Experimental study on instability and failure mechanism of sandstone under freeze-thaw and load

doi:10.21203/rs.3.rs-5305111/v1

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Experimental study on instability and failure mechanism of sandstone under freeze-thaw and load

https://doi.org/10.21203/rs.3.rs-5305111/v1

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In order to study the influence of loading rate and freeze-thaw cycles on the mechanical properties of sandstones, uniaxial compression tests were conducted on sandstone samples subjected to various freeze-thaw cycles and loading rates. Both internal and external damages were monitored throughout the tests using an acoustic emission (AE) detection system and a high-speed camera system. The effects of loading rate and freeze-thaw cycle on the typical mechanical properties, failure modes, and AE characteristics of sandstone were analyzed. In addition, attenuation models were established for the strength indices of freeze-thaw affected sandstone under different loading rates. Based on the results of the analyses, the following main conclusions are drawn: With the increase in freeze-thaw cycles and the decrease in loading rate, the uniaxial compressive strength(UCS) and elastic modulus(E) of sandstone decrease and the ductility increases, whereas the attenuation constant λ decreases as the loading rate increases. Upon complete failure, the number of tensile cracks in the sandstone exceeds that of shear cracks. As the number of freeze-thaw cycles increases and the loading rate decreases, the proportion of shear cracks gradually increases. With the increase in the loading rate, sandstone damage is primarily due to tension, and with more freeze-thaw cycles, damage is mainly due to both tension and shear. When the internal cracks in sandstone start to extend, the AE events rate and b-value signals become active. The absence of low AE events rate and a sharp decline in AE b-value can serve as precursors for predicting instability and failure of sandstones subjected to varying loading rates and freeze-thaw cycles.

Rock mechanics

Freeze-thaw cycles

Loading rate

Acoustic emission

Crack characteristics

Inner Mongolia, situated between latitudes 37°24′ and 53°23′ N, experiences substantial seasonal and diurnal temperature fluctuations, which give rise to pronounced freeze-thaw cycles in the rocks of open-pit mine slopes. These freeze-thaw processes deteriorate the mechanical properties of slope rocks, compromising their stability and elevating the risk of geological hazards such as landslides. In recent years, extensive research has been conducted on the physical properties of rocks subjected to freezing and thawing. The increase in freeze-thaw cycles reduces the strength and modulus of elasticity of the rock (Huang et al. 2022b; Wu et al. 2023), while also leading to a decline in the internal friction angle and cohesion (Gao et al. 2023). This process accelerates the shedding of surface particles (Wang et al. 2023a), promotes the expansion of rock pores (Hu et al. 2023), increases effective porosity, and results in the formation of new cracks dominated by larger pores (Liu et al. 2017; Sun et al. 2024). Additionally, it causes a reduction in the fractal dimensionality and complexity of the pore structure (Yu et al. 2024), along with a decrease in P-wave and ultrasonic pulse velocities (Çelik et al.2023; Sardana et al. 2022). The extent of rock deterioration due to freeze-thaw cycles correlates with the number of cycles, but the effect is less pronounced in rocks with smaller initial pore sizes and higher uniaxial compressive strength (UCS) (Huang et al. 2022a; Wang et al. 2024). Furthermore, the severity of freeze-thaw damage is influenced by the water saturation level of the rocks, with higher water content leading to greater damage (Song et al. 2021).

In addition to the impact of freeze-thaw cycles, the mechanical behavior of rocks under varying loading rates is crucial for ensuring the long-term stability of open-pit mine slopes. The relationship between rock mechanics and loading rate has garnered significant attention from researchers (Yao et al. 2018; Li et al. 2023). It was shown that as the loading rate increases, the strength and elastic modulus of the rock increase (Cao et al. 2019), leading to crack surface expansion with increased fragment number and decreased fragment size (Pan et al. 2023). In addition, the energy utilization rate decreases (Zhu et al. 2023), resulting in more energy required for rock fragmentation (Du et al. 2020). He et al. (2021) analyzed the damage evolution of sandstone under different loading rates, pointing out that microcracks develop more completely with more significant damage under lower loading rates. Similarly, Lajtai et al. (1991) compared the strength of brittle greywacke with ductile saline and found that loading rate has a more pronounced effect on the strength of ductile saline than on brittle greywacke. However, the strength of rock does not always increase with the increase in loading rate; there is a critical loading rate beyond which the growth rates of strength and elastic modulus of rock approach zero (Wang et al. 2023b). Currently, the crack mechanism of rocks under different loading rates is primarily analyzed from the perspectives of mechanical properties and energy evolution, with relatively few studies using other analytical methods. Moreover, most studies on the influence of loading rates on the mechanical properties of rocks rarely consider the coupling effects with other factors.

During the process of rock damage and failure, AE parameters and waveform characteristics are related to the damage evolution process (Gu et al.2024; Li et al.2021; Yuan et al.2023), and hence AE technology has been widely used to reveal the response mechanisms of rock compressive mechanical properties (Wang et al.2024; Song et al.2024). Zhao et al. (2020) established a relationship among axial stress and strain, AE events rate, and average centroid frequency, demonstrating that AE signals are closely related to axial stress and strain changes in sandstone specimens. Based on the theory of phase space reconstruction, Li et al. (2019) used the Grassberger-Procaccia algorithm to determine the fractal characteristics of AE in each stage of rock failure. Aker et al. (2014) studied AE related to shear and tensile failure around horizontal boreholes in samples under triaxial stress, correlating AE events rate with macroscopic deformation observations and the isotropy and deviation components of the seismic moment tensor with the percentage of the expected failure mechanism.

The degradation effects of loading rate and freeze-thaw cycles on the stability of sandstone have been well established. However, research on the fracture mechanisms of sandstone under the combined influence of these two factors remains limited. Building on previous work, this study conducts uniaxial compression tests combined with acoustic emission monitoring on freeze-thawed sandstone subjected to varying loading rates. The investigation aims to elucidate how these factors affect the mechanical behavior of sandstone, with damage modes and evolution patterns analyzed through high-speed camera imaging and acoustic emission data. A strength decay model for freeze-thawed sandstone under different loading rates is developed, providing a theoretical and computational foundation for assessing the stability, disaster prediction, and risk assessment of engineering rocks in cold regions.

2.1 Specimen preparation

Sandstone, a common rock type encountered in mining operations in Inner Mongolia of China, is characterized by its high water absorption and significant gravel content. For this experiment, the sandstone was sourced from an open pit mine in Inner Mongolia. The bulk material was processed into cylindrical specimens, each with a height of 100 mm and a diameter of 50 mm. The accuracy of the specimen meets the standards recommended by the International Society of Rock Mechanics and Engineering (ISRM) test regulations, ensuring that the deviations of specimen height and diameter are less than 0.3 mm, and the flatness deviation of both ends is less than 0.25°.

2.2 Test methods

To simulate the actual climatic conditions of open-pit engineering in the Inner Mongolia region, we subjected water-saturated sandstone to freezing at -30°C for 4 hours, followed by immersion in 30°C water for additional 4 hours, defining this as one freeze-thaw cycle. The study set up four groups of freeze-thaw cycles (0, 30, 50, and 70 cycles) and four loading rates (0.05, 0.10, 0.15, and 0.20 mm/min), encompassing 16 distinct conditions. Under each condition, three parallel tests were conducted.

The test equipment is shown in Fig. 1, and the experimental procedure is as follows:

(1) To ensure similar physical properties within the same group of rocks and reduce the error caused by the heterogeneity of the rocks on the test results, three sandstone pieces with similar wave velocity, T₂ values, and porosity were selected as a group.

(2) The ZYB-II vacuum pressurized water saturation device was used to fully saturate of 48 sandstone samples, which were then subjected to freeze-thaw cycle tests.

(3) Strain gauges were attached to the surface of the sandstone after freeze-thaw cycling and connected to a static strain gauge. A coupling agent was applied between the acoustic emission sensor and the sandstone to reduce noise.

(4) The sandstone specimens were placed on the loading platform, preloaded to 2 kN using the SAS-2000 uniaxial compression testing system, and the high-speed camera was focused.

(5) The uniaxial compression system axially compresses the sandstone at various loading rates until it is completely destroyed. the uniaxial compression system, AE system and high-speed camera are simultaneously activated and deactivated at the same time to record the stress-strain characteristics of the sandstone, AE signals and the evolution of external cracks during compression.

3.1 Variation law of mechanical parameters

Figure 2 displays the stress-strain curves of freeze-thaw sandstone samples subjected to various loading rates. In general, the freeze-thaw action is found to have the most significant effect on the uniaxial compressive strength (UCS) of the sandstone. The uniaxial compressive strength decreases with the increase of freeze-thaw cycles, and the deformation of sandstone increases with the increase of freeze-thaw cycles when reaching complete failure. Under the same number of freeze-thaw cycles, an increase in the loading rate results in higher stress levels and bearing capacity in the sandstone, whereas the deformation observed in the post-peak residual stage decreases.

The stress-strain curves of four groups of typical sandstone samples, subjected to loading rates of 0.05 mm/min and 0.20 mm/min and freeze-thaw cycles of 0 and 70, are shown in Fig. 3. It can be observed that the deformation of unfrozen sandstone shows little difference when it is completely destroyed under different loading rates. The uniaxial compressive strength of sandstone is the highest for 0 freeze-thaw cycles under a loading rate of 0.20 mm/min, and the lowest for 70 freeze-thaw cycles with a loading rate of 0.05 mm/min. An increase in the loading rate somewhat mitigates the impact of freeze-thaw cycles on the uniaxial compressive strength.

The mechanical parameters of sandstone samples subjected to different freeze-thaw cycles at loading rates of 0.05 mm/min and 0.20 mm/min are presented in Table 1. When the loading rate is 0.05 mm/min, the uniaxial compressive strength decreases by 69.57% after 70 freeze-thaw cycles, whereas the decrease is 37.86% at a loading rate of 0.20 mm/min. The elastic modulus(E) of sandstone decreases with an increase in freeze-thaw cycles and increases with a higher loading rate. Table 1 illustrates the decline in the elastic modulus of sandstone across different freeze-thaw cycles at both loading rates, highlighting the significant impact of freeze-thaw cycles on the elastic modulus. This impact intensifies as the number of freeze-thaw cycles increases. While the loading rate has a minimal effect on the elastic modulus of unfrozen sandstone, its influence on the elastic modulus becomes more pronounced with an increase in freeze-thaw cycles.

Table 1

Detailed table of sandstones mechanical parameters change
Group Number	0.05 mm/min				0.2 mm/min
Group Number	UCS(MPa)	Decrease (%)	E (GPa)	Decrease (%)	UCS(MPa)	Decrease (%)	E (GPa)	Decrease (%)
FT0	54.15	—	19.60	—	62.97	—	21.24	—
FT30	50.16	7.37	15.46	21.12	61.38	2.52	21.21	0.14
FT50	34.62	36.07	12.54	36.02	44.11	29.95	15.46	27.21
FT70	16.48	69.57	6.78	65.41	39.13	37.86	12.06	43.22

3.2 Exponential decay model

Mut-lutürk et al. (2004) initially introduced an exponential decay model, while Jamshidi et al.(2016) evaluated the durability of rock materials by calculating decay constants and half-lives, as illustrated in Eq. (1). This model is useful for elucidating the reduction in sandstone strength attributable to freeze-thaw cycles.

$${I_n}={I_0}{e^{ - \lambda n}}$$

where n is the number of freeze-thaw cycles; I_n and I₀ are the uniaxial compressive strength of rock after n and 0 freeze-thaw cycles, respectively; and $\:{\lambda\:}$ is the attenuation constant, indicating the characteristic parameter of frost resistance of rock. A larger $\:{\lambda\:}$, indicates a more serious deterioration of sandstone.

The changes in the uniaxial compressive strength of sandstone under different loading rates and freeze-thaw cycles are shown in Fig. 4.

By analyzing and fitting the test data, the strength index attenuation model of freeze-thaw sandstone under different loading rates is obtained, and the fitted equation is shown in Eqs. (2)-(5):

$${I_{n(0.05)}}=54.19 \times {e^{( - 0.009960n)}},{R^2}=0.9049$$

$${I_{n(0.10)}}=58.80 \times {e^{( - 0.009012n)}},{R^2}=0.8565$$

$${I_{n(0.15)}}=60.14 \times {e^{( - 0.006759n)}},{R^2}=0.9213$$

$${I_{n(0.20)}}=62.97 \times {e^{( - 0.005308n)}},{R^2}=0.8763$$

Where, I_n(0.05)、I_n(0.10)、I_n(0.15)and I_n(0.20) are respectively the uniaxial compressive strength of sandstone after $\:\text{n}$ freeze-thaw cycles at loading rates of 0.05, 0.10, 0.15 and 0.20 mm/min, respectively, MPa. The constants 54.19, 58.80, 60.14 and 62.97 are the uniaxial compressive strength of sandstone with 0 freeze-thaw cycles at loading rates of 0.05, 0.10, 0.15 and 0.20 mm/min, respectively, MPa.

It can be seen from Eqs. (2)-(5) that the attenuation constant λ is 0.00996, 0.009012, 0.006759, and 0.005308 at loading rates of 0.10, 0.15, 0.20, and 0.25 mm/min, respectively. Additionally, the attenuation constant λ decreases as the loading rate increases.

3.3 Evolution law of crack characteristics

Four groups of typical sandstone crack characteristic images are shown in Figs. 5–8. Select the images that exhibit crack development characteristics when sandstone cracks appear, develop, extend, and when the structure is completely penetrated. Analyze the crack characteristics of sandstone based on these images. In this section, we take the time node corresponding to the peak stress as the reference point and define it as $\:{t}_{p}$. The time associated with images exhibiting crack development characteristics will be represented relative to $\:{t}_{p}$.

As shown in Fig. 5, an obvious shear crack emerges in the sandstone with 0 freeze-thaw cycles at a loading rate of 0.05 mm/min, occurring 49.19 s prior to the peak stress. The crack then evolves into an X-shaped formation 12.03 s before the peak stress. At peak stress, the crack widens and is filled with sandstone debris. 19.13 s after the peak, the sandstone becomes unstable and disintegrates along the crack.

After 70 freeze-thaw cycles, particle spalling occurred on the sandstone surface due to the freeze-thaw effect. As the stress increases, the sandstone surface begins to develop from the initial freeze-thaw cracks. As depicted in Fig. 6, the cracks on the sandstone surface are distributed obliquely 100.01 s before the peak. Subsequently, the cracks start to extend, and the number of inclined cracks on the sandstone surface increases, and the bulging phenomenon becomes more pronounced. the sandstone surface is increasingly covered with inclined cracks, occurring at 19.89 s before the peak. In the post-peak residual stage, it takes 33.15 s for the crack to completely penetrate. During this stage, the cracks undergo longitudinal extension and penetration, with tensile cracks being particularly prominent. Compared to sandstone with 0 freeze-thaw cycles, sandstone subjected to more freeze-thaw cycles exhibits further crack extension throughout the loading process, with the more severe skin peeling phenomenon.

According to Fig. 7, sandstone subjected to 0 freeze-thaw cycles undergoes both complete cracking and rock burst when reaching peak stress, indicating that the increase in loading rate enhances the brittleness of the sandstone. Vertical cracks appear at the upper left position of the sandstone surface at 29.84 s before the peak; the cracks begin to expand at 5.32 s before the peak; and the cracks extend across the entire sandstone surface at 3.55 s before the peak. The time from the onset of surface cracks to complete cracking is the shortest, which is 38.1% of the time with 0 freeze-thaw cycles at a loading rate of 0.05 mm/min.

As shown in Fig. 8, under a loading rate of 0.20 mm/min, the sandstone subjected to 70 freeze-thaw cycles develops several tensile-dominated cracks along the existing freeze-thaw cracks on its surface at 107.3 s before the peak. These cracks begin to extend and expand at 15.26 s before the peak, with the cracks developing from top to bottom. Complete failure occurs at 30.23 s after the peak. Compared to sandstone with no freeze-thaw cycles at a loading rate of 0.20 mm/min, the sandstone in this case exhibits more severe fragmentation, yet its fragmentation level is still lower than that of sandstone subjected to 70 freeze-thaw cycles at a loading rate of 0.05 mm/min.

4.1 RA/AF Variation Characteristics

The RA/AF variation can be utilized to investigate the fracture mechanism of rocks (Xie et al. 2023), thereby providing a complementary validation of the findings presented in Section 3.3. In general, tensile crack corresponds to a low RA value and a high AF value, while shear crack corresponds to a high RA value and a low AF value. The calculation formulas for RA and AF are as follows:

$$\:AF（kHz）=\frac{\text{t}\text{h}\text{e}\:\text{h}\text{i}\text{t}\:\text{c}\text{o}\text{u}\text{n}\text{t}}{\text{d}\text{u}\text{r}\text{a}\text{t}\text{i}\text{o}\text{n}}$$

$$\:RA（ms/V）=\frac{\text{t}\text{h}\text{e}\:\text{r}\text{i}\text{s}\text{e}\:\text{t}\text{i}\text{m}\text{e}}{\text{a}\text{m}\text{p}\text{l}\text{i}\text{t}\text{u}\text{d}\text{e}}$$

RA and AF values can be used to qualitatively describe the variation trends of tensile and shear cracks in rocks over time during compression. The ratio of AF to RA, denoted as $\:k$, serves as the criterion to distinguish between tensile and shear cracks in rocks. Numerous scholars (Gan et al. 2020; Ohno et al. 2010) have studied the crack mechanisms of rocks using resonant sensors and found that the value of k is between 80 and 90. Therefore, this paper adopts $\:k$=85 as the threshold to differentiate between different crack types.

The variations of RA and AF in sandstone subjected to different freeze-thaw cycles at loading rates of 0.05 mm/min and 0.20 mm/min are depicted in Figs. 9,10, respectively. According to the density statistics method, RA and AF are partitioned into micro-grids, and then the number of scattered points is counted and colored according to the density of scattered points. Distinct background colors are employed to represent the different stages of uniaxial compression in sandstone, including the compaction stage, elastic deformation stage, stable crack propagation stage, unstable crack propagation stage, and post-peak residual stage. The same applies to the following figures.

As illustrated in Figs. 9,10, the majority of the densely clustered red regions are located within the tensile crack zones. Upon the occurrence of complete failure, the number of tensile cracks consistently exceeds that of shear cracks, indicating that the rupture modes predominantly involve tension-shear composite damage, with tensile damage being the primary mechanism.

With the increase in freeze-thaw cycles, the gap between the cumulative numbers of shear and tensile cracks widens in the early phase of loading, the density of the shear zone increases, and the proportion of shear cracks grows when it is completely destroyed. At a loading rate of 0.05 mm/min, as the number of freeze-thaw cycles increases, the surge in the number of tensile cracks occurs progressively later. In sandstone that has not undergone freeze-thaw cycles, the number of tensile cracks surpasses that of shear cracks during the stable crack propagation stage. However, in sandstone subjected to 50 and 70 freeze-thaw cycles, this crossover occurs only in the post-peak residual stage. Specifically, for sandstone with 50 freeze-thaw cycles, the number of tensile cracks exceeds that of shear cracks 171 seconds before complete failure, whereas for sandstone with 70 freeze-thaw cycles, this occurs 40 seconds prior to complete failure.

As the loading rate increases, the area of high-density colors in the tension region expands, and the proportion of tension cracks rises. For sandstone subjected to a loading rate of 0.20 mm/min, the initial number of shear cracks slightly exceeds that of tension cracks, but tension cracks become dominant during the compression-densification or elastic deformation stage. During the unstable crack propagation stage, the growth rate of both tension and shear cracks accelerates. By the time complete failure occurs, the crack development within the sandstone is largely complete, and the difference between the number of tension and shear cracks diminishes as the loading rate increases.

As shown in Fig. 9(d) and Fig. 10(a), the 0 freeze-thaw cycles with loading rate of 0.2 mm/min and 70 freeze-thaw cycles with loading rate of 0.05 mm/min are in sharp contrast. In the former case, tensile cracks begin to dominate at approximately 70 s, and at complete failure, the number of tensile cracks is 1.67 times that of shear cracks. In contrast, for the latter case, shear cracks dominate from the initial compaction phase to the post-peak residual phase, with tensile cracks only surpassing the number of shear cracks at 40 s before complete failure.

4.2 Variation Law of AE events rate

Establish the AE threshold at 10 mV. The AE events rate, calculated as the number of AE signals surpassing the preset threshold per second, signifies the frequency of AE signals. By examining the AE events rate, this metric can indicate the internal fracturing of sandstone. Figures 11,12 illustrate the variation in AE events rate for sandstone subjected to different freeze-thaw cycles at loading rates of 0.05 mm/min and 0.20 mm/min, respectively.

In this study, the level of internal damage and the activity of failure within the specimens are assessed by comparing the proportion of each sandstone's events rate to its peak events rate.

During the crack compaction stage, the AE events rate is high. In contrast, the AE events rate is low and relatively stable during the elastic deformation stage and the crack stable propagation stage. Prior to the failure instability of the sandstone, the AE events rate begins to increase. And it continues to rise at peak stress and throughout the residual stage after the peak. Except for the sandstone loaded at a rate of 0.05 mm/min after 50 freeze-thaw cycles, the peak events rate is all generated at the peak stress. This exception might be due to the heterogeneity of the rocks. In sandstone subjected to various freeze-thaw cycles and loading rates, the phenomenon of low AE events rate loss appears to varying degrees before complete failure, as shown by the black line in the lower right corner of Figs. 11,12. Therefore, the lack of low AE events rate can be used as an index to predict sandstone cracking and instability under different freeze-thaw cycles and loading rates.

Regarding freeze-thaw cycles, the AE events rate of unfrozen sandstone is the lowest during the crack compaction stage. As the number of freeze-thaw cycles increases, more cracks are generated in the sandstone, leading to a gradual rise in the AE events rate. At this stage, the AE event rate with 0 freeze-thaw cycles accounts for about 1/5 of the peak event rate, whereas it accounts for 1/3 of the peak event rate for 70 freeze-thaw cycles. During the elastic deformation stage and the crack stable propagation stage, the relative displacement of particles at the particle interface produces low event AE rate events, and the duration of these events decreases with the increase in freeze-thaw cycles. Sandstone that demonstrates a significant increase in AE events rate during the accelerated crack growth is more likely to be completely destroyed shortly after reaching the peak stress. With the increase in the number of freeze-thaw cycles, a large number of high AE events rate are produced in the post-peak residual stage, with a significant increase of the cumulative AE events.

The increase in the loading rate reduces the number of AE signals, shortens the time to achieve complete failure, resulting in a generally lower cumulative number of AE events compared to sandstone with a low loading rate. Sandstone subjected to a high loading rate exhibits a higher AE event rate with higher AE activities in each stage and a shorter duration of the stationary period. Under a high loading rate, the AE events rate is high in the elastic stage, and the process of internal crack compaction, development, and expansion is relatively rapid. In the post-peak residual stage, due to its longer duration for sandstones at a low loading rate, internal cracks develop, join, and converge to form macroscopic cracks, and the cumulative number of AE events increases progressively. Under high loading rates, the acoustic emission event rate of sandstone increases significantly before reaching the peak stress, peaks at the peak stress, and then the sandstone undergoes an instantaneous brittle failure and instability. Additionally, the phenomenon of missing low AE events rate is more pronounced than under low loading rates.

4.3 AE b-value variation characteristic

The concept of the AE b-value, which stems from seismological research, exhibits the change characteristics that are closely related to the development, expansion, and penetration of rock cracks (Shang et al. 2021). The calculation formula of AE is:

lgN = a-b$\:\frac{{A}_{dB}}{20}$ (8)

where N is the sum of AE data in each time window, A_dB is the AE amplitude, and a is the empirical constant.

According to the sampling frequency of AE for a total of 200 samples, a sliding window of 50 data points is employed for sampling. The AE b-value is then calculated using the least square method. An increase in the b-value indicates that small-scale cracks are predominant within the rock, and a decrease in the AE b-value suggests the occurrence of large-scale cracks within the rock. When the AE b-value fluctuates within a small range, it signifies a steady expansion of cracks within the rock. Conversely, when the AE b-value exhibits abrupt fluctuations, it indicates a rapid development of cracks within the rock (Song et al.2023).

Figures 13,14 illustrate the variations in the AE b-value and stress-strain relationship of freeze-thawed sandstone under loading rates of 0.05 and 0.20 mm/min, respectively. The overall trend of a gradually decrease in AE b-value signifies the process of crack initiation, development, and coalescence within the rock.

During the compaction phase, the b-value exhibits a high frequency of fluctuations and an overall downward trend, indicating that the cracks within the sandstone are gradually being compacted, accompanied by the formation of new cracks. Upon entering the elastic deformation stage, the fluctuations in the AE b-value stabilize and generally tend upwards, suggesting the formation and expansion of new cracks within the sandstone. For sandstone subjected to low freeze-thaw cycles and low loading rates, a significant decrease in the AE b-value is first observed during the stable development of cracks. In contrast, other sandstones only exhibit a marked reduction in the AE b-value during the unstable extension of cracks, marking the onset of crack propagation within the sandstone. In the unstable extension phase of cracks, both sandstones subjected to low freeze-thaw cycles and those with high loading rates consume a large amount of strain energy, leading to the expansion and convergence of internal cracks within the sandstone, and a sharp decrease in the AE b-value. Upon reaching the peak stress, the AE b-value continues to decrease. In the post-peak residual stage, the internal cracks in sandstone extend and interconnect. Sandstone with a high loading rate is completely destroyed immediately after the peak value, and low b-values appear frequently, with a significant decrease in the AE b-value. In contrast, under the condition of a loading rate of 0.05 mm/min, the duration of the high-frequency decline in the AE b-value signal is obviously increased, for example, in sandstone subjected to 50 and 70 freeze-thaw cycles. At the point of complete failure, cracks rapidly converge, and the AE b-value reaches its lowest point.

5.1 Strength Prediction of Sandstones under Dual-Factor Coupling

Huang et al. (Huang et al. 2022; Jamshidi et al. 2016) proposed the exponential decay model for freeze-thaw cycle rocks, and Meng et al. (2021) established the corresponding exponential decay model for sandstone under different dynamic fracturing rates. Building on the experimental findings presented in Section 3.2, this section seeks to further assess the applicability of the exponential decay model to freeze-thawed sandstones subjected to varying loading rates. Figure 15 illustrates the variation in the sandstone attenuation constant under different loading rates and further conducts a linear fitting, as shown by:

Figure15 Alt text: This figure presents the linear fitting of the attenuation constants of sandstone under different loading rates.

$$\lambda = - 0.03242 \times v+0.01181,{R^2}=0.9681$$

Where $\:v$ is the loading rate, mm/min.

Substituting Eq. (9) into Eq. (1), we can get:

$${I_{\text{n}}}={I_0}{e^{(0.03242\nu - 0.01181)n}}$$

The experimental results were substituted into the exponential decay model (10), and the model showed a good fit, as shown in Fig. 16. Thus, Eq. (10) can be utilized to estimate the variations in uniaxial compressive strength after differing numbers of freeze-thaw cycles at a loading rate between 0.05 and 0.20 mm/min. This not only compensates for the limitation of testing specific freeze-thaw cycles but also enhances the reliability of predictions regarding the uniaxial compressive strength of rocks under freeze-thaw conditions.

Figure16 Alt text: The experimental results of sandstone under different loading rates and freeze-thaw cycles are substituted into the exponential decay model (Eq. 10) and compared with the experimental values.

To assess the durability of rocks post freeze-thaw cycles, Mutlutürk (2004) introduced the concept of half-life, $\:{N}_{1/2}$, for rocks. This term refers to the number of freeze-thaw cycles a rock undergoes until its strength is reduced by half. The half-life is an important metric for evaluating a rock's resistance to frost, as depicted in:

$${I_{1/2}}=\frac{1}{2}{I_0}$$

By combining Eqs. (1) and (11), the half-life $\:{N}_{1/2}$ of the freeze-thawed sandstone discussed in this paper is determined as follows:

$${N_{1/2}}=\frac{{\ln 2}}{\lambda }$$

Similarly, if Eq. (9) is substituted into Eq. (12), we can get:

$${N_{{\text{1/2}}}}=\frac{{\ln 2}}{{( - 0.03242\nu +0.01181)}}$$

Using the aforementioned formula, we can ascertain the requisite number of freeze-thaw cycles for the strength of sandstone to degrade to half its initial value within the loading rate spectrum of [0.05, 0.20] mm/min. Our calculations reveal that at loading rates of 0.05, 0.10, 0.15, and 0.20 mm/min, the sandstone's strength reduces to half after 70, 77, 105, and 131 freeze-thaw cycles, respectively. Therefore, by considering the number of equivalent freeze-thaw cycles per year in the actual project's climate, we can approximate the time it would take for the sandstone to reach its half-life.

5.2 Damage Mechanism of Sandstone under Dual-Factor Coupling

The results presented in Sections 3.1 and 3.3 demonstrate that both freeze-thaw cycles and loading rate significantly affect the mechanical properties and crack characteristics of fully water-saturated sandstone. With an increasing number of freeze-thaw cycles, the peak strength of sandstone decreases owing to the freezing and expansion forces, which impair the cementation of internal particles. In Section 4.2, it is observed that a higher number of freeze-thaw cycles prolongs the post-peak residual phase, resulting in a greater number of high AE events rate, while the growth rate of cumulative acoustic emission events slows after reaching an inflection point. In Section 4.3, the duration of successive decreases in the AE b-value also extends. Collectively, these findings suggest that an increase in freeze-thaw cycles enhances the ductility of sandstone. Furthermore, as temperatures drop during freeze-thaw cycles, the temperature gradient between the surface and interior of the sandstone induces differential shrinkage, causing tensile stress on the sandstone surface. This coupling of tensile stress and freezing expansion forces leads to particle spalling on the sandstone surface after 70 freeze-thaw cycles, as described in Section 3.3.

An increase in loading rate reduces the efficiency with which sandstone converts absorbed energy into dissipated energy, resulting in delayed onset of damage, a significant increase in peak strength, and a shortened duration of the post-peak residual phase. Sandstone that has not undergone freeze-thaw cycles exhibits more extensive cracking and greater damage at higher loading rates, leading to enhanced brittleness. As observed in Section 3.1, the influence of loading rate on the uniaxial compressive strength of freeze-thawed sandstone, and as discussed in Section 3.2, the variation in the attenuation constant λ, indicate that within the loading rate range of [0.05, 0.20] mm/min, increased loading rate can mitigate the damaging effects of freeze-thaw cycles on sandstone to some extent. In terms of RA, AF, AE events rate, and AE b-value evolution, higher loading rates diminish the impact of freeze-thaw cycles on acoustic emission signals. However, fracture characteristics indicate that the rupture evolution of sandstone is notably governed by freeze-thaw damage. This phenomenon arises because the freezing and expansion forces during multiple freeze-thaw cycles cause microcracks to proliferate, merge, and propagate within the water-saturated sandstone, leading to the formation of multiple macroscopic fissures across varying loading rates. Consequently, the influence of water content on sandstone stability during freeze-thaw cycles is of critical importance.

AE systems are widely utilized as non-destructive monitoring tools for predicting instability damage in sandstone. Previous research has predominantly concentrated on predictive indicators under single-variable conditions, with limited studies addressing multivariable scenarios. This paper, particularly in Sections 4.2 and 4.3, demonstrates that both the AE events rate and the AE b-value remain effective predictors for freeze-thawed sandstones subjected to various loading rates. However, the AE events rate proves to be a more reliable predictor compared to the AE b-value, especially at high loading rates, where the absence of low AE events rates is more pronounced for sandstone.

5.3 Limitations

The experimental design outlined in this paper, which includes loading rates of 0.05, 0.10, 0.15, and 0.20 mm/min, represents dynamic loading conditions. However, in actual mining operations, slope rocks experience varying degrees of disturbance of loading rate. Notably, peak strength of sandstone does not consistently increase with higher loading rates. Future research should therefore focus on understanding the crack damage evolution of freeze-thawed rocks across a wider range of loading rates that covers dynamic loading. Additionally, the stability of slope rock masses is influenced by factors such as water content, initial damage, and the inherent lithology of the rock mass. Consequently, further investigation is required to gain a more comprehensive understanding of how the mechanical properties of rock are affected by multi-factor coupling.

In this study, uniaxial compression tests combined with acoustic emission monitoring were conducted on water-saturated sandstone subjected to varying loading rates and freeze-thaw cycles. By examining the mechanical properties, crack characteristics, and acoustic emission signals, the damage evolution and crack mechanisms of sandstone under the combined influence of loading rate and freeze-thaw processes were investigated. The primary conclusions drawn from this analysis are as follows:

(1) An increase in freeze-thaw cycles combined with a decrease in loading rate leads to a reduction in the uniaxial compressive strength and elastic modulus of sandstone, with strain initially decreasing and then increasing. This process also enhances the ductility of the sandstone. The attenuation constant λ decreases as the loading rate increases, indicating that higher loading rates mitigate the strength deterioration caused by freeze-thaw cycles to some extent. The relationship between uniaxial compressive strength and the combined effects of loading rate and freeze-thaw cycles can be described by an exponential decay model.

(2) With the increase of freeze-thaw cycles and the decrease of loading rate, the time from the initiation of cracks to the complete failure of the sandstone surface increases. Upon complete failure, the number of tensile cracks in sandstone exceeds that of shear cracks. The proportion of shear cracks initially increases with the increase of freeze-thaw cycles but then decreases with the increase of loading rate. As the number of freeze-thaw cycles increases, the failure mode of sandstone transitions to a blend of tension and shear failure. However, with the increase of loading rate, the sandstone predominantly exhibits tensile failure.

(3) In the stages of compaction, crack propagation, and post-peak residual deformation, the rate of AE events increases progressively, and the fluctuation range of the b-value becomes wider. As the loading rate escalates, the AE events rate throughout the entire loading cycle becomes more active, with the occurrence of high AE events rates advancing to just before the peak load. This is attributed to the rapid compaction process within the sandstone, leading to a reduction in the initial b-value. Low AE events rate omissions and significant b-value declines serve as precursors for identifying instability damage in freeze-thawed sandstones across varying loading rates. Among these indicators, the absence of low AE events rates proves to be a more effective predictive method.

Competing interests

The authors have no relevant financial or non-financial interests to disclose.

Author Contribution

Lv W.Y. provided the conceptualization, provided the funding acquisition. You R. completed the experiment and wrote the draft of the manuscript. Wang C.Y. provided the funding acquisition. Wang Z.H. Checked and corrected grammar problems. Wu Y.P. and Xie P.S. edited the manuscript. Lyu C. and Li Y.C. prepared all figures. All authors reviewed the manuscript.

Acknowledgements

This research was funded by the National Natural Science Foundation of China (No. 52464014, 52174127, 51974226), the Affiliated Universities in Inner Mongolia Autonomous Region of Research Funds (2024RCTD015), the Key Research and Development Program of Shaanxi (No. 2023-YBGY-318), the Outstanding Youth Science Fund Project of Shaanxi (2023-JC-JQ-42), and the Youth Innovation Team Project of Shaanxi University (2022-23).

Data availability

The data that support the findings of this study are available from the corresponding author, upon reasonable request.

Aker E, Kühn D, Vavryčuk V, Soldal M, Oye V (2014) Experimental investigation of acoustic emissions and their moment tensors in rock during failure. Int J Rock Mech Min 70: 286-295. http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=28744666
Cao AY, Jing GC, Ding YL, Liu S (2019) Mining-induced static and dynamic loading rate effect on rock damage and acoustic emission characteristic under uniaxial compression. Safety Sci 116: 86-96. https://doi.org/10.1016/j.ssci.2019.03.003
Çelik MY, Korucu MR (2023) The effect of Ffreeze-thaw cycles performed with salt solutions (NaCl and Na₂SO₄) on carbonate building stones. B Eng Geol Environ 82: 64. https://doi.org/10.1007/s10064-023-03072-z
Du HB, Dai F, Liu Y, Xu Y, Wei MD (2020) Dynamic response and failure mechanism of hydrostatically pressurized rocks subjected to high loading rate impacting. Soil Dyn Earthq Eng 129: 105927. https://doi.org/10.1016/j.soildyn.2019.105927
Ohno K, Ohtsu M (2010) Crack classification in concrete based on acoustic emission. Construction and Building Materials 24 (12SI): 2339-2346. https://doi.org/10.1016/j.conbuildmat.2010.05.004
Gan YX, Wu SC, Ren Y, Zhang G (2020) Evaluation indexes of granite splitting failure based on RA and AF of AE parameters. Rock and Soil Mechanics. 41 (07): 2324-2332. https://doi.org/10.16285/j.rsm.2019.1460
Gao F, Xie JX, Xiong X, Zhou KP (2023) Post-peak mechanical property and a new strain softening model for rocks subjected to freeze–thaw cycles. Environ Earth Sci 82: 531. https://doi.org/10.1007/s12665-023-11223-4
Gu C, Sun Q, Geng JS, Zhang YL, Jia HL (2024) Acoustic emission real-time monitoring and analysis of microwave thermal damage of granite. Environ Earth Sci. 83: 443. https://doi.org/10.1007/s12665-024-11745-5
He W, Huang CJ, Chen H, Zhu PZ (2021) Study on acoustic emission characteristics and damage evolution law of red sandstones under different loading rates. IOP conference series: Earth and environmental science. 861 (4): 42080. https://doi.org/10.1088/1755-1315/861/4/042080
Hu AL, Xue GB, Shang ZP, Cao Z, Wang XP, Fu YT, Huang XQ (2023) Study on pore structure and the mechanical properties of sandstone-concrete binary under freeze–thaw environment. Sci Rep-uk 13 (1): 18280. https://doi.org/10.1038/s41598-023-45576-4
Huang CC, Zhu C, Ma YF, Hewage SA (2022a) Investigating mechanical behaviors of rocks under freeze–thaw cycles using discrete element method. Rock Mech Rock Eng 55: 7517–7534. https://doi.org/10.1007/s00603-022-03027-y
Huang SB, He YB, Yu SL, Cai C (2022b) Experimental investigation and prediction model for UCS loss of unsaturated sandstones under free-thaw action. INT J MIN SCI TECHNO 32 (01): 41–49. https://doi.org/10.1016/j.ijmst.2021.10.012
Jamshidi A, Nikudel MR, Khamehchiyan M (2016) Evaluation of the durability of Gerdoee travertine after freeze–thaw cycles in fresh water and sodium sulfate solution by decay function models. Eng Geol 202: 36-43. https://doi.org/10.1016/j.enggeo.2016.01.004
Lajtal EZ, Duncan EJS, Carter BJ (1991) The effect of strain rate on rock strength. Rock Mech Rock Eng 24: 99–109. https://doi.org/10.1007/BF01032501
Li DX, Wang EY, Kong XG, Ali M, Wang DM (2019) Mechanical behaviors and acoustic emission fractal characteristics of coal specimens with a pre-existing flaw of various inclinations under uniaxial compression. Int J Rock Mech Min 116: 38-51. https://doi.org/10.1016/j.ijrmms.2019.03.022
Li HB, Liu LW, Fu SY, Liu B, Li XF (2023) Rate-dependent strength and crack damage thresholds of rocks at intermediate strain rate. Int J Rock Mech Min 171: 105590. https://doi.org/10.1016/j.ijrmms.2023.105590
Li HR, Wang ZH, Meng SR, Zhao WG, Chen F (2021) Acoustic emission activity and damage evolution characteristics of marble under triaxial stress at high temperatures. Rock Soil Mech 42 (10): 2672-2682. https://doi.org/10.16285/j.rsm.2021.5253
Liu J, Lan L, Wang RH, Wang F, Wang L, Xiao L (2017) Dynamic characteristics of sandstone under low-stress level conditions in freezing-thawing cycles. Rock and Soil Mechanics 38 (09): 2539-2550. https://doi.org/10.16285/j.rsm.2017.09.010
Meng FD, Zhai Y, Li YB, Li Y, Zhang YS (2021) Experimental study on dynamic tensile properties and energy evolution of sandstone after freeze-thaw cycles. Chinese Journal of Rock Mechanics and Engineering 40 (12): 2445-2453. https://doi.org/10.13722/j.cnki.jrme.2021.0289
Mutlutürk M, Altindag R, Türk G (2004) A decay function model for the integrity loss of rock when subjected to recurrent cycles of freezing-thawing and heating-cooling. Int J Rock Mech Min 41 (2): 237-244. http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=15467764
Pan HY, Feng GY, Ji X, Li JH, Ji B, Zhang TJ (2023) Study on deformation and failure characteristics of coal containing echelon crack-boreholes under the influence of loading rate. Chinese Journal of Rock Mechanics and Engineering. 43 (03): 1-14. https://doi.org/10.13722/j.cnki.jrme.2023.1022
Sardana S, Sinha RK, Verma AK, Singh TN (2022) Investigations into the freeze–thaw-induced alteration in microstructure and deteriorative responses of physico-mechanical properties of himalayan rock. B Eng Geol Environ 81: 269. https://doi.org/10.1007/s10064-022-02762-4
Shang XY, Lu YY， Li B，Peng K (2021) A novel method for estimating acoustic emission b value using improved magnitudes. IEEE SENS J 21 (15): 16701-16708. https://doi.org/10.1109/JSEN.2021.3076866
Song XP, Fan BW, Wang S, Zhang HW (2024) Reloading experimental research on the mechanical characteristics of cemented tailings backfill after dynamic loading action. Journal of China Coal Society. https://doi.org/10.13225/j.cnki.jccs.2023.1539
Song YJ, Yang HM, Tan H, Ren JH, Guo XX (2021) Study on damage evolution characteristics of sandstone with different saturations in freeze-thaw environment. Chinese Journal of Rock Mechanics and Engineering 40 (08): 1513-1524. https://doi.org/10.13722/j.cnki.jrme.2021.0089
Song YJ, Chen KY, Meng FD (2023) Research on acoustic emission characteristics of fractured rock damage under freeze-thaw action. Journal of Mining & Safety Engineering. 40 (02): 408-419. https://doi.org/10.13545/j.cnki.jmse.2022.0139
Sun WJ， Ma JZ， Jin JX， Li SH, Liu Q, Wang HB (2024) Quantitative Study of the Failure Characteristics of Sandstone with Freeze-Thaw Damage: Insight into the Cracking Behavior. Rock Mech Rock Eng 57: 5843–5862. https://doi.org/10.1007/s00603-024-03822-9
Wang CY, You R, Han TY (2023a) Experimental study on sandstone fracture and damage evolution law under freeze–thaw cycles. Geotech Geol Eng 41: 2923–2937. https://doi.org/10.1007/s10706-023-02437-1
Wang CY, You R, Lv WY, Sui QR, Yan YH, Zhu HJ (2024) Damage evolution and acoustic emission characteristics of sandstone under freeze–thaw cycles. ACS Omega 9 (4): 4892-4904. https://doi.org/10.1021/acsomega.3c08468
Wang JX, Liang P, Zhang YB, Yao XL, Yu GY, Guo B (2024) Research on classification of rock tensile-shear fracture based on acoustic emission RA-AF values and kneedle algorithm, Chinese Journal of Rock Mechanics and Engineering 43 (S1): 3267-3279. https://doi.org/10.13722/j.cnki.jrme.2023.0696
Wang SJ, Li ZQ, Gao ZA, Qi ZY, Sun K, Hu RL, Zhou YX (2023b) Study on strength damage model considering resistivity and failure characteristics of the frozen soil–rock mixture under different loading rates. Can Geotech J 61 (9): 1857-1872. https://doi.org/10.1139/cgj-2023-0283
Wu J, Lu YN, Wang KB, Cai Yang, Xiao C (2023) Combined effects of freeze–thaw cycles and chemical corrosion on triaxial mechanical properties of sandstone. Geomech Geophys Geo 9 (1): 57. https://doi.org/10.1007/s40948-023-00588-2
Xie HX, Li XH, Shan CH, Xia Z, Yu LQ (2023) Study on the damage mechanism and energy evolution characteristics of water-bearing coal samples under cyclic loading. Rock Mech Rock Eng 56: 1367–1385. https://doi.org/10.1007/s00603-022-03136-8
Yao W, Xia KW, Liu HW (2018) Influence of heating on the dynamic tensile strength of two mortars: Experiments and models. Int J Impact Eng 122: 407–418. https://doi.org/10.1016/j.ijimpeng.2018.09.010
Yu SL, Huang SB, Liu F, Cai HW, Ye YH (2024) Quantification of pore structure evolution and its correlation with the macroscopic properties of sandstones under freeze–thaw action. B Eng Geol Environ. 83: 3. https://doi.org/10.1007/s10064-023-03484-x
Yuan HH, Sun Q, Geng JS, Tang LY, Lv C, Zhang, YL (2023) Thermal acoustic emission characteristics and damage evolution of granite under cyclic thermal shock. Environ Earth Sci. 82 (16): 388. https://doi.org/ 10.1007/s12665-023-11075-y
Zhao K, Yang DX, Gong C, Zhuo YL, Wang XJ, Zhong W (2020) Evaluation of internal microcrack evolution in red sandstone based on time-frequency domain characteristics of acoustic emission signals. Constr Build Mater 260. https://doi.org/10.1016/j.conbuildmat.2020.120435
Zhu J, Deng JH, Wang P, Fu ZG, Pak R.Y.S, Zhao WY (2023) Mechanical behavior and failure mechanism of Rrocks under impact loading: The coupled effects of water saturation and rate dependence. Int J Geomech 23 (11). https://doi.org/10.1061/IJGNAI.GMENG-8584

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Experimental study on instability and failure mechanism of sandstone under freeze-thaw and load

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Abstract

Figures

1. Introduction

2. Materials and methods

2.1 Specimen preparation

2.2 Test methods

3. Strength characteristics and crack mode analysis

3.1 Variation law of mechanical parameters

3.2 Exponential decay model

3.3 Evolution law of crack characteristics

4. Variation Law of AE Parameters

4.1 RA/AF Variation Characteristics

4.2 Variation Law of AE events rate

4.3 AE b-value variation characteristic

5. Discussion

5.1 Strength Prediction of Sandstones under Dual-Factor Coupling

5.2 Damage Mechanism of Sandstone under Dual-Factor Coupling

5.3 Limitations

6. Conclusions

Declarations

Author Contribution

Acknowledgements

Data availability

References

Additional Declarations

Status:

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