Experimental and Numerical Investigation of Rock Failure Process under Hydromechanical Coupling Action

In order to study the initiation mechanism of rocks under hydromechanical coupling, hydromechanical coupling triaxial tests and acoustic emission tests were carried out on basalt in the Xiluodu hydropower station dam site area in southwestern China. The test results indicate that the basalt displays typical hard brittle behavior, and its peak strength increases as confining pressure rises. Conversely, the peak strength decreases gradually as the initial water pressure increases, which leads to decreased hardness. Meanwhile, tensile failure is the main crack initiation mode under hydromechanical coupling action. During the stable crack growth stage, tensile failure is predominant, complemented by shear failure, with failures mainly occurring in the rock middle position. Contrary to this, during the unstable stage, the rock failure is mainly due to shear failure. The critical pore water pressure failure criterion of rock crack initiation under hydromechanical coupling conditions is derived based on the test results and introduced into the numerical simulation. The hydromechanical coupling failure process and pore water pressure distribution law of basalt are analyzed, and the rationality of the critical pore water pressure failure criterion is verified. These findings are significant for understanding the rock failure process under hydromechanical coupling action and provide a valuable reference for future research.Hydroelectric engineering projects often involve structures such as underground power stations, water diversion tunnels, and sloping dam foundations, which are subjected to the combined action of high-ground stress and strong osmotic pressure. Therefore, research on the mechanical properties of rocks or rock masses under hydromechanical coupling has become a pressing issue in geotechnical engineering. Several scholars, including Song et al. [1], Zhu et al. [2], Yu et al. [3], Xu et al. [4], Wang et al. [5], and Wang et al. [6], have conducted hydromechanical coupling triaxial tests on limestone [1-3], sandstone [4-6], and granite [7, 8] to investigate the relationship between rock permeability, stress, strain, and pore water pressure. They have discussed the influence of pore water pressure on rock strength characteristics, deformation laws, and damage evolution. Moreover, Li et al. [9], Zhao [10], and Guo et al. [11] have employed acoustic emission (AE) signals to analyze the AE characteristics during the process of rock cracking under hydromechanical coupling.The aforementioned research has extensively demonstrated that hydromechanical coupling induces pore water pressure within the internal cracks of a rock, which significantly impacts the cracking process [12, 13]. Once the pore water pressure attains a critical level, it instigates the inception, expansion, and penetration of rock cracks, commonly referred to as hydromechanical fracturing [14]. This phenomenon is a significant factor that causes a range of engineering disasters, including water inflow in tunnels, rock slope landslides, and reservoir earthquakes. Min et al. [15] have successfully simulated the initiation and propagation of cracks under hydromechanical fracturing by employing the virtual multidimensional internal bonds model. This was achieved through the establishment of the equilibrium equation and the introduction of the Weber distribution to consider the heterogeneity of rocks. Tang et al. [16] have developed a new fracture strength criterion for rock mass containing closed and open cracks under the influence of dynamic, hydrostatic pressure, and hydrochemical damage, based on the crack tip strength factor. Bian et al. [17] have combined stress analysis of the hydraulic tunnel with crack propagation of the surrounding rocks, from macro and micro perspectives, by utilizing the fracture mechanics propagation criterion. This led to the deduction of the calculation formula of the critical pore water pressure of the crack propagation of the surrounding rock of the hydraulic tunnel under the tension shear and compression shear conditions. Sheng et al. [18] have further studied the propagation mechanism of the compressive shear crack of the surrounding rock of the hydraulic tunnel, based on the Mode I tensile failure of the crack. Cui et al. [19] have proposed two methods to calculate the critical pore water pressure for hydromechanical fracturing when the surrounding rock experiences instability damage.The above research mainly involves the hydraulic coupling failure of rocks, but there is relatively little research on the changes in pore water pressure during the hydraulic coupling failure process of rocks. At the same time, there is a lack of in-depth research to establish some qualitative understanding of the role and influence of water on rock failure. Therefore, the Xiluodu basalt is taken as the research object. The hydraulic coupling crack failure mechanism of rocks was studied through hydromechanical coupling triaxial tests, AE tests, theoretical analysis, and numerical simulation. The critical pore water pressure failure criterion for hydraulic fracturing of basalt was established. Based on this, a numerical simulation of the hydraulic coupling failure process of rocks was conducted, and the simulation results were consistent with the experimental results. The relevant research has important reference value and significance for understanding the mechanism of rock hydraulic coupling fracture and related engineering practices.The Xiluodu Hydropower Station is located in the southwestern region of China. The Xiluodu hydropower station dam site area features Emeishan basalt of the Upper Permian system (P2β) as the bedrock. The basalt specimens are dark blue in color and exhibit a fine and uniform particle composition. The samples, obtained through drilling and boring, are cut and ground into uniform cylinders with a diameter of 50 mm and a height of 100 mm. The triaxial tests are conducted using the MTS815.04 electro-hydraulic servo rigid testing machine at the Wuhan Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. The PC-II AE three-dimensional positioning real-time monitoring and display system developed by Physical Acoustics is employed for the AE acquisition. The sampling channels for this AE test are 4, with a sampling frequency of 5 MHz and a data recording threshold of 45 dB. When conducting AE testing, PDT, HDT, and HLT are set to 200, 800, and 1000 μs, respectively.Figure 1 depicts the sample installation for the triaxial compression test of basalt. In this test, the confining pressure is varied to 20, 25, and 30 MPa. For each confining pressure, an initial water pressure P is imposed with a gradient of 5, 10, and 15 MPa, respectively. Throughout the test, the initial water pressure is maintained constant. The basalt samples are confined in a closed state to ensure that P<σ2=σ3⁠, under the influence of hydromechanical coupling. To eliminate the influence of the permeable plate on axial deformation, the axial deformation of the rock sample is measured using the axial strain silicon fixed in the middle, and the measurement method is calibrated before the test. Additionally, the sample is immersed in water using the free immersion method to achieve a saturated state before the test, and the immersion time of basalt in this study is around 50 hours [20].Figure 2 illustrates the stress-strain behavior of basalt under varying water pressures at confining pressures of 20, 25, and 30 MPa. As observed in Figure 2, the post-peak stress drop of basalt is prominent, exhibiting hard, and brittle behavior. Moreover, an increase in water pressure results in a gradual decrease in the peak strength of basalt, along with a decrease in stress drop. Specifically, considering Figure 2(c), at a confining pressure of 30 MPa, when the water pressure is low (5 MPa), the post-peak curve of basalt exhibits a linear decline, indicative of typical brittle failure. However, as water pressure increases, the post-peak curve shows distinct softening characteristics, with the post-peak curve at 15 MPa water pressure demonstrating typical ductile failure. These results reveal that water pressure weakens the compressive strength of rock and reduces its hard brittleness to some extent.The interrelationships among the peak strength, confining pressure, and initial water pressure are illustrated in Figure 3. It is evident that, at a constant initial water pressure, the peak strength of basalt enhances with the addition of confining pressure, whereby a greater confining pressure yields a more marked change in peak strength. However, with a constant confining pressure, the peak strength diminishes as the initial water pressure rises. Notably, compared with the 20 and 25 MPa confining pressures, the peak strength experiences a more pronounced reduction under the 30 MPa confining pressure as the initial water pressure rises.In accordance with the characteristics of the rock failure process, the process can typically be partitioned into four stages [21]. Due to the hardness and brittleness of basalt and the high confining pressure applied, the stress-strain curve’s compaction segment in Figure 2 is either not prominent or nonexistent. Consequently, it can be inferred that the basalt compression failure process predominantly manifests in three stages, namely the elastic stage (I), the stable crack growth stage (II), and the unstable crack growth stage (III).Figure 4 illustrates the stress-time curves of basalt and AE event rate change curves under varying water pressures, with a confining pressure of 20 MPa. From Figure 4, it can be observed that the rock sample is predominantly subjected to elastic deformation, with minimal AE events during the elastic stage. Upon entering the stable crack growth stage, the occurrence of an AE event indicates the penetration of pressurized seepage into the rock’s interior and the initiation of primary cracks under hydromechanical coupling. Therefore, this paper adopts the initial AE event occurrence time as the boundary between Stage I and Stage II, considering it to signify the onset of crack formation in the rock. The unstable crack growth stage is characterized by further propagation of internal cracks in the rock under hydromechanical coupling, accompanied by a significant increase in AE event rate. It should be pointed out that in Figure 4, in order to highlight the boundary between Stage I and Stage II, the AE event rate for Stage III is not fully displayed.The Japanese code of concrete monitoring has presented a technique to differentiate fracture types based on AE parameters [22]. The average frequency (AF, kHz) is defined as the ratio of AE count to duration, while the ratio of rise time to maximum amplitude is defined as RA (ms/V). It is deemed that a high RA value and a low AF value in AE reveal rock shear failure, whereas the opposite suggests rock tensile failure.To investigate the hydromechanical coupling-induced internal crack fracturing of basalt, we utilize basalt samples subjected to a 20 MPa confining pressure and a 15 MPa initial water pressure. Figure 5 depicts the distribution of RA-AF values of basalt at different stages. The figure shows that during the elastic stage, the basalt experiences no crack fracturing. During the stable crack growth stage, the primary mode of failure is crack tensile failure, as indicated by the high and rapidly increasing AF value of AE, and the small and relatively unchanged RA value. In the unstable crack growth stage, there are two failure modes, shear and tension, within the internal cracks of basalt. The AE signals characterized by high RA values and low AF values experience a noticeable increase, while the AE signals with lower RA values and high AF values are more densely distributed, indicating that the predominant crack fracturing mode is shear failure during this stage.Figure 6 displays the three-dimensional positioning diagram of AE events in Stage II of basalt, with varying initial water pressures under a confining pressure of 20 MPa. As depicted in the figure, during Stage II, crack fracturing predominantly transpires in the central region of the rock, under the influence of hydromechanical coupling. Furthermore, the AE events significantly increase with the rise in initial water pressure, indicating that water pressure accelerates the propagation of cracks in the rock.The AE testing results demonstrate that, under the effect of hydromechanical coupling, basalt experiences tensile failure during crack initiation, which is caused by the combined influence of internal pressure seepage and external stress loading. To investigate the tensile failure of cracks, the current study assumes that the cracks are circular holes surrounded by isotropic rock materials. As the crack size is much smaller than that of the rock, the crack failure calculation model presented in Figure 7 is employed. In this model, an infinite body with a circular crack experiences two-way uniform compressive stress, and the pore water in the crack is completely filled, where the pore water pressure is equal to the initial water pressure in the absence of external load.Drawing on the principles of elastic mechanics, with the initial water pressure designated as P and the rise in water pressure as ΔP, the stress encircling the circular crack may be represented as follows [23]:where σ1 and σ3 are the maximum and minimum compressive stress, respectively; σr and σθ are the radial stress and tangential stress at the distance r from the hole center and the angle θ with the σ3 direction, respectively; R is the radius of the circular crack.When r=R⁠, that is, the stress on the circular hole wall is:From equation (2), we can see that σθ is a function of θ⁠, that is, σθ=f(θ)⁠. When θ = 0°, there is a minimum value of σθ is at its smallest value, indicating that the tensile failure of the hole wall will occur in the direction parallel to σ1⁠. At the same time, σθ reaches the tensile strength T of basalt, and ∆P also reaches its critical value ∆Pc. If the compressive stress is positive and the tensile stress is negative, then:From equation (3), we can establish a critical water pressure failure criterion for the crack:Equation (4) shows that the critical water pressure Pc of internal crack failure in the rock under the effect of hydromechanical coupling increases with the increase of confining pressure σ3 and initial water pressure P, and with the increase of initial water pressure P, the increase in the amplitude of critical water pressure ∆Pc becomes smaller.To investigate the hydromechanical coupling failure of basalt in depth, numerical simulations of hydromechanical coupling triaxial tests of basalt are performed using the FLAC3D finite difference method in this study. The model size and standard rock samples are uniform, measuring a diameter of 50 mm and a height of 100 mm. The relevant mechanics and seepage parameters are determined using the Morh-Coulomb model and are presented in Table 1. The parameters in Table 1 are mainly selected comprehensively based on experimental testing and literature [9]. The hydraulic boundary conditions of the model include an impermeable lateral boundary and permeable upper and lower-end faces. The water pressure of the upper-end face was fixed at 0 MPa, and the lower-end face was fixed at P. During the hydromechanical coupling calculation, the critical water pressure failure criterion of equation (4) was employed, and the shear and tensile failure criteria of the rocks are defined as follows:where σ1 and σ3 are the maximum and minimum principal stress, c is cohesion, φ is the angle of friction, and Nφ=1+sin(φ)1−sin(φ)⁠, σt is tensile strength, and P is the pore water pressure distributed in the rock. In order to simulate the failure process of rock, this paper assumes that if the rock is subject to shear failure or tensile failure, its shear strength or tensile strength parameters will be reduced to some extent. In this paper, it is assumed that the strength will be reduced by 50% after the rock failure [24-26].In order to avoid repetition and facilitate numerical verification, Figure 8 mainly presents the hydraulic coupling stress-strain test curves and simulation curves of basalt with initial water pressures of 5, 10, and 15 MPa under a confining pressure of 20 MPa. It can be observed that the simulated and test curves are fundamentally similar, demonstrating the reasonableness of the hydromechanical coupling calculation method and the selected mechanical and seepage parameters used in this study.Figures 9 and 10 present the failure element count curve and the plastic zone distribution of the hydromechanical coupling numerical simulation under the conditions of 20 MPa confining pressure and 10 MPa water pressure, respectively. The elements that experienced tensile failure and shear failure are colored red and blue, respectively. The points A, B, C, D, and E in Figure 10 correspond to the stress levels marked in Figure 9. The rock failure process under hydromechanical coupling can be observed as follows: Initially, the internal water pressure of the crack reaches the critical water pressure, and the crack is damaged, which manifests as tensile failure. At this stage, the number of failure elements is small and mainly concentrated in the middle of the rock. In the stable crack growth stage, a small amount of shear failure occurs, primarily on both sides of the middle of the rock and mainly between the tensile failure elements. This is due to the release of elastic deformation energy to some extent after the tensile failure of the element, resulting in stress concentration in the neighboring elements, followed by shear failure. In the unstable crack growth stage (post-peak stage), shear failure dominates. The numerical simulation results of the basalt hydromechanical coupling triaxial test are generally consistent with the understanding obtained by the AE test, which confirms that the critical water pressure failure criterion used in this paper is reasonable and can accurately describe the mechanism of crack initiation and propagation of rock under hydromechanical coupling.Figure 11 depicts the distribution of pore water pressure within the rock during triaxial compression loading, with a confining pressure of 20 MPa and water pressure of 10 MPa. It reveals that during the elastic deformation stage, the pore water pressure distribution is relatively uniform, with a value of nearly 0 MPa near the upper surface, approximately 10 MPa near the lower surface, and relatively high values in the central region, reaching a maximum of 23.3 MPa at the stress level of point A. As the crack initiates failure at point B, the uniformity of the pore water pressure distribution is lost, and a concentration of pore water pressure appears in the central region, with a maximum value of around 42 MPa, close to the critical water pressure. This is attributed to the increase in axial stress, leading to an increase in pore water pressure, ultimately causing elements to fail in tension at the critical pore water pressure, thus redistributing the stress and pore water pressure of the rock. During the stable crack growth stage, as exemplified at point C, the pore water pressure in the central region tends to decrease, and the dissipation of pore water pressure on both sides of the middle is more pronounced, which appears to be directly related to the initiation of shear failure. At the peak strength and post-peak stages, a significant change in the distribution of pore water pressure within the rock is observed. With the exception of the lower-end face, the dissipation of pore water pressure at other positions is prominent and tends toward zero.In this study, Xiluodu basalt was chosen as the research subject, and hydromechanical coupling triaxial tests, AE tests, and numerical simulation analysis were performed to draw the following conclusions:The hydromechanical coupling triaxcial tests revealed that, at a constant initial water pressure, the post-peak stress drop of basalt is conspicuous, and the peak strength increases with an increase in confining pressure, indicating a typical hard-brittle behavior. When the confining pressure remains constant, the peak strength gradually decreases with increasing initial water pressure, and the stress drop weakens, implying that water pressure weakens the compressive strength of the rock to some extent and weakens its hard brittleness.AE testing revealed that the crack initiation of basalt under hydromechanical coupling occurs due to tensile failure. In the stage of stable crack propagation, tensile failure is the main failure mode, with shear failure serving as a supplementary failure mode. These failures predominantly occur in the middle of the rock. In the post-peak stage of unstable crack propagation, rock failure is primarily due to shear failure.Based on the results of the AE test, a crack failure calculation model under hydromechanical coupling was established, and a critical water pressure failure criterion for crack initiation was derived. The critical water pressure failure criterion was integrated into the numerical simulation of the basalt hydromechanical coupling triaxial test, and the simulation results were essentially consistent with the test results. This revealed the process of basalt hydromechanical coupling fracture and the law of water pressure distribution and verified the rationality of the critical water pressure failure criterion.The hydromechanical coupling triaxcial tests revealed that, at a constant initial water pressure, the post-peak stress drop of basalt is conspicuous, and the peak strength increases with an increase in confining pressure, indicating a typical hard-brittle behavior. When the confining pressure remains constant, the peak strength gradually decreases with increasing initial water pressure, and the stress drop weakens, implying that water pressure weakens the compressive strength of the rock to some extent and weakens its hard brittleness.AE testing revealed that the crack initiation of basalt under hydromechanical coupling occurs due to tensile failure. In the stage of stable crack propagation, tensile failure is the main failure mode, with shear failure serving as a supplementary failure mode. These failures predominantly occur in the middle of the rock. In the post-peak stage of unstable crack propagation, rock failure is primarily due to shear failure.Based on the results of the AE test, a crack failure calculation model under hydromechanical coupling was established, and a critical water pressure failure criterion for crack initiation was derived. The critical water pressure failure criterion was integrated into the numerical simulation of the basalt hydromechanical coupling triaxial test, and the simulation results were essentially consistent with the test results. This revealed the process of basalt hydromechanical coupling fracture and the law of water pressure distribution and verified the rationality of the critical water pressure failure criterion.The data that support the findings of this study are available from the corresponding author upon reasonable request.The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.The study reported here is financially supported by the National Natural Science Foundation of China (Grant No. U21A20159, No. 52009129), the project of Key Laboratory of Water Grid Project and Regulation of Ministry of Water Resources (QTKS0034W23291), and Visiting Researcher Fund Program of State Key Laboratory of Water Resources Engineering and Management (Grant No. 2023SGG07). The authors want to thank all the members who give us lots of help and cooperation.