The study area is a section of a major railway line in northwestern Yunnan Province, China, crossing the Tiger Leaping Gorge of the Jinsha River. The region features steep alpine terrain, with Jade Dragon Snow Mountain and Haba Snow Mountain on opposite sides of the gorge. The peak elevation reaches 5,000 m, with a relief of over 2000 m (Figure 1). According to geological surveys, subsurface strata consist mainly of Permian and Triassic basalts, while bedrock at the bridge crossing comprises green foliated basalt and chloritized basalt. The alpine valley topography generates seasonal and diurnal temperature variations (Figure 2). The mean annual air temperature ranges between −15 °C and +15 °C, and significant F-T action is evident. Field observations also show that shallow rock masses exhibit distinct signs of F-T weathering, including fracturing and loosening near the surface. Four boreholes were drilled on both sides of the planned bridge foundation to obtain the samples for this study.

Rock samples were collected from four boreholes drilled along the slopes on both sides of the planned bridge site (Figure 1). In the laboratory, basalt core was prepared as standard cylindrical specimens with a diameter of 50 mm and a height of 100 mm following ISRM (Lamas, 2018) recommendations, resulting in 107 specimens in total (Figure 3a). All specimens consisted of dense basalt, and no vesicular structures were observed during macroscopic inspection. Four fundamental physical parameters such as dry density, porosity, P-wave velocity, and water absorption were measured under the laboratory conditions, and the results are shown in Figure 3b. The dry density of the basalt specimens range continuously from 2.75 to 3.01 g/cm³, whereas porosity and P-wave velocity exhibit noticeable variability. On this basis, the sampled basalts were considered to represent different degrees of weathering, and the average values of the physical parameters are listed in Table 1.

To identify the weathering degree of the basalt samples, three samples were randomly selected from each group and tested for uniaxial compressive strength before the FTCs. The averaged results are also reported in Table 1. Samples 1 had a higher degree of weathering with the lower strength.

Based on the engineering geological investigation data of the planned bridge and regional engineering experience, the suggested physical and mechanical parameters of fresh basalt in this study area was as follows: UCS ranging from 100 to 140 MPa, porosity of 0.3%–1.2%, and P-wave within 6.0–7.5 km/s, water absorption around 0.3%. The weathering degree of the basalt samples was evaluated by using the weathering degree criteria in the Code for Investigation of Geotechnical Engineering (GB 50021-2001, China) (Ministry of Housing and Urban-Rural Development of the People's Republic of China (MOHURD), 2009). Table 2 shows that the basalts fall into two weathering degrees: moderately weathered groups (MG) for samples 1 and slightly weathered groups (SG) for samples 2.

The freeze-thaw temperature range and the number of cycles are key parameters in freeze-thaw testing. Existing testing standards and recommendations, such as ISRM (Lamas, 2018) and ASTM (Materials, 2013), show noticeable differences in the selection of these parameters. The freeze-thaw conditions are often determined by the climatic background and engineering context of the study area.

In this study, meteorological data from the study area (Figure 2) were used as the primary reference. Considering the potential occurrence of extreme cold conditions at the engineering site, the freeze-thaw temperature range was set from ˗20 °C to +20 °C. In the laboratory, this study designed a simplified freeze-thaw scheme. The cycling temperature was fixed at ˗ 20 °C and +20 °C, with a total of 100 freeze-thaw cycles applied. Each cycle lasted 24 h, comprising a 12 h freezing stage followed by a 12 h thawing stage. The FTCs were carried out using a combination of an ultra-low-temperature freezer and a thermostatic water bath.

A total of 90 standard cylindrical specimens were selected from the SG and MG basalt groups for freeze-thaw cycle testing (FTCs). For both weathering groups, the specimens were divided into five freeze-thaw levels based on the number of cycles: 0, 25, 50, 75, and 100 cycles. Each freeze-thaw level included both SG and MG specimens, with nine independent specimens in each group. During specimen allocation, the porosity was strictly controlled: the average porosity of specimens in each group was maintained such that the relative deviation from the overall average porosity reported in Table 1 was within ±5%, and the coefficient of variation for porosity within each group was limited to below 10%. This screening and grouping criteria ensured good consistency among specimens within and across groups. The allocation of specimens to the cycle levels is summarized in Table 3.

All specimens were vacuum-saturated and sealed before the FTCs to maintain a consistent moisture condition. During the cycling, the specimens remained in a saturated state. After the specified number of cycles, the specimens were removed and tested for their physical and mechanical parameters. The freeze-thaw testing procedure is shown in Figure 4.

The test program included physical and mechanical strength parameters. Porosity, P-wave velocity, and surface features were measured as non-destructive indicators using an interval-based scheme. At every five FTCs, five specimens were selected from each of the MG5 and SG5 groups, marked and tested for porosity and P-wave velocity. Each measurement was repeated three times and the results were recorded. For the other groups (MG1 to MG4 and SG1 to SG4), four specimens were marked and tested in the same procedure. After every ten cycles, the surface features and macroscopic cracks of the specimens were inspected using a digital camera and an optical microscope. Upon completion of these non-destructive tests, the specimens underwent vacuum saturation again and were subjected to the next FTCs.

When the cumulative number of FTCs reached 25, 50, 75 and 100, nine specimens were extracted from the designated groups for mechanical testing and microscopic inspection. Four of the marked specimens were used for uniaxial compression tests at a loading rate of 0.5 mm/min, and the average uniaxial compressive strength (UCS) was calculated. Another four specimens were subjected to direct shear tests at normal stresses of 0.5, 2.5, 5.0 and 10 MPa, with a shear rate of 0.5 mm/min. Finally, the ninth specimen was examined by SEM to observe microstructural damage.

During the FTCs, notable differences in crack development were observed between the MG and SG basalt specimens. Figures 5a,b present representative appearances and macro-fracture development of specimens with different weathering degrees during 100 cycles, and the labels MG5-1 and SG5-1 denote the 1st specimens within the MG5 and SG5 groups in Table 3, respectively. In the MG specimens (Figure 5a), new cracks began to appear after 25 cycles, typically initiating at the edges of the cylindrical specimens. Between 50 and 75 cycles, the number of cracks increased significantly, and some fractures propagated from the sample periphery toward the interior. Small fragments of rock or chips were observed to spall off in zones with dense edge cracks in this stage. By 100 cycles, the MG specimens showed an extensive network of interconnected cracks around the outer regions. This crack propagation path was highlighted by the red lines in the left column of Figure 5a. The SG specimens showed a slower crack development in the Figure 5b. No obvious new cracks appeared in the first 40 cycles. A few peripheral fissures emerged after 50 cycles, but most remained short and discontinuous. After 80 cycles, the tiny fissures in SG gradually extended, and some slight spalling was noted in the edge spots. Even after 100 cycles, the SG specimens presented only few new cracks, primarily as extensions of original defects rather than forming an interconnected fracture network. Thus, the SG basalt specimens retained visually more intact and greater resistance to F-T action.

Microscopic observations via a digital microscope at magnifications of 750×-900× provided additional insights into microcrack propagation (Figure 5c, insets). In the MG samples, fine microcracks were already present initially and grew significantly with the FTCs. Between 75 and 100 cycles, microcrack coalescence led to the formation of larger discontinuities. Microfragments detached from crack edges and the crack boundaries became blurred and rough. By contrast, the SG samples initially showed almost no microcracks under the microscope. Even after dozens of cycles, only slight cracking was visible. Between 80 and 100 cycles, a few microcracks appeared and slowly grew but remained narrow and isolated. The crack edges in SG specimens remained sharp and clean, indicating minimal material removal along the cracks. These observations show more rapid microstructural degradation in MG specimens and delayed crack initiation in SG specimens.

The average mass-loss curves (Figure 5c) offered further evidence of cumulative damage. Both the MG and SG groups show a decrease in mass with increasing FTCs, because of the surface spalling and particle detachment. The SG samples display a slow and nearly linear mass-loss trend, while the MG samples show relatively greater mass reduction. In MG, the curve changes slope around 75 cycles, after which the mass-loss rate increases. This change in mass-loss occurs alongside the more extensive cracking and spalling observed in MG during the later stages of cycling. By 100 cycles, the proportion of mass lost in the MG specimens is clearly higher than that in the SG specimens.

The P-wave propagation velocity is highly sensitive to variations in rock integrity and the development of internal defects. Figure 6 shows the evolution of saturated and dry P-wave velocities for the MG and SG samples at 5-cycle intervals up to 100 cycles. Before any cycling, the saturated P-wave velocities were higher than the dry velocities for both groups, typically between 5,000 and 6,000 m/s.

In the FTCs, the saturated P-wave velocity of the MG showed a distinct three-stage evolution: a slow decline from 0 to 25 cycles, a period of accelerated reduction between 25 and 70 cycles, and a gradual leveling off between 70 and 100 cycles. In particular, the decrease in saturated velocity during the intermediate stage indicates rapid damage accumulation and crack development. After 70 cycles, the rate of decrease diminishes, with only minor additional decrease by 100 cycles. A similar pattern is reflected in the dry P-wave velocity of the MG group, although the absolute dry velocities are lower and the early-stage changes are less prominent. By comparison, both the saturated and dry P-wave velocities in the SG samples decline much more gradually and linearly, without a clear multistage pattern. The difference between the saturated and dry velocities in the SG is relatively small, suggesting that fewer pore spaces exist during the initial phase. Over the full 100 cycles, the P-wave velocity of the SG samples decreases steadily but remains modest in magnitude. The absence of distinct stages suggests that in low-porosity basalt, F-T damage accumulates at a relatively constant slow rate.

The evolution of porosity complements the P-wave velocity data. As FTCs generate and enlarge cracks, the connected porosity of the rock mass increases. Figures 7a,b present the average porosities of the MG and SG samples as a function of the number of cycles. Both groups show a linear increase in porosity with increasing cycle count, reflecting the continuous creation of new void spaces. However, the porosity of the MG samples exhibits a noticeably steeper slope, indicating a faster porosity growth rate per cycle, whereas the porosity of the SG samples increases at a slower rate. By 100 cycles, the porosity of the MG basalt samples increased by 0.5–0.6 percentage points from the initial average value of 1.54%, corresponding to roughly 30% of the initial porosity. In contrast, the porosity of the SG basalt samples increases by only 0.1–0.2 percentage points from an initial average value of 0.85%, which is a relatively minor change. Meanwhile, Figure 7c displays the porosity growth process for both groups at 5-cycle measurement intervals, which shows that MG specimens undergo greater porosity enhancement than SG specimens. These porosity trends are consistent with the P-wave velocity degradation and jointly point to more severe freeze-thaw damage in the MG basalt.

The F-T action-induced degradation in the mechanical properties was quantified by UCS and direct shear tests at several intervals. Figures 8a–f illustrate typical UCS failure mode of MG and SG samples, indicating that as damage accumulates, the failure becomes less abrupt, with more split fragments for the MG samples. The stress-strain curves shows in Figures 8g,h exhibit that, at all freeze-thaw levels, specimens of both weathering grades experience a consistent decrease in peak strength and an increase in peak strain. As summarized in Figure 9, after 100 cycles, the SG samples retained a relatively high UCS of 62.6 MPa, a 20%–25% reduction from their initial strength. whereas the UCS of the MG samples decreased to 25.3 MPa, which is lower than 50% of its initial value. The UCS results reinforce the idea that, compared with the SG basalt samples, the MG basalt samples undergo a much greater relative loss of compressive strength under FTCs.

The direct shear strength exhibited a similar decreasing trend. As shown in Table 4, at all normal stress levels (σ_n = 0.5, 2.5, 5.0, and 10.0 MPa), peak shear strength decreases monotonically with increasing cycles, with MG specimens exhibiting greater reductions than SG specimens. Under σ_n = 10 MPa, the peak shear strength of MG specimens decreases from 26.54 MPa to 12.53 MPa (a 53% reduction), while that of SG specimens decreases from 42.95 MPa to 29.56 MPa (a 31% reduction). These observations mirror the trends seen in UCS and indicate that initial weathering grade significantly influences the extent of freeze-thaw-induced shear strength degradation.

Other mechanical parameters derived from the test results also exhibit systematic reductions with increasing cycle number (Table 5). Young’s modulus, cohesion, and internal friction angle each decrease to varying degrees, indicating the losses in stiffness and shear resistance.

In nature, rock masses are continuously subjected to weathering. This process leads to that primary pores and microcracks are widely developed in the rock masses. These structural defects provide the fundamental basis for freeze-thaw damage. Previous studies have demonstrated that the phase transition of water in pores and microcracks is accompanied by volumetric expansion. It can generate substantial frost-heave-induced stresses on the order of MPa. As the stresses exceed the local tensile strength of the rock microstructure, they can induce new microcracks and facilitate the propagation of pre-existing cracks (Huang et al., 2018). When the temperature drops below 0 °C and the water freezes in these voids, the ice exerts compressive stress on the pore walls as well as induces tensile stress concentration at crack tips; upon thawing, the ice melts, and the stresses are released. Each freeze–thaw cycle can be regarded as a microscale loading-unloading process, especially in the area with concentrated stress. Under repeated cycling, frost heave stresses enlarge the defects and cause the appearance of new microcracks. This damage results in the cumulative deterioration of physical properties and mechanical strength.

In this study, the experimental results indicate that even the dense basalt with low initial porosity exhibits evident physical and mechanical degradation after FTCs under saturated conditions. This observation confirms that crack propagation induced by the water-ice phase transition plays a governing role in the freeze-thaw damage evolution. In addition, specimens with a higher initial degree of weathering (the MG group) show more severe degradation of physical parameters and more loss of strength during FTCs. This behavior suggests that a higher content of initial defects and more developed migration pathways facilitate water ingress. It can amplify the effects of freezing action. In this section, the accumulation mechanism of freeze-thaw damage in basalt is further discussed.

In this study, a damage variable approach was adopted to characterize the strength loss of basalt due to FTCs quantitatively. The F-T damage coefficient K f was defined as the ratio of a rock’s strength after FTCs of N to its initial strength before cycling, as expressed in Equation 1: K f = σ N / σ i n i (1) where σ N is the UCS after N cycles, and σ i n i is the initial UCS of the rock mass. Using the UCS data for the two weathering groups, the study first examined the general relationship between K f and N, as shown in Figure 15. The test results show that K f tends to decrease exponentially with the number of FTCs. Simple exponential decay curves can be fitted to the K f and N comparative data for both MG and SG basalts with high correlation coefficients, indicating that an exponential model is reasonable. However, a straightforward exponential function ( K f vs. N) for some constants has limitations. In particular, the best-fit exponential for the MG samples suggested that K f might drop below zero if extrapolated beyond the tested range. Obviously, K f cannot be negative; physically, as N approaches infinity, K f should approach some residual strength ratio greater than 0. The initial exponential model for the MG basalt did not capture this asymptotic behavior, indicating that it would overpredict damage for an extremely large N.

By contrast, the K f and N values of the SG samples fit the exponential comparison more effectively and presented a gradual decrease in strength, which was in line with the expectation that the SG basalt samples would approach the residual strength more slowly. For the SG basalt samples, experimental data suggest a residual K f between 0.3 and 0.5. For the MG basalt samples, introducing an asymptote is essential to avoid the nonphysical prediction of negative strength at high N.

The data was combined and nonlinear regression was performed, allowing for an asymptotic value, to create a more robust predictive model applicable to both weathering cases. In this study, a modified exponential decay function of the following form was selected: σ N = a 1 · e − N / b 1 + c 1 σ i n i (2)

Where a 1 , b 1 and c 1 are fitting constants. Here, c 1 represents the asymptotic fraction of strength as N approaches infinity (i.e., K f approaches c 1 ), a 1 represents the initial damage amplitude, and b 1 controls the rate of decay. The best-fit parameters for basalt were obtained through the utilisation of the experimental UCS data up to 100 cycles in this study: a 1 = 0.600 , b 1 = 66.98 , and c 1 = 0.415 . Thus, the combined predictive formula becomes: σ N = 0.600 · e − N / 66.98 + 0.415 σ i n i , R 2 = 0.980 (3)

This empirical formula, given by Equation 2 or Equation 3, provides a practical way to estimate the remaining UCS of basalt after N FTCs, given its initial strength. This finding suggests that for extremely large N values, the basalt ultimately retains nearly 41.5% of its original strength under the F-T conditions tested. Equation 3 yielded a high goodness of fit ( R 2 = 0.980 ) for experimental results, mainly because it sufficiently fits the SG behavior. However, for the MG samples, a single combined curve somewhat overestimates their long-term strength loss, especially since the MG loses more strength at a faster rate compared with the SG. On this basis, the model was further refined by providing separate formulations for the highly weathering degrees: one incorporating porosity growth for the MG.

For the MG basalt samples, since porosity was identified as a crucial factor, a porosity-based strength degradation model was developed. As shown in Figure 16a, the relationship between the UCS and porosity n during freezing or thawing of MG basalt could be sufficiently described by an exponential function following a Weibull distribution. The best-fit equation for the MG, denoted σ h f t , is given by: σ h f t = 4.68 · e − n / 0.763 + 0.074 σ i n i , R 2 = 0.803 (4)

This equation relates UCS to porosity n for highly weathered basalt under F-T action, with R 2 = 0.803 for the MG data. Although the goodness-of-fit is not excellent, this formula accounts for the rapid strength drop as the porosity increases and levels off to a residual value. As n increases, the exponential term decays, and capproaches 0.074, which indicates nearly 7.4% residual strength at extremely high damage.

For the SG basalt samples, a simpler cycle-count-based model was used, as the porosity changes were small and less directly tied to strength loss (Figure 16b). Based on the regression relations between the various and the damage coefficient, The SG strength, denoted by σ s f t , can be obtained by: σ s f t = 0.432 · e − N / 47.282 + 0.563 σ i n i , R 2 = 0.984 (5)

This formula is effectively the same form as Equation 4 and indeed matches the combined fit mentioned earlier. The R² was 0.984 for the SG data, indicating an excellent fit, further implying that SG strength degradation is predominantly a function of the number of cycles directly (Equation 5). Notably, the SG model’s asymptote ( c 1 = 0.563 ) aligns with the idea that 56% of the strength remains after many cycles, similar to what the combined model suggested. By contrast, the MG model (Equation 4) predicts a much lower asymptotic strength (7.4% of the initial value), reflecting the severe damage possible in already weak, cracked material.

In practical terms, these models indicate that for engineering assessments, if the initial weathering degree of basalt is known, one should select the appropriate model. If the basalt is highly weathered, then tracking the porosity increase might be essential to accurately predict strength loss because damage accelerates as new porosity is created. If the basalt is only slightly weathered, then one can reasonably predict the strength after N cycles only from the number of cycles, using an exponential decay with an asymptote as given.

Apart from the UCS, other mechanical parameters can also be expressed in a similar degradation model form. This study applied a dimensionless damage index approach to Young’s modulus ( E ), cohesion ( C ), and friction angle ( φ ) for both groups. Each parameter at N cycles (denoted by E N , C N and φ N ) was normalized by its initial value ( E i n i ,   C i n i and φ i n i ), and the decay with N was fitted. The results, shown in Figures 17a,b, indicate that E and C follow an exponential decay (Equations 6, 7), whereas φ exhibits a linear decline with N. The fitting yielded the following formulas: E N = a 2 · e − N / b 2 + c 2 E i n i (6) C N = a 3 · e − N / b 3 + c 3 C i n i (7) φ N = a 4 · N + 1 φ i n i (8) where a 2 , b 2 , and c 2 , among other variables, are constants obtained from the regression, and N is the cycle count. Equation 8 for the friction angle implies a nearly linear percentage reduction in φ with increasing number of cycles (with a 4 being a small negative slope). The exact fitting constants for experimental results are given in Table 7 along with their R 2 values. In general, these equations can serve to update slope stability model parameters after a specified number of FTCs.

The abovementioned empirical models are derived from laboratory findings and are applicable to the tested conditions of saturated F-T action involving complete freezing and thawing in each cycle. As such, they can serve as a practical reference for the engineering-oriented estimation of rock strength degradation over time. However, the predictive capability of these models is inevitably influenced by material heterogeneity and microstructural complexity.

Although the exponential relationship between the UCS damage coefficient and porosity for the MG group exhibits a significant correlation (R² = 0.803), some scatter is still evident in Figure 16a. This scatter indicates that porosity is an important factor in freeze-thaw-induced degradation of MG basalt, but it is not the sole controlling variable.

It should be noted that, although no typical primary vesicles were observed in the basalt samples used in this study, porosity manifests mainly in the form of micropores and microcracks, which are distributed heterogeneously in rock specimens. Such microstructural heterogeneity can exert mechanical effects similar to the randomly distributed vesicles, as it promotes localised frost-heaving stress concentration and preferential crack propagation paths during FTCs. Consequently, even at comparable porosity levels, significant differences may exist among specimens in terms of local pore clustering, crack orientation and connectivity. This leads to fluctuations in UCS (or K f ) under similar porosity conditions.

The scatter induced by microstructural heterogeneity is more pronounced in the SG group (Figure 16b), where the overall porosity is relatively low, making it difficult to establish a stable relationship between porosity and macroscopic mechanical degradation. Additionally, variations in initial microcrack density, mineral-matrix interface integrity, and local weathering intensity among MG specimens may interact with pore structure during FTCs, amplifying the scatter in mechanical responses further.

Therefore, the experimental results suggest that porosity can effectively predict the overall trend of weakening in MG basalt as a single parameter. However, for rocks with pronounced microstructural heterogeneity, more accurate strength prediction requires additional parameters to be incorporated, such as crack connectivity and pore-crack structural characteristics, to develop multivariable predictive models. Accordingly, the empirical relationships proposed in this study should be regarded as engineering-oriented estimation models applicable within the tested porosity range and freeze-thaw pathways.

Although this study investigates the mechanical responses and microstructural changes of dense basalt with different degrees of weathering under controlled freeze-thaw cycling, it remains necessary to clarify the applicability boundaries associated with the experimental conditions and the scope of the investigation.

The laboratory F-T cycles were conducted under fully saturated conditions following regular and symmetric temperature paths. These conditions represent an idealized and accelerated degradation scenario to a certain extent. Conversely, rock masses in natural cold-region environments are typically in an unsaturated state, and the freezing-thawing process often exhibits asymmetry in cooling and warming rates as well as in holding durations. Such differences result in alterations to the relative contributions of frost-heaving pressure and thermally induced stresses during the evolution of damage. The results presented herein primarily reflect the response of dense basalt to freeze-thaw action under saturated or near-saturated conditions, and their quantitative extrapolation to more complex natural environments should be undertaken with appropriate consideration of site-specific hydrological and thermal conditions.

In the microstructural characterisation, the present study primarily relied on SEM observations to qualitatively and semi-quantitatively analyse the initiation and propagation of microcracks in basalt. This method facilitates the clear identification of damage evolution patterns in two-dimensional sections. However, it does not provide direct quantitative information on the three-dimensional distribution and connectivity of pores and cracks. This limitation imposes constraints on the establishment of more rigorous quantitative relationships between microstructural parameters and macroscopic mechanical degradation.

Based on these considerations, future research could improve the experimental design by accounting for different degrees of rock saturation and asymmetric temperature paths. Other three-dimensional inspection techniques, such as CT and NMR, could be employed to better resolve the spatial distribution and connectivity of damage features. Coupled freeze-thaw and loading tests conducted under confining pressure or disturbance conditions may provide further insight into damage evolution. These additions would strengthen the interpretation of freeze-thaw damage mechanisms and improve the reliability and transferability of the empirical models.