Experimental study on triaxial unloading mechanical properties and acoustic emission response of shale with different water contents

Water is one of the most significant factors influencing the mechanical properties of rocks. Triaxial unloading acoustic emission (AE) tests were performed to study the unloading mechanical characteristics and damage evolution mechanism of shale with various water contents. The damage evolution characteristics of shale under triaxial unloading conditions were analyzed using AE time series parameters. The results show that when the water saturation coefficient rises, the number of AE rings and the energy value of shale decrease. Based on the results of the AE test, the ratios of the crack initiation stress and damage stress to the peak stress are 0.4 ~ 0.6 and 0.9, respectively. The closure stress, crack initiation stress, damage stress, and other characteristic stresses determined by the stress axial strain method and the AE method all decrease with the increase of the water saturation coefficient, demonstrating that water has a significant impact on the mechanical characteristics of the shale during the unloading damage process. Based on the test results, a statistical damage constitutive model is established, and it uses the AE cumulative ringing count to represent the damage variable. The calculated results of the model are in good agreement with the experimental data, indicating that the established model can more accurately depict the evolution process of shale unloading damage and failure under different water contents. The study's findings can be used as a reference for determining the extent of rock damage caused by water–rock interaction.


Introduction
Water is one of the important factors influencing the mechanical properties of rock mass. In the process of engineering construction, the initial equilibrium state of the surrounding rock mass alters due to the impact of excavation disturbance, the originally closed fissures are reopened by the unloading effect, and new fissures develop and form. The groundwater enters the rock mass along the fissures and interacts with the rock mass, affecting the mechanical properties of the surrounding rock mass. Knowledge of the influence of water-rock interactions on the mechanical behavior of rock is important for solving a range of problems relevant to many rock mechanics applications such as mining, tunneling, dam and slope stabilization (Bai et al. 2016;Song et al. 2018;Li et al. 2018;Lin et al. 2019). The surrounding rock mass of the Yijiashan Tunnel softened during construction as a result of groundwater seeping into the geological environment along the structural surface. This led to the cracking of the lining and significant deformation of the surrounding rock mass, which had a significant negative impact on the construction process and the safety of the tunnel.
Shale is a fine-grained clastic sedimentary rock formed by mixing clay minerals with tiny fragments of quartz and calcite. It has the characteristics of high clay mineral content, substantial anisotropy, and well-developed bedding fissures (Wong 1998;Lyu et al. 2015). Different clay minerals have different degrees of swelling potential. In particular, for clay minerals such as smectite and mixed-layer illite, the volume expansion can be up to 20 times that of their initial volume (Hayatdavoudi 1999). At present, the research on the mechanical properties of different types shale under water-bearing conditions has achieved rich results. Experimental evidence shows that the clay minerals swell with water, which promotes new microfractures to form and spread along the cushion of the shale formation (Morsy and Sheng 2014;Dehghanpour et al. 2013). Many experimental studies on the geomechanical behavior of various individual shales and clays revealed that the strength, deformation, and failure characteristics are closely related to water content and that mechanical parameters can be significantly reduced with a small increase in water content (Liu et al. 2014;Lyu et al. 2018). Brittle shales are predicted to possess inherent fractures and are more easily fractured by hydraulic stimulation. Therefore, the shale hardness decreases with increasing water soaking time (Wong et al. 2016). In addition, the strength, elastic modulus, and P-wave velocity of the rock material are strongly related to the applied confining pressure. Kuilaa et al. (2011) investigated the link between differential stress and velocity anisotropy in low porosity shales, and the results showed that P-wave velocity increases with confining pressure, but confining pressure has little effect on anisotropy. The orientation of maximum principal stress is important in controlling the wave velocity and velocity anisotropy behavior. Rybacki et al. (2015) studied the elastic parameters and strength of shale under confining pressures, the compressive strength increases non-linearly with increasing confining pressure and correlates almost linearly with Young's modulus.
An important phenomenon of rock failure is that the AE signal contains the characteristic information of the AE source. A good methodology for non-destructively assessing rock behavior during fracture progression is AE technique. In situ physical and mechanical monitoring during fracture formation and propagation by analyzing parameters such as waveform, number of events and cumulative AE energy plays a crucial role in revealing rock failure methods (Ohnaka and Mogi 1982;Lockner 1993;Al-Bazali et al. 2008). Tang et al. (2021) established a quantitative relationship between AE counts and the rock damage variable. Kim et al. (2015) investigated the granite damage characteristics utilizing AE energy and came to the conclusion that the AE energy method has better reliability in processing the obtained damage data compared with other evaluation methods. Amann et al. (2011) used AE monitoring for shale to help quantify the stress levels related to crack formation and propagation. Tang et al. (1997) employed the AE technology to help detect the typical stress levels during sample deformation, the tested samples have obvious horizontal bedding. Wu et al. (2017) performed a study of AE characteristics throughout the failure process in shale and the variations of a-values and b-values during sample deformation have been investigated.
Numerous experimental studies are based on the research on the strength and failure characteristics of shale with different structural modes under conventional loading conditions. However, the AE characteristics of anisotropic shale under the unloading path are not fully understood and still have important research significance. The AE characteristics of rocks can be used to predict the internal failure mechanism, which still has important research significance for engineering monitoring, drilling, and hydraulic fracturing operations.
This work takes the shale materials acquired during the excavation of the Yijiashan tunnel as the research object. By carrying out the confining pressure test of shale under different water content conditions, based on the AE test results, the variation of AE ringing count, maximum energy value, and characteristic stress with water saturation coefficient was studied, and a constitutive model of AE energy parameters representing damage variables was established and compared with the test results. The research results provide a reference for rock damage evaluation from the perspective of AE energy.

Preparation of rock samples
The rock specimens for the test were taken from the Yijiashan Tunnel in northwestern Hubei Province. The rock type is a sandy shale of the Silurian Luojiaping Formation. The dry specimens are grey-green and their overall texture is homogeneous and dense, there are no obvious flaws in the specimen appearance (Li et al. 2022). The core was drilled in the same direction and then sliced into a cylindrical specimen with a 50 mm diameter and 100 mm height to reduce dispersion caused by anisotropy between the specimens. According to the International Society for Rock Mechanics (ISRM), all specimens were polished to make the end surfaces perpendicular to the longitudinal axis within 0.02 mm, the non-parallelism of the two ends within 0.001 mm, and the top surface and the side surfaces should be perpendicular to each other with a maximum deviation of not more than 0.25° (Brown 1981). The prepared rock specimens are shown in Fig. 1. The mineral compositions of shale are measured with an X-ray spectrometer technique and the test outcomes are displayed in Fig. 1b and Table 1.
In Table 1, the main mineral components found in shale are quartz, albite, illite, and chlorite. The maximum content of quartz is about 41.7% ~ 45.5%, and the total content of clay minerals illite and chlorite is about 34.0% ~ 41.6%. Both illite and chlorite have a high water absorption capacity, which causes the water film that mineral particles have absorbed to thicken when it comes into contact with water and causes the rock's volume to expand (Zhu 1996).

Test equipment and scheme
The test was carried out on the MTS 815 electrohydraulic servo-controlled rock mechanics triaxial test system, and the AE monitoring equipment used in the test was the DISP AE test system. The acquisition system has 12 channels for recording AE activity. The AE sensor is SR150 high-sensitivity resonant sensor with a resonant frequency of 150 kHz. Eight AE sensors were used to gather AE information in the tests. Four of them were a group and distributed evenly in a plane 5 mm away from the boundary of the specimen outside on the pressure cell. The AE signal sampling rate was 10 MHz, the preamplifier gain was set at 40 dB, the signal threshold was 40 dB, and the signal filtering frequency range was 100 kH ~ 1 MHz. In order to eliminate the environmental noise of the loading system, before loading the specimen, the noise level of the loading system is determined first. After that, the corresponding processing is done on this part of the noise data. The installation method of the AE sensor and the specimen is shown in Fig. 2.
Based on the unloading method of engineering rock excavation, this test employs the scheme of keeping the axial stress unchanged and releasing the confining pressure to raise the deviatoric stress. The initial confining pressure of the test unloading is 40 MPa. In order to ensure that the rock sample can be completely destroyed after the confining pressure is released, the axial stress at the unloading point should be larger than the uniaxial compression strength and less than the triaxial compression strength. The axial stress at the unloading point is determined to be 75% of the triaxial compression strength based on the results of triaxial compression tests on shale with varying water saturation coefficients.
Taking the dry specimen as an example, the conventional triaxial compression strength at the confining pressure of 40 MPa is 281.1 MPa, and the initial axial stress of the unloading point is calculated to be 211 MPa. The specific steps of the unloading test are as follows: (1) Loading the confining pressure σ 3 and axial stress σ 1 (σ 1 = σ 3 ) simultaneously at a rate of 0.1 MPa/s until the confining pressure reaches a predetermined value of 40 MPa.  (2) Keeping the confining pressure σ 3 constant, proceed to load the axial stress σ 1 to 211 MPa at a rate of 0.1 MPa/s. Then, the axial stress is kept constant, and the confining pressure is gradually relieved at a rate of 0.1 MPa/s until the specimen failed.

Determination of water saturation coefficient
In this paper, specimens with different water contents were prepared by natural soaking, and the specimen preparation method was carried out following the Chinese National Standard (SL264-2001). The water content is determined by the change in the weight of the shale sample after soaking, which is defined as: where ω t is the water content after t days of water absorption, m w and m d are the mass of water and dry specimen, respectively. The calculation results of the water content of the specimens are given in Table 2. The basic physical parameters of shale are also presented in Table 2. The density range of all specimens is 2693.8 kg/m 3 ~ 2753.9 kg/ m 3 , the longitudinal wave velocity is in the range of 3678.1 m/s ~ 3962.8 m/s and the coefficient of variation is 0.64%. The shale used in the test has good homogeneity. The water content of the specimen is different under the same water absorption time in Table 2. For example, the water content of the saturated specimens was 1.13% and 1.42% respectively. Therefore, in order to unify the water content standard, the samples of each group were normalized by the water content for saturated specimens. Define the water saturation coefficient w s as: where ω s is the saturated water content. (

Stress-strain curve
Under the confining pressure of 40 MPa, the stress-strain curve test results of shale with varied water saturation coefficients are displayed in Fig. 3. In Fig. 3a, the values adjacent to the curve indicate the failure confining pressure value. The non-linear deformation of all specimens at the initial stage of loading is very small, the compression-dense stage is not obvious, and the deformation trend of the specimens during the unloading process is basically the same, which is related to the small porosity of the shale and the uniform dense texture. When the axial stress reaches the predetermined value of unloading, the specimen enters the unloading phase, during which the axial deformation rises slowly and is significantly smaller than the radial deformation. When the circumferential pressure is reduced until the specimen carrying capacity is less than the partial stress, the specimen is damaged and accompanied by a crisp sound. At this time, the stress reduces rapidly, and the plastic deformation near the peak stress is small. The failure process of the specimens displays clear brittle features. In addition, with the increase of the water saturation coefficient, the pre-peak plastic deformation gradually reduces, and the radial plastic deformation decreases more noticeably. In Fig. 3b, even under the high confining pressure of 40 MPa, the failure mode of the rock sample is still dominated by brittleness. The plastic yield deformation of the samples near the peak is very small, and there is almost no plastic yield plateau. Due to the impact of the confining pressure, the stress reduction after the peak is lower than that in the unloading test. Under the confining pressure, with the increase of the water saturation coefficient, the peak strength drops to variable degrees, the plastic deformation increases in the pre-peak stage of some specimens, and a plastic yield plateau appears near the peak stress. This shale is a dense hard rock and hard rocks are generally dominated by brittle damage. Some silicate rocks can still show brittle damage under hundreds of megapascals of peritectic pressure, and the unloading of the peritectic test method is equivalent to increasing the equivalent tensile stress in its radial direction, which exacerbates the occurrence of brittle damage, dominating the damage mode of the shale (Mogi 1971). The results of triaxial loading and unloading tests on specimens with different water saturation coefficients are given in Table 3. Under the condition of triaxial compression test, both the peak stress and elastic modulus of shale decrease with the increase of the water saturation coefficient. Under the condition of triaxial unloading test, the failure confining pressures of different saturation coefficient specimens are roughly the same. When the water saturation coefficient is 0.7, the peak stress and failure confining pressure are both slightly larger than the values of the water saturation coefficients of 0.2 and 0.5. If the water saturation coefficient is 0.7, the failure confining pressure is 21 MPa, and the peak stress estimated based

Unloading AE test results
The results of the AE test of shale unloading confining pressure are displayed in Fig. 4, and the cumulative ringing count of AE and the variation of AE energy value with water saturation coefficient are also shown in the figure. AE ring count refers to the number of ringing pulse exceeds the threshold value, which can reflect the signal strength and frequency of the AE event, and is widely used in the evaluation of AE activity. AE energy refers to the energy of the AE event, which is proportional to the square of the amplitude value of the observed waveform of the AE event, reflecting the intensity of the AE event. The AE results of the specimens indicate a similar variation law. In the initial compaction stage, the amplitude of AE energy is minimal, the slope of the cumulative ringing count curve is small, and the corresponding ringing count increases slowly. In the elastic stage, the AE energy amplitude has a leaping rise relative to the compaction stage. After the unloading stage, the AE began to be highly active and the energy amplitude increased dramatically, and the AE energy amplitude surged abruptly near the peak and reached the maximum value, and the corresponding cumulative ringing count curve slope also reached the maximum. In the post-peak stage, the AE energy amplitude drops abruptly and gradually weakens, indicating that the shale has evident brittle failure characteristics when the confining pressure is unloaded. In addition, a plastic yield plateau forms near the peak of the stress-strain curve of the dry specimen, and the AE activity is intense near the plateau, there are many signals with high energy values. This is due to a large amount of irrecoverable plastic deformation near the platform, and the stress wave energy in this stage is substantially larger than that in the elastic deformation stage. With the increase of the water saturation coefficient, the maximum AE energy and the quantity of AE signals with high energy values rapidly dropped at this stage. This indicates that the mechanical properties of shale are significantly weakened after water absorption, and the brittle failure characteristics near the peak are diminished. Figure 5 illustrates the maximum value of AE energy and the cumulative ringing count during the progressive failure of shale under different water saturation coefficients. It can be seen that with the increase of the water saturation coefficient, the maximum energy value and the number of cumulative ringing counts in the complete process decrease. It reveals that after water absorption, the weakening action of water on the shale reduces the energy released when the rock sample is damaged, the severity of the damage is lowered, and the brittleness is weakened. The softening of rock by water is utilized in engineering practices such as hydraulic fracturing to extract shale gas and water injection to prevent rock bursts in hard rock.

Determination of characteristic stresses
The typical stress-strain curves during rock compression are given in Fig. 6. The characteristic stress can characterize the different stages of micro-crack propagation inside the rock and the deformation characteristics in the corresponding stages. According to the features of each characteristic stress in the rock progressive failure theory, the stress-strain curve in Fig. 6 can be divided into five stages (Cai et al. 2004).
To determine the characteristic stress at different stages, Eberhardt et al. (1998) first proposed using the AE technique to determine the crack initiation stress and damage stress of rock. Based on the test results, the crack initiation stress can be used as a sign of the occurrence of AE events, and the damage stress can be used as a sign of the abrupt increase in the number of AE events. The research shows that the crack initiation stress and damage stress of rock can be more accurately determined by monitoring the AE signal. However, the AE method for estimating the crack closure stress is not applicable, while the stress axial strain method can obtain better results (Peng et al.2015). Therefore, the axial strain method is employed to determine the crack closure stress, crack initiation stress, and damage stress, while the AE monitoring method is applied in this paper.
Based on the above analysis, according to the shale AE test results in Fig. 4, the characteristic stress of specimens with different water saturation coefficients is determined by the abrupt change point of AE energy at each stage. Taking the dry sample as an example, the method for measuring the characteristic stress at each stage is provided in Fig. 7. It can be seen from the change of the AE energy amplitude in Fig. 7a that the sudden change of the AE energy amplitude during the whole compression process of the sample is divided into four times. According to the method of dividing the various stages reported in the literature (Peng et al.2015), it can be determined that the crack initiation stress and the damage stress correspond to the second and third amplitude sudden changes of the AE energy timing parameters, respectively. Therefore, their positions are established as illustrated in Fig. 7a. After the damage stress is measured, the closure stress can be determined via the axial strain method. The position of the damage stress on the stress-strain curve is point A, the maximum distance between the straight OA and the stress-strain curve is BC, and the stress value of point B is the crack closure stress. The calculated strain difference with axial stress is given in Fig. 7b, the axial stress corresponding to the maximum value of the axial strain difference is the crack closure stress, and the distance between point B and point C is the maximum axial strain  difference. Therefore, the closure stress of the dry specimen is 46.3 MPa. By the same method, the closure stress of shale was determined to be 44.2 MPa, 40.7 MPa, 35.6 MPa, and 33.8 MPa for different water saturation coefficients. Figure 8 shows the normalized results of the shale characteristic stress and its ratio to the peak stress under different water saturation coefficients. The calculation results in Fig. 8a show that with the increase of the saturation coefficient, the characteristic stress firstly decreases gradually and then decreases rapidly when it reaches the saturated state. In Fig. 8b, the ratios of closure stress, damage stress and peak stress are about 0.2 and 0.9, respectively, while the ratio of crack initiation stress slightly decreases with the rise of water saturation coefficient, and the variation range is 0.4 ~ 0.6. Therefore, it can be considered that when the water saturation coefficient is greater than 0.5, the elastic stage of the shale stress-strain curve decreases, while the stable crack propagation stage increases, which indicates that the weakening damage of water to shale occurs more in the stable crack propagation stage. In addition, the shale is homogeneous and dense, which makes the ratio of crack initiation stress and damage stress to peak stress slightly higher than that of soft rocks.

Construction of damage constitutive model
In classical damage mechanics, Kachanov (1986) defines the damage variable by the ratio of the damaged material area to the intact undamaged material area under load, and its expression is: where D is the damage variable and its value varies in the range of 0 ≤ D ≤ 1, S n represents the damaged area, while S represents the undamaged material area. Heiple et al. (1981) applied AE technology to the study of material damage and fracture processes. The results show that the ringing count in the AE timing parameters can better reflect the change in material properties. The ringing count is proportional to the strain energy released in the material during crack propagation, fracture exfoliation of inclusions, and dislocation motion between particles. Therefore, the relationship between the damage variable and the cumulative ringing count of AE can be established by using the theory of continuous damage mechanics. Assuming that the crosssectional area of the non-damaged material is S, and its AE cumulative ringing count is C when it is entirely fractured, the AE cumulative ringing count per unit area is: In the process of rock failure under load, when the damaged area of the primary control fracture surface reaches S n , the corresponding AE cumulative ringing count is: According to simultaneous Eqs. (3)-(5), the damage variable represented by the cumulative ringing count of AE is: During the test, due to different test control methods or the setting of rock failure conditions, when the testing machine stops working, the sample is not completely destroyed, and the damage variable value does not reach 1. Therefore, the damage variable critical value D u is introduced, the damage critical value is normalized by means of a linear function transformation, and the damage variable is modified as (Liu et al. 2009): where σ f and σ c represent the peak stress and residual strength, respectively.
Assuming that the damage of the rock material is isotropic and based on Lemaitre's strain equivalence hypothesis (Lemaitre 1985), the one-dimensional damage constitutive model is established as: where σ represents the nominal stress, ̃ represents the effective stress, E represents the elastic modulus, and ε represents the axial strain.
In order to establish the damage evolution model of the rock sample under triaxial conditions, it is assumed that the force of the micro-units in the sample under confining pressure satisfies the linear elastic Hooke's law: where ε v is the volumetric strain, λ is the Lame constant, and G is the shear modulus. The relationship between λ, G and Poisson's ratio μ, elastic modulus E can be expressed as follows: According to simultaneous Eqs. (7)-(10), the damage constitutive model based on AE ringing count in the triaxial state is: From the test results in Table 3, it can be observed that the elastic modulus decreases with the increase of the saturation coefficient in the test range, and their variation law can be expressed by a linear equation. However, there is no evident relationship between Poisson's ratio and the water saturation coefficient. Based on this, the saturation coefficient can be introduced into the constitutive model Eq. (11), and the unloading damage constitutive model considering the influence of the saturation coefficient can be obtained: where E (w s ) represents the elastic modulus under different water saturation coefficients, which can be determined by fitting the test results. Figure 9 displays the comparison and verification of the unloading damage constitutive model and the test results. As a reference, the model curve of the statistical damage model that was determined based on the Weibull distribution in the literature (Cao et al. 2004) is also presented in the figure. On the whole, the theoretical curve of the constitutive model has a high degree of matching with the actual test data points, and the AE model is superior to the model in the literature (Cao et al. 2004). For the elastic stage and the stable crack propagation stage, both models can describe the mechanical behavior well. After entering the unloading stage, as the confining pressure decreases, the discrepancy between the two models and the test results begins to increase gradually, and the deviation value reaches its maximum at the peak stress. For the saturated sample, the maximum deviation of the AE model is 10.1%, which is smaller than the 14.6% of the literature model. For other samples, the deviation of the AE model at the peak stress is between 1.8% and 4.9%. In the post-peak stage, the stress in the unloading test declines rapidly after reaching the peak value, the damage is severe, the brittleness is obvious, and the strain value in the residual stage is random. Therefore, the slope of the straight line in the descending segment is similarly random, and the description of the test data by the constitutive model is biased. In addition, because the AE model contains residual strength parameters, it can be seen from the comparison with the test curve that the residual strength determined by this model is roughly equivalent to the test results.

Experimental verification of damage constitutive model
There is a deviation in the determination of the peak stress by the two models, and the plastic yield stage cannot be described for the rock sample with a wide plastic plateau near the peak value. The damage model defined by the AE cumulative ringing count has high requirements for Fig. 9 Theoretical curves of unloading damage constitutive model and experimental values of shale at the confining pressure of 40 MPa. (a) w s = 0, (b) w s = 0.2, (c) w s = 0.5, (d) w s = 0.7, (e) w s = 1.0 ◂ the accurate determination of AE parameters in the process of rock fracture. In addition, the noise interference of the triaxial test is relatively large, which makes it difficult to collect its data and errors will inevitably occur. In summary, within the allowable error range, it can be considered that the AE model can better describe the changes in the unloading strength and deformation characteristics of shale under different water saturation coefficients.

Conclusion
Aiming at the problem of deformation and instability of surrounding rock caused by shale encountering water during the excavation of the Yijiashan Tunnel, an experimental study on the triaxial unloading AE characteristics of shale with varying water saturation coefficients was carried out. Based on the test results, the variation law of AE timing parameters and rock characteristic stress with water saturation coefficient is analyzed. The damage variable is defined by the AE ringing count, and a statistical damage constitutive model considering the influence of the water saturation coefficient is established, which is verified by comparison with the experimental results. The main research conclusions are as follows: (1) The stress-strain curve of shale with varying water saturation coefficients exhibits an obvious stress drop phenomenon after the peak, and the brittle failure features are obvious. Both the peak stress and elastic modulus of shale decrease with the increase of the water saturation coefficient. When the unloading failure occurs, the failure confining pressure of the specimen is roughly the same, and the axial and radial deformation decrease with the increase of the saturation coefficient. The peak stress of shale under unloading failure is smaller than that of triaxial compression, while the elastic modulus is larger than that of triaxial compression. (2) With the increase of the water saturation coefficient, the high-amplitude energy number, the maximum energy value, the cumulative ringing count, and other timing series parameters in the progressive failure process of shale all decrease. The characteristic stresses such as crack closure stress, crack initiation stress, and damage stress determined based on this account for about 0.2, 0.4 ~ 0.6, and 0.9 of the peak stress, respectively, which is basically consistent with the test results of the shale stress-strain curve. The characteristic stress showed a decreasing trend with the increase of the water saturation coefficient.

Data availability
The data used to support this study are available from the corresponding author upon request.