Freeze–thaw cycles (FTCs) often lead to severe geological disasters, significantly threatening the safety of human life and property. The physical and mechanical properties of a rock and its damage evolution are influenced by the number and duration of FTCs and the temperature variations in the rock. Therefore, understanding the physical and mechanical behavior of rock under different FTCs is of great practical significance for the stability analysis, control, and design of rock engineering in freeze–thaw zones.

The study of freeze–thaw damage in rock has attracted immense interest in rock mechanics and engineering research (Meng et al., 2024; Huang et al., 2022; Liu et al., 2023; Sun et al., 2024; Jia et al., 2023a; Jia et al., 2023b; Zhu et al., 2023; Song et al., 2022). Hou et al. (2022) studied the deterioration mechanism of anhydrite rock in freeze–thaw weathering. Jamshidi (2021) proposed a new rock mechanics prediction parameter (PMPP) to predict the strength of granite rock after FTCs. Liu et al. (2025) studied the effect of FTCs on the microstructure and macroscopic mechanical properties of sandstone. Song et al. (2023), Yang et al. (2021) proposed a phase change coupling expansion method of water ice particles based on the discrete element method, quantitatively characterized the frost heave evaluation index of pore water particles, and established the functional relationship between the evaluation index and the number of FTCs. Jin et al. (2024) observed the macroscopic morphology of slate and comprehensively analyzed the deterioration law of related mechanical properties under freeze–thaw action. Lv et al. (2023) proposed the calculation method of macroscopic damage variable based on the weighing method and established the model of mesoscopic damage variable under load using statistical damage mechanics theory. He et al. (2024) integrated mercury intrusion porosimetry (MIP) with micro-computed tomography (micro-CT) techniques to systematically investigate the microstructural evolution of cementitious specimens subjected to varying numbers of freeze-thaw cycles. Wu et al. (2024) study explores an approach to strengthen cemented rockfill by using well-graded gangue, and by partially replacing Portland cement with fly ash and a premixed low-alkalinity activator. Wu et al. (2025) reported a waste-to-wealth pathway that improves cemented gangue backfill materials by cellulose nanofibers to recycle mining wastes and partially replace cement. These studies can be summarized into four methods: microscopic, mesoscopic, macro-scopic, and an integrated macro-micro method (Zhang and Wang, 2022). However, research on rock damage characteristics under different FTCs remains limited, particularly where the cycle durations exceed 4 h.

Acoustic emission (AE) is a critical phenomenon observed during material damage and failure. It plays a vital role in evaluating material damage and failure mechanisms by capturing the characteristics of AE signals. Over the past decades, domestic and foreign researchers have extensively conducted AE characteristics, including compression, tension, shear, and fracture (Wang et al., 2020; Yang et al., 2021; Wang et al., 2019; Yang et al., 2021; Meng et al., 2020). Advancements in science and technology have also led to significant progress in AE numerical simulation and localization research (An et al., 2021; Yu et al., 2021). Theoretical and laboratory tests can provide a scientific basis for AE monitoring and predicting rock mass. Dong et al. (2022) conducted AE tests on unstable fracture of granite and provided parameters for rock instability assessment and early warning based on multiple AE indicators. The integrated machine learning model was used to construct the plastic stage identification method of rock mass crack propagation state. The study of Song et al. (2023) showed that the change in FTCs manifested an increase of ringing count in the initial loading stage, and the number and distribution of AE three-dimensional event points were closely related to the fracture dip angle. However, accurate theoretical research has not been conducted so far on the AE characteristics of rocks with different FTCs.

This study focused on red sandstone as the research subject. First, FTC tests with different FTC times were conducted. Subsequently, uniaxial compression acoustic emission tests were performed on red sandstone after different FTCs. The variation characteristics of longitudinal wave velocity, porosity, stress-strain curve, peak stress, and elastic modulus of red sandstone under different FTCs were examined. Additionally, the characteristics of AE ib value, energy rate, and ringing count in rock failure after each FTC were analyzed. The variation law of the internal microstructure of red sandstone as a function of the variation characteristics of AE RA-AF value has been discussed. Finally, the damage evolution characteristics of red sandstone under different FTCs have been quantitatively analyzed based on AE cumulative ringing counts. These results would provide a reference for the analysis, control, and design of rock engineering stability in the freeze–thaw zones.

Damage refers to the deterioration process of materials or structures caused by mesostructural defects (such as micro-cracks, micro-voids, etc.). When the rock material is subjected to load or ambient temperature changes, owing to the generation of a large number of internal micro-damages, the initiation, expansion, and connection of microcracks or micro-pores, the mechanical properties of the rock material are degraded. The release of elastic strain energy, an AE phenomenon, accompanies this process. Therefore, there must be an inevitable relationship between rock damage and the AE count rate used to quantify the progressive damage characteristics of red sandstone specimens after different FTCs under different FTCs.

The failure in which the rock directly loses its bearing capacity at a strain of less than 1% and the stress peaks under uniaxial stress state is called brittle failure. If the strain is between 1% and 2%, the stress fluctuates after reaching the peak value, causing direct failure called brittle–ductile failure. The failure of rock with a complete stress–strain curve and strain above 1%–5% is called ductile failure. In (Wu et al., 2015), the variation law of cumulative ringing count with time was determined. Rock failure is divided into three types: brittle failure, brittle–ductile failure, and ductile failure. Moreover, an exponential function can express the function relationship between AE cumulative ringing count N and time t of brittle or brittle–ductile failure of rock. From Figures 9, 10, it can be determined that the red sandstone specimen without a FTC, under the condition of freezing and thawing for 1h, was a brittle failure for 10, 20, and 30 cycles, and a brittle–ductile failure for 40 cycles. Under the condition of freezing and thawing for 2 h, 10 cycles and 20 cycles were brittle failure, and 30 cycles and 40 cycles were brittle–ductile failure.

Under the condition of displacement control, the strain of rock increases linearly with time. The relationship between strain ε and time t is as follows: ε = k t + ε 0 (2)

In the formula, ε is axial strain; k is rock strain rate; ε 0 is the initial strain of rock, which can be obtained by linear fitting according to the test data. At the same time, Reference (Wu et al., 2015) pointed out that when the rock sample is brittle or brittle-ductile failure, the function relationship between AE ringing cumulative count and time can be expressed by exponential function. N = A 1 ⁡ exp B 1 t + C (3)

The A 1 , B 1 , C from formula are obtained by fitting the experimental data. Ductile failure can be expressed by Boltzmann function (S-type growth function), namely,: N = A 1 − A 2 1 + exp t − B 1 C (4)

Where A 1 , A 2 , B 1 and C are determined by fitting the experimental data. From Equations 2–4, the coupled relationship between the cumulative number of ringing and strain of brittle or brittle-ductile damaged red sandstone AE can be derived, namely,: N = A 1 ⁡ exp B 1 ε − ε 0 k + C (5)

In addition, there is no ductile failure in all specimens in this test, so the failure mode is no longer discussed.

Based on the material damage process, Lemaitre et al. proposed the continuum damage mechanics and established the damage model, as shown in Equation 6: σ = E 1 − D ε (6)

It is assumed that the strength of rock micro-element obeys Weibull distribution function (Wu et al., 2015), that is: ϕ ε = m α ε m − 1 ⁡ exp − ε m α (7)

In the formula, the constant m and α is related to the shape and scale of the rock. The relationship between rock damage variable D and the probability density of microelement failure is: d D d ε = ϕ ε (8)

The simultaneous Equations 7, 8 can be obtained: D = ∫ 0 ε ϕ ε d ε = 1 − exp − ε m α (9)

By establishing the constitutive model of rock damage under uniaxial compression, the calculation method of and are determined in reference (Yang et al., 2005) as showing in Equation 10: m = 1 ln E ε c / σ c , α = m ε c m (10)

In the formula, σ c is the peak stress and ε c is the peak strain. The coupling relationship between AE cumulative ringing count and damage variables of red sandstone with different freeze-thaw cycles under different freeze-thaw cycle times can be obtained by simultaneous Equations 4, 8 and 9. When the rock is brittle or brittle-ductile failure. The calculation formula is shown in Equation 11: D = 1 − exp − 1 α k B 1 ln N − C A 1 + ε 0 m (11)

Applying the test data in Formula 5, the parameter values of the damage variable function of red sandstone with different FTCs under different FTCs satisfying the Weibull distribution can be obtained (Table 1). Furthermore, the relationship between AE cumulative ringing count and damage variables of red sandstone with different FTCs under different FTC times can be obtained (Figures 14, 15).

Figures 14, 15 show that the cumulative ringing count positively correlates with the damage variable in the uniaxial compression process of freeze–thaw red sandstone. With the gradual increase of axial load, the micro-pores and micro-cracks inside the red sandstone specimens gradually developed and penetrated, accompanied by the generation of a large number of AE signals. The development and penetration of these micropores and micro-cracks aggravated the deterioration process of red sandstone. After 10, 20, 30, and 40 FTCs, the final damage variable values of red sandstone, frozen and thawed for 1 h, were 0.23, 0.39, 0.42, and 0.46, respectively. The final damage variable values of red sandstone frozen and melted for 2 h under the same FTCs were 0.29, 0.41, 0.42, and 0.50, respectively. It was observed that with the increase in the number of FTCs, the final damage variable value exhibited an increasing trend. Under the same number of FTCs, the rock frozen and thawed for 2 h exhibited a higher final damage variable value than the rock frozen and thawed for 1 h, further verifying that the increase of FTC time aggravated the progressive damage inside the red sandstone to a certain extent. The cumulative ringing count–damage variable curve effectively reflects the progressive damage characteristics of red sandstone under different FTCs and the same number of FTCs and provides theoretical support for the deterioration of mechanical parameters in previous studies.

Current theoretical frameworks addressing rock FTC damage encompass volumetric expansion theory, hydrostatic pressure theory, capillary theory, and subcondensation ice theory (Jia et al., 2024). However, the freeze-thaw deterioration process in rock materials demonstrates significant complexity, wherein the dominant damage mechanism may vary across different environmental and material conditions. This mechanistic variability suggests that no singular theoretical framework can comprehensively account for the intrinsic damage mechanisms observed in practical scenarios. This study employs a multidisciplinary theoretical framework to elucidate the observed phenomena. The experimental protocol initiated with forced water saturation of red sandstone specimens followed by FTC testing. During the freezing phase, phase transition of interstitial water from liquid to solid state propagated inward from specimen surfaces. This cryogenic phase transformation generated expansive forces through ice crystallization, resulting in nucleation and propagation of microstructural defects. Concomitantly, terminal regions of pre-existing micropores exhibited hydraulic fracturing characteristics (Jia et al., 2016), a phenomenon attributed to elevated hydraulic pressures within confined microstructural spaces caused by differential phase transformation rates between peripheral ice layers and internal aqueous phases. The thawing phase induces phase transformation from ice to aqueous phase, while residual deformation space generated by cryogenic expansion remains irrecoverable, resulting in permanent structural deterioration. Experimental investigations have demonstrated (Qiao et al., 2020) that ice-phase ablation within fissures triggers abrupt volumetric contraction of pore fillings, producing pronounced hydraulic rebound effects in fractured rock masses. Notably, the resultant expansion forces during this phase significantly exceed those generated during the freezing process. Furthermore, the water-ice phase transition exhibits non-uniform propagation velocity and intensity across specimen cross-sections under varying FTC durations. This spatial-temporal heterogeneity in phase transformation kinetics leads to progressive amplification of damage differentials in red sandstone through successive FTC iterations. Consequently, specimens undergoing extended-duration FTC regimens exhibit premature bearing capacity degradation compared to those subjected to shorter FTC exposures, attributable to accelerated cyclic stress accumulation mechanisms.

Contemporary analysis of geotechnical challenges in southern China reveals a prevailing tendency within conventional analytical paradigms to predominantly attribute rock engineering failures to pluvial climatic conditions (Yang et al., 2016). This perspective notably overlooks the widespread distribution of short time frozen ground within the region, as quantitatively delineated in Figure 2. The 2008 cryogenic disaster exemplifies this oversight, where sustained cryogenic precipitation events precipitated widespread geological instabilities across southern provinces. Significantly, critical infrastructure projects such as the South-North Water Transfer Scheme encounter multifaceted engineering challenges including: altered mechanical behavior of argillaceous formations; stability optimization of expansive rock canal slopes; bearing capacity degradation in alluvial foundations; and subsidence management in mining-affected corridors (Zhou et al., 2002). These geotechnical systems remain vulnerable to cyclic freeze-thaw actions of varying durations, particularly given the project’s trans-regional climatic exposure. Furthermore, operational parameters such as soft rock slope reinforcement efficacy and structural integrity of fluvial crossings demonstrate particular sensitivity to FTC-induced material deterioration. These case studies collectively underscore the critical need for differentiated assessment of FTC-induced geotechnical risks based on temporal phase-transition characteristics.

(1) With the increase of FTCs, the longitudinal wave velocity, peak stress, and elastic modulus of red sandstone had different degrees of reduction. The reduction rate of red sandstone after freezing and thawing for 2 h was higher than that of red sandstone after freezing and thawing for 1 h. An increased porosity was observed in specimens with extended freeze–thaw exposure.