The Influence of Freeze-Thaw Cycles on the Mechanical Properties of Loess Under Temperature Variations

Abstract

Freeze-thaw (F-T) cycle tests and triaxial shear tests are conducted under varying freezing ambient temperatures and different F-T cycles for remolded loess. The results indicate that nearly all stress–strain curves of remolded loess exhibit strain-hardening behavior under varying freezing ambient temperatures and different F-T cycles. A decrease in freezing temperature alters the yield strain of loess and diminishes its resistance to deformation. As the freezing temperature decreases and the number of F-T cycles increases, the failure deviatoric stress of loess initially decreases, then increases, and eventually stabilizes. The most detrimental freezing temperature is −12 °C, which significantly exacerbates the adverse effects of F-T cycles on failure deviatoric stress. The strength indices initially decrease and then increase with decreasing freezing temperatures, while they first decrease and then stabilize with an increasing number of F-T cycles. Notably, the deterioration of cohesion is significantly greater than that of the internal friction angle. A quantitative analysis is conducted to examine the relationship between failure deviatoric stress, shear strength index, temperature, and freeze-thaw cycles. The fitting results effectively quantify the influence of different variables on the strength characteristics of loess. The findings of this research have significant theoretical implications for practical engineering applications in the northwest loess region.

1. Introduction

Loess is a typical Quaternary aeolian sediment found in arid and semi-arid regions, characterized by its unique material composition and structural properties. It is widely distributed throughout the northwestern part of China [1,2,3]. The seasonal temperature variations and the differences between day and night temperatures are significant in northwest China, with low temperatures during winter and at night. These periodic temperature changes lead to repeated cycles of freezing and thawing in the loess soil, which can result in various hazards, such as subgrade deformation and slope failure [4,5,6,7]. These issues pose serious threats to the quality of construction projects and the safety of people’s lives. In light of the continued advancement of the “Belt and Road” Initiative, there has been a notable shift in the emphasis of infrastructure development, particularly concerning high-speed railways and highways, towards the northwestern loess region. Consequently, loess projects, such as roadbeds and slopes, are likely to undergo F-T cycles during both construction and operation [8,9,10,11]. It is imperative to investigate the impact of F-T cycles on the mechanical properties of soil for the purposes of practical engineering applications.

To date, numerous experts have conducted various studies on the effects of F-T cycles on the mechanical properties of different types of soil. Zhao et al. [12] conducted a study examining the effects of F-T cycles on the shear strength of loess through the application of triaxial testing methods. The findings reveal that an increase in the number of F-T cycles correlates with a reduction in both the internal friction angle (φ) and cohesion (c). This change pattern closely resembles the microstructural characteristics of the particles. Notably, both parameters exhibit significant changes before reaching five cycles and tend to stabilize after 15 cycles. Zhang et al. [13] investigated the changes in loess strength under F-T cycles. The results indicated that as the number of F-T cycles increased, the strength of the soil exhibited varying degrees of deterioration. Yang et al. [14] conducted triaxial shear tests on intact loess under F-T conditions and found that F-T cycles significantly weakened the failure strength, shear strength, cohesion, and initial tangent modulus of intact loess. However, there was no noticeable effect on the internal friction angle. Ghazavi et al. [15] conducted a study examining the effects of F-T cycles on the compressive strength of fiber-reinforced clay. The results indicated that the unconfined compressive strength of the soil decreased by 20 to 25% with an increase in the number of F-T cycles. Tang et al. [16] conducted consolidated undrained triaxial tests to investigate the impact of F-T cycles on the strength of expansive soil. The results indicated that the elastic modulus, failure strength, and shear strength parameters of the soil significantly decreased with an increasing number of F-T cycles. Wang et al. [17] performed direct shear tests on coarse salt soil samples that were exposed to F-T cycles. The results indicated a decline in cohesion as the F-T cycles advanced, whereas the φ exhibited no significant changes due to the F-T cycles. Chu et al. [18] conducted F-T cycle tests and triaxial shear tests to investigate the mechanical properties of loess at varying moisture contents. The results indicate that the failure mode of the stress–strain curve for loess is influenced by both moisture content and the number of F-T cycles. As the number of F-T cycles increases, the failure strength and shear strength parameters of loess gradually decrease before stabilizing. Guo et al. [19] conducted triaxial tests on the paleosoil subjected to various F-T cycles. The results indicated that the F-T cycles compromised the structure of the paleosoil, with the stress corresponding to the strain being greater under high confining pressure and low moisture conditions. It is evident that various environmental factors exert distinct effects on the mechanical properties of different soil types [20,21,22,23,24,25,26,27].

The F-T cycle alters the internal temperature of the soil by responding to changes in the external environmental temperature, causing the soil to repeatedly undergo the processes of freezing and melting. During the F-T cycle, the initial structure of soil is compromised, leading to alterations in microstructure, such as particle diameter and pore volume. Consequently, the macroscopic physical parameters and mechanical properties deteriorate due to changes in microstructure [28,29,30,31,32,33]. In loess engineering, issues such as frost heaving, thawing, and sinking have significantly compromised construction quality, leading to various degrees of engineering accidents [34,35]. Severe weather conditions, including heavy snow, freezing temperatures, strong winds, high temperatures, and both heavy and continuous rainfall, exacerbate the F-T cycle. Therefore, environmental temperature is a significant factor influencing soil properties. Investigating the effects of freezing and thawing temperature changes on the strength characteristics of loess is crucial for addressing the challenges posed by freezing and thawing disasters in loess engineering. Therefore, based on the application of the F-T cycle test followed by triaxial shear testing, this study investigates the evolution of the stress–strain characteristics, failure deviator stress, and shear strength index of loess as the temperature of the freeze-thaw environment changes.

2. Soil Materials and Test Methods

2.1. Preparation of Test Materials and Soil Samples

The loess samples were obtained from a construction site of a subway station currently under development in Xi’an City, Shaanxi Province, China. The locations and environmental conditions of the soil sampling are illustrated in Figure 1a,b, with the sampling depth ranging from 13.0 to 14.0 m. The soil samples exhibited a yellow-brown coloration, lacked distinct bedding, and were classified as Late Pleistocene loess (Q₃^eol). The original soil sample size was cut into approximately 30 cm × 30 cm × 30 cm blocks. Following successful collection, the samples were promptly wrapped and sealed with black plastic film and tape to mitigate water loss and prevent damage to the soil samples. The fundamental physical property indices of the soil samples, as determined through laboratory analyses, are presented in

Table 1. Basic physical properties of soil samples.

Specific Gravity of Soil Grain	Moisture Content (%)	Dry Density (g∙cm−3)	Limit of Plastic (%)	Liquid Limit (%)	Index of Plasticity
2.71	22.9	1.5	18.4	35.0	16.6

.

Subsequent to the processes of cutting, drying, and pulverizing the soil sample, the resultant material was subjected to sieving through a mesh with a pore diameter of 2 mm. The sifted soil was then weighed, and distilled water was uniformly sprayed onto it. Subsequently, the soil was placed into a sealed bag and allowed to equilibrate for 24 h to achieve a uniform target moisture content of ω = 18.4%. Thereafter, based on the desired dry density of ρ_d = 1.5 g/cm³, the necessary mass of wet soil was determined. The soil was then compacted in three layers using a compaction method, ensuring that each layer had an equal weight. Upon completion of the compaction process, the surface of each layer was shaved to create a cylindrical remolded loess sample with a diameter of 39.1 mm and a height of 80 mm.

2.2. Test Equipment

A high-low temperature test chamber designated as XT5402-TC400-R60 was utilized for the testing. The external dimensions of the test chamber are 860 mm × 960 mm × 1780 mm (W × L × H), while the internal dimensions are 700 mm × 700 mm × 800 mm, as illustrated in Figure 2a. The dynamic constant temperature control system design of the test chamber effectively meets the precise temperature control requirements across the entire range, achieving an optimal constant temperature fluctuation of ±0.5 °C. This makes it suitable for environmental condition testing within a temperature range of −60 °C to +100 °C. Additionally, the programmable temperature control function allows for automatic temperature adjustments.

The experiment employed the TSZ30-2.0 strain-controlled triaxial testing apparatus, which consists of three primary components: the testing machine (including the load cell, pressure chamber, elevating platform, sensors, etc.), the pressure control system, and the PC-based data acquisition system, as illustrated in Figure 2b. This apparatus is engineered to evaluate the strength and deformation properties of soil specimens subjected to axial static loading conditions. The triaxial apparatus can accommodate sample sizes of 39.1 mm × 80 mm and 61.8 mm × 125 mm, and it allows for controlling strain rates ranging from 0.0024 to 4.5 mm/min.

2.3. Test Scheme

The remolded loess samples wrapped in plastic wrap were placed in the high-low temperature test chamber. According the variation curve of annual daily minimum temperature in Xi ‘an City from 1970 to 2020 (Figure 3), the minimum value of annual daily minimum temperature was −16 °C and the maximum value was −5.4 °C. The freezing temperature was set to −5, −8, −12, and −16 °C, and the melting temperature was set to 25 °C. The samples were frozen for 12 h at low temperature and melted for 12 h at high temperature. A freeze-thaw cycle of 24 h was used to ensure full freezing and complete melting of the samples. The frequency of F-T cycles is established at 1, 5, 10, and 20, respectively.

Upon completion of the freeze-thaw cycle test, which achieved the predetermined number of cycles, the remolded loess samples were extracted. The plastic wrap that had been applied to the surface was subsequently removed, and the triaxial shear test was conducted. The confining pressures of triaxial shear tests were set to 100, 200 and 300, respectively. The shearing rate was controlled to 0.012%/min. The detailed freeze-thaw cycle and triaxial shear test protocols are shown in

Table 2. Scheme of F-T cycle test and triaxial shear test.

Test Number	Low Temperature (°C)	High Temperature (℃)	Number of F-T Cycles	Confining Pressure (kPa)
1-1	−5	25	1	100, 200, 300
1-5			5	100, 200, 300
1-10			10	100, 200, 300
1-20			20	100, 200, 300
2-1	−8	25	1	100, 200, 300
2-5			5	100, 200, 300
2-10			10	100, 200, 300
2-20			20	100, 200, 300
3-1	−12	25	1	100, 200, 300
3-5			5	100, 200, 300
3-10			10	100, 200, 300
3-10			20	100, 200, 300
4-1	−16	25	1	100, 200, 300
4-5			5	100, 200, 300
4-10			10	100, 200, 300
4-20			20	100, 200, 300

.

3. Experimental Results

3.1. Stress–Strain Characteristics

Figure 4 illustrates the stress–strain relationships of remolded loess samples subjected to various freezing temperatures, using 10 F-T cycles as a representative example. As can be seen from the figure, the stress–strain curves are similar in terms of the morphological distribution but show some local differences due to the different freezing temperatures. The stress–strain curves corresponding to each freezing temperature are all strain hardening, which indicates that the freezing temperature has little effect on the morphological characteristics of the stress–strain curves.

When the freezing temperature is higher than −12 °C, the deviatoric stress corresponding to the same strain gradually decreases as the freezing temperature drops. This indicates that lower freezing temperatures can compromise the soil structure and reduce soil strength. Conversely, when the freezing temperature falls below −12 °C, the deviatoric stress corresponding to the same strain gradually increases with decreasing temperature, although the variation range is relatively small. The yield strain of the reshaped loess samples at freezing temperatures of −5 °C, −8 °C, −12 °C, and −16 °C decreased from 1.5% to 0.5%. This indicates that the resistance to deformation gradually diminished as the freezing temperature decreased.

Figure 5 illustrates the stress–strain curves of remolded loess samples subjected to different F-T cycles (taking a freezing temperature of −12 °C as an example). It can be noted that the stress–strain curves associated with the various numbers of cycles demonstrate a general tendency towards strain hardening behavior. Only the stress–strain curve at 10 F-T cycles and a confining pressure of 100 demonstrates a slight softening. The findings suggest that the quantity of F-T cycles exerts minimal influence on the morphological properties of the stress–strain curve.

For a given confining pressure, the position of the stress–strain curve gradually decreases as the number of cycles increases. The deviatoric stress after 10 F-T cycles is slightly greater than that after 20 cycles, indicating that the initial number of F-T cycles significantly influences the stress–strain curve. However, this influence diminishes as the number of cycles increases. F-T cycles alter the structural characteristics of the soil, including its particles and pore structure, which in turn affects the soil’s strength and deformation properties. These changes in strength and deformation characteristics can be represented by the stress–strain curve. After 10 F-T cycles, the soil structure reaches a stable equilibrium state, and the stress–strain curve is no longer significantly affected by additional F-T cycles.

3.2. Failure Deviatoric Stress

The deviatoric stress corresponding to a 15% axial strain (ε₁), or peak deviatoric stress, is designated as the failure deviatoric stress (σ₁–σ₃)_f [36]. Figure 6 illustrates the relationship between failure deviatoric stress and freezing temperature (−5 °C, −8 °C, −12 °C, −16 °C) under various F-T cycles (1, 5, 10, 20). It is observed that as the freezing temperature decreases, the overall failure deviatoric stress also diminishes. Furthermore, the relationship exhibits a trend characterized by an initial decrease followed by an increase as the freezing temperature continues to decline. In the context of varying freeze-thaw effects, it was observed that as the freezing temperature decreased from −5 °C to −12 °C, the failure deviatoric stress of the sample exhibited a gradual decline. Conversely, when the temperature was further reduced from −12 °C to −16 °C, the failure deviatoric stress of the sample demonstrated a gradual increase. It can be inferred that the freezing temperature serves as a significant determinant of the deviatoric stress associated with sample failure. Notably, a freezing temperature of −12 °C emerges as the most detrimental, resulting in the most pronounced adverse effects on the deviatoric stress during F-T cycles.

As the number of F-T cycles escalates from 1 to 20, there is a marked reduction in the failure deviatoric stress of the sample subjected to a consistent freezing temperature. This observation suggests that an increase in the number of F-T cycles exacerbates the detrimental impact of freezing temperatures on the failure deviatoric stress of the sample. An elevation in confining pressure (σ₃) from 100 kPa to 300 kPa results in a substantial rise in the failure deviatoric stress of the sample subjected to identical freezing temperatures. This observation suggests that elevated confining pressure may mitigate the adverse effects of freezing temperatures on the failure deviatoric stress of the sample.

During the freezing process, the surface of the soil freezes first, causing the unfrozen water film on the surface of the ice crystals to become thinner. At this stage, the pore water pressure decreases, generating suction that causes the internal water in the soil to migrate to the surface, replenishing the thin unfrozen water film on the ice crystals. This process allows the ice crystals to expand continuously, and the freezing front gradually penetrates deeper into the soil, resulting in further freezing. When the soil thaws, the ice crystals on the surface melt first, causing a drop in pore water pressure within the soil and generating suction that allows soil water to migrate backward. This back-and-forth movement of soil moisture disrupts the soil structure. Uneven distribution of water within the soil can easily lead to the formation of a weak structural surface, which limits the overall strength of the soil. The F-T effect results in the continuous migration of water within the soil and ongoing changes to the soil structure, thereby affecting the soil’s strength behavior [37,38,39,40].

Figure 7 illustrates the correlation between failure deviatoric stress and the number of F-T cycles (1, 5, 10, 20) for remolded loess samples subjected to various freezing temperatures (−5 °C, −8 °C, −12 °C, −16 °C). The analysis indicates that the failure deviatoric stress of the remade loess sample exhibits an overall decline, characterized by an initial decrease followed by a stabilization as F-T cycles increase. As the cycles increased from 1 to 10, there was a progressive decline in the failure deviatoric stress of the sample. Subsequently, when the cycles rose from 11 to 20, the failure deviatoric stress exhibited a tendency to stabilize. It can be inferred that the frequency of F-T cycles serves as a significant determinant of the failure deviatoric stress of the sample. Furthermore, the observation that the failure deviatoric stress does not return to its original value after stabilization suggests that the damage inflicted on the sample by F-T cycles is irreversible.

3.3. Shear Strength Index

Figure 8 and Figure 9 illustrate the correlation between the shear strength parameters of the remolded loess samples, specifically, cohesion (c) and internal friction angle (φ), in relation to variations in freezing temperature. The data presented in the figure indicate that, under various cycles of F-T, the shear strength index of remolded loess samples exhibits a general decline. Notably, the reduction in c attributed to freezing temperatures is significantly more pronounced than the decrease observed in the φ. As the freezing temperature decreases, both the c and φ exhibit analogous patterns of variation, initially decreasing before subsequently increasing. When the freezing temperature ranges between −12 °C and −5 °C, both the c and φ exhibit a decline as the freezing temperature decreases. Conversely, within the range of −16 °C to −12 °C, both the c and φ increase as the freezing temperature decreases. Specifically, when comparing the freezing temperature of −5 °C to that of −12 °C, the average reductions in cohesion and internal friction angle are 7.39% and 1.19%, respectively. In contrast, when comparing −12 °C to −16 °C, the average increases in the c and φ are 1.95% and 0.41%, respectively. This indicates that −12 °C represents the most detrimental freezing temperature, at which the c and φ of the remolded loess sample reach their minimum values.

Figure 10 and Figure 11 illustrate the correlation between the shear strength index and F-T cycles under various freezing temperatures. Research indicates that the shear strength index of remolded loess samples generally declines at various freezing temperatures. Furthermore, the extent of deterioration in the c due to F-T cycles is markedly more pronounced than that observed in the φ. The c and φ exhibit analogous patterns of change in response to the increasing number of F-T cycles, demonstrating an initial decline followed by a stabilization phase. Notably, the reduction in c and the variability in the φ are more pronounced at elevated freezing temperatures. Prior to reaching 10 F-T cycles, both the c and φ experience significant variations across different freezing temperatures, with values ranging from 84.00 kPa to 73.93 kPa and 21.26° to 20.65°, respectively. On average, the c and φ decreased by 11.99% and 2.87%, respectively. Following 10 cycles of F-T, the alterations in cohesion and internal friction angle under varying freezing temperatures are minimal, with values ranging from 79.08 kPa to 73.00 kPa and 20.83° to 20.60°, respectively. The average reductions in the c and φ during this phase are 7.69% and 1.10%, respectively.

4. Quantitative Analysis

4.1. Effect of Quantitative Analysis on Failure Stress

To enhance the quantification of the effects of the temperature and F-T cycles on failure deviatoric stress, the concept of the stress reduction coefficient (K_σ) [41] is introduced. The formulation of the stress reduction coefficient is presented in Equation (1):

$$K_{\sigma }={\displaystyle \frac{{({\sigma }_1-{\sigma }_3)}_{\mathrm{f}}}{{({\sigma }_1-{\sigma }_3)}_{\mathrm{f}0}}}$$

(1)

where K_σ is the stress reduction coefficient; (σ₁ − σ₃)_f0 is the failure deviatoric stress at initial conditions; (σ₁ − σ₃)_f is the failure deviatoric stress under different freezing temperatures and F-T cycles.

The correlation between the stress reduction coefficient (K_σ) and the freezing temperature (T) can be described by Equation (2). The fitting results are illustrated in Figure 12, and the corresponding fitting parameters are detailed in

Table 3. Fitting parameters of Kσ and T.

Confining Pressure	F-T Cycles	A1	A2	A3	R2
100 kPa	1	1.13171	0.03333	0.00129	0.97704
	5	1.11959	0.02976	0.00118	0.99960
	10	1.10368	0.02622	0.00110	0.99994
	20	1.10584	0.02676	0.00116	0.98896
200 kPa	1	1.11778	0.02969	0.00124	0.99950
	5	1.07335	0.01896	0.00077	0.94388
	10	1.06422	0.01608	0.00066	0.99669
	20	1.08434	0.02193	0.00094	0.96299
300 kPa	1	1.10042	0.02549	0.00099	0.97400
	5	1.08792	0.02221	0.00090	0.99533
	10	1.07143	0.01801	0.00076	0.99742
	20	1.08054	0.02054	0.00090	0.99687

.

$$K_{\sigma }=A_1+A_{2}T+A_3{T}^2$$

(2)

where A₁, A₂, and A₃ are the fitting parameters.

The correlation between the stress reduction coefficient (K_σ) and the F-T cycles (N) can be described by Equation (3). The fitting results are illustrated in Figure 13, and the corresponding fitting parameters are detailed in

Table 4. Fitting parameters of Kσ and N.

Confining Pressure	Temperature	B1	B2	B3	R2	RSS
100 kPa	−5 °C	0.91733	0.09549	7.35857	0.99606	1.32 × 10−5
	−8 °C	0.94200	0.06526	10.24322	0.98075	2.69 × 10−5
	−12 °C	0.94789	0.05924	7.53427	0.99884	1.48 × 10−6
	−16 °C	0.97263	0.03156	7.22874	0.99893	3.90 × 10−7
200 kPa	−5 °C	0.95603	0.0554	4.69084	0.96076	4.68 × 10−5
	−8 °C	0.95877	0.04522	9.65966	0.99393	4.14 × 10−6
	−12 °C	0.96465	0.03942	21.20856	0.81459	6.17 × 10−5
	−16 °C	0.97181	0.03525	4.61872	0.99362	2.97 × 10−6
300 kPa	−5 °C	0.93767	0.07366	6.37583	0.99294	1.44 × 10−5
	−8 °C	0.95655	0.04862	9.09249	0.99968	2.56 × 10−7
	−12 °C	0.95960	0.04593	7.79612	0.9999	1.07 × 10−10
	−16 °C	0.97897	0.02497	5.97741	0.99832	3.95 × 10−7

.

$$K_{\sigma }=B_1+B_2{e}^{-{\displaystyle \frac{N}{B_3}}}$$

(3)

where B₁, B₂, and B₃ are the fitting parameters.

4.2. Effect of Quantitative Analysis on Shear Strength Index

Considering the impact of freezing temperature (T) and F-T cycles on the shear strength index, the cohesion © can be fitted and analyzed using Equation (4). The fitting results are illustrated in Figure 14 and

Table 5. Fitting parameters.

Temperature (°C)	C1	C2	C3	m	R2
−5	84.00	77.75	6.33673	3	0.99079
−8	78.66	74.69	7.54184	3	0.98114
−12	76.36	73.00	6.90083	3	0.98218
−16	77.42	74.97	5.93750	3	0.99072

.

$$y={\displaystyle \frac{C_1-C_2}{1+{(\frac{x}{C_3})}^m}}+C_2$$

(4)

where y represents c; x represents F-T cycles; C₁, C₂, C₃, and m represent fitting parameters.

Based on the fitting parameters of c detailed in Table 5, it is evident that the association between C₁, C₂, and C₃ with freezing temperature conforms to the quadratic polynomial model, as illustrated in Equation (5). The fitting results are presented in Figure 15.

$$y=D_1+D_{2}x+D_3{x}^2$$

(5)

where y represents C₁, C₂, and C₃; x represents the freezing temperature; D₁, D₂, and D₃ represent fitting parameters.

Based on the fitting results, the relationships between the fitting parameters of cohesion (C₁, C₂, and C₃) and freezing temperature (T) are presented in Equations (6)–(8).

$$C_1=97.38352+3.36428T+0.13260T^2$$

(6)

$$C_2=87.30247+2.41211T+0.10245T^2$$

(7)

$$C_3=3.62885-0.76193T-0.03893T^2$$

(8)

5. Conclusions and Prospects

5.1. Conclusions

(1) The temperature and F-T cycles have little impact on the morphological characteristics of the stress–strain curves. A decrease in freezing temperature alters the yield strain of loess and reduces its resistance to deformation. Additionally, the effect of F-T cycles on the stress–strain curve of loess diminishes as the number of cycles increases.

(2) As the temperature of freezing decreases and F-T cycles increase, the failure deviatoric stress in loess demonstrates a pattern characterized by an initial decline, followed by an increase, and ultimately a state of stabilization. The most adverse freezing temperature is −12 °C, which markedly exacerbates the effects of freeze-thaw cycles on the degradation of failure deviatoric stress. Freezing temperatures ranging from −5 °C to −12 °C exacerbate the negative effects of the number of F-T cycles on failure deviatoric stress, while temperatures between −12 °C and −16 °C can inhibit or counteract this deterioration.

(3) The cohesion (c) and internal friction angle (φ) of loess exhibit a trend of initially decreasing and then increasing as the freezing temperature decreases. Additionally, they show a trend of first decreasing and then stabilizing with an increase in the number of F-T cycles. Notably, the degree of deterioration in cohesion is significantly greater than that of the internal friction angle. Compared to a freezing temperature of −5 °C, the c and φ decrease by an average of 7.39% and 1.19%, respectively. In contrast, when compared to a freezing temperature of −12 °C, the c and φ increase by an average of 1.95% and 0.41%, respectively. After 10 cycles of F-T, the c decreases by an average of 11.99% and 7.69%, while the φ decreases by an average of 2.87% and 1.10%.

(4) The relationship between the stress reduction coefficient (K_σ) and both the freezing temperature and the number of F-T cycles is best fitted by a quadratic polynomial model and an exponential model, respectively. The fitting results effectively quantify the impact of the temperature and F-T cycles on the failure deviatoric stress.

(5) Considering the effects of freezing temperatures and F-T cycles, both the logistic model and the quadratic polynomial model are employed to quantitatively analyze c. The fitting results effectively quantify the impact of freezing temperatures (T) and F-T cycles (N) on shear strength index.

5.2. Prospects

(1) This study focuses solely on the evolution of the mechanical properties of loess in response to changes in freezing temperature. However, melting temperature may also impact the stress–strain curve, failure deviatoric stress, and shear strength index of loess. The next step should involve a comprehensive analysis of how both melting and freezing temperature variations affect the strength characteristics of loess.

(2) At present, this study has only conducted research on the loess of Xi’an under the regional temperature conditions of Xi’an. The next step should involve conducting research on loess in various areas of Northwest China under different temperature conditions.

(3) Only macroscopic mechanical properties were examined in this study. In the next phase, the structural changes in the soil under varying freeze-thaw conditions should be analyzed both qualitatively and quantitatively from a microscopic perspective by incorporating microscopic testing methods.

(4) At present, this study is limited to the experimental stage as conducted in the laboratory. The next step should involve selecting representative projects and performing specific engineering simulation analyses based on the quantitative formulas derived from the tests and utilizing numerical analysis software.