Fatigue damage evolution mechanism of sandstone under Freeze–Thaw and loading rate coupling based on NMR and AE techniques

The influence of freeze-thaw damage effects on the fatigue mechanical response characteristics and damage mechanisms of sandstone was examined. Three loading rates (0.2, 0.4, and 0.6 kN/s) and four freeze-thaw cycles (0, 15, 30, and 45 cycles) were used in cyclic loading-unloading tests to accomplish this. The sandstone’s physical parameters, pore structure evolution, stress-strain behavior, and microcrack propagation characteristics were all carefully examined using nuclear magnetic resonance and acoustic emission techniques. The findings showed that the mass of saturated sandstone rose by 0.26% over the first 15 freeze-thaw cycles. However, the mass dropped by 0.17% and 1.01%, respectively, when the number of freeze-thaw cycles reached 30 and 45. The percentage of macropores increased from 45% to 63% after 45 cycles, suggesting that frost heave forces encouraged the spread of microcracks and the formation of linked fissures, which progressively weakened the structure. The loading rate also played a big influence. In comparison to a rate of 0.2 kN/s, a greater loading rate (0.6 kN/s) reduced slow crack development, increasing the cyclic strength by 14.8%. The strength degradation rate surpassed 24% when the number of freeze-thaw cycles reached 30 or more, indicating that even at high loading rates, freeze-thaw damage continued to be the primary cause. Microcracks started to appear at 15 cycles, with tensile cracks outnumbering shear cracks. However, the percentage of shear cracks rose with increasing loading rates, almost equaling or even exceeding that of tensile cracks. The connectivity between pores and cracks greatly improved with 30 and 45 cycles, and high loading rates were more likely to induce rapid and abrupt instability behavior by favoring shear crack dominance. Under identical freeze-thaw circumstances, increasing loading rates increased the ratio of shear cracks, demonstrating that local stress distributions altered crack propagation routes. This study provides theoretical insights for evaluating the stability of rock engineering in cold climates by elucidating how loading rates and cyclic freeze-thaw processes govern the fatigue mechanical behavior of sandstone.

1 Introduction

As open-pit mining operations in cold climates continue to grow, rock masses often experience the combined effects of periodic loading and unloading during real service as well as periodic freezing and thawing. Through the frost heaving force produced by pore water phase change, the freeze-thaw cycle initiates and spreads microcracks inside the rock mass, severely reducing the rock mass’s durability, compressive strength, and elastic modulus (Han et al., 2024; Huang et al., 2022b; Feng et al., 2022). Meanwhile, by altering the stress route, the cyclic loading and unloading loads brought about by excavation disturbances have an impact on the crack propagation pattern (Zhou et al., 2024). The difference in loading rate directly impacts the mechanical response characteristics and failure mechanism of the rock mass. The superposition of these two mechanisms exacerbates the damage accumulation process of engineering rock formations, posing a major threat to their structural stability. Therefore, examining the impact of freeze-thaw damage on the fatigue mechanical response characteristics and damage process of sandstone under varied loading rates is of major scientific interest and application value for the stability evaluation of rock mass engineering in cold climates.

In recent years, the evolution of pore structure, microscopic damage development, and energy dissipation patterns of rocks under cyclic freezing and thawing conditions have been systematically studied by combining experiments with numerical simulation (Feng et al., 2022; Zhang J. et al., 2024; Gao et al., 2020; Zhang et al., 2025a; b; Kun et al., 2025; Fu et al., 2023; Hu and Yang, 2020; Qiu et al., 2025). Substantial research achievements have been made. The research results indicate that with the increase in the number of cyclic freezing and thawing cycles, the uniaxial compressive strength, tensile strength, and shear strength of rocks all show a significant downward trend (Chen et al., 2014; Zhang et al., 2022). Different types of rocks exhibit varying sensitivities to cyclic freezing and thawing, which is primarily related to factors such as the mineral composition, pore structure, and water absorption of the rocks. For instance, rocks containing more hydrophilic minerals are more prone to damage and deterioration during cyclic freezing and thawing (Huang et al., 2022a; Zhao et al., 2022). This is because hydrophilic minerals adsorb more water, thereby exacerbating the destructive effects of frost heaving forces on the rocks. Advanced detection techniques such as CT scanning and NMR reveal the progressive characteristics of freezing and thawing damage (Zhang L. et al., 2024; Yang et al., 2024). The initial stages of freezing and thawing mainly manifest as adjustments in the internal pore structure of the rocks and the initiation of local microcracks. When the number of freezing and thawing cycles exceeds a critical value, the internal crack network of the rocks gradually connects and forms dominant fracture surfaces, ultimately leading to significant deterioration in the macroscopic mechanical properties of the rocks (Liu et al., 2025; Huang et al., 2025). It has also been found that there is a significant correlation between the critical threshold of energy accumulation-release during freezing and thawing and the spatiotemporal evolution of internal defects in the rocks (Gao et al., 2020; Song et al., 2024). This provides a new theoretical perspective for explaining the mechanism of freezing and thawing damage.

Numerous experimental studies have demonstrated that variations in loading rate significantly impact the strength, deformation characteristics, and failure modes of rocks (Zou et al., 2024; Wei et al., 2022; Zhang et al., 2018; Zhang and Wong, 2013). In comparison, as the loading rate increases, the strength of rocks gradually rises, and the elastic modulus also improves. Under high-speed loading conditions, the crack propagation within the rock is constrained by inertial effects (Guo et al., 2023; Woo et al., 2025). The crack propagation speed is relatively slow, enabling the rock to withstand greater loads. An increase in loading rate also leads to enhanced brittleness of rocks. The plastic deformation stage is shortened. When the loading rate is low, rocks undergo significant plastic deformation during the stressing process, exhibiting ductile failure characteristics. However, when the loading rate is high, rocks reach peak strength and fail within a short period of time. Plastic deformation is not fully developed, exhibiting obvious brittle failure characteristics (Lee et al., 2016). Low-rate loading allows the crack system to form a complex damage network through bifurcation and turning. High-rate loading, on the other hand, enhances rock strength by limiting the slow expansion of cracks, but it exacerbates local energy accumulation. Currently, research on the impact of loading rate on the mechanical properties of rocks has yielded considerable results. However, there are still many issues to be further investigated regarding the intrinsic relationship between loading rate and changes in rock microstructure, as well as the mechanical response characteristics of rocks under complex loading conditions.

Existing research has primarily focused on studies of single mechanisms. There is a lack of systematic exploration into the fatigue behavior of sandstone under conditions of freeze-thaw damage and different loading rates (Song et al., 2022). Specifically, certain achievements have been made in the study of pore structure evolution and microcrack propagation characteristics induced by cyclic freeze-thaw (Cao et al., 2018; Ma et al., 2022). Additionally, the mechanisms of damage evolution and crack propagation during cyclic loading and unloading have been partially revealed (Wang et al., 2025; Chen et al., 2024; Li et al., 2021; Wang et al., 2021). However, a comprehensive theoretical framework for the interaction mechanism between the two has not yet been established. Consequently, the regulatory effects of different loading rates on the fatigue mechanical response of sandstone under freeze-thaw damage and its underlying mechanisms remain unclear. This not only constrains our understanding of rock mass failure patterns in complex environments but also affects the scientific nature of engineering safety design and risk prevention and control.

This study aims to clarify the mechanism of microstructural changes and crack evolution induced by cyclic freeze-thaw, as well as the regulatory effect of loading rate on the crack propagation process. This, in turn, clarifies the fatigue damage mechanism of sandstone under the combined action of these two factors. A thorough analysis of the fatigue response of sandstone under different loading rates under cyclic freeze-thaw conditions is conducted through laboratory tests. Consequently, the research findings can provide a theoretical basis for rock mass stability assessment and safety design in open-pit mining projects in cold regions.

2 The test material and solution

2.1 Test materials

This study focuses on natural sandstone as the research object. Standard specimens were prepared in accordance with the specifications of the International Society for Rock Mechanics (ISRM). Systematic physical and mechanical property tests were conducted. The samples were taken from the same fresh rock block. Visual inspection and hammering methods were used to eliminate surface cracks, bedding, and other defects. Diamond drill bits were used to process them into φ50 mm × 100 mm standard cylinders. The parallelism of the end faces of the rock specimens was tested. The error was strictly controlled within ±0.02 mm to ensure uniform transmission of axial load.

X-ray diffraction analysis (Figure 1) reveals that the mineral composition of the sample primarily consists of quartz (45.3%), feldspar (28.7%), and mica (12.5%). Additionally, it contains a high content of hydrophilic clay minerals, specifically kaolinite (9.2%) and illite (4.3%). This unique mineral composition not only directly affects the physical and mechanical properties of sandstone. The moisture adsorption-desorption effect of hydrophilic minerals during cyclic freeze-thaw processes significantly exacerbates rock damage and deterioration.

Figure 1

Figure 1. Diffraction pattern of mineral composition.

Before the experiment, basic physical parameters such as dimensions, mass, and wave velocity of all rock specimens were measured. The average mass was approximately 489.25 g, the average density was approximately 2.35 g/cm³, and the longitudinal wave velocity was approximately 2,108 m/s. Based on the mass-wave velocity dual-parameter control method, specimens with similar physical properties were selected. The coefficient of variation was below 3%, significantly reducing the interference of material heterogeneity on the experimental results. Through the standardized sample preparation process and strict screening criteria mentioned above, a highly reliable experimental sample system was constructed. This laid a solid foundation for revealing the fatigue damage evolution mechanism of sandstone under the combined action of freezing-thawing and loading-unloading.

2.2 Freeze-thaw cycles test scheme

After completing the screening and numbering of sandstone specimens, a saturation test was conducted on the sandstone specimens using the vacuum saturation method. The specimens were placed in a dedicated saturation container and filled with an appropriate amount of distilled water until the surface of the specimens was completely submerged. The vacuum pump system was connected. And a constant pressure of 0.1 MPa was applied, followed by continuous air extraction for 4 h. During the air extraction process, the state of bubble evolution was monitored in real-time through a transparent observation window. The specimens were deemed to have reached saturation when the bubbles completely disappeared. After the air extraction was completed, the specimens were soaked under constant pressure for more than 24 h to ensure that the internal pores of the sandstone specimens were filled with water.

Environmental simulation experiments were conducted using an open-cycle freeze-thaw testing machine. Based on the typical climatic characteristics of open-pit mines, the freezing temperature was set at −20 °C (±1 °C) and the thawing temperature at 20 °C (±1 °C), with a single cycle period of 24 h (12 h for freezing and 12 h for thawing). The experiment was set up with four freeze-thaw gradients: 0, 15, 30, and 45 cycles.

To improve the engineering relevance of the selected freeze–thaw (F–T) cycle numbers, we relate the laboratory cycles to seasonal climatic exposure in cold regions. Field-scale freeze–thaw action is commonly characterized by the annual frequency of ground-surface freeze–thaw events, which varies with regional temperature fluctuations and moisture conditions (Zhang J. et al., 2024). In laboratory simulation, freeze–thaw processes are commonly simulated by applying repeated freezing and thawing cycles under controlled temperature conditions to reproduce long-term climatic action (Chen et al., 2014; Zhou et al., 2024). Therefore, the selected cycle numbers (0, 15, 30, and 45) are intended to represent progressive stages of F–T exposure: 0 cycles correspond to intact rock prior to climatic action, 15 cycles represent an early-stage exposure level, 30 cycles represent a medium exposure stage with accumulated damage, and 45 cycles represent a severe exposure stage. Similar cycle ranges and stepwise gradients have been widely used in rock F–T studies to capture progressive deterioration and damage evolution (Chen et al., 2014; Liu et al., 2025; Zhou et al., 2024). This design enables systematic investigation of the staged evolution of physical parameters, pore structure, and mechanical degradation of sandstone under cyclic F–T conditions.

All specimens underwent freeze–thaw (F–T) cycling under saturated conditions. During thawing, specimens were immersed in distilled water in sealed containers to minimize evaporation. The water level was checked once per cycle (every 24 h) at the start of thawing and replenished to keep the water surface 10–20 mm above the specimen; the typical replenishment volume was 50–150 mL per container per cycle. This procedure ensured saturation throughout F–T cycling (Figure 2).

Figure 2

Figure 2. A roadmap for the research programmer.

The Macro MR12-150H-I low-field nuclear magnetic resonance system was employed for pore characteristic analysis. Samples were taken for testing at the freeze-thaw cycles of 5, 10, 15, 20, 25, 30, 35, 40, and 45. These intermediate-cycle NMR measurements were performed to track the continuous evolution of pore structure throughout the freeze–thaw process and to identify possible damage-transition thresholds (e.g., accelerated pore coarsening or connectivity enhancement). In contrast, mechanical tests were conducted at 0, 15, 30, and 45 cycles as representative exposure stages to evaluate strength degradation at key points along the freeze–thaw damage trajectory. The testing environment was strictly controlled at a temperature of (20 ± 1)°C and a humidity of (50 ± 5)%. A dedicated constant temperature and humidity chamber was used to maintain the saturation state of the specimens. Pore distribution characteristic parameters were obtained through inversion of the T₂ spectrum. The system analyzed the dynamic evolution law of sandstone pore structure under the effect of cyclic freeze-thaw.

2.3 Loading test scheme

This experiment utilizes the RMT-150C rock mechanics testing machine for quasi-static loading tests. The machine boasts a displacement control accuracy of 0.001 mm/s and a force control accuracy of 0.1 kN/s, meeting high-precision loading requirements. Based on the stress control mode, three loading rate gradients of 0.2, 0.4, and 0.6 kN/s are set.

The loading rates of 0.2, 0.4, and 0.6 kN/s were selected to represent three typical quasi-static stress-controlled disturbance intensities while ensuring stable control accuracy and reliable acquisition of stress–strain and AE signals. These rates are within the commonly adopted range in laboratory cyclic loading–unloading studies on rocks, enabling systematic comparison of rate effects while avoiding dynamic impact conditions. In practical open-pit mining and slope engineering, rock masses are repeatedly disturbed by excavation, blasting-induced stress redistribution, and operational activities, which can be idealized as intermittent loading–unloading processes with different disturbance intensities. Therefore, the adopted graded cyclic loading scheme, in which the peak stress is increased stepwise while unloading to a baseline stress between stages, is intended to simulate progressive stress accumulation and repeated disturbance in engineering conditions and to capture the staged evolution of fatigue damage and crack propagation. It should be noted that these loading rates are not direct in-situ measurements of mining-induced stress rates; rather, they are laboratory-controlled proxies used to represent different disturbance intensities under quasi-static conditions. During system commissioning, we confirmed that stable force control and reliable AE acquisition could be achieved at these three rates for the present specimen size and strength level.

The study focuses on the impact of loading rate on the mechanical behavior of sandstone. A graded cyclic loading strategy is employed during the loading process. The first level is loaded to 2.5 MPa and then unloaded to the baseline stress of 0 MPa. The second level is loaded to 5 MPa and then unloaded repeatedly. Each subsequent level is incrementally increased by 2.5 MPa until the specimen is damaged.

The AE signals are collected using the PCI-II AE system developed by American Physical Acoustics Corporation. A 40 dB gain preamplifier is configured to enhance the signal-to-noise ratio. The system sampling frequency is set to 10 MSPS. It can fully capture the micro-fracture AE signals in the characteristic frequency band of 10–1,000 kHz. The AE sensor array adopts a four-channel spatial positioning topology. R6α broadband sensors (frequency range 50–800 kHz) are symmetrically arranged in a 120° circumferential direction in the middle of the test piece. The sensor coupling uses a high-conductivity acoustic silicone grease medium to ensure that the acoustic wave transmission efficiency is over 95%. Prior to formal testing, sensor coupling and system configuration were verified through standard calibration procedures to ensure reliable signal acquisition and acceptable source localization accuracy for crack evolution analysis (Zhou et al., 2024).

3 Freeze-thaw cycles on physical properties of sandstone

3.1 Quality change characteristics of sandstone

During the cyclic freeze-thaw process, the mass change of sandstone in a saturated state serves as one of the crucial indicators for characterizing the evolution of its internal structural damage. Table 1 presents the mass measurement results of saturated sandstone specimens subjected to varying numbers of freeze-thaw cycles.

Table 1

Table 1. Measurement results of saturated sandstone specimens under different freeze-thaw cycles.

As shown in Table 1, the sandstone specimens exhibited an increase in quality during the initial stage of cyclic freeze-thaw. The initial average quality of 512.27 g increased to 513.62 g after 15 cycles, with a quality change rate of +0.26%. This quality increase is attributed to the adjustment of pore structure during the freeze-thaw process. During the freezing phase, the volume expansion resulting from the phase transition of pore water (with ice density being approximately 9% lower than that of water) triggers a coupled frost heaving and shear stress effect. This drives the migration of free water towards unfilled micropores, promoting the filling effect of water migration in rock pores. When the number of freeze-thaw cycles increases to 30, the average mass of the specimens decreases to 511.45 g, with the quality change rate turning negative at −0.17%. The deterioration of pore sorting leads to improved hydraulic connectivity. At this point, the tensile-shear composite stress field generated by the frost heaving force causes the expansion of primary fractures. The debris particles generated by structural disintegration are lost with the pore water during the melting phase. After 45 cycles, the quality of the specimens drops sharply to 507.10 g (with a mass loss rate of approximately −1.01%).

This quality loss is primarily attributed to the cumulative damage to the internal structure of the rock caused by repeated freeze-thaw cycles. Under the influence of frost heaving forces, pores and fractures continuously expand and connect, leading to a gradual loosening of the structure. During the melting phase, pore water is more prone to loss. Simultaneously, surface particles shed due to the loosening of the structure. The pattern of quality change indicates that the effects of cyclic freeze-thaw on sandstone exhibit distinct phased characteristics. Initially, there is an increase in quality, reflecting the adjustment process of the internal structure of the rock. Later, it manifests as a loss of quality, visually reflecting the damage and deterioration of the internal structure. This characteristic of quality change provides an important basis for further studying the evolution of the physical and mechanical properties of sandstone under cyclic freeze-thaw conditions.

3.2 Pore structure evolution law of sandstone specimen

NMR technology provides an effective research method for exploring the evolution of sandstone pore structure under cyclic freeze-thaw conditions. Based on the NMR test results of sandstone specimens subjected to different numbers of freeze-thaw cycles, this study quantitatively analyzes key pore structure parameters such as porosity and pore size distribution through relaxation time T₂ spectroscopy. Figure 3 illustrates the variation pattern of sandstone porosity under different numbers of freeze-thaw cycles.

Figure 3

Figure 3. Evolution characteristics of sandstone pore structure under different freeze-thaw cycles. (a) Pore distribution characteristics, (b) porosity change characteristics.

It should be noted that the pore size classification adopted in this study is based on an operational T₂-range definition rather than a universal pore-radius criterion. Specifically, the T₂ spectrum is divided into three ranges: 0.001–10 m corresponding to micropores, 10–100 m corresponding to mesopores, and 100–10000 m corresponding to macropores. Although pore-size terminology and threshold values vary among different studies, the above T₂-based classification is explicitly defined and consistently applied throughout this work to ensure reproducibility and facilitate relative comparison under identical NMR testing conditions (Zhang et al., 2025).

As shown in Figure 3, the porosity of sandstone demonstrates a notable nonlinear growth pattern with the increasing number of freeze-thaw cycles. During the initial freeze-thaw phase (0-15 cycles), the cumulative increase in porosity is merely 1.28%. This phase is primarily influenced by the limited expansion of primary pores. The structural stability is maintained due to the cementation between quartz particles. The response of the pore system to frost heaving stress exhibits a gradual development characteristic. After the number of cycles exceeds 15, the pore evolution enters an accelerated growth phase. After 30 freeze-thaw cycles, the porosity increases by 4.07% compared to the initial value. The increase reaches 26.79% at 45 cycles. This nonlinear mutation characteristic is closely related to the expansion behavior of the microcrack system. The cumulative damage caused by repeated phase transitions leads to the penetration of microcracks between particles, forming a secondary pore network. The volume expansion effect of pore water during freezing (approximately 9%) continuously acts on the existing primary pores, promoting a shift in pore size distribution towards larger pores. It is worth noting that the internal porosity of the sandstone specimen significantly increases after 40 freeze-thaw cycles, indicating that the internal freeze-thaw damage effect of sandstone is relatively significant currently.

Quantitative analysis based on pore size distribution characteristics reveals that cyclic freeze-thawing significantly alters the topological structure of the sandstone pore system (Figure 4). In the initial state, the pore system is predominantly composed of micro-pores and meso-pores, accounting for 55% of the total. Macro-pores make up 45%. Following 15 cycles of freeze-thawing, the proportion of micro-pores and meso-pores climbs to 56%. When the number of cycles escalates to 45, the proportion of macro-pores surges to 63%, marking an increase of 19% compared to the 15-cycle stage. This pore coarsening effect demonstrates a typical three-stage evolution pattern. In the initial stage (0-15 cycles), cumulative damage resulting from phase transitions of micro-pore water leads to the detachment of intergranular cement, thereby forming isolated secondary pores. In the transition stage (15-30 cycles), the connectivity of the pore network enhances, and the T₂ spectrum indicates an accelerated rate of transformation from mesopores to macropores. In the drastic change stage (30-45 cycles), upon exceeding the percolation threshold, dominant seepage channels emerge, and the volume fraction of macropores increases exponentially.

Figure 4

Figure 4. Evolution characteristics of sandstone pore size under different freeze-thaw cycles.

4 Fatigue mechanical properties and crack evolution characteristics of freeze-thawed sandstone under different loading rates

4.1 Characteristics of stress-strain curve

A series of stress-strain curves were obtained through graded cyclic loading tests conducted on sandstone under various conditions, including different numbers of freeze-thaw cycles and loading rates. Figure 5 illustrates the stress-strain curves of sandstone specimens subjected to different freeze-thaw cycles and a loading rate of 0.2 kN/s.

Figure 5

Figure 5. Stress-strain curve of sandstone specimen with loading rate of 0.2 kN/s under different freeze-thaw cycles.

As depicted in Figure 5, the cyclic loading-unloading strength of sandstone specimens demonstrates a notable nonlinear attenuation trend as the number of freeze-thaw cycles increases. The cyclic loading-unloading strength of unfrozen sandstone specimens stands at 14.45 MPa. However, after 15 freeze-thaw cycles, its strength drops to 13.73 MPa, representing a decrease of approximately 6.92%. As the number of freeze-thaw cycles increases to 30 and 45, the cyclic loading-unloading strength of sandstone specimens decreases to 12.64 MPa and 10.05 MPa, respectively. The corresponding decreases expand to 12.52% and 30.44%. The cumulative damage effect caused by cyclic freeze-thawing exacerbates the deterioration of the sandstone microstructure, which is the fundamental reason for the continuous attenuation of its bearing capacity. Cyclic freeze-thawing significantly weakens the energy dissipation capacity of sandstone. Unfrozen sandstone specimens exhibit a large hysteresis loop area during the graded loading process, indicating that the material possesses excellent elastic recovery capacity and energy storage performance. As the number of freeze-thaw cycles increases, the hysteresis loops gradually become sparser. When the number of freeze-thaw cycles reaches 30, the slope of the unloading path significantly increases, reflecting an intensified accumulation of irreversible deformation. After 45 freeze-thaw cycles, it is indicated that energy is mainly released through crack propagation rather than plastic deformation. This transition confirms that freeze-thawing exacerbates the inter-particle cementation failure through the crystallization pressure generated by pore water phase transition, promoting the development of a connected microcrack network, ultimately leading to the simultaneous deterioration of the material’s mechanical properties and energy absorption capacity. Figure 6 illustrates the stress-strain curves of sandstone specimens under different freeze-thaw cycles at a loading rate of 0.4 kN/s.

Figure 6

Figure 6. Stress-strain curve of sandstone specimen with loading rate of 0.4 kN/s under different freeze-thaw cycles.

As shown in Figure 6, cyclic freeze-thawing has a significant deteriorating effect on the cyclic loading-unloading strength of sandstone. The cyclic loading-unloading strength of sandstone specimens without freeze-thawing is 16.49 MPa. As the number of freeze-thaw cycles increases, the cyclic loading-unloading strength gradually decreases, reducing to 15.28 MPa (after 15 freeze-thaw cycles), 12.75 MPa (after 30 freeze-thaw cycles), and 10.92 MPa (after 45 freeze-thaw cycles), respectively. Among them, the impact of 15 freeze-thaw cycles on the cyclic loading-unloading strength is relatively minor. However, when the number of freeze-thaw cycles reaches 30 or more, the rate of decay in cyclic loading-unloading strength accelerates, indicating that the gradual accumulation and weakening of microcracks caused by cyclic freeze-thawing gradually reduce the load-bearing capacity of sandstone. Under conditions without freeze-thawing or with minimal freeze-thawing (15 cycles), sandstone still exhibits certain strain hardening characteristics during cyclic loading. The slope of the curve does not significantly decrease at high stress levels. However, when the number of freeze-thaw cycles reaches 30 or more, the slope of the curve significantly decreases. After 45 freeze-thaw cycles, the curve exhibits obvious strain softening. The above experimental results indicate that freeze-thaw damage increases the number of microcracks within sandstone and weakens the material’s plastic deformation capacity, ultimately leading to a transition from ductile failure to brittle failure. Compared with the experimental results obtained at a loading rate of 0.2 kN/s, the cyclic loading-unloading strength of sandstone at a loading rate of 0.4 kN/s is generally higher, indicating that an increase in loading rate inhibits the expansion of some microcracks, resulting in higher cyclic loading-unloading strength of the rock. However, the deteriorating effect of freeze-thawing on the cyclic loading-unloading strength of sandstone remains significant. Especially when the number of freeze-thaw cycles reaches 30 or more, the decrease in cyclic loading-unloading strength becomes more pronounced, indicating that the microscopic damage caused by freeze-thawing still dominates the failure process under higher loading rates. Figure 7 shows the stress-strain curves of sandstone specimens at a loading rate of 0.6 kN/s under different freeze-thaw cycles.

Figure 7

Figure 7. Stress-strain curve of sandstone specimen with loading rate of 0.6 kN/s under different freeze-thaw cycles.

As depicted in Figure 7, cyclic freeze-thawing significantly diminishes the cyclic loading-unloading strength of sandstone. However, this effect is influenced by the loading rate. The cyclic loading-unloading strengths of the samples under different freeze-thaw cycles are as follows: 17.55 MPa (0 freeze-thaw cycles), 16.01 MPa (15 freeze-thaw cycles, approximately 8.78% lower than that of 0 cycles), 13.23 MPa (30 freeze-thaw cycles, approximately 24.61% lower than that of 0 cycles), and 12.70 MPa (45 freeze-thaw cycles, approximately 27.64% lower than that of 0 cycles). Compared to a loading rate of 0.4 kN/s, the cyclic loading-unloading strength under various freeze-thaw conditions are all improved at a loading rate of 0.6 kN/s. This indicates that a faster loading rate inhibits the expansion of some cracks, resulting in higher strength of sandstone. Cyclic freeze-thawing changes the strain evolution mode of sandstone. Samples without freeze-thawing or with minimal freeze-thawing (0 and 15 cycles) still exhibit certain strain hardening characteristics during cyclic loading. That is, the slope of the curve does not significantly decrease at high stress levels. However, as the number of freeze-thaw cycles increases (30 cycles and above), the slope of the curve significantly decreases, indicating that the material enters a strain softening stage. This is manifested as a shortened elastic phase and enhanced plastic deformation. Freeze-thaw damage increases the number of micro-cracks within sandstone, weakening the material’s plastic deformation capacity and ultimately leading to an evolution from ductile failure to brittle failure.

4.2 Micro-crack evolution characteristics

During the deformation and failure process of rocks, the elastic strain energy stored internally is instantly released in the form of elastic waves, leading to AE phenomena. Therefore, AE signals can effectively indicate the development of internal microcracks (Meng et al., 2016). As a non-destructive testing technique, AE is widely applied in monitoring fields such as rock crack propagation and damage identification. During the development of shear cracks and tensile cracks, rocks generate different modes of AE signals, resulting in significant differences in the waveform characteristics of AE signals (Zhao et al., 2024). The RA value (the ratio of rise time to amplitude) and AF value (average frequency) of AE signals are key parameters for describing waveform characteristics (Du et al., 2020; Chen et al., 2022). AE signals associated with the formation of tensile cracks have relatively short rise times and durations, while their amplitudes and ringing counts are relatively large, as shown in Figure 8. Conversely, AE signals associated with the formation of shear cracks exhibit opposite characteristics (Xiao et al., 2023). The definitions of the RA and AF values of AE signals are as Equations 1, 2 (Zhao et al., 2024; Yue et al., 2020).

$\text{RA value}=\frac{\text{Rise}\text{Time}\left(\text{RT}\right)}{\text{Maximum}\text{Amplitude}\left(\text{MA}\right)}(1)$

$\text{AF value}=\frac{\text{AE}\text{Counts}\left(\text{AC}\right)}{\text{Duration}\text{Time}\left(\text{DT}\right)}(2)$

Figure 8

Figure 8. Crack growth mode classification based on AF/RA index analysis.

Where, RT represents the rise time of the AE waveform, measured in ms. MA denotes the amplitude, expressed in dB. AC stands for the AE ringing count, and DT signifies the duration of AE, also measured in ms.

The effectiveness of RA–AF parameters for distinguishing tensile and shear crack modes has been widely validated in acoustic emission studies, with tensile cracking generally associated with lower RA and higher AF values and shear cracking characterized by higher RA and lower AF values due to frictional sliding effects (Ding et al., 2025). To reduce subjectivity arising from signal dispersion and overlap, a Gaussian Mixture Model (GMM) is adopted to statistically cluster AE events in the RA–AF feature space, thereby improving the robustness of crack mode classification (Li et al., 2020).

The evolution process of microcracks, including their initiation, propagation, and coalescence, can reveal the fatigue failure mechanism of sandstone from a microscopic perspective under different numbers of freeze-thaw cycles and loading rates. To investigate the evolution characteristics of microcracks in sandstone during fatigue under different numbers of freeze-thaw cycles, this study systematically analyzes the crack evolution characteristics of the samples using the AF and RA values of AE signals. To avoid interference from subjective factors on the experimental results, this study employs the Gaussian Mixture Model (GMM) to statistically analyze the tensile cracks and shear cracks generated in sandstone specimens during cyclic loading and unloading tests under different numbers of freeze-thaw cycles. The results are shown in Figure 9. Due to space limitations, the principle of the GMM algorithm will not be elaborated further. For detailed principles, please refer to the literature (Zhao et al., 2021).

Figure 9

Figure 9. Crack evolution characteristics of sandstone specimens during cyclic loading and unloading tests under different cycles of freezing and thawing. (a) 0.2 kN/s, (b) 0.4 kN/s, (c) 0.6 kN/s.

As evident from Figures 4, 9, the internal structure of sandstone specimens without undergoing freeze-thaw cycling remains relatively intact, with tensile failure being the primary mode at low loading rates. When the loading rate escalates to 0.6 kN/s, the proportion of shear cracks markedly rises. As the number of freeze-thaw cycles climbs to 15, microcracks start to proliferate. Local weakened areas expand, with the proportion of tensile cracks still surpassing that of shear cracks. Nevertheless, under high loading rates, the proportion of shear cracks approaches or even surpasses that of tensile cracks. As the number of freeze-thaw cycles increases to 30 and 45, the connectivity between sandstone pores and cracks significantly improves. High loading rates are more prone to induce overall instability in a short period of time. Consequently, the proportion of shear cracks also further increases. At the same number of freeze-thaw cycles, increasing the loading rate also promotes an increase in the proportion of shear cracks. Freeze-thaw degradation provides channels for the penetration of microcracks. High loading rates accelerate the formation and expansion of shear cracks by intensifying local stress concentration. These two factors jointly determine the evolutionary trend of sandstone fatigue failure mode, which gradually shifts from being dominated by tensile cracks in the early stage to being dominated by shear cracks in the later stage.

Comparing the AE signals of various samples under 0, 15, 30, and 45 cycles of freeze-thaw conditions and different loading rates, it was found that there were significant differences in the distribution patterns and evolution processes of cracks under the combined effects of freeze-thaw cycles and loading rates. As the number of freeze-thaw cycles increased, the internal microcracks of sandstone increased and gradually connected, leading to local stress concentration and increased susceptibility to shear failure. At the same time, the increase in loading rate accelerated the connection of cracks to a certain extent, further increasing the proportion of shear cracks. When the number of freeze-thaw cycles was relatively low (such as 0 or 15), tensile cracks dominated at lower loading rates (0.2 kN/s). Large-scale connected cracks had not yet formed inside the rock, and cracks were mainly characterized by local tensile failure. However, at high loading rates (0.6 kN/s), even with a relatively small number of freeze-thaw cycles, microcracks were prone to rapidly expanding along the path of least resistance, leading to an increase in the proportion of local shear failure. As the number of freeze-thaw cycles increased to 30 or 45, microcrack expansion and pore connectivity became more significant, resulting in overall structural deterioration of sandstone. Especially at high loading rates, shear failure became the dominant form.

In summary, cyclic freeze-thaw and loading rate have significant superimposed effects on the fatigue failure process of sandstone. Although a unified quantitative strength prediction model is not established in this study, the experimental results provide a quantitative basis for future development of strength models incorporating freeze–thaw cycles and loading rate effects. Cyclic freeze-thaw weakens the overall structure of the rock, making it more prone to generating and connecting microcracks. The loading rate exacerbates the occurrence of damage by affecting the speed and direction of crack propagation. The statistical results of the proportions of tensile cracks and shear cracks are of great significance for revealing the mechanism of rock failure. They also provide a reference for reasonably controlling the loading method and evaluating structural stability in rock engineering in cold regions.

5 Discussion

5.1 Influence of freeze-thaw cycles and loading rate on fatigue mechanical properties of sandstone

Rocks in cold regions undergo long-term freeze-thaw cycling, leading to significant changes in both their mechanical properties and internal microstructure. During the freeze-thaw process, the phase change of pore water induces volume expansion, which in turn triggers the generation and propagation of microcracks, resulting in the gradual deterioration of the overall structure of sandstone. Meanwhile, the loading rate significantly impacts the deformation and failure mode of sandstone. A lower loading rate provides ample time for cracks to propagate, whereas a higher loading rate may inhibit their slow expansion, leading to faster failure and instability of sandstone specimens.

To deeply explore the superimposed effect of cyclic freeze-thaw and loading rate, this study systematically analyzes the fatigue mechanical response characteristics of sandstone under different numbers of cyclic freeze-thaw (0, 15, 30, 45) and loading rates (0.2 kN/s, 0.4 kN/s, 0.6 kN/s) through cyclic loading and unloading tests and NMR test data. It reveals the mechanism of freeze-thaw damage on the fatigue mechanical properties of sandstone and discusses the regulating effect of loading rate on crack propagation behavior.

The NMR test results indicate that the freeze-thaw cycling significantly alters the pore structure of sandstone (Figures 3, 4). The pores of unfrozen sandstone are predominantly mesopores (45%) and macropores (45%), with a low content of micropores (10%). As the number of freeze-thaw cycles increases, the micropore content gradually decreases. The proportion of mesopores first increases and then stabilizes, while the proportion of macropores significantly rises. This suggests that freeze-thaw action accelerates the expansion and connectivity of microcracks. Ultimately, through fractures are formed, making the internal structure of sandstone looser. Specifically, when the number of freeze-thaw cycles increases to 30, the proportion of mesopores reaches its maximum (47%) and then stabilizes. Meanwhile, the proportion of macropores increases from 41% to 45%. This indicates that freeze-thaw damage mainly promotes the expansion of microcracks into mesopores and macropores, ultimately forming larger fractured structures. After 45 freeze-thaw cycles, the proportion of macropores increases to 63%, significantly higher than the initial state. A large area of fracture connectivity has appeared within the sandstone, leading to significant strength deterioration. The main mechanism of freeze-thaw cycling lies in the initiation and expansion of microcracks. When the frost heaving force exceeds the tensile strength of the internal particles of sandstone, microcracks begin to form. They gradually expand and connect with each other as the number of freeze-thaw cycles increases, resulting in a decrease in the overall strength of sandstone. In addition, the uneven expansion and contraction of different mineral components further exacerbate the stress concentration between mineral particles, accelerating the evolution of cracks.

The cyclic loading and unloading strength of sandstone gradually decreases with an increase in the number of freeze-thaw cycles, but it slightly increases with a higher loading rate (Figure 10). The cyclic loading and unloading strength of unfrozen sandstone exhibits relatively minimal changes under different loading rates. However, after undergoing 15 or more freeze-thaw cycles, the cyclic loading and unloading strength significantly decays. Furthermore, a high loading rate has a more pronounced effect on enhancing the cyclic loading and unloading strength. The accumulation of freeze-thaw damage observed in the experimental results heightens the sensitivity of sandstone to loading rates.

Figure 10

Figure 10. Cyclic loading and unloading strength of sandstone under different cylices freeze-thaw and loading rates.

The intermediate-cycle NMR results provide a continuous microstructural basis for interpreting the staged mechanical degradation. Specifically, the porosity shows a slow-growth stage at low F–T cycles, followed by an accelerated increase after approximately 15–30 cycles, which is consistent with the observed acceleration of strength loss at 30 cycles and beyond. To further strengthen the quantitative linkage, we performed a correlation analysis between porosity and cyclic loading–unloading strength using the paired data at 0, 15, 30, and 45 cycles. The results indicate a clear negative correlation, demonstrating that pore growth and pore coarsening captured by NMR are key microstructural drivers for strength degradation under freeze–thaw action.

At low loading rates, cracks have ample time to expand slowly. The crack propagation path is significantly influenced by the heterogeneity of the rock’s internal structure. It often propagates along weak internal surfaces of the rock, such as pores, microcracks, and mineral grain boundaries. Therefore, the crack propagation path is relatively tortuous. At high loading rates, due to the short loading time, crack propagation is affected by inertial effects. When external forces are rapidly applied, the stress within the rock does not have time to distribute evenly, resulting in stress concentration in local areas. This makes cracks tend to propagate rapidly in the direction of least resistance, leading to a relatively straight crack propagation path.

From a fracture-mechanics perspective, the suppression of slow crack propagation observed at higher loading rates in this study can be explained by time-dependent crack growth mechanisms. Increasing the loading rate shortens the time available for subcritical crack growth (e.g., stress-corrosion and environmentally assisted cracking), thereby limiting stable crack extension before peak stress is reached. Meanwhile, rapid loading restricts microcrack nucleation, growth, and interaction, delays crack coalescence, and leads to a higher apparent strength. As a result, failure tends to shift from progressive and stable crack accumulation toward abrupt crack coalescence and more brittle instability at higher loading rates.

There are significant differences in the stress-strain curves of sandstone specimens under different numbers of freeze-thaw cycles and loading rates. Under non-freeze-thaw conditions, the stress-strain curve of sandstone exhibits typical elastic deformation characteristics, accompanied by a certain degree of plastic deformation. As the number of freeze-thaw cycles increases, the elastic deformation phase gradually shortens. Plastic deformation increases, and the slope of the curve gradually decreases. After 30 or more freeze-thaw cycles, the strain hardening effect of sandstone is significantly weakened. The slope of the stress-strain curve decreases, and the unloading path becomes steeper. The material failure mode transitions from ductile to brittle.

There is a notable synergistic effect between freeze-thaw damage and loading rate. After experiencing freeze-thaw cycling damage, sandstone contains numerous microcracks and pores, rendering its structure more porous. During the loading process, these defects serve as preferential paths for crack propagation, heightening sandstone’s sensitivity to the loading rate. At elevated loading rates, the internal structure deterioration caused by freeze-thaw damage makes cracks more prone to rapid propagation and coalescence, thereby hastening the destruction of sandstone. To further verify the microstructural basis of the above macroscopic and mesoscopic observations, representative SEM images were analyzed, as discussed in the following section.

5.2 SEM observations of microstructural evolution

To provide direct microstructural evidence for the pore and crack evolution inferred from NMR and AE analyses, representative SEM images corresponding to different freeze–thaw damage levels were examined, as shown in Figure 11. In the undamaged or weakly damaged state (Figure 11a), the sandstone matrix exhibits dense cementation and only isolated micropores or microcracks, indicating an intact pore–grain framework.

Figure 11

Figure 11. SEM images of sandstone microstructural evolution under different freeze–thaw damage levels. (a) 0 cycles (Initial intact state), (b) 15 cycles (Initial damage stage), (c) 30 cycles (Damage progression stage), (d) 45 cycles (Severe damage stage).

With increasing freeze–thaw damage (Figures 11b,c), microcracks preferentially initiate along grain–cement interfaces, reflecting the sensitivity of cementation to repeated freeze–thaw-induced stresses. As damage accumulates, the density of microcracks increases and partial crack coalescence becomes evident, accompanied by a clear coarsening of pore structures.

In the severely damaged state (Figure 11d), multiple microcracks interconnect to form a crack network, resulting in significantly enhanced pore connectivity and structural degradation. These SEM observations qualitatively corroborate the pore coarsening revealed by the T₂-based NMR results and the crack evolution and mode transition identified by AE monitoring, thereby contributing a triangulated interpretation of freeze–thaw-induced damage mechanisms in sandstone.

5.3 Deterioration mechanism of sandstone under cyclic freeze-thaw conditions

Under cyclic freeze-thaw conditions, the deterioration of sandstone’s mechanical properties primarily stems from the initiation, propagation, and coalescence of internal microcracks caused by the repeated freezing and melting of pore water, as illustrated in Figure 12. The core mechanism can be summarized as follows.

Figure 12

Figure 12. Schematic diagram of deterioration of sandstone under cyclic freeze-thaw conditions.

When the temperature drops below freezing, the water within the pores of sandstone freezes and undergoes a volume expansion (approximately 9%). This frost heaving force is exerted on the cementation interfaces between pore walls and mineral particles, inducing tensile stress within the rock. When the frost heaving force surpasses the tensile strength of sandstone, existing microcracks become activated or new microcracks are initiated. These cracks persist in expanding during multiple cycles of freezing and thawing, ultimately leading to the formation of through fractures, which results in a decrease in macroscopic strength.

Sandstone typically consists of various minerals, including quartz, feldspar, mica, and clay minerals (Figure 1). Different minerals exhibit varying coefficients of thermal expansion during both low and elevated temperatures. Repeated freeze-thaw cycles can induce stress concentration at the interfaces between adjacent mineral particles, further triggering or exacerbating the expansion of microcracks. Additionally, the water-absorption expansion of clay minerals can also intensify pore deformation and interparticle interface damage.

During repeated freeze-thaw cycles, initially dispersed microcracks continuously expand and connect, forming a larger-scale fracture network. NMR tests indicate that the pore structure of sandstone gradually transitions from micropores to mesopores and macropores, with an overall increase in porosity. The increase in pores enhances the permeability of water within the rock, further exacerbating the damage caused by subsequent freeze-thaw cycles. In practical environments, water flow during the melting phase may lead to processes such as dissolution, salting-out, or chemical erosion, further weakening the mineral particle interfaces and pore walls. Coupled with the physical expansion and contraction effects brought about by low-temperature cycles, this promotes significant deterioration of sandstone in a relatively short period of time.

Due to the continuous accumulation and connectivity of microcracks, the bearing capacity and deformation capacity of sandstone will significantly decrease with the increase in the number of freeze-thaw cycles. This is specifically manifested as the attenuation of peak stress and elastic modulus. Furthermore, the crack propagation gradually transitions from ductile failure to brittle failure. In later cycles, the material often exhibits steep fracture characteristics during unloading. In summary, the deterioration mechanism of sandstone under cyclic freeze-thaw conditions is caused by the combined effects of pore water phase change, uneven thermal expansion of minerals, and dynamic evolution of pore structure. These mechanisms are coupled and accumulate over time, ultimately leading to a significant decrease in the macroscopic strength and durability of sandstone, posing a serious threat to the stability of rock engineering in cold regions.

It should be noted that all specimens in this study were obtained from a single sandstone block with a fixed mineral composition, which was intended to minimize lithological variability and to isolate the coupled effects of freeze–thaw cycles and loading rate; thus, the reported quantitative results are representative of the investigated sandstone. For sandstones with different genesis or higher clay mineral contents, freeze–thaw damage may develop more rapidly and critical deterioration thresholds may shift. Nevertheless, the qualitative damage evolution mechanisms identified—such as pore coarsening, microcrack initiation and coalescence, and loading-rate-dependent crack-mode transition—are expected to remain applicable to sandstones with similar pore–cement structures under comparable conditions, and further comparative experimental or numerical studies are suggested to extend the universality of these findings.

6 Conclusion

The effects of freeze-thaw damage on the fatigue mechanical response properties and damage mechanisms of sandstone under varied loading and unloading rates are investigated in this work using experiments. The key findings are as follows.

1. At the commencement of the freeze-thaw cycle (15 cycles), the mass of sandstone experiences a modest rise. However, there is a noticeable decrease in mass and a noteworthy rise in porosity when the number of freeze-thaw cycles increases (30 and 45 cycles). This implies that the interior structure of sandstone is more severely damaged and deteriorated by the freeze-thaw cycle. The pore structure of sandstone is drastically changed by the freeze-thaw cycle, with the fraction of mesopores and macropores greatly increasing and micropores gradually decreasing. This suggests that the growth and connection of microcracks are accelerated by the freeze-thaw action, which eventually results in the creation of through fractures and increases the porosity of the sandstone’s internal structure.

2. Sandstone’s peak strength is increased and crack propagation is somewhat inhibited by an increase in loading rate. However, the breakdown process of sandstone is still primarily influenced by the cumulative effect of freeze-thaw degradation. Sandstone tends to collapse more brittlely under high loading rates. Sandstone’s peak strength is greater at a loading rate of 0.6 kN/s than it is at 0.2 kN/s. Nevertheless, the peak strength still drops noticeably as the number of freeze-thaw cycles rises to 30 or more. This implies that even at high loading rates, the cumulative impact of freeze-thaw damage is still considerable.

3. The number of microcracks in the sandstone started to rise after 15 cycles of freeze-thaw. With the percentage of tensile cracks remaining higher than that of shear cracks, the localized weak spots grew. Nevertheless, the percentage of shear cracks approached or even exceeded that of tensile cracks at high loading rates. The connectivity between sandstone pores and cracks greatly improved when the number of freeze-thaw cycles was raised to 30 and 45. The fraction of shear cracks increased further because of the high loading rates’ propensity to cause overall instability quickly. Increasing the loading rate also increased the percentage of shear cracks at the same number of freeze-thaw cycles.

4. Sandstone’s internal microcracks grow and progressively join as the number of freeze-thaw cycles rises, creating a concentrated area of stress that is more likely to cause shear fracture. To a certain degree, crack penetration is accelerated by an increase in loading rate. By altering the pace and direction of crack propagation, the loading rate makes failure more likely.

Data availability statement

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.

Author contributions

DS: Validation, Conceptualization, Methodology, Writing – review and editing, Software, Writing – original draft, Resources, Investigation, Formal Analysis, Visualization. XW: Writing – review and editing, Validation, Resources, Formal Analysis, Writing – original draft, Data curation, Methodology, Investigation, Visualization. DY: Methodology, Supervision, Conceptualization, Writing – review and editing.

Funding

The author(s) declared that financial support was received for this work and/or its publication. This work was supported by Natural Science Foundation of Jiangxi Province (No. 20224BAB213052).

Conflict of interest

The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The author(s) declared that generative AI was not used in the creation of this manuscript.

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