Experimental Study on Anisotropic Mechanical Characteristics of Shale under Triaxial Loading

Abstract

Shale is composed of a rock matrix and bedding planes with a layered structure, resulting in significant anisotropy in its mechanical properties. In order to study the anisotropic mechanical properties of shale, the shale samples were prepared in different orientations with respect to the bedding planes, and the composition and microstructure of shale were first analyzed by X-ray diffractometer (XRD) and scanning electron microscope (SEM), and then the uniaxial and triaxial compression experiment on shale samples with five different bedding angles (the angle between the loading direction and the normal direction of the bedding planes, 0°, 30°, 45°, 60°, and 90°) were conducted under five confining pressures (0, 10, 20, 30, and 40 MPa), respectively; meanwhile, the acoustic emission (AE) test was carried out in the uniaxial test. The results indicate that the mechanical properties and parameters of shale have obvious anisotropy, and the AE characteristics of shale samples with different bedding angles are significantly different during uniaxial loading. Furthermore, the compressive strength and elastic modulus of the shale samples first decrease and then increase with the increase in the bedding angle under different confining pressures. Moreover, according to the anisotropic grade of compressive strength, the shale has moderate anisotropy. In addition, the failure mode of the shale samples is also anisotropic, and varies with the bedding angle and confining pressure.

1. Introduction

Shale, as a common sedimentary rock, has a layered structure formed by an ordered parallel arrangement of a high-strength rock matrix and low-strength bedding planes [1,2]. Due to the different physical and mechanical properties of the rock matrix and bedding planes, there are significant differences in the mechanical and deformation properties of the shale between the parallel bedding planes direction and the vertical bedding planes direction, resulting in the macroscopic mechanical properties of shale being controlled by bedding planes, exhibiting significant anisotropic mechanical characteristics [3,4,5]. Excavating a tunnel in shale formations can cause disturbances to the surrounding rock mass, leading to the opening or sliding of the bedding planes within the shale, reducing its macroscopic mechanical parameters such as strength and modulus, resulting in damage and deterioration of surrounding rock mass [6]. This leads to engineering disasters such as tunnel collapse, asymmetric large deformation, and support cracking, which not only seriously affects the construction progress, but also endangers construction safety. Therefore, it is vital to systematically investigate the anisotropic mechanical properties of shale under triaxial loading, which is meant to provide a theoretical basis for the design of support and excavation parameters for tunnels in shale or other layered rock formations.

Anisotropy of rock materials refers to the characteristics of mechanical parameters, structural properties, and constitutive relationships that change with direction, and numerous scholars have carried out studies on the anisotropy of rock materials [7,8,9]. Meanwhile, shale is often known for its remarkable intrinsic anisotropic properties, including strength, brittleness, acoustic velocity, permeability, fracture toughness, etc. [10,11,12,13,14,15]. Various studies have first focused on the anisotropy of the basic mechanical properties of shale. For example, Lo et al. [16] studied the elastically anisotropy of Chicopee shale and found that the elastic anisotropy of shale is due to the combined effects of pores or cracks and mineral grain orientation and decreases with increasing confining pressure. Niandou et al. [17] investigated the anisotropic mechanical behavior of the Tournemire shale and found that the plastic deformation and failure mode of the Tournemire shale is anisotropic and strongly depends on confining pressure. Geng et al. [18] addressed that the brittleness anisotropy of Longmaxi shale samples was bedding angle-dependent, and the anisotropy of brittleness decreased with increasing confining pressure through the triaxial experiments under various confining pressure. Yang et al. [19] conducted an experimental study on the mechanical behavior and brittleness characteristics of Longmaxi shale, and the anisotropic behavior of shale specimens under conventional triaxial compression, including the strength, brittleness, deformation, and failure behaviors, was analyzed. Wang et al. [20] studied the damage evolution and acoustic emission (AE) characteristics during failure process of anisotropic shale and revealed the effect of different layer inclination angles between the loading direction and the bedding planes. Ma et al. [21] analyzed the characteristics of the anisotropic tensile strength of layered rocks and three different anisotropic tensile failure criteria were reviewed and compared. Zhang et al. [22] investigated the tensile mechanical properties and damage patterns of shale with different various orientations of the bedding planes by conducting a Brazilian splitting test and an AE test. Wang et al. [23] conducted a high-temperature triaxial permeability testing machine to study anisotropic permeability of oil shale at stresses that emulate in situ conditions. Mayr et al. [24] proposed the porosity deformation approach (PDA) to the elastic anisotropy of shale under triaxial loading and found that the velocity change due to hydrostatic loading can be used to predict elastic anisotropy under additional axial loading. Wilczynski et al. [25] studied the anisotropy of strength and elastic properties of lower Paleozoic shales from the Baltic basin, Poland, and found that the shale was characterized by VTI type (vertical transverse isotropy) internal anisotropy. Xu et al. [26] adopted a finite-element–based continuum damage mechanics model to capture sample size effects and the influence of intrinsic anisotropy on the stress–strain response of shale and investigated deformation and stiffness anisotropy induced by damage propagation in a rock brittle deformation regime. Xie et al. [27] studied the anisotropic characteristics of the failure mechanism by conducting AE monitoring tests on shale specimens with seven different bedding inclination angles under uniaxial cyclic loading and unloading. Kong et al. [28] explored the anisotropy of the mechanical properties of shale and the energy evolution of its failure through the cyclic loading and unloading experiments of shale specimens with seven different bedding orientations.

On the other hand, in terms of dynamic mechanical properties of shale, some efforts had also been conducted to investigate the mechanical properties of shale under dynamic loads with different strain rates, including anisotropic characteristics of strength, elastic modulus, failure mode, etc. [29,30,31,32,33,34]. In addition, geologists engaged in the development of unconventional shale gas and shale oil had carried out a lot of research on the anisotropy of elastic wave velocity of shale. Vernik et al. [35] implemented ultrasonic velocity and anisotropy measurements on a variety of shale with different clay and kerogen content, clay mineralogy, and porosity at a wide range of effective pressure, and found that the elastic anisotropy of shale increased substantially with compaction. Kuila et al. [36] investigated the ultrasonic velocity response of low porosity shale in Western Australia to both isotropic and anisotropic stress fields and to evaluate the velocity response to the changing stress field. Wang et al. [37] conducted real-time ultrasonic and mechanical experiments of Longmaxi formation shale under uniaxial deformation; the results suggest that shale govern the intrinsic P- and S-wave velocity anisotropy, and pronounced bedding planes have a significant influence on the mechanical properties and velocity responses of shale. Dewhurst et al. [38] performed multiple stage triaxial tests of Norwegian Sea shale and evaluated rock strength and the evolution of ultrasonic response during rock deformation. They found that the S-wave anisotropy was significantly affected by the increasing stress anisotropy. Zhubayev et al. [39] studied the velocity and attenuation anisotropy of P- and S-waves in dry Whitby Mudstone samples as a function of stress by ultrasonic experiments and found the degree of anisotropy to be as large as 70% for velocity and attenuation, and the sensitivity of P-wave anisotropy change with applied stress to be more conspicuous than for S-waves.

Meanwhile, hydraulic fracturing is the key technology for efficient exploitation of shale gas and oil [40,41,42]. In the process of hydraulic fracturing, the initiation and propagation of hydraulic fractures is controlled by the fracture toughness of shale. As an anisotropic material, the fracture toughness of shale varies in different directions. Chandler et al. [43] conducted fracture toughness measurements on Mancos shale determined in all three principal fracture orientations using a modified short-rod methodology, and significant anisotropy was observed in shale fracture toughness measurements. Kramarov et al. [44] measured the anisotropic nature of mode I fracture toughness of Mancos shale by combining semi-circular bend test (SCB) and digital image correlation (DIC), and the experiments were carried out in different notch orientations with respect to bedding. Inskip et al. [45] characterized fracture toughness from Nash Point shale in multiple orientations, including angles oblique to the three principal fracture orientations, and found that the fracture toughness of Nash Point shale is mechanically highly anisotropic. Shi et al. [46] employed shale samples with different bedding angles (the angle between loading axis and bedding planes) for cracked chevron notched Brazilian disc test (CCNBD) and Brazilian disc test, to characterize the bedding-plane-induced fracture toughness anisotropy in shale and its relationship with other physical and mechanical properties. Guo et al. [47] carried out a series of fracture experiments on the Longmaxi shale specimens with five bedding orientations after constructing in situ temperatures, and the results revealed that increasing in situ temperature decreases the fracture toughness but increases the fracture toughness anisotropy. Wang et al. [48] utilized real-time ultrasonic detection and post-test CT imaging to reveal anisotropic energy and ultrasonic characteristics of black shale under triaxial deformation, indicating that the strain energy evolution and fracture anisotropy were bedding orientation dependent.

In summary, although some scholars have studied the intrinsic anisotropic properties of shale, there is still no clear and unified understanding of the shale’s anisotropic mechanical behaviors under triaxial loading. Thus, it is necessary to systematically investigate the anisotropic mechanical properties of shale under triaxial loading, which is meant to provide reference basis for the design of tunnel excavation and support in shale formation. In this work, the composition and microstructure of shale in western Hubei were tested using XRD and SEM, and then a uniaxial AE compression test and triaxial compression test were carried out. Moreover, the anisotropy characteristics of shale’s compressive strength, deformation parameter, and failure modes were studied, as well as the anisotropic index of shale’s mechanical parameters. Finally, the reason for the mechanical anisotropy of shale under triaxial loading was discussed in detail.

2. Experimental Methodology

2.1. Shale Samples Preparation

The shale cores used in the experiment were taken from a traffic tunnel in a shale formation in the western Hubei province, China. The large shale blocks, as shown in Figure 1a, were selected at the tunnel construction site and were drilled to obtain shale cores, and then the cores were cut and polished into standard cylindrical shale samples. The diameter and height of the prepared cylindrical shale samples are 50 mm and 100 mm, respectively, and the flatness deviation at both ends of the samples is within 0.02 mm, whereas the deviation along the height direction does not exceed 0.1 mm. At the same time, in order to determine the anisotropic mechanical properties of shale, the angle θ between the static loading direction and the normal direction of the bedding planes of the shale samples was defined as the bedding angle. Shale samples with bedding angles of 0°, 30°, 45°, 60°, and 90° were prepared, and there were 15 samples for each bedding angle, as shown in Figure 1b.

The composition and microstructure of shale are the internal factors that determine its mechanical behavior and anisotropic characteristics [3]. By using X-ray diffractometer (XRD) to analyze the mineral composition of the shale samples, it can be found that the shale composition is mainly divided into clay minerals and other minerals. The proportions of each component were as follows: quartz 41.9%, illite 28.4%, albite 11.6%, chlorite 8.8%, kaolinite 8.6%, and hematite 0.7%. The XRD results indicated that the mineral composition of the shale is mainly composed of quartz and illite, which account for about 70% of the total composition.

Meanwhile, the remaining shale fragments after sample preparation were selected, and the microstructure of shale samples was observed by scanning electron microscope (SEM). The scanning results are shown in Figure 2, and it can be found that the layered structure of shale was significant. In Figure 2a, the electron microscope was scanning in the direction of the bedding planes, and the organic matter (inside the red solid circle) mixed on the bedding planes can be seen. The flaky bedding structure can also be clearly identified. In Figure 2b, the electron microscope was scanning in the direction perpendicular to the bedding planes, and it can be seen that the microcracks (inside the red dotted ellipse) between bedding planes are completely developed; most of the pores are between 5 μm and 10 μm, and impurities were filled with them.

2.2. Experimental Set Up and Procedure

The uniaxial and triaxial loading tests were carried out on the prepared shale samples by using the TAW-2000 rock triaxial testing machine, as shown in Figure 3a, and the samples were fully dried before the test. In the test, the radial strain of the samples was collected by a chain extensometer, while the axial strain was collected by axial extensometers matched to the triaxial testing machine, which were set at the middle height position of the samples. In addition, a DS-5 acoustic emission (AE) instrument, as shown in Figure 3b, was used in the uniaxial test to record the AE signals during the uniaxial loading, and the AE recording probes were installed on the surface of the samples, as shown in Figure 3c. It is worth noting that due to the limitation of the space inside the confining pressure loading cylinder in the triaxial test, as shown in Figure 3d, the AE signals of the samples were not collected during the triaxial test.

The confining pressures σ₃ set in uniaxial and triaxial compression tests were 0, 10, 20, 30, and 40 MPa, respectively. During the experiment, the axial displacement was used to control the static loading rate of 0.1 mm/min, and the loading was terminated in the following two cases: the first case was that the bearing capacity of the samples dropped rapidly, causing the oil cylinder to fall back, and the second case was that the axial strain reached 104 με. In the triaxial compression test, the axial compression pressure and confining pressure were applied to the design value at the rate of 0.05 MPa/s synchronously, and then axial displacement control loading was carried out. During the loading process, the stress and strain data of the samples were recorded simultaneously by the data acquisition system, and each group of loading conditions contained three shale samples. In the test, 15 shale samples of each bedding angle were prepared, and the IDs of shale samples with 5 bedding angles under different confining pressure σ₃ are shown in

Table 1. IDs of shale samples under different confining pressures.

Bedding Angle θ (°)	IDs of Shale Samples
	σ3 = 0 MPa	σ3 = 10 MPa	σ3 = 20 MPa	σ3 = 30 MPa	σ3 = 40 MPa
0	A1, A2, A3	A4, A5, A6	A7, A8, A9	A10, A11, A12	A13, A14, A15
30	B1, B2, B3	B7, B8, B 9	B7, B8, B9	B10, B11, B12	B13, B14, B15
45	C1, C2, C3	C 4, C5, C6	C7, C8, C9	C10, C11, C12	C13, C14, C15
60	D1, D2, D3	D 4, D5, D6	D7, D8, D9	D10, D11, D12	D13, D14, D15
90	E1, E2, E3	E4, E5, E6	E7, E8, E9	E10, E11, E12	E13, E14, E15

.

3. Experimental Results

3.1. Uniaxial Compression Results and Acoustic Emission Characteristics

The stress–strain curves of shale samples with different bedding angles in uniaxial compression tests, as well as the variation of AE hits, AE cumulative hits, and AE ringing counts with time, are shown in Figure 4. It can be observed that the uniaxial compressive strength of shale samples varies with the bedding angle, and the average uniaxial compressive strength of shale samples with bedding angles θ of 0°, 30°, 45°, 60°, and 90° is 171.4, 113.0, 98.6, 61.0, and 117.7 MPa, respectively. This indicates that the uniaxial compressive strength of shale samples first decreases and then increases with the increasing of the bedding angle, and the AE characteristic parameters of shale samples with different bedding angles under uniaxial compression are not identical, as explained below.

(1) θ = 0°: As shown in Figure 4, at first, the sample enters the compaction stage, and the stress increases slowly. Because the loading direction is perpendicular to the bedding planes which have weak stiffness relative to the shale matrix, the bedding planes are compacted before the shale matrix. In this process, no new microcracks are generated, so only a small number of AE ringing counts and AE hits can be detected. Secondly, as the sample enters into the elastic stage, the stress–strain curve of the sample shows a linear growth trend, and the microcracks in the sample slowly increase, so the AE ringing counts increase slightly. Moreover, most of the collected AE signals do not exceed the threshold, so the AE hits remain relatively low. Subsequently, in the plastic stage, the volume strain of the sample gradually increases, new microcracks are constantly generated, and the original closed microcracks continue to expand, resulting in a rapid increase in AE ringing counts and AE hits. Finally, in the failure stage, the microcracks in the sample are penetrated and the main cracks run through the sample, resulting in the specimen reaching the peak strength and failure. Meanwhile, the AE ringing counts, AE hits, and AE cumulative hits increase sharply and reach the peak.

(2) θ = 30°: As shown in Figure 4, the original microcracks of the shale matrix and bedding planes in the sample are simultaneously compacted during the compaction stage, so the AE ringing counts and AE hits begin to increase at this stage. As the sample enters the elastic stage, the microcracks inside the sample increase uniformly, and the AE ringing counts also maintain a stable growth. During this period, only a small amount of the AE signal exceeds the threshold value, so the AE hits are collected intermittently, and the AE cumulative hits continue to increase. After entering the plastic stage, the number of microcracks in the sample continue to increase, and the AE ringing counts further increase. However, the AE signal in this stage hardly exceeds the threshold value, so there are no AE hits generated. Finally, the AE ringing counts, AE hits, and AE cumulative hits of the shale sample increase sharply and reach the peak in the failure stage.

(3) θ = 45° and 60°: As shown in Figure 4, the uniaxial AE test data of the samples with bedding angles of 45° and 60° are relatively similar. During the compaction stage, the microcracks inside the sample begin to be compacted, and the stress–strain curve slowly grows. In this process, the microcracks are compacted, the AE ringing counts are collected relatively evenly, and the AE hits are also relatively uniform. Then, in the elastic stage, the stress–strain curve shows a linear growth, and the microcracks are still compacted, with only a small number of microcracks generated. Therefore, the collected AE ringing counts and AE hits still maintain the trend of the previous stage. In the plastic stage, the AE ringing counts and AE hits of the sample are the same as those in the elastic stage. Finally, in the failure stage, as the sample reaches peak strength, the AE ringing counts instantly increase to the maximum, and the AE hits increase rapidly at the same time, leading to the failure of the sample. The reason for the variation of the AE data above is that the shear failure along the bedding plane is the main feature of the shale samples under uniaxial loading at the bedding angles of 45° and 60°.

(4) θ = 90°: As shown in Figure 4, because the loading direction is parallel to the bedding planes, the static load is mainly borne by the shale matrix. Due to the high strength and brittleness of the shale matrix, the microcracks in the shale matrix continue to develop during the compaction, elastic and plastic stages, resulting in the AE ringing counts remaining basically stable, whereas, with the increase in strain, the AE hits and AE cumulative hits increase steadily. In the failure stage, the sample reaches the peak strength, and the AE ringing counts and the AE hits quickly reach the maximum value. Meanwhile, the main cracks in the sample appear and the tensile failure along the bedding surface occurs.

3.2. Triaxial Compression Results

The stress–strain curves of the triaxial compression test for shale samples with different bedding angles are shown in Figure 5, and the stress–strain curves of the uniaxial compression test are also added in Figure 5 for comparative analysis. From this figure, it can be found that:

(1) For shale samples with different bedding angles θ, the characteristics of stress–strain curves before peak strength are the same as those of homogeneous rocks, all showing obvious compaction stage (which gradually disappears with the increase in confining pressure σ₃), elastic deformation stage, and yield stage (or unstable fracture development stage). For the post-peak stress–strain curve, the shale samples with bedding angles of 0°, 30°, 45°, and 60° show obvious brittle failure characteristics, and their bearing capacity decreases rapidly after the peak strength, with no obvious strain softening behavior. On the other hand, the samples with a 90° bedding angle show completely different ductile failure characteristics, and the stress–strain curves which do not decrease significantly after reaching the peak strength but fluctuate up and down while the strain increases, maintaining relative stability. The characteristic that the peak strength of the 90° bedding angle samples is approximately equal to the residual strength is more pronounced at higher confining pressure σ₃, and their stress–strain curve are similar to the ideal elastic–plastic model.

The reason for the unique stress–strain curve characteristics of the 90° bedding angle samples is that under the Poisson effect, radial tensile stresses are generated inside the samples, while for the 90° bedding angle samples, the tensile stresses act vertically on the bedding planes with extremely low tensile strength, resulting in tensile cracks along the bedding planes of the samples, so the axial stresses will decrease temporarily. However, the rock matrix is not destroyed yet, so the axial stresses will increase again. From the beginning of the phenomenon of stresses drop, the load-bearing mode of the samples is changed from bearing by a complete cylinder to multiple independent cylinders. At the same time, with the increase in axial stresses, these shale matrix columns will also be stretched and broken into more new columns under the Poisson effect, and their rupture (or instability) is also independent under axial loading. After the bearing failure of the columns with weak strength, the columns with higher strength continue to bear the load, and finally the unique up-and-down fluctuation stress–strain curve characteristics of the 90° bedding angle samples are formed.

(2) As the confining pressure σ₃ increases, the compressive strength σ_cs of shale samples with different bedding angles increases, and the axial and radial peak strains of the samples also increase. At the same time, it can be found that the strength of shale samples with different bedding angles under different confining pressures σ₃ is also different, showing obvious anisotropic characteristics, which will be analyzed in detail in Section 4.

(3) For the shale samples with bedding angles 0° and 30° under high confining pressure σ₃ conditions, the stress–strain curves show a significant yield stage after the liner elastic stage. During this stage, the tangent modulus of the stress–strain curves gradually decreases. However, the stress–strain curves of shale samples with 60° and 90° bedding angles do not show a significant yield stage before failure, and the axial strains and radial strains exhibit an approximate linear relationship with stress before peak strength, while the plastic deformation is small. The main reason for this phenomenon is the difference in yield characteristics between the rock matrix and bedding planes. After the compaction stage, the microcracks in the rock matrix and bedding planes are fully compacted, but the mechanical properties of the two materials are quite different. As shown in Figure 5a,e, under the same axial stress, the brittle-plastic characteristics of the stress–-strain curves are different. At high bedding angles of nearly 90°, the axial stress is mainly borne by the shale matrix. Therefore, based on the stress–strain curves, it can be inferred that the rock matrix has strong rigidity characteristics, i.e., high elastic modulus, so it will not produce obvious plastic deformation before failure. For shale samples with a lower bedding angle, axial stress is jointly borne by the matrix and bedding planes in the samples, and the strong plastic characteristics of the sample are mainly caused by the weak bedding planes. Moreover, because the plastic deformation of the bedding planes inside the samples is fully demonstrated under the action of axial stress, the failure strain of the samples with a 0° bedding angle is greater than that of samples with other bedding angles under the same confining pressure.

4. Analysis of Anisotropic Mechanical Characteristics of Shale

According to the results of the uniaxial and triaxial tests of the shale, it can be found that mechanical parameters such as the strength and modulus of shale samples with different bedding angles show significant anisotropy. Therefore, this section focuses on analyzing the anisotropy of mechanical behavior of shale samples and the reasons for its occurrence.

4.1. Compressive Strength Anisotropy of Shale

The compressive strength of all the shale samples with different bedding structures obtained from uniaxial and triaxial compression tests are sorted out, and the average values of the compressive strength of shale samples under the same loading condition are used as the compressive strength σ_cs to carry out anisotropic analysis; meanwhile, the relationship curves of compressive strength σ_cs and bedding angle θ with confining pressure σ₃ are drawn, as shown in

Table 2. Compressive strength of shale under different confining pressures.

Bedding Angle θ (°)	Confining Pressure σ3 (MPa)	IDs of Shale Samples	Compressive Strength of Each Shale Samples (MPa)	Average Values of Compressive Strength σcs (MPa)
0	0	A1, A2, A3	180.0, 165.7, 168.5	171.4
	10	A4, A5, A6	203.1, 219.4, 196.4	206.3
	20	A7, A8, A9	227.4, 237.3, 221.1	228.6
	30	A10, A11, A12	244.7, 255.5, 240.2	246.8
	40	A13, A14, A15	281.4, 270.8, 285.1	279.1
30	0	B1, B2, B3	112.8, 106.3, 119.9	113.0
	10	B7, B8, B9	142.5, 146.3, 157.9	148.9
	20	B7, B8, B9	170.4, 177.5, 170.2	172.7
	30	B10, B11, B12	191.4, 200.8, 187.7	193.3
	40	B13, B14, B15	199.4, 241.5, 199.3	213.4
45	0	C1, C2, C3	93.7, 102.9, 99.2	98.6
	10	C4, C5, C6	153.0, 150.1, 155.3	152.8
	20	C7, C8, C9	143.2, 140.8, 139.9	141.3
	30	C10, C11, C12	163.8, 161.7, 166.2	163.9
	40	C13, C14, C15	184.2, 190.3, 177.8	184.1
60	0	D1, D2, D3	65.0, 59.4, 58.6	61.0
	10	D4, D5, D6	74.8, 79.1, 77.1	77.0
	20	D7, D8, D9	104.0, 107.1, 106.6	105.9
	30	D10, D11, D12	110.1, 105.4, 114.8	110.1
	40	D13, D14, D15	130.5, 130.8, 130.2	130.5
90	0	E1, E2, E3	117.4, 115.8, 119.9	117.7
	10	E4, E5, E6	234.3, 216.6, 225.3	225.4
	20	E7, E8, E9	200.9, 203.8, 210.0	204.9
	30	E10, E11, E12	221.6, 228.0, 210.4	220.0
	40	E13, E14, E15	291.6, 307.4, 302.5	300.5

and Figure 6.

As shown in Table 2 and Figure 6a, the compressive strength σ_cs of the shale samples exhibits significant anisotropy, and σ_cs under the same confining pressure σ₃ shows a “U-shaped” trend of first decreasing and then increasing with the increase in the bedding angle θ. Secondly, the minimum value of σ_cs of shale samples with or without confining pressure σ₃ is achieved at the bedding angle of 60°, which is consistent with the experimental results of other researchers [9,17,19]. On the other hand, with the increase in confining pressure, the bedding angle θ corresponding to the maximum value of σ_cs tends to change from 0° to 90°. When confining pressure σ₃ is between 0 MPa and 30 MPa, the bedding angle corresponding to the maximum value of σ_cs is obtained at 0°, while at the higher confining pressure of 40 MPa, the maximum value is obtained at a bedding angle of 90°. It can be seen that the sensitivity of σ_cs to the confining pressure under different bedding angles is different.

In addition, the compressive strength σ_cs of shale samples at the same bedding angle θ mostly increases with the confining pressure σ₃, which conforms to the effect of confining pressure in the traditional rock triaxial test, as shown in Figure 6b. Moreover, within the confining pressure σ₃ range of 0 MPa to 40 MPa in the test, the compressive strength σ_cs and confining pressure σ₃ show an approximate linear relationship. Therefore, the curve between compressive strength σ_cs and confining pressure σ₃ in Figure 6b is fitted by Equation (1), and the coefficient A and B in Equation (1) represent the sensitivity of compressive strength of confining pressure at this bedding angle and the uniaxial compressive strength, respectively.

$${\sigma }_{\mathrm{cs}}=A{\sigma }_3+B$$

(1)

Table 3. Parameter values of Equation (1).

Bedding Angle θ (°)	A	B	R-Square	Removed Abnormal Data (σ3, σcs) [R-Square before Removing Abnormal Data]
0	2.559	175.273	0.988	/
30	2.452	119.208	0.984	/
45	2.148	98.667	1.000	(10, 152.8) [0.816]
60	1.722	62.453	0.965	/
90	4.282	114.427	0.954	(10, 225.4) [0.763]

shows the values of coefficient A and B obtained by linear fitting of the experimental data according to Equation (1). It is worth noting that some abnormal data in Figure 6b were excluded in the fitting process. The reason why these data are considered abnormal is that they violate the trend of rock compressive strength increasing with the confining pressure in traditional rock triaxial tests, which is also followed by most of the data in the triaxial tests in this paper. Therefore, in order to ensure that the fitted equation can be applied to most test data, and to increase the accuracy of linear fitting (that is, to improve the value of R-square) and the safety of subsequent strength criteria, some abnormal data are removed, as shown in Table 3, and the fitting index R-square before and after abnormal data are removed is also given in the table.

As can be seen from Table 3, R-square values are all greater than 0.95, indicating that the linear relationship between shale compressive strength σ_cs and confining pressure σ₃ is very significant after removing some abnormal data. The fitting curve and the measured data are drawn in Figure 7, and it is not difficult to find that due to the difference in the sensitivity coefficient of bedding angle θ, the critical point of confining pressure is about 35 MPa between the shale compressive strength at a 90° bedding angle and the shale compressive strength at a 0° bedding angle. When the confining pressure σ₃ is near the critical point, the bedding angle corresponding to the maximum shale strength will be transformed.

According to the linear relationship between compressive strength σ_cs and confining pressure σ₃ of shale, it can be considered that the shale samples with different bedding angles basically obey the Mohr–Coulomb strength theory under the minimum principal stress of nearly 0~40 MPa, and the principal stress expression of Mohr–Coulomb strength theory is as shown in Equation (2).

$${\sigma }_{\mathrm{cs}}=\frac{1+\sin \phi }{1-\sin \phi }{\sigma }_3+\frac{2c\cdot \cos \phi }{1-\sin \phi }$$

(2)

where c is cohesion and φ is the internal friction angle. According to the data in Table 2, the values of c and φ of shale samples with five bedding angles are shown in

Table 4. Parameters in Mohr–Coulomb strength criterion of shale samples.

Bedding Angle θ (°)	Cohesion c (MPa)	Internal Friction Angle φ (°)
0	54.784	25.979
30	38.064	24.874
45	33.661	21.388
60	23.796	15.382
90	27.649	38.415

.

Figure 8 shows the variation of the cohesion c and the internal friction angle φ of the shale samples with the bedding angle θ. It can be seen that the c and φ of samples decrease first and then increase with the increase in the bedding angle θ, and both obtain the minimum value when the bedding angle θ is 60°, which is the same as the variation of compressive strength σ_cs with the increase in bedding angle θ. The difference is that the maximum cohesion c obtained when θ is 0°, while the maximum internal friction angle φ is obtained when θ is 90°.

4.2. Compressive Deformation Parameter Anisotropy of Shale

Modulus and Poisson’s ratio are the main parameters used to characterize the compressive deformation characteristics of rock, and the elastic modulus E_θ, 50% strength deformation modulus E₅₀, and Poisson’s ratio v_θ of shale with different bedding angles are discussed, respectively. The average values of shale compressive deformation parameters measured by uniaxial and triaxial compression tests are shown in

Table 5. Deformation parameters of shale under uniaxial and triaxial compression.

Bedding Angle θ (°)	Confining Pressure σ3 (MPa)	Elastic Modulus Eθ (GPa)	Poisson’s Ratio vθ	50% Strength Deformation Modulus E50 (GPa)
0	0	27.59	0.124	25.94
	10	30.95	0.148	30.14
	20	33.53	0.153	33.03
	30	34.38	0.188	34.19
	40	34.48	0.172	33.62
30	0	27.56	0.127	22.32
	10	28.73	0.148	26.53
	20	29.54	0.171	29.12
	30	33.56	0.173	33.42
	40	33.75	0.167	32.83
45	0	28.13	0.111	25.18
	10	30.96	0.181	30.25
	20	31.18	0.159	30.67
	30	32.01	0.158	31.67
	40	33.93	0.170	33.41
60	0	33.53	0.177	24.36
	10	35.37	0.191	30.21
	20	34.96	0.186	35.21
	30	35.52	0.184	35.93
	40	38.21	0.200	38.30
90	0	48.24	0.165	44.35
	10	52.75	0.158	46.02
	20	54.19	0.141	54.36
	30	59.30	0.146	59.07
	40	64.60	0.220	64.55

.

According to Table 5, the values of elastic modulus E_θ and 50% strength deformation modulus E₅₀ are close when the confining pressure σ₃ is no less than 20 MPa, but there are some differences when the confining pressure is lower than 20 MPa. The reason for this phenomenon is that the compaction stage of shale stress–strain curve under low confining pressure conditions has different effects on the calculation process of these two moduli. The E_θ is calculated based on the straight section of the stress–strain curve, which reflects the deformation of rock in the linear elastic stage. However, the E₅₀ reflects the average deformation of rock in the early compaction stage, and its value will be affected by the compaction stage, so is slightly lower than E_θ. The ratio of elastic modulus E_θ to the 50% strength deformation modulus E₅₀ of shale samples under different confining pressures are listed in

Table 6. The ratio of E_θ to E₅₀ of shale samples under different confining pressures.

Bedding Angle θ (°)	Confining Pressure σ3 (MPa)
	0	10	20	30	40
0	0.940	0.974	0.985	0.994	0.975
30	0.810	0.923	0.986	0.996	0.973
45	0.895	0.977	0.984	0.989	0.985
60	0.726	0.854	1.007	1.012	1.002
90	0.919	0.872	1.003	0.996	0.999

, and it can be found that with the increase in the confining pressure applied synchronously in the first stage of the triaxial compression test, the value of E_θ/E₅₀ rises and approaches 1, indicating that the compaction stage of the shale samples is gradually shortened. At the same time, when the confining pressure σ₃ is greater than 20 MPa, the values of E_θ/E₅₀ of shale samples at five bedding angles are all close to 1, showing that shale samples can be fully compacted under the action of confining pressure σ₃.

On the other hand, according to Table 5, it can be found that with the increase in confining pressure, the elastic modulus E_θ and 50% strength deformation modulus E₅₀ both increase, and the changes are similar. Therefore, only the variation of elastic modulus E_θ with confining pressure σ₃ is analyzed, and the change curve of elastic modulus E_θ with respect to confining pressure σ₃ is sorted out, as shown in Figure 9.

It can be found from Figure 9 that the elastic modulus E_θ with confining pressure σ₃ show an approximate linear growth relationship, so the E_θ and σ₃ are linearly fitted, and the obtained linear fitting parameters and fitting index R-square are listed in

Table 7. Parameter values of Equation (3).

Bedding Angle θ (°)	C	D	R-Square
0	0.172	28.745	0.858
30	0.172	27.182	0.911
45	0.126	28.712	0.910
60	0.095	33.615	0.784
90	0.393	47.964	0.971

, and the linear fitting equation is shown in Equation (3).

$$E_{\mathsf{\theta }}=C{\sigma }_3+D$$

(3)

where C and D represent the sensitivity of shale elastic modulus E_θ to confining pressure σ₃ and the uniaxial compressive elastic modulus of shale at this bedding angle.

It can be seen from Table 7 that the fitting index R-square of linear fitting between the elastic modulus E_θ and confining pressure σ₃ of shale samples with different bedding angles are close to or greater than 0.8, indicating that E_θ and confining pressure σ₃ basically obey a linear relationship. The comparison between the linear fitting function and the experimental results is sorted out, as shown in Figure 10. It can be observed that the sensitivity of the E_θ to the confining pressure effect is different under various bedding angles. Combined with the sensitivity coefficients in Table 3 and Table 7, it is found that the variation of shale elastic modulus E_θ sensitivity to confining pressure σ₃ with bedding angle θ is very similar to that of the compressive strength σ_cs sensitivity. The sensitivity coefficient C decreases slowly in the bedding angle θ range of 0°~60°, and the growth of elastic modulus E_θ decreases gradually with the increase in confining pressure σ₃, while the sensitivity coefficient increases rapidly in the range of 60°~90°, showing that the growth of E_θ increases rapidly with the confining pressure σ₃.

In addition to the elastic modulus E_θ, Poisson’s ratio is also a very important elastic constant, and the variation curves of Poisson’s ratio v_θ and confining pressure σ₃ of shale samples obtained by uniaxial and triaxial tests are shown in Figure 11, and it can be found that the variation of Poisson’s ratio v_θ of shale with confining pressure σ₃ is disordered. According to the transverse isotropic properties and the experimental scheme, the Poisson’s ratio v_θ of shale samples with a bedding angle of 0° measured by the chain extensometer is a constant, while the v_θ measured by the samples with other bedding angles are all mixed data of v_θ in different directions. Therefore, only the relationship between v_θ and confining pressure σ₃ for samples with a bedding angle of 0° is discussed. As shown in Figure 11, v_θ and σ₃ for shale samples with a bedding angle of 0° are approximately positively correlated.

On the other hand, according to the data in Table 5, the variation curves of elastic modulus E_θ and 50% strength deformation modulus E₅₀ of shale samples with bedding angle θ under different confining pressures σ₃ are drawn, as shown in Figure 12.

It can be seen from Figure 12 that the E_θ and E₅₀ of shale have similar variation trends with the bedding angle, and the anisotropic characteristics are obvious. Both the E_θ and E₅₀ show a changing trend of first decreasing and then increasing with the increase in the bedding angle θ, and the variation is gentle when the bedding angle θ is less than 45°, while the change is drastic when the angle is greater than 45°. Within the designed confining pressure range in the test, the maximum values of E_θ and E₅₀ of shale are obtained when the bedding angle is 90°, while the bedding angle corresponding to the minimum value is basically 30°. In addition, the relationship between the Poisson’s ratio v_θ of shale and the bedding angle θ in this experiment is unclear, so no further specific analysis is made.

4.3. Anisotropic Index of Shale’s Mechanical Parameters

Anisotropic index R_c is an important parameter to quantitatively evaluate the anisotropic degree of the mechanical properties of materials. Singh et al. [49] proposed a formula for calculating the anisotropic index R_c of rock materials, which is the uniaxial compressive strength of the materials at a 90° bedding angle divided by the minimum uniaxial compressive strength of the rock materials within 0°~90° bedding angles, and the classification standard of anisotropic degree is also given, as shown in

Table 8. Classification criteria for anisotropy degree of rock materials proposed by Singh et al. [49].

Grade	Range of Anisotropy Index Rc
Isotropy	1.0 < Rc ≤ 1.1
Low anisotropy	1.1 < Rc ≤ 2.0
Moderate anisotropy	2.0 < Rc ≤ 4.0
High anisotropy	4.0 < Rc ≤ 6.0
Very high anisotropy	6.0 < Rc

.

The calculation method of the anisotropic index R_c used in this paper adopts the calculation formula proposed by Niandou et al. [17], as shown in Equation (4), and the anisotropic R_c is calculated by the ratio of the maximum value to the minimum value of the physical and mechanical parameters of shale at different bedding angles. In this paper, the compressive strength σ_cs and elastic modulus E_θ of shale samples are selected for calculating anisotropic indexes, and

Table 9. Shale anisotropic indexes under different confining pressures σ₃.

Selected Mechanical Parameters	Confining Pressure σ3 (MPa)
	0	10	20	30	40
Compressive strength σcs	2.811	2.928	2.158	2.242	2.302
Elastic modulus Eθ	1.751	1.836	1.834	1.853	1.914

shows the anisotropic indexes calculated by the σ_cs and E_θ of shale samples in Table 2 and Table 5.

$$R_c=\frac{{(parameter)}_{\max }}{{(parameter)}_{\min }}$$

(4)

According to the anisotropic indexes of the compressive strength σ_cs of the shale, combined with the anisotropic grading standard in Table 8, it is determined that the shale has a moderate degree of anisotropy. In the confining pressure σ₃ range of 0~40 MPa, the bedding angle θ corresponds to the extreme values of the compressive strength σ_cs and elastic modulus E_θ of shale changes, which increases the complexity of analyzing the anisotropy. The fitting curves of the anisotropic indexes of σ_cs and E_θ with σ₃ are sorted out, as shown in Figure 13, and the functional expressions of the fitting curves are shown in Equations (5) and (6).

For compressive strength σ_cs, the fitting formula is as follows:

$$\{\begin{array}{l}{R}_c=\frac{2.559{\sigma }_3+175.273}{1.722{\sigma }_3+62.453},(0\mathrm{MPa}\le {\sigma }_3\le 35.314\mathrm{MPa}),\\ R_c=\frac{4.282{\sigma }_3+114.427}{1.722{\sigma }_3+62.453},(35.314\mathrm{MPa}<{\sigma }_3\le 40\mathrm{MPa}).\end{array}$$

(5)

For elastic modulus E_θ, the fitting formula is as follows:

$$\{\begin{array}{l}{R}_c=\frac{0.393{\sigma }_3+47.964}{0.172{\sigma }_3+27.182},(0\mathrm{MPa}\le {\sigma }_3\le 33.261\mathrm{MPa}),\\ R_c=\frac{0.393{\sigma }_3+47.964}{0.126{\sigma }_3+28.712},(33.261\mathrm{MPa}<{\sigma }_3\le 40\mathrm{MPa}).\end{array}$$

(6)

According to Figure 13, the anisotropic indexes of shale are obviously affected by confining pressure σ₃, and the anisotropic indexes of elastic modulus E_θ are positively correlated with σ₃, while the anisotropic indexes of compressive strength σ_cs are negatively correlated with σ₃ in the range of 0 to 35.314 MPa, and when the σ₃ is greater than 35.314 MPa, the indexes of compressive strength σ_cs are positively correlated with σ₃. The reason is that the compressive strength of shale samples with a 90° bedding angle will increase rapidly with σ₃, and its growth rate is greater than that of the samples with a 0° bedding angle. When the σ₃ increases from 30 MPa to 40 MPa, the compressive strength of shale samples with a 90° bedding angle exceeds that of samples with a 0° bedding angle, which becomes the maximum compressive strength of shale with different bedding angles. As a result, the anisotropic index of compressive strength has a transition value between the σ₃ of 30 MPa and 40 MPa, that is, the minimum value. The anisotropy of strength and deformation parameters of shale samples is closely related to the obvious differences in layered structure and mechanical properties of constituent materials, and the macro failure mode of shale samples is also deeply related to the anisotropic characteristics.

4.4. Anisotropy Characteristics of Shale Compression Failure Modes

The strength and deformation characteristics of rock are closely related to the failure mode. Unlike isotropic materials, the failure modes of shale samples in uniaxial and triaxial compression tests are affected by the confining pressure σ₃ and the bedding angle θ, and there are many kinds of failure modes.

Table 10. Failure modes of representative shale samples under uniaxial and triaxial compression.

Bedding Angle θ (°)	Confining Pressure σ3 (MPa)
	0	10	20	30	40
0
30
45
60
90

lists the failure modes of representative shale samples in uniaxial and triaxial compression tests, and the main fractures of the failure samples are marked by a red curve, and the bedding angle θ of each sample is marked by a white straight line.

The composition of shale can be simplified into the shale matrix and bedding planes, and the failure modes of shale can be decomposed into four basic failure modes—tensile failure and shear failure of shale matrix and tensile failure and shear failure of bedding planes [33]—while the different failure modes of shale samples presented in Table 10 are combinations of these four basic failure modes. According to Table 10, the following conclusions can be drawn:

(1) Consistent with isotropic materials, confining pressure σ₃ can significantly change the failure modes of shale samples. Compared with triaxial compression, there are more penetrating fractures in shale samples under uniaxial compression, and their distribution is more complex. The reason for this phenomenon is that the uniaxial compression experiment lacks the constraint effect of radial stress.

(2) The uniaxial failure mode of the samples with a 0° bedding angle is a composite failure of tension and shear, and the friction cone at the end is the product of the hoop effect, and this failure mode is relatively complex, including four types of basic failure modes. With the application of confining pressure σ₃, the failure mode of the samples with a 0° bedding angle changes to the through-bedding plane shear failure mode with a single fracture, and the fracture is not parallel to the bedding planes, which is the shear failure mode of rock matrix. In addition to the secondary fractures produced by uniaxial compression, the failure mode of samples with a 30° bedding angle is the same as that of samples with a 0° bedding angle, which is dominated by the shear failure mode of the shale matrix.

(3) The failure mode of the samples with a 45° bedding angle is mainly a composite failure mode of shear failure through the bedding planes and shear failure along the bedding planes. The failure surface of the composite failure mode is approximately composed of two failure angles; one is the angle of the bedding planes, and the other is the angle higher than the bedding angles. At the same time, a small number of shale samples with a 45° bedding angle also show pure shear failure mode along the bedding planes. The failure mode of the samples with a 60° bedding angle is mainly shear failure along the bedding planes. In addition, a small amount of composite shear failure between rock matrix and bedding planes occurs in samples with a 60° bedding angle.

(4) The failure mode of the shale samples with a 90° bedding angle is different from that of the samples with the other bedding angles; there are tensile cracks parallel to the bedding planes caused by the Poisson effect in the samples. Therefore, it can be considered that the failure mode of the samples with a 90° bedding angle belongs to the tensile failure mode of the bedding planes. As the confining pressure σ₃ increases, some shear cracks through the bedding planes will appear on the samples. It can be seen that as the restraining of confining pressure σ₃ on the tensile failure of bedding planes increases, the failure mode of the samples with a 90° bedding angle begins to gradually change into the shear failure mode of rock matrix.

5. Discussion

Based on the experimental results and analysis, the reason for the compressive strength σ_cs, elastic modulus E_θ, anisotropic index of σ_cs and E_θ, and failure modes of shale samples having different sensitivities to the variation of confining pressure σ₃ is systematically analyzed:

(1) The reason for the σ_cs and E_θ of shale samples having confining pressure effects is that the spherical stress σ_m whose value is equal to σ₃ has a compaction effect on the samples. Under the action of spherical stress σ_m, the microcracks inside the samples are closed, and the density, compressive strength σ_cs, and elastic modulus E_θ increase, which is the same for homogeneous rock and shale.

(2) The first difference is that the basic failure mode of shale changes from shear failure to tensile failure as the bedding angle θ increases. According to Table 10, it can be seen that the failure surface tendency of all samples is the same as the bedding planes’ tendency except for the samples with a 0° bedding angle, because shale is more prone to deformation along the bedding planes under deviatoric stress. Therefore, the three-dimensional stress condition of the samples can be simplified to the plane stress condition (ignoring the influence of the bedding planes’ direction), and it is easy to ascertain that the plane spherical stress σ_m has a limited constraint effect on the shear stress generated by the deviatoric stress on the shear failure surface. The radial stress component of the spherical stress σ_m can effectively suppress the radial strain of the samples, thereby reducing the possibility of the tensile failure of the sample. It is found that the spherical stress σ_m has different restraining performance on the shear stress and radial strain, which are the main factors causing shear failure and tensile failure, and as the confining pressure increases from 0 to 40 MPa, the increase percentages of the compressive strength σ_cs and elastic modulus E_θ of the shale samples with bedding angles are 0°, 30°, 45°, 60°, and 90° are 62.8%, 88.87%, 86.7%, 114.1%, and 155.2% and 24%, 22%, 20.6%, 13.9%, and 33.9%, respectively, so the sensitivity of the shale samples with a high bedding angle (90°) dominated by tensile failure to the change in confining pressure is significantly greater than that of the samples with medium and low bedding angles (0°~60°) dominated by shear failure.

(3) The second difference is that the failure site of shale samples changes from the combination of the rock matrix and bedding planes to bedding planes. Combined with the failure images of shale samples shown in Table 10 and the values of cohesion c and internal friction angle φ in Table 4, it can be seen that the shear strength of the bedding planes is significantly weaker than that of the rock matrix. With the increase in the bedding angle, the shear failure characteristics of the samples are gradually dominated by the bedding planes, which leads to the phenomenon that the sensitivity of the shale samples to the change in confining pressure decreases when the basic failure mode is the shear failure. At the same time, it is observed that the failure modes of shale samples with 0°~30° low bedding angles are the same, so the sensitivity of compressive strength σ_cs and elastic modulus E_θ to confining pressure changes little in this range.

(4) The anisotropy index of the shale mechanical parameters is obviously affected by confining pressure, and the variation of anisotropy index of different mechanical parameters is different with the increase in confining pressure. Within the confining pressure range of the test, the anisotropic index of compressive strength basically decreases with the increase in confining pressure, while the anisotropy index of elastic modulus increases gradually. At present, it is generally believed that under a sufficiently high stress environment, the anisotropy of the rocks will gradually disappear and eventually tend to be isotropic, resulting in the anisotropy index of its mechanical parameters being close to 1. Therefore, combined with the experimental results in this paper, it can be concluded that with the increasing confining pressure, the anisotropy index of the mechanical parameters of shale does not monotonically decrease to 1.

(5) With the increase in confining pressure, the evolution of the failure modes of shale samples with different bedding angles under uniaxial and triaxial compression is as follows: 1. For the 0° bedding angle sample: The failure mode changes from a composite mode that includes both splitting failure perpendicular to the bedding planes and shear failure through the rock matrix to a shear failure mode through the rock matrix; 2. For the 30° bedding angle sample: The failure mode changes from a composite mode that includes both local splitting failure and shear failure through the rock matrix to a shear failure mode through the rock matrix; 3. For the 45° bedding angle sample: The failure modes of the samples are both a mixed mode that includes shear failure through the shale matrix and along the bedding planes; 4. For the 60° bedding angle sample: The failure mode changes from a composite mode that includes shear failure through the shale matrix and along the bedding plane to a shear failure mode along the bedding planes; 5. For the 90° bedding angle sample: The failure mode of the sample gradually evolved from the splitting failure along the bedding plane to the shear failure mode through the rock matrix. Therefore, it can be found that under different confining pressure conditions, although the failure modes of shale samples with different bedding angles have different evolution rules, the failure modes of shale samples all tend to evolve in the direction of shear failure mode through the rock matrix with the increase in confining pressure, and the anisotropy of the failure modes of shale samples with different bedding angles is gradually weakened.

6. Conclusions

(1) The AE characteristics of shale samples with different bedding angles in the compaction, elastic, plastic, and failure stages are significantly different during uniaxial loading, and the variation of AE hits, AE cumulative hits, and AE ringing counts with time are closely related to the angle between loading direction and bedding planes and the progressive failure mode of those samples.

(2) The uniaxial and triaxial compressive strength σ_cs of shale samples is anisotropic. Under different confining pressures, the compressive strength of shale samples first decreases and then increases with the increase in the bedding angle. The compressive strength of shale samples reaches the minimum value when the bedding angle is 60°, while the maximum values of compressive strength are obtained at the bedding angle of 0° when the confining pressure is 0~30 MPa and obtained at the bedding angle of 90° when the confining pressure is 40 MPa. At the same time, the compressive strength and confining pressure of shale samples with the same bedding angle conform to the linear growth relationship.

(3) The elastic modulus E_θ of shale samples also has anisotropic characteristics. Under the designed confining pressure, the elastic modulus of shale samples decreases first and then increases with the increase in the bedding angle, and the maximum values of elastic modulus are obtained when the bedding angle is 90°, while the bedding angle where the minimum value is located tends to increase gradually from 30° with the increase in confining pressure. The elastic modulus of shale samples with the same bedding angle has a linear growth relationship with confining pressure, while the variation of Poisson’s ratio with the bedding angle or confining pressure is disordered.

(4) According to the anisotropic grade of compressive strength σ_cs, the shale samples have moderate anisotropy. The variation of anisotropic index of compressive strength and elastic modulus of shale with confining pressure is different. In the confining pressure range of 0~35 MPa, the anisotropic index of compressive strength decreases with the increase in confining pressure, while the anisotropy index of elastic modulus increases gradually.

(5) The failure mode of shale samples is also anisotropic. In the uniaxial and triaxial experiment, the shale samples with 0° and 30° bedding angles mainly undergo through-bedding plane shear failure, and the samples with a 45° bedding angle mainly experience the composite failure of through-bedding plane shear failure and along-bedding plane shear failure. The failure mode of shale samples with a 60° bedding angle is mainly along-bedding plane shear failure, while the samples with a 90° bedding angle are dominated by tensile failure and will be accompanied by some tensile and shear cracks through the bedding planes under high confining pressures.