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. 2024 May 2;9(19):21528–21537. doi: 10.1021/acsomega.4c02233

Experimental Study on the Response of Cracked Sandstone to the Intermediate Principal Stress Coupled with Pore Pressure

Qinming Liang †,‡, Gun Huang †,‡,*, Jie Zheng §, Weile Geng ∥, Jinyong Huang †,‡, Guowen Sun ⊥,*
PMCID: PMC11097356  PMID: 38764677

Abstract

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Underground fractured rock masses are susceptible to failure under the combined influence of true triaxial stresses and pore pressure, posing severe threats to personnel and production safety of underground engineering. To investigate the influence of intermediate principal stress (σ2) on the mechanical and water diffusion volume change (ΔV) characteristics during the failure process of cracked rocks under stable pore pressure, this study conducted true triaxial strength experiments on cracked sandstone with stable pore pressure. The results demonstrated that with the increase of σ2, crack initiation stress (σci), crack damage stress (σcd) and the peak stress (σ1,peak) of cracked sandstone initially increase and then decrease. Conversely, ΔV tends to decrease first and then increase with the increase of σ2. This inverse relationship indicates that under elevated σ2, the decreased strength of cracked rock could lead to an increase in ΔV, which may increase the probability of water inrush disasters. The findings of this study provide a theoretical reference for the stability of rock mass engineering and the prevention of water inrush disasters.

Introduction

With the exhaustion of shallow energy resources and sustainable utilization of underground space, human endeavors have inevitably extended into deeper regions of the Earth.1−3 The rock masses in deep underground engineering are characterized by inherent heterogeneity, often containing an abundance of structural planes such as joints, fissures, and faults.4,5 Meanwhile, the intricate geological structures typically subject the fractured rock underground to true three-dimensional stress with high geostress and elevated pore pressure.2 The presence of pore pressure in the cracked causes a decrease in the strength of the rock masses, reducing its stability and increasing its susceptibility to failure under stress perturbations.6,7 During the rock failure process, the water diffusion volume change (i.e., ΔV) can potentially lead to water inrush disaster, significantly jeopardizing the safe construction of underground engineering. Therefore, it is crucial to investigate the mechanical and ΔV characteristics in the failure process of cracked rocks under the influence of true triaxial stress and pore pressure. Such research can provide theoretical foundations for mitigating the risks associated with water and mud inrush disasters in underground engineering.

Since Mogi first developed a true triaxial loading test apparatus applicable to rock strength properties,8,9 the σ2 effect of intact rock strength has been extensively experimentally verified by numerous researchers worldwide.10,11 These studies consistently show that with increasing σ2, the strength of intact rocks first increases and then decreases.12,13 In addition, significant progress has also been made in studying the σ2 effect of fractured rock strength. Chang et al.14 discovered that increased σ2 leads to higher rock strength, while crack initiation stress (σci) under true triaxial stress first increases and then decreases. Concurrently, other researchers have also conducted true triaxial compression experiments on foliated phylite and jointed marble, respectively.15−17 The strength of these fractured rocks exhibits a σ2 effect similar to that of intact rocks.

The effect of water on rock mechanical behavior has achieved remarkable accomplishments.18−20 The existence of pore water pressure significantly reduces rock strength and poses a serious threat to the stability of underground rock masses. To further understand the failure behavior of fractured rocks under hydro-mechanical coupling conditions, existing studies have conducted hydro-mechanical experiments on rock (and rock-like) materials under various stress conditions. Lin et al.21 investigated the failure behavior of cracked sandstone under different dip angles and pore pressure conditions with uniaxial compression experiment. The results showed that specimens under pore pressure had much lower strength than specimens without pore pressure. Meanwhile, under the same pore pressure condition, crack dip angle significantly affected the failure mode of the specimens. Moreover, increasing pore pressure in the crack accelerates wing crack propagation and inhibits secondary crack initiation, leading to tensile failure of the specimens.22 Further studies have shown that the application of pore pressure to the crack surfaces under uniaxial stress conditions has a significant effect on the location, angle, and strength of the crack initiation.23 This indicates that the mechanical characteristics and deformation properties of rocks are significantly altered when pore pressure is applied to the crack surfaces. Apart from uniaxial stress situations, some researchers have observed that the combined effects of shear loading and pore pressure more easily induces failure in cracked rock. Furthermore, pore pressure causes local stress redistribution around crack tips.24,25 Since the difficulty in sealing internal pore pressure in cracks under uniaxial compression, conventional triaxial experiments are now extensively adopted to investigate the influences of crack inclinations, confining pressure, and pore pressure on hydro-mechanical characteristics of rock materials.26 Kou et al.27 investigate the mechanical behavior of rock-like materials under different pore pressure. They observed that the strength of specimens decreased with increasing pore pressure under constant confining pressure conditions. Additionally, scanning electron microscope (SEM) results further indicated that roughness of fracture surfaces decreased at crack initiation with increasing pore pressure. Regarding failure modes under various confining pressures, Wang et al.28 discovered that failure patterns of metamorphic rocks under hydro-mechanical coupling were significantly associated with confining pressure. Lower confining pressure led to splitting failure while higher confining pressure resulted in shear failure. Liu et al.29 conducted extensive experiments to investigate the mechanical properties of limestone under hydro-mechanical coupling conditions. They analyzed the fracture patterns of single-fractured limestone using linear elastic fracture mechanics. Based on this findings, they derived a compressive-shear fracture criterion under hydro-mechanical coupling, providing a theoretical reference for underground engineering projects. Additionally, previous studies have demonstrated that the thresholds of σci and crack damage stress (σcd) both decreased with increasing pore pressure under conventional triaxial stress conditions. Furthermore, elevating pore pressure resulted in a transition of the failure mode of the specimens from pure shear failure to mixed tensile-shear failure.30 Moreover, Zhou et al.31 identified a new type of crack called horizontal coupled crack (HCC), caused by pore pressure under conventional triaxial stress conditions. Microscopic analysis revealed that HCC begin as tensile cracks from pre-existing crack tips, but transform into mixed tensile-shear fractures when reaching the edges of the specimens. Additional, Kou et al.32 investigated the hydro-mechanical coupling characteristics of rock-like specimens under unloading conditions. They established a relationship between three-dimensional fractal dimension, mechanical strength, and permeability, unveiling the hydro-mechanical coupling failure mechanism. These research findings provide valuable theoretical references for underground engineering and a foundation for stability analysis of water-rich jointed rock masses. The significant impact of hydro-mechanical coupling on the mechanical properties of rocks and rock-like materials has been comprehensively validated through rock mechanics experiments. Furthermore, some researchers have performed mechanical experiments on intact shale specimens under combined true triaxial stresses and varying water pressure conditions, analyzing the variation of water flux during the process of rock deformation and failure.33 The results demonstrate that water flux exhibits a clear relationship with the volumetric strain of rocks during the loading process, which is affected by water pressure and the degree of saturation of the shale.

Stable pore pressure is often applied directly to the cracks in hydro-mechanical coupling experiments on cracked rock. During the process of rock deformation and failure, water infiltrates into other fractures as internal microcracks develop to a certain extent, leading to changes in ΔV. The penetration of water into the internal fractures of rocks significantly affects their strength. However, current research on the variation of ΔV during the deformation and failure process of specimens remains limited. Particularly under true triaxial stress conditions, how σ2 affects ΔV during the deformation and failure process of rocks necessitates further investigation.

As summarized above, the influence of σ2 on the strength of both intact and fractured rocks has achieved remarkable progress. Numerous studies have also been conducted on the mechanical properties of rocks and rock-like materials under hydro-mechanical coupling, including uniaxial and conventional triaxial conditions. However, due to the inherent complex physicomechanical properties of rocks, leading to certain disparities between rock-like specimens and real rocks in physical and mechanical properties. Although underground rock masses often experience true triaxial stress states, current research on the mechanical properties of rocks under hydro-mechanical coupling often overlooks the influence of σ2. Furthermore, there is a lack of experimental research on the impact of σ2 on ΔV during the failure process of cracked sandstone under pore pressure. Therefore, it is essential to conduct true triaxial strength experiments on rocks under hydro-mechanical coupling. To further investigate the effect of σ2 on the mechanical properties of cracked rocks and the variations of ΔV during the failure process under stable pore pressure.

In this study, true triaxial strength experiments were performed on cracked sandstone under different σ2 conditions with stable pore pressure. The experimental results characterize the variation of σci, σcd, σ1,peak and ΔV during the failure process of fractured sandstone under hydro-mechanical coupling with vary σ2. The findings of this research provide theoretical references for the stability of underground rock mass engineering and the prevention of water inrush incidents.

Materials and Methods

To investigate the impact of different σ2 on the mechanical properties of fractured rocks and the variation of ΔV during the failure process under stable pore pressure, the red sandstones were selected for true triaxial strength experiments. These sandstones were taken from outcrops in Kunming, Yunnan Province, southwest China. The density of this rock is 2260 kg/m3, and the uniaxial compression strength is determined to be 41.6 MPa. Young’s modulus and Poisson’s ratio of sample are 5.4 GPa and 0.36, respectively. Initially, large blocks of red sandstone were cut into cubes measuring 100 mm × 100 mm × 100 mm. Subsequently, a 3 mm drill bit was used to bore holes in the center of the cubic specimens. Prefabricated crack was then created using a diamond wire cutter. The cracks had an inclination of 45°, a length of 20 mm, and a width of 0.5 mm. After the fabrication of the pre- fabricated crack, water injection holes of 3 mm diameter were drilled above the crack to ensure connectivity between the boreholes and the crack, facilitating the application of stable pore pressure within the crack later in the experiments. The sample preparation process is illustrated in Figure 1 (a), and the completed specimens are shown in Figure 1 (b).

Figure 1.

Figure 1

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Experimental rock samples. (a) Schematic diagram of sample processing process. (b) Sandstone specimen containing prefabricated crack.

The experiments were conducted utilized the multifunctional true triaxial geophysical (TTG) apparatus,34 as depicted in Figure 2. This system comprises a true triaxial pressure chamber, stress loading, sealed permeation, and data acquisition monitoring systems. The true triaxial pressure chamber is equipped with six independent loading indenters, each capable of applying force to the rock specimens either through displacement or force control. The four indenters aligned along the X and Y axes can exert a maximum pressure of 6000 kN, while the two indenters on the Z axis can apply up to 4000 kN. A servo system facilitates the generation of a maximum confining pressure of 60 MPa within the chamber, enabling the execution of experiments related to seepage or hydraulic fracturing. The experimental setup incorporates three novel modes of force and displacement control: force control and tracing mode, displacement control and tracing mode, and a displacement tracing with force correction mode. These configurations significantly mitigate the imbalance of forces applied in the loading directions. Additionally, Linear Variable Differential Transformers (LVDTs) are used to capture displacements throughout experiment.

Figure 2.

Figure 2

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True triaxial geophysical apparatus and stress setting path.

The experimental stress path involved applying the minimum principal stress (σ3) along the fissure strike direction, while σ2 was applied perpendicular to the fissure strike direction. Each indenter of TTG is equipped with an LVDT to record the displacement changes during the experiments. The stress settings in this experiment were based on the geostress calculation formula proposed by Stephansson.35 Taking the stress state at a depth of 500 m underground as a reference, the calculated minimum principal stress was 17.25 MPa. For the convenience of setting the stress scheme in the experiment and subsequent analysis, the minimum principal stress was set to 15 MPa. Consequently, the intermediate principal stress was set sequentially at 15, 20, 25, 30, 35 MPa. The detailed experimental programs are given in Table 1.

Table 1. Experimental Stress Programs.

Sample number (σ3)/MPa (σ2)/MPa (Pore Pressure)/MPa v/mm·s–1
1# 15 15 2 0.002
2# 15 20
3# 15 25
4# 15 30
5# 15 35
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A stress loading path recommended by International Society for Rock Mechanics (ISRM) was adopted,36 with the experimental loading path depicted in Figure 3. The specific steps were as follows:

  • (1)

    Initially, the sandstone specimen was wrapped in heat shrink tubing and put into the true triaxial pressure chamber. The purpose of wrapping with heat-shrink tubing is to ensure complete sealing of the pore pressure during the experimental process. A force control method was used to load up to the hydrostatic pressure stage (σ1 = σ2 = σ3).

  • (2)

    Subsequently, σ1 and σ2 were continuously increased to preset values, and pore pressure of 2 MPa was applied. Upon completion of loading, the experiment moved to the next loading stage after the stress state had stabilized.

  • (3)

    Finally, σ1 was incrementally increased at a rate of v = 0.002 mm/s using a displacement-controlled approach until the specimen failed. Throughout this process, σ2, σ3, and pore pressure were maintained constant.

Figure 3.

Figure 3

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Loading path used in true triaxial compression experiments.

Results

σci and σcd Characteristics of Cracked Sandstone

σci and σcd thresholds play a significant role in the failure process of rocks. Various theoretical approaches based on fracture volumetric strain have been suggested by scholars to determine the compressive-shear σci for rocks.37,38 Therefore, in this study, these methods were employed to determine σci and σcd of cracked sandstone. The volumetric strain (εv) of the rock can be obtained from the sum of the strain components in the three principal stress directions, and the calculation method is as follows:39

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The volumetric strain of rock consists of crack volumetric strain (εcv) and elastic volumetric strain (εev):

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where ε1 is the strain in the direction of σ1; ε2 is the strain in the direction of σ2; ε3 is the strain in the direction of σ3; μ is the Poisson’s ratio; E is the elastic modulus, and both of which parameters are determined based on the elastic deformation stage.40

The σci and σcd of the experimental results were determined using the method described above, and schematic representations of the critical stress determinations are shown in Figure 4. In the initial phase of rock loading and deformation, the microfractures existing inside the rock are compressed, resulting in the stress–strain curve approximating a linear increase. At this time, εcv also gradually increases. As the loading continues, the internal fractures of the rock begin to develop, and it can be clearly seen that the curve of εcv gradually increases to a peak. The stress corresponding to this peak is σci. With further increase in load, the internal cracks of the rock continue to develop, and εv curve of the rock grows to a peak. The stress corresponding to this peak is σcd, indicating the onset of unstable expansion of internal fractures.

Figure 4.

Figure 4

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Stress–strain diagram showing the stages of crack development under true triaxial compression and pore pressure conditions.

The deviatoric stress corresponding to the point where εcv shifts from increasing to decreasing is identified as the σci for cracked sandstone. Then, σcd corresponds to the deviatoric stress value at which εv begins to decrease, indicating the beginning of unstable crack propagation. The stress threshold results under different σ2 conditions were determined by this method, are presented in Figure 5 and Table 2.

Figure 5.

Figure 5

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Results of critical stress under different σ2. (a) The results of σci. (b) The results of σcd.

Table 2. Characteristic Stresses of Sandstone Samples under Different σ2.

Sample number σ2/MPa σci/MPa σcd/MPa
1# 15 50.14 96.35
2# 20 82.45 104.13
3# 25 90.05 122.73
4# 30 100.57 107.65
5# 35 72.97 104.41
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As observed from Figure 5, the σci and σcd of cracked sandstone both exhibit a trend of first increasing and then decreasing with the increase of σ2. Notably, for σci, when σ2 increases from 15 to 30 MPa, σci escalates from 50.14 to 100.57 MPa, marking an increase of 100.58%. The maximum value of σci is attained at σ2 = 30 MPa. σci corresponds to the beginning of stable crack propagation within the rock, indicating that an increase in σ2 from 15 to 30 MPa can significantly inhibit crack development, thereby enhancing the load-bearing capacity of rocks to a certain extent. However, when σ2 increases from 30 to 35 MPa, a significant decrease in σci is observed, dropping from 100.57 to 72.97 MPa. This indicates that σci at σ2 = 35 MPa is only marginally higher than that at σ2 = 15 MPa. This indicates that in our experiments, once σci reaches its peak value (that is, when σ2 = 30 MPa), a slight increase in σ2 (from 30 to 35 MPa) can significantly reduce the magnitude of this stress. This could be attributed to the development of certain extents of fracturing within the rock at a certain threshold of σ2, consequently reducing the threshold of σci. When σ2 increases from 15 to 25 MPa, σcd rises from 96.35 to 122.73 MPa, an increase of 27.38%. Moreover, the maximum value of σcd is reached at σ2 = 25 MPa. Subsequent schemes with increased σ2 lead to a gradual decline in σcd. σcd corresponds to the beginning of unstable crack propagation within the rock, peaking at σ2 = 25 MPa, which slightly differs from σci. This indicates that σ2 has different degrees of influence on the stable development and unstable propagation of internal cracks in the rocks. Unstable crack propagation is typically linked to rock failure. Therefore, to further investigate the impact of σ2 on the mechanical characteristics of cracked rocks, we analyzed the variation of σ1,peak in the experiments.

σ1,peak Characteristics of Cracked Sandstone

σ1,peak of cracked sandstone under stable pore pressure and varying σ2 conditions is shown in Figure 6. At σ3 = 15 MPa, σ1,peak of cracked sandstone exhibits a pattern of initially increasing and then decreasing with the increase of σ2. During the increase of σ2 from 15 to 25 MPa, σ1,peak of cracked sandstone rises from 114.16 to 152.28 MPa, an increase of 33.39%. However, as σ2 further increases from 25 to 35 MPa, σ1,peak decreases from 152.28 to 142.64 MPa. Our experimental results demonstrate that σ2 also have a significant impact on the strength of rocks with prefabricated fissures and stable pore pressure. Furthermore, this effect is similar to σ2 effect on the strength of intact rocks. That is, as σ2 increases, the strength of various types of intact rocks displays a trend of first increasing and then decreasing.41 However, the trend of increasing and then decreasing strength typically requires a larger range of σ2 change in intact rocks. In contrast, the range of σ2 change is relatively smaller in the present study.

Figure 6.

Figure 6

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Strength of cracked sandstone with pore pressure under different σ2.

Analyzing the results from Figure 5 and Figure 6, it is clear that σ1,peak and σcd of cracked sandstone have a stronger correlation. The maximum values for both were observed at σ2 = 25 MPa. This suggests that the impact of σcd on σ1,peak is more significant than that of σci, since it marks the beginning of unstable crack propagation within the rock. Based on the analysis above, it is evident that σ2 can significantly impact the mechanical properties of cracked sandstone when subjected to pore pressure. The variation in σ1,peak causes different fracture formation in the rocks. For the cracked sandstone in this study, the presence of stable pore pressure in the pre-existing cracks spreads to varying degrees as the fractures develop, leading to alterations in ΔV. Therefore, we further investigated the influence of different σ2 on the ΔV during the failure process of cracked sandstone when subjected to stable pore pressure.

ΔV Characteristics in the Deformation and Failure Process of Cracked Sandstone

The experiment utilized the pore pressure stabilization control method, resulting in a change of the monitored water diffusion volume (V) due to microfractures development of cracked rocks during the loading process. The variation of V and σ1 was analyzed under different σ2 conditions from the beginning of displacement-controlled loading stage to the moment of σ1,peak, as shown in Figure 7. It is evident from the Figure 7, during the initial stage of displacement-controlled loading, specifically prior to Point A. There are no obvious microfractures present in the rock, and V does not show significant changes. The slight variations observed in the curve are attributed to minor fluctuations in the servo control equipment. As loading progresses beyond Point A, sufficient development of microfractures in the rock enable the pore pressure acting on the crack surfaces to dissipate into the surrounding area, resulting in a reduction of the preset pore pressure. Since the pore pressure control mode is pressure-controlled, the servo control system compensates water quantity by changing V, thereby maintaining the applied pore pressure stable at 2 MPa, which results in V exhibiting an upward trend in the latter stages of loading. To uniformly analyze the variation of ΔV under different σ2 during the experimental process, we defined that ΔV = VA - VB, specifically, the AB phase in the Figure 7.

Figure 7.

Figure 7

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Variation of V and σ1 under different σ2. (a) The results of σ2 = 15 MPa. (b) The results of σ2 = 20 MPa. (c) The results of σ2 = 25 MPa. (d) The results of σ2 = 30 MPa. (e) The results of σ2 = 35 MPa. (f) Variations of ΔV under different σ2.

Figure 7 (f) illustrates the relationship between ΔV and σ2 during the failure process of cracked sandstone. It can be observed that ΔV initially decreases and then increases with the increase of σ2, reaching its minimum value at σ2 = 25 MPa. From the results in Figure 5 and Figure 6, it is clear that both the σci, σcd and σ1,peak of cracked sandstone exhibit a trend of first increasing and then decreasing with the increase of σ2. This may be due to the increase in σ2 altering the crack propagation within fractured sandstone, thereby affecting its σci and σcd. During the experiment, when the applied stress exceeds σci, cracks developed stably, and water in the pre-existing crack does not easily penetrate these microfractures. Therefore, the variation patterns of σci and ΔV do not exhibit a strong correlation (the peak of σci occurs at σ2 = 30 MPa, while the peak of ΔV occurs at σ2 = 25 MPa). σcd is the threshold for unstable crack propagation in the rock. When the applied stress exceeds σcd, the internal fractures in the rock become more developed, allowing water in the pre-existing crack to infiltrate the newly formed cracks, resulting in a strong correlation between σcd and ΔV (both peaking at σ2 = 25 MPa). These indicated a strong correlation between ΔV and σcd, σ1,peak during the progressive failure process of cracked sandstone. Both σcd and σ1,peak reach their maximum values at σ2 = 25 MPa, while ΔV reaches the minimum value when σ2 = 25 MPa. Therefore, from the above results, it can be concluded that with the increase in σ2, the increase in σcd and σ1,peak corresponds to a decrease in ΔV, and the decrease in σcd and σ1,peak corresponds to an increase in ΔV. This demonstrates that under steady pore pressure, the mechanical characteristics of cracked rocks significantly influence the variation in ΔV, providing theoretical references for rock deformation and failure under hydro-mechanical coupling.

Discussion

As underground tunnels, mining operations, and other underground engineering projects expand to greater depths, they often encounter complex stress states characterized by high geostress, high geothermal conditions, and high pore pressure.2 To address the mechanical characteristics of cracked sandstone under the combined influence of high geostress and pore pressure, this study conducted a series of true triaxial compression experiments under stable pore pressure with different σ2. From the experimental results, it is apparent that σ1,peak of cracked sandstone containing pore pressure exhibits a trend of initially increasing and then decreasing under various σ2 conditions. According to previous research, σ2 also has a similar impact on the σ1,peak of intact rocks.12,42−44 However, σ1,peak of intact rocks typically exhibits this trend over a larger range of σ2, while for the cracked sandstone with pore pressure in this study, this trend appears within a relatively smaller range of σ2 variation (15–35 MPa). Previous studies have shown that pre-existing cracks significantly affect the strength of rocks under various stress conditions, including uniaxial, biaxial, conventional triaxial, and true triaxial.45−48 Additionally, researchers have investigated the hydro-mechanical coupling characteristics of brittle materials (rocks, gypsum) under uniaxial and conventional triaxial stress conditions, indicating that pore pressure existed in cracks can significantly impact the strength of brittle materials. Therefore, as the specimens in this experiment contain prefabricated crack and are subject to pore pressure on the crack surfaces, the σ2 effect on their σ1,peak does not entirely align with that of intact rocks. Hence, in the smaller range of σ2 variation, σ1,peak of fractured sandstone exhibits an initial increase followed by a decrease.

From the results of this study, it can be observed that σci, σcd and σ1,peak of cracked sandstone under different σ2 conditions have corresponding relationships with the changes in ΔV during the failure process, as shown in Figure 8. With increasing σ2, σci and σ1,peak exhibit an approximately inverted U-shaped variation trend, and σcd displays an inverted V-shaped change. Overall, all three parameters demonstrate a trend of initially increasing and then decreasing. However, ΔV shows a V-shaped variation pattern, characterized by an initial decrease followed by an increase. Furthermore, both σcd and σ1,peak reach their maximum values at σ2 = 25 MPa, whereas ΔV reaches its minimum value at this point. These experimental findings indicate that σ2 significantly influences the mechanical properties of cracked sandstone, which consistent with exist studies. Then, these changes in mechanical properties directly affect the variation in ΔV during rock failure. As underground resource extraction and engineering construction gradually advance into deeper parts of the Earth, under smaller increases in σ2 (such as σ2 = 15, 20, 25 MPa in this study), both σcd and σ1,peak exhibit an increasing trend. In these circumstances, the absence of internal water inrush channels within the rock mass results in higher rock strength. Current research also supports this view. Underground tunnels or caverns with relatively intact surrounding rock often possess higher strength and have a relatively lower probability of experiencing water inrush or similar geological disasters.49,50 Additionally, ΔV demonstrates a declining trend under stable water supply under relative lower σ2. However, when the increase in σ2 becomes more significant (such as σ2 = 30, 35 MPa in this study), σcd and σ1,peak of the cracked rock start to decline, resulting in a decrease in rock strength and heightened development of internal water inrush channels in the cracked rock. This leads to an increase in ΔV under relative higher σ2. Existing research findings indicate that the volume of water inflow is one of the critical indicators guiding the assessment of underground water inrush disasters.51,52 Although there remains a certain discrepancy between the conditions of water supply in our experiments and actual site conditions, a preliminary correlation between ΔV and rock strength has been established. Therefore, it could be considered as one of the potential indicators in subsequent evaluations of water inrush risk under specific conditions. However, we also fully recognize that the factors determining the occurrence of water inrush events are multifaceted, including but not limited to the mechanical properties of rocks, the extent of fracture development, and the dynamics of groundwater conditions. Thus, our study emphasizes that research into water inrush accidents must not only consider geological and hydrogeological conditions but also the effects of different intermediate principal stresses on the mechanical and hydraulic properties of rock masses. Furthermore, future research needs to elucidate how these variations affect the stability of rocks and the risk of water inrush, as well as the interactions between these factors, to more comprehensively understand the mechanisms behind the occurrence of water inrush.

Figure 8.

Figure 8

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Relationships between σci, σcd, σ1,peak and ΔV under different σ2..

Conclusion

This study conducted experimental research on the mechanical and ΔV characteristics of cracked sandstone during the failure process with stable pore pressure under varying σ2. The experimental results demonstrate that σ2 significantly influences σci, σcd, σ1,peak and ΔV of cracked sandstone. The specific conclusions are as follows:

  • (1)

    Under stable pore pressure, σ2 significantly influences σ1,peak of cracked sandstone, with a similar effect to that of σ2 on the strength of intact rocks. As σ2 increases, σci, σcd and σ1,peak of cracked sandstone all exhibit a trend of first increasing and then decreasing.

  • (2)

    With the increase of σ2, ΔV during the failure process of cracked sandstone shows a trend of initially decreasing and then increasing, which is contrary to the variation patterns of σci, σcd and σ1,peak. Both σcd and σ1,peak reach their maximum values at σ2 = 25 MPa, while ΔV reaches its minimum value at the same σ2.

  • (3)

    The influence of σ2 on ΔV during the failure process of cracked sandstone suggests that under conditions of higher σ2, underground rock masses may have an increased probability of water and mud inrush disasters due to the increase in ΔV.

Acknowledgments

The authors gratefully acknowledge the financial supported by the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJZD-K202203402), and National Natural Science Foundation of China (51674049).

The authors declare no competing financial interest.

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