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. 2026 Feb 10;11(7):12662–12674. doi: 10.1021/acsomega.5c12996

Study on the Physico-Mechanical Properties and Damage Mechanisms of Weakly Cemented Sandstone under Freeze–Thaw Cycles

Shi Tan †, Ning Wang ‡,*, Wenjuan Li §, Lianchun Zhou †, Mingdong Yu †
PMCID: PMC12947199  PMID: 41768735

Abstract

Weakly cemented sandstone is a critical rock type in cold-region engineering. It is characterized by a loose fabric and well-developed pores, which makes it highly sensitive to freeze–thaw disturbance. In this study, weakly cemented sandstone from Gansu Province, China, was investigated. Freeze–thaw cycling tests were performed. Uniaxial compression, ultrasonic P-wave measurements, nuclear magnetic resonance (NMR), and fractal theory were combined to clarify the evolution mechanism of freeze–thaw damage. The results show a typical three-stage deterioration in physical and mechanical properties. The uniaxial compressive strength (UCS) and elastic modulus (E) decreased by 59.09 and 66.37%, respectively. The failure pattern shifted from a single dominant crack to cooperative failure with multiple cracks. Porosity increased from 12.86 to 22.21%. The proportion of micropores first increased and then decreased, whereas macropores became dominant, indicating an evolutionary trend of micropore activation, mesopore expansion, and macropore predominance. The pore fractal dimension decreased, indicating that pore growth was accompanied by enhanced connectivity and structural simplification. Pearson correlation analysis further demonstrated strong coupling between pore structure parameters and mass, P-wave velocity, UCS, E, and fracture patterns. These findings comprehensively clarified the multiscale damage evolution mechanism of weakly cemented sandstone under freeze–thaw cycles and revealed a sequential damage development path characterized by pore expansion, structural simplification, mechanical degradation, and increasing complexity of fracture patterns. This study provides scientific insights and experimental support for stability evaluation of rock masses in cold region engineering.

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1. Introduction

With the increasing intensity of mineral resource development in cold regions, the engineering stability of weakly cemented sandstone, a common ore-bearing rock mass, has received growing attention. This type of rock is characterized by low cementation strength and a loose structure and is therefore particularly vulnerable in cold environments. Under such conditions, long-term exposure to severe seasonal temperature fluctuations leads to frequent freeze–thaw cycles. Consequently, microstructural damage progressively accumulates, which in turn induces pronounced deterioration in macroscopic mechanical properties and ultimately results in instabilities such as slope failures. − Therefore, the freeze–thaw damage evolution of weakly cemented sandstone needs to be revealed at the microscale. This is essential for clarifying the degradation mechanisms and thereby improving the long-term stability of engineering projects in cold regions.

Current studies on the effects of freeze–thaw action on rocks have primarily focused on the evolution of macroscopic physical and mechanical properties. − Accordingly, uniaxial compression tests, Brazilian splitting tests, and ultrasonic velocity measurements have been widely used to systematically reveal the degradation trends of key parameters, including uniaxial compressive strength (UCS), elastic modulus (E), and P-wave velocity, under freeze–thaw cycles. For example, Li et al. conducted freeze–thaw tests on Huashan granite over a temperature range of −20 to 20 °C for up to 100 cycles. The UCS and E decreased by 38.4 and 21.5%, respectively. Notably, the strength degradation rate did not increase monotonically with cycle number. Instead, the average degradation rate varied from 0.1 to 2.4% across different stages. Moreover, several studies have developed damage constitutive models based on mechanical tests. − For instance, Feng et al. carried out triaxial compression tests on saturated sandstone after different numbers of freeze–thaw cycles (0, 20, 40, 60) under various confining pressures (3, 5, 10 MPa). They proposed a damage constitutive model based on energy dissipation theory and the minimum energy consumption principle to describe triaxial mechanical behavior. However, despite these advances, research has largely remained at the macroscale. , Therefore, a systematic characterization of the dynamic evolution of microstructural features during freeze–thaw cycling is still lacking. This gap hinders a clear understanding of the physical mechanisms underlying macroscopic degradation.

In fact, freeze–thaw damage is primarily driven by water–ice phase transitions and moisture migration, which disturb and enlarge the microscale pore structure. − During freezing and thawing, volumetric expansion and crystallization pressure generated by pore-water freezing, together with the migration and redistribution of unfrozen water under a temperature gradient, can induce local stress concentrations. − Consequently, cementation bonds may fracture and grain-to-grain contacts may degrade, thereby promoting microcrack initiation. With continued freeze–thaw cycling, these microcracks propagate and coalesce, and eventually develop into through-going macroscopic cracks. Therefore, establishing a damage-evolution pathway from the pore scale to the structural scale is essential for understanding freeze–thaw deterioration mechanisms. In recent years, nuclear magnetic resonance (NMR) has attracted increasing attention in rock-damage studies because it is highly sensitive to changes in pore-size distribution and can nondestructively track the dynamic evolution of pore structures. − With advances in spectrum inversion and parameter-identification techniques, NMR has been extended from static characterization to dynamic monitoring and damage-index construction under freeze–thaw cycling, as well as under coupled freeze–thaw and loading conditions. For example, Su et al. proposed a model to quantify unfrozen water content during freeze–thaw processes, and NMR was then used to verify the evolution of pore-size distribution and unfrozen water content in red sandstone subjected to freeze–thaw cycles. In addition, complementary methods such as computed tomography (CT) and scanning electron microscopy (SEM) have been employed to reveal pore enlargement, microcrack initiation, and crack-network connectivity under freeze–thaw action, ,− thereby providing supporting evidence for mechanistic interpretation and microscale model development. However, most existing studies focus on well-cemented rocks, whereas research on pore-structure evolution of weakly cemented sandstone under freeze–thaw cycles remains limited.

Based on this, weakly cemented sandstone from a coal mine in Gansu was selected as the research object. NMR tests and uniaxial compression experiments were conducted under freeze–thaw cycles. Accordingly, the evolution of key parameters, including mass, wave velocity, porosity, pore-size distribution, mechanical properties, and failure mode, was systematically characterized. Furthermore, fractal theory was introduced to quantitatively describe the geometric features of the pore structure. Meanwhile, Pearson correlation analysis was employed to establish relationships between macroscopic mechanical responses and microstructural parameters. As a result, the multiscale propagation pathway and degradation mechanism of freeze–thaw damage in weakly cemented sandstone were clarified. Overall, these results provide theoretical support and experimental references for evaluating the stability of rock masses in cold regions.

2. Material and Methods

2.1. Test Material

As shown in Figure , the specimens used in this study were collected from a Jurassic weakly cemented sandstone layer in a coal mine in Gansu. The stratum was formed in a fluvial–lacustrine depositional environment and exhibits typical sedimentary and structural characteristics. To reduce the influence of sample heterogeneity, all specimens were obtained from the same depth. The lithology is weakly cemented sandstone with a reddish-brown appearance. At the macroscopic scale, no obvious bedding structures or structural damage were observed. According to the Chinese standard GB/T 23561.9-2009 for determining the physical and mechanical properties of coal and rock, the samples were prepared as standard cylindrical specimens, each with a diameter of 50 mm and a height of 100 mm. Meanwhile, the flatness and parallelism errors at the specimen ends were strictly controlled within 0.02 mm. The basic physical properties are listed in Table .

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Field sampling site, specimen morphology, and microscopic characteristics of the weakly cemented sandstone.

1. Physical Properties of Saturated Weakly Cemented Sandstone.

m (g) Porosity (%) P-wave (km/s) UCS (MPa) E (GPa)
437.86 12.86 2.45 35.52 5.67
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Under an orthogonally polarized petrographic microscope, the specimens exhibited typical features of weakly cemented sandstone. The detrital framework was dominated by quartz (70%) and feldspar (25%). Grain sizes were mainly 0.1–0.5 mm. Sorting was moderate. Most grains were angular to subangular. The grain arrangement was disordered, and no distinct bedding was observed. Although the framework minerals were primarily high-strength quartz and feldspar, the cement content was very low (2–3%). The cement was mainly cryptocrystalline clay. It occurred as dispersed patches or as discontinuous infill within intergranular pores. As a result, grain contacts were mostly point contacts or locally cemented contacts, and the rock was primarily grain-supported. These microstructural characteristics indicate weak cementation, a loose fabric, and weak intergranular bonding, which is consistent with the definition of weakly cemented rock. −

2.2. Experimental Steps and Equipment

As shown in Figure , a multistage testing procedure was established to systematically evaluate the effects of freeze–thaw action on the physical and mechanical properties of weakly cemented sandstone. The procedure included freeze–thaw treatment, microstructural detection, and mechanical property testing. First, all sandstone specimens were oven-dried at 105 °C for 24 h and then allowed to cool naturally to room temperature. The specimens were then saturated using a vacuum–pressure saturation system. A vacuum of −0.1 MPa was applied for 6 h. Distilled water was then introduced, and a pressure of 30 MPa was applied and maintained for 24 h to ensure full saturation. Saturation was verified by the gravimetric method to maintain consistency among groups. Full saturation was preserved during subsequent freeze–thaw conditioning and all follow-up tests. After saturation, freeze–thaw cycling was conducted in a programmable temperature chamber. The temperature range was selected with reference to the Standard for Test Methods of Engineering Rock Mass (GB/T 50266-2013), typical cold-region climatic conditions in China, and commonly used settings in previous studies. The freezing and thawing temperatures were set to −20 and 20 °C, respectively. , Each freezing and thawing stage lasted 12 h, yielding a 24 h cycle. The specimens remained saturated throughout the cycling process. A total of 0, 5, 15, 30, 45, and 60 freeze–thaw cycles were applied to capture damage evolution at different degradation stages. This cycle scheme was designed according to the typical progression of freeze–thaw damage, in which damage remains relatively stable at early stages, then develops, and finally accelerates. It therefore covers the full evolution from the intact state to the accelerated damage stage.

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Test system.

After the completion of freeze–thaw cycles, the specimens were weighed and tested for P-wave velocity to obtain mass variation and structural integrity indicators under freeze–thaw damage. The evolution of porosity and pore size distribution was analyzed using a MicroMR12-150H-I low-field nuclear magnetic resonance instrument. The specimens were then placed on a WAW-1000 kN uniaxial loading machine. Loading was applied under displacement control at a rate of 0.15 mm/min. Complete stress–strain curves were recorded. Mechanical parameters including UCS and E were extracted. No fewer than three parallel specimens were prepared for each freeze–thaw cycle group to ensure the reliability and representativeness of the experimental results.

2.3. Testing Principle

2.3.1. NMR

As a nondestructive testing method, NMR technology has significant application value in rock physics and reservoir characterization. − This technique detects the relaxation behavior of hydrogen nuclei in pore fluids under an applied magnetic field. Quantitative characterization of pore structure, fluid occurrence, and permeability in rocks can be achieved. The fundamental principle is that the distribution of transverse relaxation time (T 2) is directly related to pore size. The cumulative amplitude of the T 2 spectrum is proportional to the total amount of hydrogen nuclei in the sample, which can be converted to effective porosity. The observed transverse relaxation rate is governed by three mechanisms. It is expressed as

1T2=1T2B+1T2S+1T2D 1

Where T 2 is the transverse relaxation time. T 2B is the bulk relaxation time. T 2S is the surface relaxation time. T 2D is the diffusion relaxation time. In low-field nuclear magnetic resonance testing, the effects of bulk and diffusion relaxation are generally negligible. eq can be simplified as

1T2=1T2S=p2(SV)=Fsp2r 2

Based on the above principle, the T 2 curve can be directly converted into a pore size distribution curve.

2.3.2. Fractal Calculation of Pores

The pore structure of rock is highly heterogeneous and spans multiple length scales. Fractal theory offers an effective framework for describing such irregular geometries. Accordingly, it has been widely applied to quantify the geometric properties of complex pore systems. − In NMR measurements, the transverse relaxation time (T 2) is positively correlated with pore radius. Therefore, the T 2 distribution can be used to characterize pore-size distribution in rock. Within the fractal framework, the normalized cumulative pore volume fraction (S v) is defined as the ratio of the cumulative pore volume of pores smaller than that corresponding to a given T 2 to the total pore volume. It can be expressed as follows:

Sv=(T2T2max)3−D 3

Where T 2max is the maximum transverse relaxation time, and D is the pore fractal dimension.

lg⁡(Sv)=(3−D)lg(T2)+(D−3)lg(T2max⁡) 4

By taking the common logarithm of both sides of the above equation, a linear relationship can be obtained as follows:

lg⁡(Sv)=(3−D)lg(T2)+(D−3)lg(T2max⁡) 5

A linear regression of the S v and T 2 data in a double-logarithmic coordinate system yields the slope (k). The D can then be calculated directly from

D=3−k 6

D is a dimensionless parameter ranging from 2 to 3. − Values closer to 2 indicate a simpler pore geometry with smoother pore surfaces. Values closer to 3 indicate a more irregular, space-filling pore network, with higher effective specific surface area and greater heterogeneity.

3. Result Analysis

3.1. Evolution of Mass and P-wave Velocity

Figure illustrates the evolution of mass and P-wave velocity of weakly cemented sandstone under freeze–thaw cycles. The specimen mass increased from 437.86 to 454.83 g, showing a continuous upward trend with a clear stage-wise variation. During the first five cycles, the mass increased by only 0.09%, indicating that the internal structure remained relatively intact. At this stage, only a limited number of microcracks were initiated, and their influence on water absorption was minimal. Between 15 and 45 cycles, microcracks gradually expanded and began to interconnect, leading to the formation of additional water-absorption channels. Accordingly, the stage-wise mass increase rose from 0.48 to 0.91%, exhibiting a stable growth trend. By the 60th cycle, the increase rate sharply reached 1.68%, suggesting substantial structural deterioration. At this stage, porosity and pore connectivity increased significantly, and the water absorption capacity was markedly enhanced. Compared to mass variation, P-wave velocity attenuation proved more sensitive. The P-wave velocity decreased from 2.45 to 1.46 km/s, reflecting progressive degradation of structural integrity. In the early stage, the velocity reduction was limited to −1.22%, suggesting that a well-connected microcrack network had not yet formed and the impact on P-wave propagation remained minimal. However, during cycles 15 to 45, the stage-wise change rate dropped from −3.72 to −12.32%, indicating accelerated development of internal cracking and disruption of the P-wave transmission path. By the 60th cycle, the stage-wise change rate reached −21.08%, demonstrating that crack connectivity had significantly increased and the rock structure was severely deteriorated. P-wave propagation was most severely hindered at this stage.

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Evolution of mass and P-wave velocity of weakly cemented sandstone under freeze–thaw cycles.

Overall, both mass increase and P-wave velocity reduction exhibited a typical three-stage trend: an initial stable stage, a steady development stage, and an accelerated deterioration stage. This trend reflects the coupled evolution of pore connectivity and skeleton integrity during freeze–thaw damage. At the early stage, freeze–thaw action mainly affected pre-existing pores. Water filling caused only a slight mass increase, and the P-wave velocity decreased marginally. With continued cycling, repeated frost-heaving stress degraded cementation and promoted microcrack growth as well as pore-network connectivity. Consequently, water retention increased and mass rose steadily. Meanwhile, crack development and weakened grain contacts enhanced wave scattering and reduced stiffness, leading to a continuous decrease in velocity. At the late stage, extensive pore coalescence and severe structural degradation induced an accelerated response. Therefore, mass gain primarily reflects enhanced pore connectivity and effective water-storage space, whereas velocity loss indicates reduced structural integrity. Together, these indices characterize the evolution of freeze–thaw damage.

3.2. Evolution of Mechanical Properties

Figure and Table present the evolution of stress–strain curves and the corresponding variation in mechanical properties of weakly cemented sandstone under freeze–thaw cycles. Overall, the macroscopic mechanical properties progressively deteriorated with increasing freeze–thaw cycles, and the extent of degradation became more pronounced. The UCS decreased from 35.52 to 14.53 MPa, marking a reduction of 59.09%, while the E declined from 5.67 to 1.91 GPa, corresponding to a 66.37% decrease. Notably, the reduction in E was slightly greater than that in UCS, suggesting that the material’s elastic deformation capacity was more sensitive to freeze–thaw effects. This response is closely associated with the intrinsic structural characteristics of weakly cemented sandstone, including poorly bonded interfaces, well-developed porosity, and the propensity for microcrack initiation and propagation. The stage-wise change rate showed strong consistency with the trends of mass increase and P-wave velocity attenuation, further validating the coupled and systematic nature of freeze–thaw damage evolution. Moreover, the shape of the stress–strain curve underwent distinct transformations. With an increasing number of freeze–thaw cycles, the initial compaction stage became progressively extended, indicating that pore closure and rearrangement of the internal skeleton structure occurred more readily at the early loading stage. This behavior implies that freeze–thaw cycling enhanced internal porosity and structural looseness, thereby increasing irreversible deformation during initial loading.

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Mechanical characteristics of weakly cemented sandstone under freeze–thaw cycles.

2. Average Values of UCS and E for Weakly Cemented Sandstone under Freeze-Thaw Cycles.

Number of cycles (n) UCS (MPa) SD E (GPa) SD
0 35.52 1.42 5.67 0.58
5 33.68 1.51 5.24 0.48
15 29.03 1.62 4.41 0.23
30 24.59 1.35 3.59 0.28
45 19.96 1.54 2.83 0.27
60 14.53 1.36 1.91 0.21
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In summary, freeze–thaw cycles not only caused a significant reduction in the strength and stiffness of weakly cemented sandstone but also altered the characteristics of the stress–strain curve. These changes were the macroscopic manifestations of multiple damage effects, including microcrack accumulation, enhanced pore connectivity, and weakened cementation interfaces within the material.

3.3. Failure Patterns

Figure illustrates the failure patterns of weakly cemented sandstone under freeze–thaw cycles. With continued cycling, the failure mode evolved progressively from a single dominant crack to a complex network of multiple cracks, accompanied by continuous degradation of structural integrity. The specimen without freeze–thaw treatment exhibited a typical single shear failure surface with clear crack orientation, reflecting a relatively intact internal structure. After 15 cycles, the main crack remained dominant, but small secondary cracks appeared on both sides, and local structural loosening was observed, indicating the initiation and outward propagation of microcracks. Between 30 and 45 cycles, crack development intensified, characterized by increased crack density, intersection, branching, and overlapping, along with local shear spalling. By the 60th cycle, a large number of cracks had developed in multiple directions and exhibited high connectivity. Intersecting shear surfaces and visible fragmentation indicated that structural integrity was nearly completely lost. The failure mode thus transitioned from early single-crack dominance to a typical multicrack cooperative mechanism.

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Failure patterns of weakly cemented sandstone under different freeze–thaw cycles.

Overall, the freeze–thaw cycles did not alter the dominant mechanism of shear failure but significantly increased the number, connectivity, and spatial complexity of cracks. The fracture pattern exhibited a trend of evolution from a simple form to a complex network.

To further quantify the complexity and spatial distribution characteristics of fracture patterns, the box-counting dimension method was introduced for fractal analysis of fracture images. The binary fracture image was divided into grids at different scales. The number of boxes N(ε) occupied by fractures at each scale was counted. A log–log plot of N(ε) versus box size ε was constructed. The fractal dimension D of the fractures was calculated by fitting the relationship.

D=−limε→0⁡log⁡N(ε)log⁡ε 7

Where N(ε) denotes the number of boxes with side length ε that are occupied by fractures.

A larger D indicates a denser and more spatially extended crack distribution, with increased branching and intersections, and thus a more complex crack network. Figure shows the fitting results of the fractal dimension of failure patterns in weakly cemented sandstone subjected to freeze–thaw cycles. Overall, D increased markedly with the number of cycles, rising from 1.21 to 1.87. This trend reflects a clear transition of the fracture network from a simple to a highly complex state.At the initial stage (n = 0–5), D increased slightly from 1.21 to 1.25, indicating that the fracture pattern remained relatively simple. During the accelerated degradation stage (n = 15–45), D increased from 1.37 to 1.64, reflecting an increase in crack density and a more irregular spatial distribution. By the 60th cycle, D rose rapidly to 1.87, indicating that the fracture network had become highly connected and densely distributed, with pronounced multilevel branching. At this stage, the specimen structure had entered a severely degraded state. It should be emphasized that the fractal dimension quantitatively characterizes the evolution of fracture network complexity. Its variation is highly consistent with mass increase, P-wave velocity attenuation, and reductions in UCS and E. This consistency indicates that the increasing complexity of the crack network is a macroscopic manifestation of freeze–thaw damage.

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Fitting results of the fractal dimension of failure patterns in weakly cemented sandstone under different freeze–thaw cycles.

In summary, the D provides an effective quantitative indicator of fracture-pattern complexity and connectivity. As freeze–thaw cycles increase, isolated cracks gradually evolve into an interconnected multicrack network. This evolution signifies a transition in failure mode from dominance by a single weak plane to a global and diffuse degradation process. Consequently, conventional support strategies that focus mainly on localized discontinuities become less effective. Therefore, support design in cold regions should shift from local control to systematic reinforcement and overall confinement. Furthermore, auxiliary measures such as grouting and void filling, drainage and seepage control, and thermal insulation with freeze-mitigation should be integrated. Together, these measures can delay crack propagation and coalescence, maintain rock-mass integrity, and improve long-term durability.

3.4. Pore Characteristics

3.4.1. T2 Curve

Figure shows the NMR characteristics of weakly cemented sandstone after freeze–thaw cycles. Overall, all T 2 spectra exhibited a distinct bimodal distribution, which differs from the typical trimodal pattern commonly observed in conventional sandstone. This indicates that the pore type distribution in the rock was relatively concentrated and that the pore size structure exhibited certain particularities. The first peak appeared in the range of 0.1–8.5 ms, corresponding mainly to micropores. The second peak was distributed between 8.5–1000 ms, reflecting the presence of mesopores and macropores. The area of the second peak was significantly larger than that of the first, indicating that the pore system was dominated by mesopores and macropores. No distinct trough was observed between the two peaks, suggesting good connectivity across different pore scales. With the progression of freeze–thaw cycles, the T 2 spectra shifted toward longer relaxation times, and the signal amplitude continued to increase. This reflects a process of pore expansion and systematic growth in total pore volume. In the early stage of freeze–thaw cycling, changes in the first peak were the most pronounced, indicating that the initiation of microcracks and the opening of previously closed micropores were the dominant mechanisms. In the middle and late stages, the amplitude and position of the second peak changed significantly, indicating that the expansion of mesopores and macropores and the connection of fracture networks had become the primary failure modes. The pore structure evolved from dispersed damage to through-going damage.

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NMR characteristics of weakly cemented sandstone under freeze–thaw cycles.

Corresponding to the changes in T 2 spectral shape, porosity and T 2 spectral area also exhibited a coupled evolution (Figure b). Porosity increased from 12.86 to 22.21%, representing a rise of 72.73%. The T 2 spectral area increased from 109174.49 to 197690.21, representing a rise of 81.17%. Both parameters showed a nonlinear growth pattern, indicating that freeze–thaw damage involved not only the accumulation of pore number but also the reconstruction of pore structure.

3.4.2. Pore distribution

The morphological analysis of the T 2 spectra preliminarily revealed the pore distribution characteristics and the evolution trend of freeze–thaw-induced damage. To further clarify the evolution behavior of pores at different scales, a quantitative classification was conducted based on the correlation between T 2 relaxation time and pore radius. The pores were categorized into three types: micropores (<0.1 μm), mesopores (0.1–1 μm), and macropores (>1 μm). −

Figure illustrates the pore structure evolution of weakly cemented sandstone under freeze–thaw cycles. The results indicate that freeze–thaw action not only led to an overall increase in pore volume but also induced significant restructuring of the pore–throat system. In the initial state, micropores, mesopores, and macropores accounted for 18.90, 39.18, and 42.92% of the total pore volume, respectively. This indicates that the pore system was dominated by mesopores and macropores. This observation was highly consistent with the characteristics of the T 2 spectra. During the early stage of freeze–thaw cycling, the porosity of micropores increased from 2.43 to 3.37%, with their proportion rising to 24.16%. This implies that the nucleation of microcracks and the activation of previously closed micropores constituted the dominant damage mechanism at this stage. Although slight increases in mesopore and macropore volumes were observed concurrently, their relative proportions slightly decreased, indicating that the pore structure had entered a phase of scattered adjustment. In the midterm stage, mesopore porosity steadily increased from 5.16 to 5.96%, while macropore porosity rose from 5.42 to 6.22%, resulting in a combined proportion recovery to 39.37%. This suggests that the freeze–thaw damage mechanism gradually shifted toward the expansion and interconnection of mesopores and macropores. Mesopores served as bridges within the pore network, promoting the transformation of the damage mode from isolated point-like features to a more networked structure. During the late stage of freeze–thaw cycling, the total porosity increased significantly from 18.28 to 22.21%. Notably, macropore porosity surged from 7.48 to 10.61%, accounting for 47.76% of the total, with the first emergence of a new pore size class within the range of 16–25 μm. This reflects substantial damage to the matrix skeleton and indicates that fracture development had entered a stage of macroscopic interconnection. In the same period, the proportion of micropores declined to 18.33%, highlighting their diminished contribution to the overall pore system.

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Pore distribution of weakly cemented sandstone under freeze–thaw cycles.

In summary, the pore structure of weakly cemented sandstone exhibited a distinct stage-wise evolution under freeze–thaw cycles. In the early stage, the development was dominated by the growth of micropores, corresponding to the initiation of microdamage and the activation of previously closed micropores. During the middle stage, mesopore expansion and enhanced connectivity became dominant, indicating the formation of a pore network. In the later stage, rapid growth of macropores occurred, accompanied by the emergence of a new pore size class, suggesting skeleton degradation and fracture interconnection. This multiscale progressive mechanism, characterized as “micropore activation–mesopore expansion–macropore domination”, comprehensively reveals the full evolution process of freeze–thaw damage from microscopic initiation to macroscopic failure.

3.4.3. Fractal Characteristics of Pores

The pore distribution analysis in Section revealed the stage-wise evolution of pore structure under freeze–thaw cycles. However, it has limited capability in characterizing the spatial complexity and heterogeneity of the pore system. Therefore, this section further quantifies the spatial geometric features of pores at different scales using fractal theory.

Figure presents the pore fractal dimensions of weakly cemented sandstone under different numbers of freeze–thaw cycles. The results indicate that the total pore fractal dimension (D t), mesopore fractal dimension (D e), and macropore fractal dimension (D a) were all distributed within the range of 2–3, suggesting good statistical self-similarity. In contrast, the micropore fractal dimension (Di) remained below 2.0, indicating the absence of typical fractal characteristics and suggesting that the spatial distribution of micropores was discrete and random. With the progression of freeze–thaw cycles, D t, D e, and D a exhibited systematic reductions. Specifically, D t decreased from 2.68 to 2.47, D e from 2.88 to 2.72, and D a from 2.97 to 2.84. This change indicates that freeze–thaw action drives the pore system to evolve from a complex, multiscale heterogeneous structure toward a network with higher connectivity and a simplified geometry. This trend is attributed to frost-heaving stress, which preferentially propagates and connects pre-existing weak pathways, causing dispersed and tortuous micropores to gradually coalesce into more continuous backbone channels. At the same time, the channelization process suppresses fine-scale boundary roughness and multilevel branching, thereby simplifying the overall pore geometry. Notably, throughout the entire evolution process, a consistent hierarchy of fractal dimensions was maintained, with D a > D e > D t. This pattern reveals a pronounced scale effect in pore geometry complexity. The macropore system, influenced by crack propagation and overlapping, exhibited the highest surface roughness and geometric irregularity. The mesopores, functioning as transitional structures within the pore network, showed intermediate complexity. In contrast, the total pore fractal dimension was the lowest, reflecting a tendency toward structural homogenization during the multiscale coevolution of the pore system.

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Fractal dimension fitting of pores in weakly cemented sandstone under different freeze–thaw cycles.

Further analysis of the relationship between porosity and fractal dimension (Figure ) shows that D t, D e, and D a are all significantly and negatively correlated with porosity. This trend indicates that an increase in porosity reflects not only pore-volume expansion but also a reduction in pore geometric complexity. From an engineering stability perspective, porosity describes changes in pore volume at a quantitative scale. In contrast, the fractal dimension characterizes the roughness, hierarchical organization, and connectivity pattern of the pore network from a geometric and topological perspective. It can therefore capture the extent to which the pore system evolves from a dispersed, multilevel structure toward channelized and through-going pathways. As the fractal dimension decreases, effective connected channels are more likely to form. Meanwhile, skeleton continuity and overall stiffness tend to deteriorate, which is consistent with P-wave velocity attenuation and the degradation of mechanical properties such as UCS and E. Therefore, the fractal dimension can serve as a complementary indicator to porosity for quantitatively assessing the accumulation of freeze–thaw damage and the associated deterioration in rock-mass stability.

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Relationship between porosity and fractal dimension of weakly cemented sandstone under freeze–thaw cycles.

3.5. Damage Evolution Law

3.5.1. Microscopic Damage Mechanism

To deepen the understanding of the internal degradation process of weakly cemented sandstone, it is crucial to reveal the underlying microscopic damage mechanism induced by freeze–thaw cycles. Owing to its high porosity and loose structure, the material exhibited a nonlinear, multipath evolution characterized by “pore disturbance–cementation degradation–fracture network expansion” (Figure ).

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Schematic diagram of damage to weakly cemented sandstone under freeze–thaw cycles.

In the initial stage of freeze–thaw cycles, external moisture was intruded along pore channels and filled the primary micropores and microcracks. Due to the fact that the cementing material in weakly cemented sandstone mainly consisted of clay minerals or weak sericite, hydration reactions with water readily occurred, leading to a reduction in cementation strength. Damage at this stage was primarily manifested as the relaxation of cemented structures, weakening of particle interfaces, and the reactivation of previously closed pores. These changes provided potential pathways and stress concentration zones for subsequent frost heave damage. When the temperature dropped below the freezing point, pore water froze and expanded by approximately 9% in volume. The resulting frost heave pressure could reach up to 60 MPa, far exceeding the tensile strength of weakly cemented sandstone. This pressure was concentrated on pore walls and crack tips, promoting the initiation and propagation of microcracks. Cracks in this period predominantly developed along particle contacts or weak cementation planes, displaying discontinuous and nonpenetrative characteristics. The damage mechanism during this stage could be summarized as “localized microcrack initiation–restricted propagation.” As the freeze–thaw process progressed into the midterm stage, the number of microcracks continued to increase and began to interconnect. The pore structure evolved from low connectivity and weak interlinkage toward high connectivity and multiscale interaction. The linkage of cracks expanded local weak zones into structurally reconstructed regions. Some cracks even exhibited tendencies to propagate across layers, indicating that damage had advanced from local deterioration to a systematic topological reconstruction. In the later stages of freeze–thaw cycles, a coupled evolution between microcracks and the pore system was observed. Bridging structures were formed between cracks, which penetrated in multiple directions and eventually intertwined into a complex fracture network. The failure paths gradually broke through the original weak cementation interfaces and achieved cross-scale connections through mechanisms such as intergranular debonding and pore-edge splitting. At this stage, the fracture network exhibited self-sustaining characteristics, resulting in a typical “fracture–pore synergistic instability” behavior.

3.5.2. Macroscopic and Microscopic Damage Correlation

To reveal the multiscale damage evolution pathway of weakly cemented sandstone under freeze–thaw cycles, a systematic Pearson correlation analysis was performed. As shown in Figure , freeze–thaw cycling induced a clear coupling between pore characteristics and mechanical responses of the rock mass.

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Pearson correlation coefficient matrix of key parameters of weakly cemented sandstone under freeze–thaw cycles.

At the microscopic scale, the correlation coefficients between porosity and T 2 spectral area were both close to 1.00, indicating a highly synchronized growth trend during the accumulation of freeze–thaw-induced damage. Simultaneously, these microscopic indicators exhibited significant negative correlations with the D t, D e, D a, with r values less than −0.93. This relationship suggests that freeze–thaw cycling caused continuous pore-volume expansion and enhanced pore-network connectivity. As a result, the original multiscale fractal geometry was progressively simplified and degraded, leading to a consistent decrease in pore fractal dimensions. At the macroscopic scale, the P-wave velocity, UCS, and E were strongly negatively correlated with porosity, T 2 spectral area, and m, with correlation coefficients below −0.96. In contrast, they were significantly positively correlated with D t, D e, and D a, with r values exceeding 0.94. This indicates that mechanical degradation was driven not only by pore-volume expansion. It was also controlled by the transformation of the pore system from a complex multilevel structure to a coarser and more interconnected network. Higher pore fractal dimensions imply a more complete hierarchical structure and more uniform load transfer paths, which are beneficial for maintaining the overall strength of the rock. Conversely, the reduction in fractal dimensions reflects the weakening and degradation of the load-bearing skeleton, which imposes a significant adverse effect on strength and stiffness. The D of the failure pattern exhibited particularly strong correlations. It showed extremely strong positive correlations with porosity, T 2 spectral area, and m, with correlation coefficients around 0.99, and strong negative correlations with P-wave velocity, UCS, E, and pore fractal dimensions, with r values below −0.97. It showed extremely strong positive correlations with porosity, T 2 spectral area, and m, with correlation coefficients of approximately 0.99. In contrast, it exhibited strong negative correlations with P-wave velocity, UCS, E, and pore fractal dimensions, with r values lower than −0.97. As a quantitative measure of the complexity of the final crack network, an increase in D indicates that the fracture system develops a more tortuous and highly branched macroscopic failure path. This behavior can be explained as follows. Although freeze–thaw cycling may make the pore geometry appear statistically more uniform at the microscale, it also weakens the rock skeleton and creates numerous potential weak planes. Under external loading, these weak planes act as multiple crack-initiation sites. Cracks then propagate and coalesce through competing weak zones, which ultimately produces a tortuous and branched fracture network with higher complexity.

Further analysis indicates that pore expansion is the dominant driver of freeze–thaw damage evolution. Porosity and the T 2 spectral area vary almost identically, and both represent the pore-volume dimension. A decrease in pore fractal dimension reflects the loss of structural hierarchy and geometric complexity. It mediates the transfer from microscale damage to macroscale deterioration and is closely associated with the reductions in P-wave velocity, UCS, and E. In contrast, the fractal dimension of fracture morphology is an outcome metric that characterizes the connectivity and complexity of the crack network. The correlation matrix further indicates pronounced multicollinearity. Porosity and the T 2 spectral area are highly synchronous and interchangeable. D t, D e, and D a are strongly correlated with each other, as are P-wave velocity, UCS, and E. Moreover, D is positively correlated with pore-volume indicators but negatively correlated with mechanical indices and pore fractal dimensions, suggesting a common underlying damage process. Overall, freeze–thaw damage in weakly cemented sandstone follows a multiscale chain: pore expansion leads to structural simplification, which drives mechanical deterioration and ultimately results in fracture-pattern complexity.

4. Conclusion

In this study, weakly cemented sandstone from Gansu Province was selected as the research subject. Through systematic freeze–thaw cycling tests integrated with NMR, uniaxial compression, P-wave velocity measurements, and fractal analysis, the damage evolution mechanism under freeze–thaw cycles was revealed in a multiscale and full-process manner. A cross-scale correlation from microscopic mechanisms to macroscopic responses was established by means of the Pearson correlation coefficient matrix. The main conclusions are as follows:

  • (1)

    With increasing freeze–thaw cycles, the physicomechanical properties of weakly cemented sandstone exhibited a typical three-stage degradation pattern. The UCS and E decreased from 35.52 MPa and 5.67 GPa to 14.53 MPa and 1.91 GPa, representing reductions of 59.09 and 66.37%. The P-wave velocity was markedly reduced, indicating a weakening of structural integrity. The mass increased from 437.86 to 454.83 g, reflecting enhanced pore connectivity and improved water absorption capacity. The D of the failure pattern increased from 1.21 to 1.87, with a growth of 54.55%, indicating that the macroscopic failure mode evolved from a single crack to a complex multicrack network. Therefore, cold-region engineering should adopt systematic reinforcement and overall confinement, supplemented by drainage and seepage-control measures as well as thermal insulation and freeze-mitigation treatments. These measures can limit water uptake and frost heave, delay the coalescence of the crack network, and improve the long-term durability of the rock mass.

  • (2)

    As freeze–thaw cycles progressed, porosity increased from 12.86 to 22.21%, and the T 2 spectral area rose from 109174.49 to 197690.21, with corresponding increases of 72.73 and 81.17%. The pore structure exhibited a three-stage evolution characterized by “micropore activation–mesopore expansion–macropore domination”. In the early stage, the proportion of micropores increased from 18.90 to 24.16%. In the later stage, the proportion of macropores reached 47.76%, and a new pore size class of 16–25 μm appeared, indicating skeleton degradation and macroscopic fracture coalescence. These results reveal the full evolution process of freeze–thaw damage from microscopic initiation to macroscopic instability.

  • (3)

    In the pore structure of weakly cemented sandstone, the distributions of total pores, mesopores, and macropores exhibited evident fractal characteristics, with their fractal dimensions consistently ranging from 2.47 to 2.97. In contrast, the fractal dimension of micropores remained below 2 throughout, indicating the absence of fractal behavior. As freeze–thaw cycles progressed, the fractal dimensions D t, D e, and D a systematically decreased from 2.68, 2.88, and 2.97 to 2.47, 2.72, and 2.84, respectively. The order D a > D e > D t was maintained at all stages, reflecting a pronounced scale dependence of pore geometric complexity. All three fractal dimensions showed negative correlations with porosity, indicating that freeze–thaw processes not only facilitated pore volume expansion but also drove the evolution of the pore system toward a more regularized, homogenized, and interconnected structure.

  • (4)

    The Pearson correlation matrix indicated strong correlations between microscopic structural parameters such as porosity and T 2 spectral area and macroscopic mechanical indices including UCS, E, and P-wave velocity. This finding demonstrated the dominant role of pore evolution in the overall mechanical degradation of the rock mass. Meanwhile, the fractal dimension of fracture patterns, as a quantitative descriptor of the final failure geometry, exhibited strong correlations with both pore structure evolution and mechanical property deterioration. These results revealed a hierarchical transmission mechanism of freeze–thaw damage between microscopic porosity and macroscopic failure. In summary, the damage evolution of weakly cemented sandstone under freeze–thaw cycles can be characterized as a multiscale chain process of pore expansion, structural simplification, mechanical degradation, and fracture complexity.

This study has several limitations. All samples were obtained from a single mining area and stratum, failing to encompass weakly cemented sandstones of different origins and cementation types. Freeze thaw experiments were conducted under constant temperature amplitude and pure-water saturation, without considering field factors such as temperature fluctuations, unsaturated conditions, and salt effects. Mechanical characterization relied mainly on uniaxial compression and static elastic modulus tests, lacking systematic multiaxial, tensile, shear, and other diversified tests, as well as meso-damage monitoring techniques such as micro-CT and acoustic emission. Future research should expand the geological representativeness of samples, introduce more field-realistic environmental simulation protocols, and integrate multiscale observation with multiparameter mechanical testing to establish a more comprehensive damage assessment framework.

Acknowledgments

The authors would like to gratefully acknowledge the supports from the Research on Three Prepositions of Advanced Precontrol for Coal Mine Safety Production and Integrated Technology of Ecological Environmental Protection at Shanxi Shuozhou Pinglu District Hou’an Coal Co., Ltd. (No. 117480070).

Shi Tan: Writing-original draft. Ning Wang: Project administration, Methodology. Wenjuan Li: Investigation, Visualization, Methodology. Lianchun Zhou: Formal analysis, Data curation. Mingdong Yu: Project administration, Methodology.

The authors declare no competing financial interest.

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