm)			Silt fraction (0.005–0.075 mm)		Sand fraction (0.075–2 mm)
38.26%			53.53%		8.21%

. Particle size distribution was measured by sieving and hydrometer analysis (Figure 3). The inorganic soil was then classified as lean clay (CL) based on the Unified Soil Classification System (USCS) [37]. The results of chemical analysis on soluble salt are summarized in

Table 2. Contents of soluble salt of natural saline soil.

Item	Total	Na+	K+	Ca2+	Mg2+	SO42−	HCO3−	CO32−	Cl−
Content (%)	0.5	0.0999	0.0012	0.0073	0.0044	0.0089	0.1929	0	0.0141

Note: The data were measured on the basis of the filtrate of 1:5 soil–water extractive.

. The total soluble salt content is 0.5%, significantly exceeding the threshold for saline soil (0.3%) specified by the classification criteria for special soils in GB 50021-2001 [23]. Among cations, Na⁺ accounts for 88.6%, while among anions, HCO₃⁻ constitutes 89.3%. Both ions dominate in comparable proportions, indicating that NaHCO₃ is the primary salt type. Thus, the soil can be classified as a carbonate saline soil.

3. Experimental Approaches

3.1. Specimen Preparation

The experimental scheme was planned based on the control variate method (

Table 3. List of experimental schemes.

Group Label	Moisture Content (%)	Salt Content (%)	Freeze–Thaw Cycle	Confining Pressure (kPa)
MC	16, 20, 24	0.5	0	100
SC	20	0, 0.5, 1.0, 1.5, 2.0	0	100
FT	20	0.5	0, 1, 3, 5, 10, 30, 60	100
CP	20	0.5	0	100, 150, 200

MC is the abbreviation of moisture content; SC is the abbreviation of salt content; FT is the abbreviation of freeze–thaw cycle; CP is the abbreviation of confining pressure.

). For the soils of group MC (moisture content), SC (salt content, only the 0.5% salt content sample), FT (freeze–thaw cycle), and CP (confining pressure), which contained the natural salt content, the collected soil samples were firstly air-dried and dried in an oven at 105 °C. Afterward, the dry saline soil was pulverized and passed through a 2 mm sieve. For the other SC group (0%, 1.0%, 1.5%, and 2.0%), the collected soil samples were desalinized with daily deionized water for 15 days to remove the soluble salt, and the dried, sieved samples were obtained after the above treatments (the salt content was 0). According to the data in Table 2, Na⁺ and HCO₃⁻ were the major cation and anion, respectively; therefore, the NaHCO₃ powder was selected to prepare artificial saline soil samples (including 1.0%, 1.5% and 2.0% of group SC).

The experiment was conducted using the controlled variable method. Considering the need for a clear differentiation between various sample variables, the moisture content was set at ±4% of the optimum moisture content; the salt content was varied in increments of 0.5%, ranging from 0 to 2.0%. The soil undergoes at least one freeze–thaw cycle annually [30,38]. For the soil with shallow burial depth, this situation may occur once a day in the early winter or at the end of winter. Therefore, it was necessary to design a sufficient number of freeze–thaw cycles. Moreover, as the remolded saline soil initially possesses high strength, its properties may deteriorate more significantly during the early stages of freeze–thaw cycles. Consequently, based on the team’s previous research [39], the number of freeze–thaw cycles was selected with representative values of 0, 1, 3, 5, 10, 30, and 60. The sieved dry saline soil samples, deionized water, and NaHCO₃ powder in calculated dosages for different experimental combinations were uniformly mixed and sealed in plastic bags to achieve a more homogeneous distribution of moisture and salt. Considering the relative stability of the maximum dry density of saline soil at low salt contents [40,41], based on the maximum dry density (1.74 g/cm³), the samples were then compacted at a compaction degree of 90% by using a metal mold, namely, the dry density of prepared specimens was 1.566 g/cm³. The 90% compaction degree was chosen to simulate weak zones in field construction resulting from common factors such as uneven compaction and moisture control variability. Damage in linear infrastructure projects, such as uneven pavement surfaces, often initiates precisely in these weak zones. Additionally, the 90% compaction degree helps prevent excessively high initial strength from masking or attenuating the degradation of dynamic soil properties under multi-factor interactions.

The layered compaction method was employed by dividing the sample into three layers. Prior to the addition of each subsequent layer, the surface of the compacted layer was scarified. To eliminate the effect of size variations and surface damage of specimens caused by freeze–thaw cycles in subsequent dynamic triaxial tests, the specimens prepared for freeze–thaw cycles were made larger. Therefore, the prepared specimens were 50 mm in diameter and 100 mm in height (Figure 4a), and all of them were sealed with plastic film and stored in moisturizing containers to prevent moisture loss. For group FT, the soil specimens to be subjected to freeze–thaw regimes were next put in a self-made apparatus for freezing (Figure 4b). The temperatures were set to −20 °C and 20 °C, respectively, according to the environmental temperature (Figure 1b); in addition, in order to realize complete freezing and thawing of free water in soil [2,42], a complete cycle included 12 h of freezing process and 12 h of thawing process. Before conducting the dynamic triaxial tests, each specimen was carefully trimmed into a size of 39.1 mm in diameter and 80 mm in height using a rotatable soil cutter tool to fit the apparatus for dynamic triaxial tests (Figure 4c).

3.2. Dynamic Triaxial Test

As shown in Figure 4d, a TAJ-20 computer-controlled electro-hydraulic servo triaxial test apparatus manufactured by Tianshui Hongshan Testing Machine Co., Ltd, Gansu province, China, was employed for the dynamic triaxial tests. First, each soil specimen was isotopically consolidated (σ_1c = σ_3c = 100 kPa, consolidation ratio K_C = 1) in the chamber of this apparatus, and the consolidation process was terminated when the volumetric deformation (i.e., the volume of drained water) of the specimen was less than 0.01 cm³ per hour [43]. After consolidation, the drain valve was closed to create an undrained condition. Seeing that the target vibration mainly originates from passing vehicles or trains, one-way sinusoidal loading was imposed on consolidated saline soil specimens. Based on existing methods [44,45], the vibration frequency and amplitude of simulated loadings were set to 1 Hz and 0.024 kN, respectively. The data were automatically recorded by the equipped software during the whole dynamic test. The 5% of dynamic axial strain of specimens was deemed as the failure criterion [30,43].

4. Experimental Results and Analyses

4.1. Dynamic Strength

The dynamic strength (τ_d) is a basic parameter that reflects the stability of soil under dynamic loading. It is defined as the relationship between half of the dynamic axial stress amplitude generated by axial cyclic loadings and the number of vibration cycles (N_F) corresponding to the failure criterion. Generally, it can be calculated by Equation (1) [3,5,7,30]:

$${\tau }_d={\sigma }_d/2,$$

(1)

where σ_d denotes the dynamic axial stress. The experimental data are shown in Figure 5. Zhang et al. [46] indicated that for a given failure criterion, the τ_d induced by the same cyclic loading does not decrease indefinitely with increasing N_F, and proposed a corresponding formula:

$${\tau }_d/{\sigma }_3=a{N}_0/N_F+b ({\sigma }_3\ne 0),$$

(2)

where σ₃ denotes the confining pressure; N₀ = 1 denotes the reference vibration cycle; a and b denote two dimensionless parameters, and their values for this study are summarized in

Table 4. Fitted parameters for Equations (2) and (3).

Moisture Content	Salt Content	Freeze–Thaw Cycle	Confining Pressure	Linear Fitting by Equation (2)			Logarithmic Fitting by Equation (3)
				a	b	R2	a′	b′	R2
16%	0.5%	0	100 kPa	2.4015	0.5084	0.7971	0.0688	0.8456	0.9453
20%				1.2259	0.4591	0.9718	0.0394	0.6455	0.9909
24%				1.0060	0.3148	0.8178	0.0460	0.5289	0.9657
20%	0	0	100 kPa	1.1476	0.5121	0.7440	0.0431	0.7160	0.9392
	1.0%			2.5054	0.3587	0.9490	0.0632	0.6712	0.9996
	1.5%			2.0532	0.3182	0.9490	0.0599	0.6079	0.9970
	2.0%			1.1166	0.3193	0.6297	0.0482	0.5412	0.7817
20%	0.5%	1	100 kPa	2.0394	0.3952	0.7755	0.0652	0.7056	0.9156
		3		0.8721	0.3765	0.7764	0.0472	0.5867	0.8980
		5		1.5897	0.3297	0.9999	0.0434	0.5450	0.9535
		10		1.0944	0.2827	0.7362	0.0520	0.5217	0.9263
		30		1.9124	0.2847	0.7452	0.0714	0.6130	0.8739
		60		1.2636	0.2711	0.6675	0.0489	0.4973	0.7935
20%	0.5%	0	150 kPa	1.6357	0.4413	0.7924	0.0456	0.6626	0.9260
			200 kPa	2.0413	0.3880	0.9758	0.0563	0.6655	0.9880

. Equation (2) demonstrates the linear relationship between τ_d/σ₃ and N_F, and the minimum τ_d equals bσ₃ (N_F → +∞). In the present research, however, it is found that the relationship between τ_d/σ₃ and N_F is better described by a logarithmic function (Figure 5) rather than linear, since the soil cannot be regarded as an ideal linearly elastic material; thus, the relationship can be written as Equation (3):

$${\tau }_d=\left[a^{\prime }{\mathrm{l}\mathrm{n}(N}_0/N_F\right)+b^{\prime }]{\sigma }_3=-a^{\prime }{\sigma }_3\mathrm{l}\mathrm{n}{N}_F+b^{\prime }{\sigma }_3({\sigma }_3\ne 0),$$

(3)

where a′ and b′ denote two dimensionless parameters, and their values are summarized in Table 4. Parameter a′, which fluctuates between 0.0394 and 0.0714, representing the rate of loss of τ_d with increasing N_F, a higher a′ means a faster rate of loss. Parameter b′, which ranges from 0.4973 to 0.8156, representing the magnitude of τ_d, a higher b′ means a greater residual τ_d. In addition, from Table 4, it is clear that the fitting degree (R²) of logarithmic fitting is higher than linear fitting; in another aspect, the soil structure becomes denser after undergoing more vibration cycles, and the rate of reduction in dynamic strength is bound to decrease. Furthermore, Figure 6 demonstrates that the fitting degrees (R²) of the logarithmic fitting show a more concentrated distribution compared to those from Equation (2). The median and mean R² values of the logarithmic fitting are as high as 0.9392 and 0.9263, respectively. Therefore, although no outliers are observed in either fitting method, the logarithmic relationship in Equation (3) is clearly more reasonable and acceptable for predicting the relationship between the τ_d and N_F of saline soil.

Figure 5a indicates that τ_d decreases by approximately 35% to 42% with increasing moisture content from 16% to 24%. Figure 5b illustrates that the existence of soluble salt can weaken the τ_d of saline soil in comparison with non-saline soil (salt content is 0%), a 0.5% increase in salt content leads to about 10% decline in τ_d; when the salt content of saline soil is greater than 1.5%, the dynamic strength tends to stabilize, especially after experiencing more N_F. Figure 5c manifests that the increasing freeze–thaw cycles continuously reduce the τ_d of saline soil, whereas the τ_d is apt to be stable after suffering approximately five freeze–thaw cycles, which is consistent with the study of Cui, Ma, Liu, and Wang [30]. Figure 5d presents a positive relationship where the τ_d increases significantly with increasing confining pressure, and the increment of τ_d tends to decrease with increasing N_F.

4.2. Dynamic Elastic Modulus

The backbone curves for dynamic triaxial tests are the foundation of further analyses of dynamic parameters. According to Hardin and Drnevich [47] (applicable to the case of K_c = 1), the backbone curves can be described as hyperbolic curves by adopting the following relationship [7,19,47,48]:

$${\sigma }_d={\epsilon }_d/(B{\epsilon }_d+A),$$

(4)

where ε_d denotes the dynamic axial strain, A and B denote two fitting parameters (MPa⁻¹), and their values are listed in

Table 5. Summary of fitted parameters A and B for Equation (4).

Moisture Content	Salt Content	Freeze–Thaw Cycle	Confining Pressure	A (MPa−1)	B (MPa−1)	R2
16%	0.5%	0	100 kPa	0.00224	9.121	0.9994
20%				0.00635	9.233	0.9979
24%				0.01753	14.400	0.9910
20%	0	0	100 kPa	0.00203	9.422	0.9984
	1.0%			0.01283	12.770	0.9929
	1.5%			0.01557	16.480	0.9874
	2.0%			0.02635	15.380	0.9973
20%	0.5%	1	100 kPa	0.00941	9.245	0.9983
		3		0.01045	13.070	0.9993
		5		0.01499	15.190	0.9961
		10		0.02577	15.420	0.9957
		30		0.03360	12.350	0.9914
		60		0.04542	15.170	0.9884
20%	0.5%	0	150 kPa	0.00265	5.896	0.9991
			200 kPa	0.00114	4.748	0.9978

. The fitted backbone curves, influenced by the four factors (moisture content, salt content, freeze–thaw cycle, and confining pressure), are plotted in Figure 7.

It is clear that the shape of all the backbone curves exhibits a steeper and approximately linear curve at first, and then it becomes flatter. This trend is similar to the strain-hardening behavior in conventional triaxial results, with the turning point of ε_d being about 0.1%. Furthermore, the changes in four factors obviously affect the σ_d, whereas with increasing salt content (Figure 7b) and freeze–thaw cycle (Figure 7c), the variation in σ_d is gradually converged, indicating that the effects of these two factors may be limited. In contrast, decreasing moisture content (Figure 7a) and increasing confining pressure (Figure 7d) in this study markedly improve the real-time σ_d during dynamic compression, highlighting the importance of moisture characteristics and constrained design of subgrade soil in engineering projects.

The dynamic elastic modulus E_d, namely the dynamic Young’s modulus, is a key parameter in soil dynamics [48], and it can be determined from the backbone curves using the following formula [15,19,48]:

$$E_d={\sigma }_d/{\epsilon }_d,$$

(5)

The results of E_d are presented in Figure 8. It is interesting to observe that with the progressive small deformation (ε_d < 0.5%) of soil specimens, the E_d quickly converges to a constant value, and the constant value generally begins to appear when the ε_d exceeds 0.2%. The rate of convergence is high, especially under lower moisture content, lower salt content, fewer freeze–thaw cycles, and higher confining pressure. Taking the soil specimen at a moisture content of 16% as an example (Figure 8a), near 0.1% ε_d causes a 74% reduction in the E_d. Such results reveal that the loss of E_d of saline soil mainly occurs soon after the instantaneous loading. The E_d of saline soil specimens subjected to more than five freeze–thaw cycles is almost the same (Figure 8c). With increasing moisture content, salt content and freeze–thaw cycles (no more than five cycles), the E_d decreases apparently; with increasing confining pressure, the E_d increases conspicuously; with increasing ε_d (< 0.5%), the E_d corresponding to the above four factors stabilizes at a range of 14–45 MPa, 10–40 MPa, 9–25 MPa, and 20–60 MPa, respectively (Figure 8).

To investigate the influences of four factors on the maximum dynamic elastic modulus E_dmax (corresponding to ε_d = 0), E_dmax is defined as follows:

$$E_{dmax}=1/A,$$

(6)

where A is a parameter of Equation (4), which can be determined by referring to Table 5. Hence, the E_dmax is demonstrated in Figure 9, and its variation is fitted by the following power function:

$$E_{dmax}={f\left(x\right)=\alpha x}^{\beta }$$

(7)

where α and β denote two fitting parameters, and x denotes the numerical value of each influential factor. Parameter β is an exponent that determines the nonlinear intensity and direction of the relationship between the variable x (e.g., moisture content, salt content, number of freeze–thaw cycles) and the maximum dynamic elastic modulus E_dmax. The absolute value of β reflects the sensitivity or intensity of the influence of factor x on E_dmax. Parameter α is the baseline state coefficient of the system. Its value collectively represents the inherent “baseline” stiffness potential of the soil—determined by its mineral composition, initial pore structure, and particle arrangement under specific experimental conditions (e.g., 90% compaction degree, specific soil type), before being influenced by other fixed experimental conditions (such as initial density, soil type, etc.).

Figure 9a shows that when the moisture content of saline soil is lower than the plastic limit (18.5%), the E_dmax is fairly high, and even a slight decrease in moisture content will arouse significant increment in E_dmax; when the moisture content exceeds the liquid limit (32.4%), the soil will lose almost all the strength and the E_dmax will be close to 0; such a rule shows that the E_dmax is closely associated with the consistency state of saline soil. Interestingly, as the results presented in Figure 9b show, the E_dmax can be weakened due to the existence of salinity, and it gradually remains unchanged (around 30 MPa) with increasing salt content. Figure 9c shows that the E_dmax remains nearly constant after five freeze–thaw cycles (around 30 MPa); as numerous freeze–thaw cycles occur in a year, the experimental value of E_dmax of saline soil corresponding to more than five freeze–thaw cycles in the seasonally frozen region can be used as a reference in practical subgrade construction. Figure 9d illustrates that the E_dmax of saline soil specimens is strongly affected by the confining condition, which indirectly shows the importance of compaction of subgrade soil.

Regarding the model proposed in Equation (7), the value of α varies significantly with changes in external constraints such as confining pressure (compare the fitted curves under different confining pressures in Figure 9d). This demonstrates that α is not a fixed material constant but rather a system-state-dependent parameter, which incorporates all factors influencing stiffness that are not captured by the x^β term. As for parameter β, when x represents moisture content, salt content, or the number of freeze–thaw cycles, β is negative (see Figure 9a–c). This clearly indicates that E_dmax decreases as these factors increase, reflecting their destructive effect on the soil structure. In contrast, when x represents confining pressure, β is positive (Figure 9d), indicating that E_dmax increases with higher confining pressure. This trend is fully consistent with the understanding that confining pressure enhances soil densification and strengthens interparticle friction and interlocking effects. A comparison of Figure 9a,b shows that the curve for moisture content variation is steeper, and its corresponding |β| value is generally larger than that for salt content variation. This suggests that, within the experimental framework of this study, small changes in moisture content have a more pronounced weakening effect on soil stiffness than equivalent changes in salt content. This quantitative relationship provides a theoretical basis for prioritizing moisture control in engineering practice. Therefore, the model proposed in Equation (7) possesses considerable scientific significance.

5. Discussion on Factors Affecting Dynamic Behavior

Before the conduction of dynamic triaxial tests, the initial physical and chemical states of saline soils play predominant roles in influencing the mechanical characteristics. Thus, for the same experimental conditions of cyclic loadings, static analyses can first be used to understand the mechanism of variation due to the state changes in the soils themselves.

5.1. Moisture Content

The reduction in dynamic strength (τ_d) and dynamic elastic modulus (E_d) with increasing moisture content is a complex process governed by shifts in the soil’s hydraulic state. Water plays a key role in reducing interparticle attractions [49]. In the remolded, compacted state at low moisture content, the soil benefits from matric suction resulting from capillary forces in the partially saturated pores. This suction contributes significantly to the apparent cohesion and, hence, the initial stiffness and strength. As the moisture content increases, this matric suction diminishes, leading to a loss of capillary-induced strength.

Critically, under undrained cyclic loading, as employed in this study, the increased degree of saturation facilitates the rapid development and accumulation of excess pore water pressure. The inability of pore water to drain during loading cycles means that the effective stress acting on the soil skeleton is progressively reduced. This decrease in effective stress is a primary driver for the softening of the soil and the degradation of its dynamic properties (τ_d and E_d). Therefore, the influence of moisture content extends beyond a simple lubricating effect; it fundamentally alters the soil’s response by weakening the soil fabric through loss of suction and promoting pore pressure buildup under dynamic excitation, which collectively lead to the observed significant deterioration in performance. Moreover, from another perspective, with a constant salt content, increasing moisture content lowers the concentration of pore solution of saline soil, which, according to the Gouy–Chapman diffuse-double-layer theory for clayey soils, means the thickness of the loosely bound water film of clay grain is easily affected by the concentration of pore solution. Accordingly, increasing moisture content thickens the diffuse double layer and increases the electrokinetic potential, and also weakens the strength of saline soil eventually [50].

Many studies have drawn a conclusion that the shear strength of soil decreases monotonously with increasing moisture content [51,52,53]. Supported by the above theories and back to the current study, increasing moisture content from 16% to 24% leads to a significant reduction in the dynamic strength (τ_d), dynamic elastic modulus (E_d), and maximum dynamic elastic modulus (E_dmax) of saline soil. This conclusion is in good agreement with Liu et al. [6]. It should be noted that the soil specimens in this group were not subjected to a freeze–thaw cycle, and the pore water in the soil maintains a liquid state. Therefore, the consequences of the variation trend of the dynamic modulus of frozen soils from Ling et al. [3] and Zhu et al. [7] are contradictory to current results.

5.2. Salt Content

In this study, the τ_d, E_d, and E_dmax decrease monotonically with increasing salt content up to 2.0%. This observed weakening behavior at low to moderate salinity levels can be fundamentally attributed to the specific chemical composition of the soil and the resulting physicochemical interactions.

The presence of NaHCO₃, the predominant salt, imparts a weakly alkaline environment to the pore water. In this alkaline environment, NaHCO₃ readily dissociates into Na⁺ and HCO₃⁻ ions. The monovalent Na⁺ are known for their strong hydration capacity and their tendency to promote the development of a thick, hydrated diffuse double layer around clay particles. Furthermore, the alkaline condition (high pH) tends to increase the negative surface charge of clay minerals, significantly expanding the thickness of the diffuse double layer surrounding the clay particles, generating strong repulsive forces between adjacent clay particles. In cohesive soils, these repulsive forces can overcome the natural attractive Van der Waals forces, leading to a phenomenon known as particle dispersion [22].

Consequently, an increase in salt content results in a more dispersed soil structure and a greater effective distance between particles, thereby directly weakening inter-particle bonds and the soil’s cohesion. Under static conditions, this dispersion effect already leads to a reduction in strength. Under cyclic loading, this pre-weakened, dispersed structure is subjected to repeated shear stresses. The poorly connected soil structure is more susceptible to particle reorientation and accumulation of permanent strains, accelerating the degradation of the soil’s stiffness (manifested as a lower E_d and E_dmax) and its resistance to cyclic failure (manifested as a lower τ_d). Therefore, the increase in salt content, within the tested range, exacerbates the soil’s inherent susceptibility to deterioration under dynamic loading by enhancing its dispersity, leading to the continuous decline in dynamic parameters.

5.3. Freeze–Thaw Cycles

The frost heaving and salt expansion of saline soil during freeze–thaw cycles can break the coarse aggregates into fragments and deteriorate the soil microstructure [20], and then the soil strength decreases [54,55]; moreover, a few cycles can cause a considerable reduction in the resilient modulus [56,57]. Our results accord with the empirical results, but it should be noted that the τ_d, E_d, and E_dmax seem irrelevant to more than five freeze–thaw cycles. The result is similar to that of Elif et al. [5], in which they ascribed it to the formation of a new dynamic equilibrium in soil texture. As for the saline soil specimens that have undergone freeze–thaw treatments, less than five freeze–thaw cycles disintegrate most of the loosely aggregated particles into finer grains, and more cycles do not cause significant changes. Macroscopically, the τ_d, E_d, and E_dmax decrease significantly at first and then enter a relatively constant stage.

5.4. Confining Pressure

The results demonstrate a significant positive correlation between confining pressure and the dynamic parameters (τ_d, E_d, and E_dmax). This well-established phenomenon can be interpreted through the fundamental principle of increased effective stress. Under higher confining pressure, the soil skeleton experiences greater compression.

While direct microstructural evidence (e.g., SEM imaging) for the tested saline soil is not available in this study, the macroscopic mechanical response is consistent with well-documented mechanisms observed in other cohesive soils. It is reasonable to infer that the increase in confining pressure leads to a more compact soil fabric through processes such as the closing of pre-existing micro-fissures, compression of larger pores, and a rearrangement of soil particles into a denser, more oriented structure. This particle rearrangement likely evolves from point-to-point contacts to more stable face-to-face contacts, thereby enhancing interparticle interlocking and frictional resistance. The findings of Ling et al. [19] on frozen soil and Chen et al. [43] on loess, although from different soil types, support this general principle of fabric densification under confinement. Therefore, the enhancement of dynamic properties with increasing confining pressure observed here is attributed to this inferred densification of the soil microstructure and the consequent improvement in interparticle forces.

5.5. Practical Insights for Subgrade Performance

Based on the experimental findings, this study provides practical insights for the design and maintenance of subgrades in saline soil areas of seasonally frozen regions. The logarithmic relationship between dynamic strength and vibration cycles offers a quantitative basis for predicting long-term cumulative deformation under traffic loading, thereby supporting the durability design of roadbeds. The observed sharp decline in elastic modulus at low axial strains (<0.2%) highlights the need to strictly control initial deformation during construction. Furthermore, the significant weakening effects of moisture content, salt content, and freeze–thaw cycles emphasize the importance of implementing effective drainage measures and salt content control to mitigate material degradation. The stabilization of dynamic parameters after five freeze–thaw cycles suggests that pre-freeze–thaw conditioning or targeted reinforcement strategies could be applied to enhance post-thaw stability. Finally, the confining pressure dependence of dynamic properties supports the use of proper compaction techniques to ensure sufficient lateral constraint in subgrade construction.

6. Conclusions

Symmetrical cyclic loading and freeze–thaw cycles constitute essential external factors in saline soil subgrade design in seasonally frozen regions. By conducting a series of dynamic triaxial tests on a type of carbonate saline soil in west Jilin Province, China, this study investigated the effects of various moisture contents, salt contents, freeze–thaw cycles, and confining pressures on the dynamic characteristics, including dynamic strength, backbone curve, and elastic modulus, and the following conclusions are mainly drawn:

(1)

The relationship between the dynamic strength of saline soil and increasing vibration cycles can be well described by logarithmic functions.

(2)

With increasing dynamic axial strains, the reductions in real-time dynamic elastic moduli are especially significant when the dynamic axial strains are small (<0.2%), then the dynamic strength and elastic modulus basically begin to stabilize at higher dynamic axial strains (>0.2%).

(3)

The dynamic strength and elastic modulus (including the maximum dynamic elastic modulus) both decrease with increasing moisture content, salt content, and freeze–thaw cycle, and increase considerably with increasing confining pressure. In particular, the dispersion of clay particles induced by NaHCO₃, the dominant salt in this carbonate saline soil, is identified as the primary mechanism responsible for the observed decrease in dynamic parameters with increasing salt content. Moreover, these dynamic parameters remain almost constant after undergoing five freeze–thaw cycles. The variations in maximum elastic moduli with the above variables can be well expressed by power functions.

In summary, the evolution patterns of dynamic parameters revealed in this study highlight the necessity to control filler moisture/salt content and enhance drainage and lateral confinement in subgrade design. Future work should focus on developing design guidelines based on the logarithmic and power function models for long-term performance prediction and freeze–thaw protection of regional subgrades.