Introduction

Shale oil and gas are unconventional resources with great development potential. Shale reservoirs are characterized by strong compactness, low permeability and anisotropic strength characteristics, which are difficult to be exploited (Sone and Zoback 2013; Rybacki et al. 2015; Gupta et al. 2021; Li et al. 2022). To increase production, hydraulic fracturing must be carried out on the reservoirs. The tensile strength and failure mode of shale are closely related to fracturing design (Nath and Mokhtari 2018; Yang et al. 2019), and the research on mechanical properties of shale can provide important guidance for fracturing stimulation.

Due to the arrangement of mineral particles, the internal natural fractures of shale are relatively developed in the process of sedimentary diagenesis, and its appearance also has obvious layered structure (Geng et al. 2016; Na et al. 2017). Many researchers conducted experimental work on the mechanical behavior and failure of layered rocks. Tavallali and vervoort (2010) conducted Brazilian test on stratified sandstone to investigate the effect of the layer orientation on failure strength and failure pattern of layered sandstone. Mokhtari and Tutuncu (2016) explored the tensile strength and tensile fracture patterns in shales by conducting splitting tests on a variety of shale formations and discussed the effect of lamination or natural fracture angle on tensile strength and fracture pattern. Mighani et al. (2016) studied fracture initiation and propagation during Brazilian tests, and investigated the influence of anisotropy on fracturing by rotating the sample-fabric direction relative to the loading axis. The damage evolution and acoustic emission (AE) characteristics during failure process of anisotropic shale have been investigated by Wang et al (2016). Li et al. (2017) experimentally examined the effects of water content, mineralogy and lamination on tensile strength of organic-rich shales. Yu et al. (2020) took sandstone as the research object, conducted triaxial compression test with permeability and revealed the failure characteristics and permeability evolution law of sandstone under different bedding dip angles. Li et al. (2020) conducted Brazilian splitting test on slate with different sizes and different bedding angles, revealing the relationship between rock tensile strength, specimen size and bedding angle.

As a supplement to laboratory tests, numerical simulation studies based on rock mechanical test results can be used to improve the understanding of the test conclusions. Bahaaddini et al. (2013) used particle flow three-dimensional model (PFC3D) to study the influence of bedding geometric parameters on rock strength and mechanical properties. Yang and Huang (2014) studied the meso-mechanical mechanism of bedding rock based on the complete Brazilian disk rock test results and combined with the particle flow two-dimensional model (PFC2D). Duan and Kwok (2015) and Tan et al. (2015) presented numerical simulations using discrete element modeling to study the fracture patterns of transversely isotropic rocks using data of layered slate tested via the Brazilian method.

Based on the cohesive zone model in ABAQUS, Meng et al. (2021) investigated the effects of the number and strength of bedding plane on the fracture and crack distributions of specimens.

The above studies mainly focus on the influence of bedding plane on the tensile strength and failure pattern of layered rock. However, the meso-mechanism of layered shale and mechanical properties caused by natural fractures needs further study. In this paper, PFC2D program is used to establish a particle flow model that reflects the two factors of shale bedding geometry and natural fractures distribution. The meso-fracture mechanism and mechanical properties of layered shale are studied and verified by Brazilian splitting test. The effects of bedding angle, bond strength and natural fracture distribution on the tensile strength and fracture evolution characteristics of layered shale are discussed from the meso–macro perspective.

Construction of particle flow model

The motion and interaction of finite size particles are simulated by particle flow code (PFC) program from the mesoscopic point of view. These particles are rigid bodies with finite mass and can be translated, rotated and extruded (Cundall and Strack 1979). Particles interact in pairs through internal force and moment, and the contact force is related to the overlap of particles.

To characterize the constitutive of macroscopic materials and reflect the real macroscopic mechanical properties of shale reservoirs, it is necessary to give the corresponding contact model between mesoscopic particles. Therefore, it is essential to select an appropriate contact model. The layered shale particle flow model constructed in this paper is shown in Fig. 1, which mainly includes three type models: shale matrix contact model, bedding plane contact model and natural fracture model.

Fig. 1
figure 1

Contact model of layered shale

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Matrix contact model of layered shale

The linear parallel bond model (referred to as PB model) is selected as the contact model between shale matrix particles in this model (Park and Min 2015; Nguyen et al. 2017). PB model regards the rock as an inhomogeneous material composed of bonded particles and allows particles to be bonded together at contacts, which can transfer tension, pressure, shear and bending moment. Bond failure modes between particles are divided into tensile failure and shear failure.

The PB model provides two kinds of interaction behavior. The first behavior is non-bonded, which is equivalent to the linear model. The mutual slip between particles satisfies the Coulomb’s theory. The second behavior is a parallel bond. When there is a bond between particles, it acts parallel to the first behavior and can resist tension and bending moment. When the force exceeds the corresponding bond strength, the bond breaks. Then, the bond failure stress redistribution, which lead to adjacent bond failure or local progressive failure. The finial model degenerates into a linear model. (Duan et al. 2016).

In each calculation step, the force and moment of PB contact model are updated as follows:

$$\overline{F}_{n} = \left( {\overline{F}_{n} } \right)_{0} + \overline{k}_{n} \overline{A}\Delta \delta_{n}$$
(1)
$$\overline{F}_{s} = \left( {\overline{F}_{s} } \right)_{0} - \overline{k}_{s} \overline{A}\Delta \delta_{s}$$
(2)
$$\overline{M}_{b} = \left( {\overline{M}_{b} } \right)_{0} - \overline{k}_{n} \overline{I}\theta_{b}$$
(3)

where \(\overline{F}_{{\text{n}}}\) is the normal contact force updated in the current step, N; \(\left( {\overline{F}_{{\text{n}}} } \right)_{0}\) is the initial value of \(\overline{F}_{{\text{n}}}\); \(\overline{k}_{{\text{n}}}\) is the bond normal stiffness, N·mm−3; \(\overline{A}\) is the cross-sectional area, mm2; \(\Delta \delta_{{\text{n}}}\) is the relative increment of normal displacement, mm; \(\overline{F}_{{\text{s}}}\) is the shear contact force updated in the current time step, N; \(\left( {\overline{F}_{{\text{s}}} } \right)_{0}\) is the initial value of \(\overline{F}_{{\text{s}}}\); \(\overline{k}_{{\text{s}}}\) is the bond shear stiffness, N mm−3; \(\Delta \delta_{{\text{s}}}\) is the relative increment of shear displacement, mm; \(\overline{M}_{{\text{b}}}\) is the moment updated for the current step, N·mm; \(\left( {\overline{M}_{{\text{b}}} } \right)_{0}\) is the initial value of \(\overline{M}_{{\text{b}}}\) in the calculation step. \(\overline{I}\) is the moment of inertia of the parallel bond cross section, mm4; \(\theta_{{\text{b}}}\) is the relative bend-rotation increment.

The bond strength envelope equation between particles in the parallel bond model is as follows:

$$\sigma_{\max } = \frac{{ - \overline{F}_{n} }}{{\overline{A}}} + \frac{{\overline{M}_{b} }}{{\overline{I}}}\overline{R}$$
(4)
$$\tau_{\max } = \frac{{\overline{F}_{s} }}{{\overline{A}}}$$
(5)

where \(\sigma_{\max }\) is the maximum tensile stress of parallel bond, MPa; \(\tau_{\max }\) is the maximum shear stress of parallel bond, MPa; \(\overline{R}\) is the effective radius of parallel bond contact, mm.

The parallel bond model occurs tensile failure, if

$$\sigma_{\max } \ge \overline{\sigma }_{c}$$
(6)

On the other hand, shear failure appears, if

$$\tau_{\max } \ge \overline{\tau }_{c}$$
(7)

where the \(\overline{\sigma }_{{\text{c}}}\) is the normal strength of PB, MPa; \(\overline{\tau }_{{\text{c}}}\) is the shear strength of PB, MPa.

Layered shale bedding model

The anisotropy of shale is largely related to the properties of bedding plane, so this paper further embeds different angles of bedding plane in shale contact to study its mechanical properties. The angle between the loading direction and the normal line of the bedding plane is defined as the bedding angle \(\theta\). In setting the location of the bedding, a new contact model is needed to replace the original PB model. Different contact states between particles on both sides of the bedding are used to simulate different mechanical behaviors.

Through the dfn add fracture command stream, a new shale bedding planes contact model with different angles is established. The new contact model adopts the smooth joint contact model (SJ model), which allows dislocation and slip between two adjacent particles (Bahaaddini et al. 2015; Mehranpour and Kulatilake 2017). The SJ model simulates the behavior of an interface, regardless of the local particle contact orientation along the interface. Compared with the PB model, the SJ model does not have the ability to resist rotation.

The force and magnitude of SJ contact model in each calculation time step are updated as:

$$F_{n} = \left( {F_{n} } \right)_{0} - k_{n} A\Delta \delta_{n}^{e}$$
(8)
$$F_{s} = \left( {F_{s} } \right)_{0} - k_{s} A\Delta \delta_{s}^{e}$$
(9)

where \(F_{{\text{n}}}^{{}}\) is the normal contact force of the current time step update of SJ model, N; \(F_{{\text{s}}}^{{}}\) is the shear contact force of current time step update, N; \((F_{{\text{n}}} )_{0}\) is the initial value of \(F_{{\text{n}}}^{{}}\); \((F_{{\text{s}}} )_{0}\) is the initial value of \(F_{{\text{s}}}^{{}}\); A is the area of the smooth joint cross section, mm2; \(k_{n}\), \(k_{{\text{s}}}\) is the SJ normal stiffness and shear stiffness, respectively, N·mm−3; \(\Delta \delta_{{\text{n}}}^{{\text{e}}} \,\), \(\Delta \delta_{{\text{s}}}^{{\text{e}}}\) is the elastic part of the relative increment of SJ normal displacement and shear displacement, respectively, mm.

According to the bond state coefficient (sj) of the SJ model, the smooth joint contact model is divided into bond model (for sj = 3) and non-bond model (for sj < 3).

In the bond model, the tensile failure mode occurs in the bedding, as follows:

$$F_{n}^{{}} \ge \sigma_{c} A$$
(10)

Otherwise, the bedding fails in shear mode, as follows:

$$F_{s}^{{}} \ge \tau_{c} A$$
(11)

where \(\sigma_{{\text{c}}}\) is the normal bond strength of bedding, MPa; \(\tau_{{\text{c}}}\) is shear bond strength, MPa.

In the non-bond model, for \(F_{{\text{s}}}^{{}} < \mu F_{{\text{n}}}^{{}}\), particles cannot slide against each other, and the shear contact force is given as:

$$\left( {F_{s} } \right)_{0} = F_{s}$$
(12)

Otherwise, the particles slide each other, the shear contact force is given as:

$$\left( {F_{s} } \right)_{0} = \mu F_{n}$$
(13)

The normal contact force is changed as the shear displacement increases:

$$\left( {F_{n} } \right)^{*} = F_{n} + \left( {\frac{{\left| {F_{s} } \right| - \mu F_{n} }}{{k_{s} }}} \right)k_{n} \tan \psi$$
(14)

where \(\left( {F_{{\text{n}}} } \right)^{*}\) is the update value of normal contact force, N; \(\mu\) is the friction coefficient; and \(\psi\) is the dilatancy angle, (°).

The SJ model can set weaker tensile and shear strength parameters than the PB model. When the strength exceeds the strength criterion, the bonds of SJ model break and produce corresponding tensile or shear cracks, which can describe the failure of shale more accurately. Therefore, the SJ model is often used to simulate shale bedding or initial cracks, etc.

Natural fracture model

In this paper, a new random function is defined by dfn add fracture command. The discrete fracture model is generated to characterize natural fractures, and further investigate the influence of natural fractures on the mechanical properties of layered shale.

The dip angle of natural fracture model is defined to obey Gaussian distribution. The mean and variance of dip angle are modified by multiplying the returned Gaussian random number by a factor or adding offset. To reflect strong regularity, this paper defines the probability density function as follows:

$$p(\theta_{n} ) = \frac{1}{{30\sqrt {2\pi } }}e^{{ - \frac{{(\theta_{n} - 30)^{2} }}{{2 \times 30^{2} }}}}$$
(15)

where random variable \(\theta\) n is natural fracture dip angle; \(p(\theta_{{\text{n}}} )\) is the probability density distribution function of \(\theta\) n.

The size and position coordinates of natural fractures obey uniform distribution on the disk profile. Finally, a certain size, angle and number of micro-fractures were randomly generated in the four quadrants of the disk. As with the contact model of bedding plane, natural fractures are given SJ contact model.

Brazilian splitting simulation test of layered shale

Numerical specimen preparation

The Brazilian split test was carried out by using the core obtained from the field to calibrate the particle flow model coefficient. Brazilian split test shale samples were collected from Changqing oilfield. As shown in Fig. 2, the shale specimens appear gray and black, showing obvious bedding lines. The tensile strength of the specimen is obtained by the following formula:

$$\sigma_{t} = \frac{2P}{{\pi Dt}}$$
(16)

where \(\sigma_{{\text{t}}}\) is the tensile strength of the specimen, MPa; P is the peak load of Brazilian test, N; D and t are the diameter and thickness of the specimen, respectively, mm.

Fig. 2
figure 2

Brazilian splitting test specimen of bedding shale

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Based on sizes of Brazilian test cores, particle flow specimens of layered shale were constructed. The preparation process was as follows:

  1. (1)

    Initial particles generated. The real cylinder specimen with diameter of 25 mm and thickness of 20 mm was simplified to a flat disk with diameter of 25 mm. To reduce the influence of particle sizes and numbers on the macroscopic mechanical properties, this paper set the specimen composed of 5000 mutually bonded particles, and the ratio of maximum particle size to minimum particle size is 5. After the particles generated, the particles in the model were uniformly loaded by the cycle command stream, thus reducing the overlap between particles.

  2. (2)

    Sample servo. The servo program compiled by Fish language was used to servo the specimen to make the specimen compacted uniformly.

  3. (3)

    Defined particles contact models. First, PB model was given between layered shale matrix particles. Next, the size and position coordinates of each direction were defined by the model dfn add fracture command stream to generate a complete bedding plane. Finally, a certain number of natural fracture models were randomly generated by defining random functions that obey statistical laws in Fish language. Both bedding planes and natural fractures used SJ models.

  4. (4)

    Model loading. The Brazilian disk specimen was loaded until the model failed by applying a certain speed to the upper and lower loading walls. Figure 3 shows the loading mode of the specimen.

Fig. 3
figure 3

Brazilian disk particle flow model of layered shale

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Comparison of particle flow model results and experiments

The microscopic parameters of the model reflect the macroscopic mechanical properties of rock. To determine a set of microscopic parameters which can properly reflect the macroscopic mechanical properties of shale specimens, the trial and error method was used, and the simulation results were compared with the laboratory test data. The specific microscopic parameters of the contact model are shown in Table 1 and Table 2.

Table 1 Micro-parameters of PB model for layered shale
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Table 2 Micro-parameters of SJ model for layered shale
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Figure 4 shows the load–displacement curve and final failure pattern obtained by test and simulation under Brazilian splitting test. It can be seen from the result that the PFC numerical simulation curve matches well with the test curve, and the slopes of the two are approximately equal in the elastic stage. The limit failure mode of the numerical simulation is also the same as that of the laboratory test.

Fig. 4
figure 4

Comparison of load–displacement curves by Brazilian test and simulation

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The discrete fracture model is used to replace the natural fracture model to study its influence on the mechanical properties of layered shale. As shown in Fig. 4, only considering the effect of bedding plane, the peak load is about 0.9 KN, which is close to the peak value of the actual test. But the peak displacement is about 0.012 mm, which is lower than the test result 0.018 mm.

When the influence of natural fracture is considered, the peak load of the curve is about 0.8 KN, and the peak displacement is about 0.016 mm. Since the natural fracture is a weak plane with low bond strength, when it acts with the bedding plane, the fracture resistance of the shale is reduced. When subjected to load compression, the crack connects the bedding and the natural fracture, and the peak displacement increases.

In summary, only consider bedding factor, the slope of PFC numerical simulation curve and experimental curve in the elastic stage is approximately equal, but the deformation is relatively small. Compared with the test results, the combination of parallel bond contact model and smooth joint contact model can accurately reflect the Brazilian splitting load–displacement change law of layered shale, which verifies the effectiveness of the PFC model.

Failure modes analysis under the Brazilian test

The PFC model provides insights on the relationship between the failure modes and micro-level failure mechanism of shale under the Brazilian test. A series of Brazilian simulation tests is conducted to investigate the factors that affect the mechanical characteristics and fracture patterns of layered shale, such as the bedding orientation angles, the bedding plane properties and natural fractures.

Influence of bedding angle on failure pattern

Figure 5 shows the failure pattern and crack distribution of Brazilian disk with different bedding angles. Disk red line segment represents tensile crack, and black represents shear crack. With the lamination angle changes, there are mainly three failure patterns: tensile failure of shale matrix, tensile failure along bedding plane, and tensile–shear composite failure along shale matrix and bedding.

Fig. 5
figure 5

Failure behavior of shale with different bedding angles

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When \(\theta { = }0^\circ\), the shale matrix reached the tensile strength limit and tensile failure occurred. Tensile cracks were generated along the shale matrix, and the cracks propagated along the direction perpendicular to the bedding plane. When \(\theta { = 9}0^\circ\), the shale bedding reached the tensile strength limit and tensile failure generated. Tensile cracks were extended along the bedding plane, and the direction of crack propagation was parallel to the direction of load and bedding plane.

When \(15^\circ \le \theta \le 75^\circ\), except for the tensile cracks caused by matrix failure, some shear cracks along the bedding direction are also generated due to the slip effect of the bedding plane. The shear cracks mainly appear at medium or high-level angles along the bedding plane, as shown in the disk specimens with bedding dip angles of 45°, 60° and 75°. The research results are consistent with the physical test results of Li et al. (2017), which verifies the reliability of the simulation results in this paper.

To investigate the meso–macro fracture mechanism of rock from the mesoscopic perspective, the mesoscopic force chain and crack evolution process of layered shale are discussed in detail by taking the specimens with 15° and 75° bedding orientation.

Figures 6 and 7 show the mesoscopic force chain evolution diagrams of 15° and 75° layered shales. Black represents compression, and red represents tension. At the initial loading stage, the particles are squeezed by the compression load, and the force chain is concentrated in the middle of the disk along the direction of the force. The contact force between particles is small, and the force chain is sparse. There is almost no obvious crack at this stage.

Fig. 6
figure 6

Mesoscopic force chain evolution process for shale with 15°bedding plane

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Fig. 7
figure 7

Mesoscopic force chain evolution process for shale with 75°bedding plane

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With the increase in load, the extrusion between particles increases, and tensile cracks begin to initiate from the top and bottom of the disk specimen. When the load reaches the peak value, the contact force reaches the maximum, and the mesoscopic cracks in the disk expand to form the initial fracture zone, and a dense force chain appears. Due to the large compression at the top and bottom of the specimen, the local failure of the specimen occurs, the distance between particles increases, and the contact force decreases, resulting in the relative sliding between particles and the generation of shear cracks in the disk, which can be seen from Figs. 6b and 7b. At the same time, there is still low contact force in the area without cracks in the disk which reflects the heterogeneity of rock.

At the post-peak stage, macro fracture zone formed by continuous propagation and coalescence of micro-cracks. At this time, the specimen is destroyed, the contact force between particles is reduced, and the force chain is significantly weakened.

Effect of bond strength ratio on failure characteristics

The bond strength ratio of bedding plane has a significant effect on the fracture characteristics of rock specimens. The tensile or shear failure mode of the specimen is closely related to the normal bond strength and cohesive force of the bedding plane.

In this study, the bond strength ratio is defined as the ratio of the normal bond strength to the cohesion of the bedding plane. Taking the bedding angle of 75° as an example, by keeping the normal bond strength of the bedding plane unchanged and changing the bond cohesion, the influence of the change ratio of the bond strength on the failure pattern and peak strength of the Brazilian disk specimen were studied.

It can be seen from the evolution process in Fig. 8, the failure pattern and peak strength of the specimen are different under different bond strength ratios of the bedding planes. When the cohesive force decreases gradually to the bond strength ratio of 1.8, the specimen shows a trend of shear failure to the weak plane, the crack gradually extends to the bedding plane, and the peak strength of the specimen decreases slightly. When the ratio exceeds 1.8, with the increase in the ratio, the crack completely propagates along the bedding plane, and the peak strength of the specimen decreases obviously.

Fig. 8
figure 8

Evolution law of bond strength failure characteristics

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In other words, with the gradual decrease in bond cohesion, the ratio of normal bond strength to bond cohesion of the bedding plane increases, and the shear strength of the bedding plane decreases gradually. The shear failure of the disk specimen is easier to occur along the bedding plane, and the peak strength of the specimen reduces with the increase in the ratio.

Influence of natural fractures on fracture characteristics

Considering the influence of natural fractures, Fig. 9 shows the results of failure patterns and crack distribution of 0°, 30°, 60° and 90° layered shale specimens. The blue line segment in the disk represents the natural crack. When the bedding angle is 0° or 90°, the tensile crack is approximately parallel to the load direction, and the specimen is subjected to tensile failure. The shear crack propagates along the bedding plane as the bedding angle is 30° or 60°.

Fig. 9
figure 9

Failure behavior of layered shale considering natural fractures

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From the perspective of failure pattern, 0° is the splitting tensile failure of shale matrix, 30° and 60° are the tensile and shear composite failure of shale matrix and bedding, and 90° is the tensile failure along the bedding splitting.

As the rock specimen splitting fracture meets the natural fracture in the expansion process, complex fracture system with tensile fractures, bedding fractures and natural fracture cooperative propagation is generated. Due to the weak bond strength of natural fractures, it is easy to connect and expand into the new fracture system, such as the yellow circle identification in the diagram. At the same time, the shear cracks propagating along the bedding plane in the 30° and 60° disks are also significantly increased.

Tensile strength variation characteristics of layered shale

Figure 10 shows the relationship between the tensile strength of shale specimens and the bedding angle. Due to the influence of weak bedding plane, shale has poor splitting resistance. With the increase in bedding angle, the tensile strength decreases gradually. Considering the influence of bedding plane, the maximum tensile strength appears at 0°, which is 1.28 MPa. The minimum value appears at 90°, which is 1.02 MPa. In the range of \(30^\circ < \theta < {60}^\circ\), the tensile strength decreases rapidly with the increase in the bedding angle.

Fig. 10
figure 10

Relationship between tensile strength and bedding angle

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Considering the influence of bedding plane and natural fractures, the tensile strength decreases greatly with the increase in bedding angle, and the tensile strength is 1.15 –0.89 MPa. On the interval of \(0^\circ < \theta < 30^\circ\), the tensile strength varies greatly. At \(\theta = 0^\circ\), the tensile strength is 1.18 MPa, while it decreases to 1.0 MPa at \(\theta = 30^\circ\), with a descent range of 19.4%. The fluctuation of tensile strength is small as \(60^\circ \le \theta \le 90^\circ\). Natural cracks have obvious influence on the tensile strength of the layer.

Conclusions

Based on two-dimensional particle flow code PFC2D program, the failure mechanical behavior of layered shale under Brazilian splitting test was simulated. The effects of different bedding angles, bedding plane bond strength ratio and natural fractures on the failure characteristics of shale were studied from the microscopic point of view. The conclusions are as follows:

  1. 1)

    An PFC numerical model is developed to analyze the failure behavior and anisotropic characteristics of layered shale. The parallel bond (PB) model is used to establish the shale disk specimen. Then, the smooth joint (SJ) model is inserted into the locations of bedding plane in shale, which to simulate the behavior of laminations. Furthermore, the discrete SJ model is generated to characterize the influence of natural fractures. Simulation results are compared to experimental results and good agreement can be found.

  2. 2)

    The PFC simulation reveals that tensile fracture in the rock matrix and shear fracture along bedding plane are the main fracture pattern of shale disk specimens under Brazilian tests. When the bedding angle \(\theta\) is \({0}^\circ\), it is manifested as shale matrix tensile failure. When the bedding angle \(\theta\) is \({90}^\circ\), it is shown as the splitting tensile failure along the bedding. When the bedding angle is in the range of 15° to 75°, it is presented as tensile and shear composite fracture of shale bedding and matrix.

  3. 3)

    The macroscopic fracture modes rock are the results of the continuous evolution of mesoscopic force chain and mesoscopic cracks between particles. When the load increases to the peak strength, the micro-cracks propagate to form the initial tensile fracture zone, and dense force chain appears. The relative sliding between particles leads to local shear cracks. In the post-peak stage, the contact force between particles decreases and the force chain effect is significantly weakened.

  4. 4)

    Impacts of the bond strength of bedding and natural fractures contributes to the tensile strength anisotropy and consequent fracture patterns change. With the decrease in cohesive force and the increase in bonding strength ratio, the shear failure of disk specimens along the bedding plane is more likely. The tensile strength decreases significantly as considering the natural fractures effect. Moreover, a complex fracture network system is generated due to the collaborative propagation of tensile fractures, bedding fractures and natural fractures.