1 Introduction

With the advancement of unconventional oil and gas drilling technologies in China, the extraction of shale oil and gas is gradually moving toward deeper formations. The geological environment in these formations is more complex, characterized by higher heterogeneity, and increased drilling difficulties. These challenges significantly limit development efficiency and production safety. Therefore, there is an urgent need for research on the mechanical properties of deep shale oil and gas as a theoretical basis for industrial-scale extraction [11, 24, 42].

In order to effectively extract shale oil and gas, it is necessary to create a stable flow system through artificial fractures after reservoir fracturing. This helps to improve the overall flow characteristics of the reservoir [9, 46]. The generation, expansion, and stability of fracture networks are closely related to the mechanical properties of shale. Therefore, a comprehensive understanding of the mechanical behavior of shale is crucial for the successful exploitation of deep shale oil and gas resources [28].

The mechanical properties of shale during oil and gas drilling are primarily influenced by sedimentation and external environmental factors. These factors include the shale's bedding structure, moisture content, and surrounding pressure. Scholars from both domestic and international research communities have conducted extensive analysis and research on these aspects. For instance, Borja et al. [4] proposed a constitutive model based on damage mechanics and plastic flow theory, which accurately describes the elastic, plastic, and damage behavior of soil. Ip et al. [18,19,20] pointed out that the anisotropic and unsaturated behaviors of geomaterials can have a strong interdependence. They demonstrated through numerical simulations the role of saturation-dependent stiffness and hydraulic anisotropy in shrinkage behavior. Zhou et al. [61] conducted laboratory mechanical tests and direct shear experiments on the Fuling shale to ascertain its anisotropic characteristics. Wang et al. [41] studied the fracture properties of shale under the combined effects of bedding and fractures, demonstrating that the layering effect of the rock strengthens with increasing bedding angle. Chandler et al. [8] measured the fracture toughness of the Mancos shale and found that the shale fractures preferentially occurred along planes with the lowest toughness. Zhao et al. [54] investigated the influence of moisture content on characteristic stress of red sandstone and, in conjunction with acoustic emission systems, concluded that an increase in moisture content leads to a transition from brittle failure to ductile failure. Shen et al. [31] conducted infrared monitoring experiments on sandstone samples with varying moisture contents under uniaxial compression and observed that the change in infrared images and MIRT gradually transitions from a decrease-rise-sudden change to a rise-anomalous-sudden change with increasing moisture content. Xie et al. [44] studied the mechanical behavior differences during the transition from brittle to ductile deformation at different depths and pointed out that the increase in depth leads to an increase in the proportion of hard phases and medium mineral content, resulting in increased brittleness of the rocks. However, higher stress levels can inhibit the growth of rock brittleness. Taheri et al. [36] evaluated the damage threshold characteristics of rocks under different confining pressures and found that the closure stress of rock fractures decreases with increasing confining pressure.

These aforementioned studies contribute to a comprehensive understanding of the mechanical properties of shale under various conditions. By considering the effects of bedding structure, moisture content, and surrounding pressure, we can gain valuable insights into the behavior of shale during drilling operations. This knowledge is essential for optimizing drilling techniques, ensuring wellbore stability, and enhancing the efficiency and safety of shale oil and gas extraction. The aforementioned analysis indicates that many scholars [5, 16, 21] have studied the variations in the mechanical properties of rocks from individual perspectives such as bedding structure, moisture content, and confining pressure. However, in practical wellbore stability and hydraulic fracturing engineering problems, the effects of bedding structure, moisture content, and confining pressure on the rock formation often occur in combination. It is essential to consider the comprehensive effects of anisotropy, hydration, brittleness, and other factors. Unfortunately, there is still a lack of experimental research on the coupled effects of bedding structure, moisture content, and confining pressure on shale formations. The comprehensive understanding of the mechanical properties of laminated shale under the combined influence of multiple factors is yet to be summarized.

To address the aforementioned issues, this study focuses on the deep Longmaxi shale as the research object and conducts a series of experimental investigations. By comprehensively considering the combined effects of bedding structure, moisture content, and confining pressure, the aim is to understand the mechanical behavior and variations of the Longmaxi shale. This research aims to provide valuable insights into the coupled influence of these factors on the stability of wellbores and the effectiveness of hydraulic fracturing in shale formations. The experimental research conducted in this study will contribute to a more comprehensive understanding of the mechanical properties of laminated shale under real-life conditions. The findings will not only enhance our knowledge of the fundamental behavior of shale formations but also help in optimizing drilling and hydraulic fracturing techniques for the efficient and safe extraction of shale oil and gas resources.

2 Experimental approach

2.1 Samples studied

The experimental shale cores were extracted from the deep Longmaxi Formation in the Sichuan Basin, China. This formation represents a typical lithological unit characterized by the development of black shale layers. To ensure the representativeness of the samples, the selection of core samples took into consideration the significant differences in lithology, total organic carbon (TOC) content, and stratigraphy. Therefore, the results of this study can to some extent reflect the characteristics of the layered shale reservoirs in the research area. TOC content is one of the important indicators for assessing the abundance of organic matter, which can accurately evaluate the content of combustible organic compounds in shale and is of significance for assessing the petroleum and natural gas resource potential of shale. In this experiment, the Rapid CS Cube carbon–sulfur analyzer (instrument measurement accuracy ≤ 1% RSD) was used to determine the TOC content of the shale core samples. The test samples were 0.1–0.5 g of powder (200-mesh particle size). Prior to the experiment, the powder samples were treated with a dilute hydrochloric acid solution in a volume ratio of 1:7 to remove inorganic carbon, followed by drying at 60–80 °C, and finally being combusted in a high-temperature oxygen flow [38]. The CO2 content was detected by an infrared detector, and the TOC content of the samples was calculated accordingly, as shown in Fig. 1. The TOC content in the shale samples ranged from 0.5 to 5.78%, with an average of 3.82%, indicating a relatively high content and abundance of organic matter in the rock. A higher content of organic matter generally suggests greater potential for petroleum and natural gas resources in the rock. Therefore, based on the TOC content, it can be inferred that the shale under investigation may have good development potential for petroleum and natural gas.

Fig. 1
figure 1

TOC content of the specimens; dashed line represents the average value

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In addition to the TOC content, other factors need to be considered to evaluate the reservoir characteristics and development prospects of shale. X-ray diffraction (XRD) analysis of samples from different stratigraphic positions was conducted to determine the mineral composition. For the analysis, an appropriate amount of 200-mesh powder samples was subjected to X-ray diffraction using conditions of a tube voltage of 35 kV, tube current of 30 mA, Cu target radiation source with λ = 1.54 Å, scanning range of 2θ = 5°–80°, and a scanning speed of 2°/min [1]. The mineral content in the samples was determined by observing the characteristic diffraction peak intensities of different mineral crystals in the X-ray diffraction patterns, as shown in Fig. 2.

Fig. 2
figure 2

XRD mineral composition analysis chart: (a) whole rock mineral composition analysis of the six samples and (b) clay mineral mass fraction analysis of the six samples

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From Fig. 2a, it is evident that the shale sample primarily consists of quartz and clay minerals, along with varying amounts of plagioclase, calcite, and dolomite. Quartz, as the main brittle mineral in this shale interval, has a content ranging from 40.94 to 62.34%, with an average of 54.97%. Brittle minerals make the rock more prone to natural and induced fractures under external forces. They are one of the important factors affecting the development of pore and microcrack networks in shale.

Simultaneously, the clay content in the shale interval ranges from 10.94 to 43.29%, with an average of 26.61%. Clay minerals are prone to hydration and swelling in the presence of water, which is one of the key factors leading to rock degradation and wellbore instability. Due to the different hydration swellability of different clay minerals, further analysis specific to clay minerals is necessary, as shown in Fig. 2b. The results indicate that the shale sample is mainly composed of illite, with some illite/smectite interlayers. The relative content of illite ranges from 40.32 to 64.77%, with an average of 56.57%. When immersed, water molecules in the drilling fluid can combine with illite, forming a hydration film on its surface, leading to the expansion and extension of pores and fractures in shale and subsequently inducing wellbore instability. Therefore, when designing drilling fluids and optimizing wellbore performance for this formation, the weakening effect of water on the rock needs to be considered.

The development and aperture size of microfractures in shale can induce hydraulic fracturing, intensifying rock fragmentation, and subsequently impacting the stability of shale wellbore. Environmental scanning electron microscopy (ESEM) provides an effective means to observe the oriented arrangement of clay minerals, cementation structures, and distribution of microfractures within shale, offering strong support for analyzing shale genesis, assessing mineral resources, and predicting the potential for combustible gases in shale. The microstructural features, occurrence patterns, and pore-throat development characteristics of shale clay minerals were analyzed through ESEM, as shown in Fig. 3a.

Fig. 3
figure 3

Comparison of ESEM images of the original and soaked shale samples: (a) ESEM image of the original shale and (b) ESEM image of the saturated shale

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From the figure, it can be observed that the shale interval exhibits well-developed bedding planes and microfractures, indicating that the shale is more prone to damage along these microfractures and bedding surfaces. Additionally, it is hypothesized that in areas with high microfracture development and concentrated structural stress, these conditions provide pathways for the invasion of external fluids such as drilling fluid, thereby influencing shale saturation and weakening the strength of shale wellbore. This can lead to shale fracturing, spalling, and even wellbore instability and failure. To validate this hypothesis, shale samples immersed in a water solution were subjected to ESEM analysis, as shown in Fig. 3b. The microstructural images demonstrate that the immersion of shale significantly promotes the development of internal pores and microfractures, resulting in a relatively loose overall structure compared to the in situ shale [59].

Through the study of shale samples, the author has initially summarized the impact mechanism of moisture content on the physical and chemical properties of shale, explaining its effects on the following aspects:

  1. (1)

    The infiltration of water solution softens and lubricates the rock particles. As the moisture content increases, the friction and bonding forces between the soil particles decrease under the influence of the water solution.

  2. (2)

    Hydration-induced expansion of clay minerals. Shale, being a sedimentary rock, contains a certain amount of clay minerals such as illite and montmorillonite. The infiltration of water solution into the rock easily combines with the clay minerals, causing hydration-induced expansion [27]. This expands the internal pores and cracks of the rock, leading to the deterioration of its internal structure and a reduction in its compressive strength.

  3. (3)

    Since the bedding planes are weak interfaces characterized by numerous pores and microcracks, the presence of water solution not only weakens the overall strength of that particular section but also induces increased porosity and microcrack propagation. This leads to the absorption of more water by the bedding planes, causing secondary weakening and making the shale more prone to failure along these planes [62].

Merely studying the physicochemical characteristics of rocks is insufficient for practical engineering applications. Therefore, it is necessary to conduct in-depth research on the influence of moisture content on the structure and strength characteristics of shale under different moisture conditions.

2.2 Sample preparation

During core drilling, the inclination angle of the coring bit was carefully controlled relative to the bedding orientation, resulting in a set of 63 shale core specimens with different tilt angles (θ) of 0°, 15°, 30°, 45°, 60°, 75°, and 90° (Where 90° represents the direction parallel to the bedding plane.). Each core had a diameter of 50 mm, with nine specimens obtained for each bedding orientation.

To ensure that the shale cores remained isolated from external fluids, air cooling was employed during the coring process, and residual rock debris was removed. The two ends of the shale cores were then carefully trimmed and polished, resulting in standardized cylindrical specimens with dimensions of Φ50mm × 100 mm. A schematic representation of the sample preparation procedure is presented in Fig. 4.

Fig. 4
figure 4

Test rock sample preparation (θ means the angle between the normal direction of bedding plane and loading direction.)

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The strict sample selection and preparation procedures described above ensured the quality and representativeness of the shale core specimens. These prepared specimens were ready for subsequent laboratory testing and analysis, enabling a comprehensive investigation of the mechanical properties and behavior of the Longmaxi shale under controlled conditions. The subsequent sections will provide detailed insights into the experimental methods and results obtained from these prepared shale specimens.

2.3 Vacuum water absorption test

To investigate the detrimental effects of moisture content on the mechanical properties of laminated shale during oil and gas drilling, a vacuum water absorption test was conducted to simulate the in situ conditions of shale oil and gas reservoirs. In this test, distilled water was used as the soaking solution. Before the water absorption test, a preliminary experiment was conducted to determine the appropriate soaking duration for the shale specimens. The moisture content (ω) of the shale samples was measured at different soaking time durations (t). Based on the trends observed in the variation of moisture content with soaking time, it was determined that the shale samples reached a stable state and had near-saturation after 48 h of soaking. Therefore, soaking durations of 24 and 48 h were selected for the water absorption test.

Subsequently, the shale samples were subjected to the water absorption test. The 63 shale samples were divided into three groups, with each group comprising three specimens for each of the seven different bedding angles. This experimental design aimed to capture the influence of both moisture content and bedding angle on the mechanical properties of the shale samples. The specific experimental procedures and workflow are depicted in Fig. 5a.

Fig. 5
figure 5

Water absorption experiment and triaxial compression experiment: (a) flowchart of the water absorption test; (b) water absorption test equipment; and (c) rock triaxial testing system

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Firstly, to ensure the homogeneity of the experimental materials, it is necessary to dry the 63 shale samples for 24 h. It should be noted that high temperatures can cause rock samples to expand and undergo plastic deformation, so the drying temperature should not be too high. We followed the experimental procedures of other scholars [52] and conducted control experiments, and found that the plastic deformation of shale occurs within the allowable error range when the drying temperature is chosen as 80 °C, meeting the requirements of the experiment. After drying, the shale samples were weighed, and two groups were placed in vacuum vessels. The vessels were evacuated to create a vacuum environment, and distilled water was poured into the vessels until the shale samples were completely submerged. After 24 h, one group of samples was removed from the vessels and weighed. After 48 h, the remaining group was removed and weighed. Throughout the experiment, all shale samples were stored in sealed bags to minimize contact with the surrounding environment.

In the 24-h and 48-h water absorption tests, the average moisture content of the shale samples was determined to be 0.63 and 0.97%, respectively, with a range of 0.542–0.683% and 0.886–1.047%, respectively. Since the moisture content of the shale samples within the same soaking duration was relatively similar, the average values were chosen to represent the overall moisture content of each group of samples. Assuming that the moisture content of the dried shale samples was 0, we can obtain three different moisture content gradients of ω = 0, 0.63%, and 0.97% for further analysis.

2.4 Triaxial compression test

Using a triaxial servo-controlled rock mechanics testing system, a series of compression tests were conducted on shale specimens with different bedding angles and moisture contents after vacuum water absorption. The testing apparatus is illustrated in Fig. 5c. The system had a maximum load capacity of 1000 kN and a confining pressure limit of 80 MPa.

To simulate the stress conditions at different depths of the in situ shale formations, three confining pressure gradients of 0, 25, and 50 MPa were planned for the laboratory compression tests. The shale specimens were placed inside the apparatus and sealed. The confining pressure was gradually increased to the predetermined value at a loading rate of 0.03 MPa/s. Axial load was then applied until the specimens experienced fracturing failure.

3 Geomechanical behaviors of shale

3.1 Influence of different conditions on shale mechanical properties

Through the processing and analysis of triaxial test data, stress–strain curves at different bedding angles, moisture contents, and confining pressures were obtained, as partially shown in Fig. 6. Prior to reaching the peak stress, the curves exhibited linear elasticity, and the elastic limit approached the yield limit. The rock suddenly fractured upon reaching the ultimate compressive strength, resulting in a rapid drop in the curve. By comparing the variations in shale stress–strain curves under different conditions, the influence of each factor on the mechanical properties of shale can be determined.

Fig. 6
figure 6

Stress–strain relationship

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3.1.1 Influence of bedding angle on the mechanical properties of shale

By analyzing curves 1, 2, 3, and 4 in Fig. 6, the stress–strain curve patterns of dry shale specimens at different bedding angles under unconfined conditions can be deduced. From the figure, it is evident that the peak strength, yield strength, and residual strength of dry shale exhibit a "U-shaped" variation trend with an increase in the inclination angle. The shale specimens demonstrate a maximum peak strength of 74.36 MPa at an inclination angle of 90°, while the minimum peak strength of 54.11 MPa is observed at an inclination angle of 30°, resulting in a difference of 27.23%.

The slope of the stress–strain curve in the elastic deformation stage shows a trend consistent with the strength variation, decreasing and then increasing with increasing inclination angle. The influence of the bedding angle on the yield stage of dry shale specimens is not significant. However, due to the brittleness of dry shale specimens, all curves exhibit a sharp drop after the peak stress, indicating a catastrophic failure mode.

The analysis reveals a clear anisotropic behavior of shale under the influence of bedding planes, which can be considered as a set of weak structural interfaces and closed fractures. These weak planes tend to weaken the overall strength of the rock, while the presence of closed fractures facilitates sliding failure along these planes under shear stress. Under a 30° inclination angle, stress primarily acts along the bedding planes, resulting in shear failure of fractures and weak interfaces within the rock. Simultaneously, the presence of bedding planes decreases the contact area between rock particles, leading to localized stress concentration and further promoting the occurrence of failure. Bedding planes play a role in weakening the overall strength and stability of the rock, making it more prone to failure when subjected to external stress.

3.1.2 Influence of moisture content on the mechanical properties of shale

By analyzing curves 1, 5, and 6 in Fig. 6, the stress–strain curve patterns of shale specimens at an inclination angle of θ = 0° under the influence of moisture content can be deduced. The curves demonstrate a gradual flattening trend with increasing moisture content. In the pre-peak stage, the slope of the curve decreases with increasing moisture content, resulting in a shorter elastic deformation stage and a faster development of plastic deformation.

Moreover, the peak strength of the shale gradually decreases with increasing moisture content, with a reduction of approximately 25.07% when the shale reaches saturation. The effect of moisture content in the post-peak failure stage is characterized by a slower and prolonged curve, indicating a decrease in shale's brittleness and an enhancement of ductility due to hydration, exhibiting certain plastic characteristics.

3.1.3 Influence of confining pressure on the mechanical properties of shale

In triaxial tests, by varying the confining pressure, the stress environment of shale at different depths can be restored, enabling the study of the strength and deformation characteristics of shale at different depths. Curves 1, 7, and 8 in Fig. 6 present the stress–strain curves of dry shale specimens at an inclination angle of 0° under three different confining pressures. It can be observed that the yield strength, peak strength, and residual strength of the shale increase with increasing confining pressure, indicating that the rock becomes harder and offers greater resistance to failure with increasing burial depth.

However, as the confining pressure increases, the proportion of the post-peak curve drop decreases from 84.87% under no confining pressure to 39.77% at σ3 = 50 MPa. This suggests that the presence of confining pressure significantly reduces the brittleness of shale.

In triaxial loading conditions, comparing the experimental data with uniaxial loading, we found that shale exhibits higher strength when loaded parallel to the bedding planes under high confining pressure. This may be attributed to the presence of confining pressure compressing the internal bedding structure of shale, which weakens the bonding effect between bedding planes, the density of bedding planes, the strength of weak structure surfaces, and the brittleness of shale, all of which affect the elastic modulus of shale [35].

3.2 Evolutionary law of anisotropy under the influence of moisture content and confining pressure

Shale, as a unique sedimentary rock, exhibits pronounced anisotropy due to its microstructural characteristics and fracture system. Moisture content and confining pressure are two crucial factors that influence shale performance and behavior. Increasing moisture content and applying confining pressure both have significant impacts on the physical and mechanical properties of shale. This anisotropy plays a vital role in the engineering behavior and resource extraction of shale. Understanding the evolutionary relationship of shale anisotropy is crucial for the rational design of development plans and predicting rock behavior in shale development.

3.2.1 Evolutionary law of anisotropy and moisture content

Elastic modulus serves as a crucial mechanical parameter that reflects the ease of elastic deformation in rock materials and is indicative of their deformation characteristics. Therefore, the degree of anisotropy of shale can be constructed by the magnitude of the variation in the elastic modulus. After analyzing the results of numerous rock saturation-related experiments, Hu et al. [17] suggested that there exists an approximate linear relationship between saturation and elastic modulus:

$$E\left( \omega \right) = E_{sat} + \left( {1.0 - \frac{\omega }{{n_{eff} }}} \right)a_x$$
(1)

Among them, E(ω) represents the elastic modulus at a given moisture content, in GPa; Esat is the elastic modulus of the rock in a saturated state, in GPa; the coefficient ax is the slope of the line, representing the rate of change of the elastic modulus with moisture content; and neff is the effective porosity of the rock, which is taken as 1.15% for shale in this study. To specifically analyze the evolutionary relationship between anisotropy and moisture content in shale, Ip et al. [18] introduced the concept of anisotropy degree Er, defined as the ratio of elastic moduli:

$$E_r \left( \omega \right) = \frac{{E_{2,sat} + \left( {1.0 - \frac{\omega }{{n_{eff} }}} \right)a_{x2} }}{{E_{1,sat} + \left( {1.0 - \frac{\omega }{{n_{eff} }}} \right)a_{x1} }}$$
(2)

where E1 and E2 represent the minimum and maximum elastic moduli under the influence of anisotropy, in GPa; and Esat represents the elastic modulus of the rock in a saturated state, in GPa. Figure 7 shows the variation of the elastic modulus and anisotropy degree of shale with moisture content in a vacuum water absorption test. E1 is taken as the elastic modulus at an inclination angle of 30°, and E2 is taken as the elastic modulus at an inclination angle of 90°. The data are fitted and analyzed using Eqs. (1) and (2).

Fig. 7
figure 7

Variation of the elastic modulus and anisotropy degree of shale with moisture content; dashed lines represent the fitting curves

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Although the elastic modulus of shale decreases with increasing moisture content, the slope of the fitting curve for E1 is lower than that of E2, indicating that E2 is more influenced by moisture content and the gap between the two values decreases with increasing moisture content. According to Eq. (2), a higher anisotropy ratio indicates a greater degree of anisotropy in the rock. As moisture content increases, the anisotropy degree curve shows a clear decreasing trend, indicating that moisture content weakens the anisotropy degree of shale. This may be because the presence of water fills the pores and cracks in the shale, especially as water gradually saturates, water molecules preferentially form a connected network within the bedding planes, increasing the permeability of the shale in the bedding direction. The bedding planes of shale are longer and more exposed at an inclination angle of 90°, making it easier for water to flow through connected pores and cracks, leading to a faster decrease in the elastic modulus of shale. Therefore, with increasing moisture content, the anisotropy in the bedding direction may decrease [3]. These observations reveal that the weakening effect of water is particularly prominent in rock masses with layered structures, and thus, the coupled effects of shale's anisotropy and hydration should be given more attention in the construction of engineering structures such as oil and gas drilling and tunneling, as well as in the management of geological hazards.

3.2.2 Evolutionary law of anisotropy under varying confining pressure

The influence of anisotropy on the elastic modulus of shale under confining pressure is shown in Fig. 8a. As the confining pressure increases, the elastic modulus of shale increases significantly. The elastic modulus of shale still decreases with increasing moisture content, similar to the situation without confining pressure. When the inclination angle is 90°, the decrease rate of elastic modulus E2 with increasing moisture content is still faster than that of E1 when the inclination angle is 30°. Therefore, the evolution of moisture content in shale is minimally affected by confining pressure, and the influence of confining pressure on shale anisotropy can be studied using the anisotropy model in Eq. (2). Figure 8b compares the anisotropy degrees of shale under different confining pressures, revealing that the anisotropy degree of shale increases with increasing confining pressure. For dry shale samples, the anisotropy degree increases by 4.30% when the confining pressure increases from 0 to 50 MPa, while for water-saturated shale samples, the anisotropy degree increases by 3.78%. This indicates that shale anisotropy becomes more pronounced under confining pressure conditions.

Fig. 8
figure 8

Comparison of anisotropy degree of aquifer bedding shale under different confining pressures: (a) relationship between elastic modulus of shale and moisture content under different confining pressures and (b) relationship between anisotropy degree of shale and moisture content under different confining pressures; dashed lines represent the fitting curves

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The reason behind these phenomena is that in the confining pressure environment, the fluids in the shale's pores are compacted, resulting in a reduction of pore space. The closure of pores increases the density, overall stiffness, and strength of the shale. Additionally, as the confining pressure increases, shale may undergo elastic and plastic deformation, leading to changes in the microstructure of the rock, especially the presence of bedding structures. Overall, the anisotropy of elastic modulus and compressive strength exhibits opposite trends with increasing confining pressure. The increase in anisotropy of elastic modulus is mainly due to the significant pressure densification effect on interbedded pores and microcracks, while the decrease in anisotropy of compressive strength is caused by the change in fracturing mechanism of bedding planes after being suppressed by confining pressure. Therefore, when dealing with high stress conditions in shale formations, neglecting the anisotropy of elastic modulus would lead to significant errors in the analysis and design of engineering problems. Additionally, when the propensity for bedding plane fracturing is inhibited to a greater extent, the anisotropy of strength will be reduced, which is beneficial to the stability of wellbore.

3.3 Evolution of shale mechanical properties under the coupled influence of bedding structure and moisture content

In the process of oil and gas drilling, the stress state of rock formations can be disturbed, and both the wellbore and the hydrocarbon reservoir can be exposed to a water solution environment for an extended period. The angle between the principal stress and the bedding planes directly affects the mechanical properties of shale [47]. Compared to other rocks, shale is more susceptible to the weakening effects of water on its weak bedding planes [29, 32]. Through the analysis of the evolution relationship between anisotropy and moisture content in Sect. 3.2, it can be observed that an increase in moisture content leads to the softening of the bedding structure. Moreover, the different bedding structures and changes in moisture content can both affect the mechanical properties of shale. Therefore, there exists a coupled relationship between the influence of bedding structure and moisture content on shale's mechanical properties. Based on this, the present study further investigates the evolutionary patterns of shale's mechanical characteristics under the coupled influence of bedding structure and moisture content.

3.3.1 Evolution of strength characteristics of shale

Figure 9 illustrates the variation patterns of key strength characteristics of shale under uniaxial compression with different moisture contents and inclination angles. Analysis reveals that under different moisture content conditions, the strength variation patterns of shale influenced by bedding angle are generally consistent with those of dry shale specimens [30, 34, 55]. However, as the moisture content increases, the influence of bedding angle on the strength properties of shale becomes more significant. For dry shale with ω = 0, the peak strength of shale is maximally different by 27.23%, the yield strength is maximally different by 37.71%, and the residual strength is maximally different by 40.45% due to the influence of anisotropy. As the moisture content of shale increases, the differences in strength gradually increase. When the moisture content approaches the saturated state, i.e., ω = 0.97%, the maximum and minimum values of peak strength, yield strength, and residual strength of shale differ by 34.08, 47.99, and 59.82%, respectively. This indicates that the influence of bedding angle on the strength of shale becomes more pronounced under the effect of water degradation. Moreover, as the moisture content increases, the drop in yield strength for shale is more significant compared to the peak strength and residual strength. This indicates that the moisture content has a greater influence on the brittleness characteristics of shale.

Fig. 9
figure 9

Variation of key strength characteristics of shale with moisture content

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3.3.2 Evolution of deformation characteristics of shale

From the previous discussions, it is clear that the elastic modulus serves as a representative indicator of the mechanical properties of rock. The anisotropy induced by shale bedding planes can be effectively equivalent to a set of weak planes or closed cracks parallel to the bedding planes. The presence of weak planes reduces the overall strength of the rock, and under shear stress, the rock slides along the closed crack surfaces, causing additional deformation. The increase in moisture content also leads to the growth of closed cracks and the deterioration of weak structural planes in shale, thereby affecting the elastic modulus of the rock. Therefore, the elastic modulus varies with the inclination angle of the bedding planes and the moisture content. Based on this hypothesis, an equivalent elastic modulus model can be established to consider the induced anisotropy by the bedding planes. Fjær et al. [14] proposed a stiffness prediction model for laminated weak planes, which only includes the shale elastic modulus variation model caused by the bedding planes as described below:

$$E_\theta = \left( {1 - \eta \sin^2 2\theta - \rho \cos^4 \theta } \right)E_{90{\circ} }$$
(3)

Among them, Eθ represents the elastic modulus of shale at different bedding angles; θ represents the inclination angle in degrees (in Fig. 4); η represents the number of weak microelements in the weak plane or bedding plane; ρ represents the transitional normal compliance associated with the weak microelements; and E90° represents the elastic modulus of shale at θ = 90° (when the sample is loaded parallel to the bedding direction) under the corresponding confining pressure. The elastic modulus prediction model given by Eq. (1) is used to fit the experimental data (Fig. 10), and the parameter values of the fitting curves for different moisture contents are listed in Table 1.

Fig. 10
figure 10

Variation of elastic modulus of shale with bedding angle under different water conditions; dashed lines represent the fitting curves

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Table 1 The fitting parameters of elastic modulus of shale under different confining pressures
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The variation of elastic modulus in shale influenced by bedding plane anisotropy and moisture content is depicted in Fig. 10. From the figure, it can be observed that, similarly to the influence of anisotropy, the elastic modulus also exhibits a "U-shaped" variation trend with the bedding angle [40]. The inclination angle is near 30°, the elastic modulus reaches its minimum value, indicating that the shale sample is more prone to experience shear deformation along the bedding planes at this angle. Moreover, the minimum elastic modulus corresponds to the smallest compressive strength at θ = 30°, which aligns with the more significant plastic strain observed in the mechanical characteristics of the sample at this bedding angle compared to others. Comparatively analyzing the variation of elastic modulus in shale under different moisture contents, it can be generally concluded that the deformability of the rock demonstrates a reduction in elastic modulus with increasing moisture content.

Specifically, the influence of moisture content on the deformation parameters of the rock is most evident at inclination angles of θ = 30° and θ = 90°, where the elastic modulus of the shale sample decreases by 11.45% and 13.23%, respectively. At θ = 0°, the moisture content has a less pronounced effect, resulting in an 8.76% reduction in elastic modulus. These observations indicate the anisotropic impact of moisture content on the deformation characteristics of shale. At θ = 30° and θ = 90°, the bedding planes of shale are longer and subject to higher stress, making the rock more prone to shear displacement along these planes. With an increase in moisture content, the pores and fractures in the shale bedding structure may be filled with water, leading to a reduction in shale brittleness. Simultaneously, an increase in moisture content directly results in a decrease in shale strength. Therefore, under the coupling effect of bedding structure and moisture content, shale gradually tends toward isotropy, and the overall mechanical properties approach a minimum. In other words, the mechanical characteristics of shale at different bedding angles tend to saturate at the mechanical performance of shale with an inclination angle of 30° under saturated conditions.

Hence, in shale engineering design and resource extraction, the coupling effect of bedding and moisture content needs to be fully considered to accurately assess rock mechanical properties and formulate rational design and extraction plans. This ensures reducing risks and guaranteeing the long-term performance of shale-related projects [49].

3.4 Failure modes and mechanisms of shale

The results from the previous sections indicate that shale exhibits the highest compressive strength when the inclination angle θ = 90°, while a lower compressive strength is observed when θ approaches 30°. However, the corresponding peak stress–strain relationship remains relatively unchanged, suggesting a relationship with the anisotropic characteristics of shale. Figure 11 illustrates the typical failure patterns of shale with different inclination angles under various conditions.

Fig. 11
figure 11

Failure features of the specimens after triaxial compression tests

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During the compression loading of shale, once the axial stress reaches its peak strength, the sudden release of energy leads to the rapid formation of macroscopic cracks that traverse the entire specimen, resulting in the loss of its load-carrying capacity [12]. This results in tensile and shear fracture surfaces, exhibiting distinct characteristics of layered brittle rock failure and significant anisotropy. The specific failure modes of shale specimens under different conditions are compared as follows:

  1. (1)

    Comparison of failure modes of shale specimens with different inclination angles under uniaxial compression. When θ = 90°, the dominant failure mode of shale specimens is tensional splitting along the bedding planes. Multiple tension fractures, parallel to the bedding planes and traversing both ends of the specimen, are observed. During continued loading, the rock plate is subjected to compression and bending until partial buckling occurs, leading to fracture. When θ = 60°, shale specimens exhibit a uniform fracture surface along the 30° bedding planes, indicating significant shear displacement along the bedding planes [58]. For θ = 30°, shale specimens exhibit a single shear failure surface traversing the bedding planes. The rock samples fracture along multiple bedding planes, extending toward the center of the specimen, and eventually connecting through the 60° bedding plane. When θ = 0°, shale specimens display a tensile failure surface traversing the bedding planes. Under uniaxial loading, the vertical deformation of the rock sample is constrained, forcing the specimen to exhibit tensile failure along the bedding planes after accumulating considerable lateral tension. Additionally, due to the presence of horizontal bedding, the rock samples crack along the bedding planes, resulting in several fractured parts [39, 57]. Overall, the presence of weak bedding planes is the primary cause of the anisotropic behavior in the failure mechanism of shale under uniaxial compression.

  2. (2)

    Comparison of failure modes of shale specimens with different moisture contents under uniaxial compression. The failure patterns of shale specimens saturated with water through vacuum suction saturation are similar to those of dry specimens under uniaxial loading. However, by observing the failure images of saturated shale, it is evident that the failure is more complete after water saturation. Both tensile splitting and shear failure penetrate the layered structure of the rock. Furthermore, post-failure shale exhibits partial structural fragmentation due to softening. This indicates that the moisture content has a minimal influence on the failure mode of shale but exacerbates the deterioration of the overall structure of shale due to the presence of bedding planes. This may be attributed to the lubrication effect of water on rock particles, reducing the cohesion and adhesion of the rock and further weakening the stability of the bedding structure.

  3. (3)

    Comparison of failure modes of shale specimens under triaxial and uniaxial compression. Under confining pressure, the predominant failure mode of shale is shear failure, and at higher confining pressures, a single shear fracture surface is typically observed, indicating a significant reduction in brittleness [2]. In contrast with the various failure modes observed under uniaxial compression, shale exhibits two types of failure modes under confining pressure. The first mode is single shear plane failure, as shown in the last column of Fig. 11. Although the position of the shear plane varies with the inclination angle of 30°,60°, and 90°, there is always a primary shear surface that generally traverses both ends of the specimen, partially coinciding with the bedding plane. The second mode is conjugate shear failure. Shale specimens with an inclination angle of 0° exhibit multiple parallel shear failure surfaces that intersect and divide the rock sample into multiple blocks, ultimately forming conjugate shear fracture surfaces. Comparing the failure mechanisms under uniaxial and triaxial compression reveals that the influence of weak bedding planes on the failure mechanism significantly diminishes under confined pressure. Instead, the inclination angle of bedding planes and the effect of confining pressure have a greater impact on the failure mechanism, resulting in increased anisotropy as the confining pressure increases.

4 Constitutive model

4.1 Development of the constitutive model

In Sect. 3, we analyzed the mechanical properties and deformation characteristics of laminated shales under different moisture contents and confining pressures based on the stress–strain curve of shales. We introduced an elastic modulus model to fit and predict these patterns, which laid the foundation for a deeper understanding of the mechanical behavior of shales. This section aims to further derive the constitutive model for the stress–strain curve of shales. In developing the constitutive model, we will combine the previously proposed elastic modulus fitting formula and simplify the influence of shale anisotropy into variations of the elastic modulus. By introducing appropriate physical assumptions and deformation theories, we will establish a constitutive model capable of describing the mechanical behavior of laminated shales.

Simply analyzing the raw triaxial compression test data may be insufficient due to the challenges of obtaining complete stress–strain curves and the inherent heterogeneity of shale. Thus, many researchers [1, 26, 45] have proposed constitutive models based on the stress–strain relationship to describe the mechanical properties and behavior of shale samples under loading conditions. Due to the comprehensive consideration of shale anisotropy and water damage effects in the elastic modulus E, the rock material can be simplified as isotropic during the establishment of the damage constitutive model [56]. Based on the Lemaitre strain equivalence theory and the concept of effective stress, the equilibrium relationship between the maximum principal stress σ1 and the effective maximum principal stress σ1* under loading can be expressed as follows:

$$\sigma_1 = \sigma_1^* \left( {1 - D_m } \right)$$
(4)
$$\sigma_1^* = E\varepsilon_1^*$$
(5)

where Dm represents the damage variable induced by triaxial loading. From laboratory test results, it is known that rock materials in the post-peak stage of the stress–strain curve typically retain a certain bearing capacity, known as residual stress σr [7]. Therefore, to better capture the shale’s failure process, the residual stress is considered based on Eq. (4):

$$\sigma_1 = \sigma_1^* \left( {1 - D_m } \right) + \sigma_{\text{r}} D_m$$
(6)

Substituting Eq. (5) into Eq. (6), we obtain the stress–strain constitutive relationship for shale:

$$\sigma_1 = E\left( {1 - D_m } \right)\varepsilon_1^* + \sigma_r D_m$$
(7)

Assuming that the statistical distribution of rock microelement strength follows the Weibull distribution [60]:

$$P(F) = \frac{m}{F_0 }\left( {\frac{F}{F_0 }} \right)^{m - 1} \exp \left[ { - \left( {\frac{F}{F_0 }} \right)^m } \right]$$
(8)

where F represents the stochastic distribution variable of microelement strength, m and F0 are Weibull distribution parameters. Considering the rock as a series of defective microelements, the strength criterion of rock microelements can be unified as follows:

$$f\left( {\sigma^* } \right) - k = 0$$
(9)

where f(σ*) is the stress function, and k is the material parameter. As the stress state changes, when f f(σ*) > k, it indicates the yielding or failure of the rock microelement. Thus, the function f(σ*) can reflect the degree of microelement failure and serve as the distribution variable of stochastic distribution of microelement strength. The damage variable Dm induced by triaxial loading in rock is defined as the ratio of the number of failed microelements Nf to the total number of microelements N, combined with Eqs. (8) and (9), we have:

$$D_m = \frac{N_f }{N} = 1 - \exp \left[ { - \left( {\frac{f(\sigma^* )}{{F_0 }}} \right)^m } \right]$$
(10)

During the triaxial loading process, the deformation coordination relationship between the failed and unfailed parts of the rock microelement is that the effective strain is equal to the axial strain, i.e., ε*1 = ε1 [10]. Since rock damage mainly occurs in the axial direction and the confining pressure has a negligible effect on rock damage, we can assume σ2* = σ3* = σ3. Substituting Eq. (10) into Eq. (7), we finally obtain the damage constitutive relationship between stress and strain:

$$\sigma_1 = \left[ {E\varepsilon_1 - \sigma_r } \right]\exp \left[ { - \left( {\frac{f(\sigma^* )}{{F_0 }}} \right)^m } \right] + \sigma_r$$
(11)

where the values of m and F0 can be obtained by fitting experimental data using the peak point method. The Hoek–Brown strength criterion [10] considers the influence of low stress and tensile stress areas, as well as the effect of confining pressure on rock strength, better capturing the nonlinear characteristics of rock failure. The Hoek–Brown strength criterion in the form of effective stress invariants can be expressed as follows:

$$f\left( {\sigma^* } \right) = m_i \sigma_{ci} \frac{I_1^* }{3} + 4J_2^* \cos^2 \theta_\sigma + m_i \sigma_{ci} \sqrt {J_2^* } \left( {\cos \theta_\sigma + \frac{\sin \theta_\sigma }{{\sqrt {3} }}} \right)$$
(12)

where mi is a material constant reflecting the intact strength of the rock, which can be obtained by fitting experimental data; σci is the uniaxial compressive strength of the rock, MPa; I1* is the first invariant of effective stress, I1* = σ1* + σ2* + σ3*; J2* is the second invariant of effective stress, J2* = [(σ1*-σ2*)2 + (σ2*-σ3*)2 + (σ3*-σ1*)2]/6; and θσ is the Lode angle. In conventional triaxial compression tests, ε*2 = ε*3, θσ = 30°. Therefore, combining Eq. (5) and Eq. (12), equation can be simplified as follows:

$$f\left( {\sigma^* } \right) = m_i \sigma_{ci} E\varepsilon_1 + \left( {E\varepsilon_1 - \sigma_3 } \right)^2$$
(13)

4.2 Fitting of the stress–strain curve

The fitting curves obtained, as shown in Fig. 12, combined with the experimental data, allow for the analysis of the mechanical properties of shale under different conditions.

Fig. 12
figure 12

Stress–strain curves of bedding shales under different conditions: (a) different bedding angles; (b) different moisture content; and (c) different confining pressures

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By examining the overall trend of the curves for each group, it can be observed that the shale samples underwent elastic deformation, yielding, and residual stress stages during the loading process [25, 33]. With variations in inclination angle, moisture content, and confining pressure, the curves exhibit distinct regularities in each stage. Based on these observations, it becomes possible to further understand the effects of individual conditions on the strength and deformation characteristics of the shale specimens [6]. The subsequent sections will discuss the application of this model and provide insights into the stress–strain relationship and key mechanical characteristics of the Longmaxi shale obtained from its implementation.

5 Quantitative analysis of shale evaluation index based on energy evolution

5.1 Energy evolution during rock full stress–strain failure process

From the perspective of the dynamic energy evolution of rock, the process of rock failure involves continuously absorbing external energy until the stress reaches the peak strength, and then releasing energy continuously. In other words, the deformation and failure of the rock is essentially the result of energy dissipation and release. The complete stress–strain curve of the rock is actually the external manifestation of the internal energy state transformation. Throughout the process of elastic deformation, microcrack evolution, and ultimately failure, the rock material is always involved in energy exchange with the external environment. On the one hand, it stores the energy transmitted from the outside, and on the other hand, it releases energy to the outside world in various forms to maintain energy balance [23, 51]. Therefore, the energy evolution associated with each physical process during the loading of rocks is reflected in the stress–strain diagram (Fig. 12).

Under external forces, rocks initially undergo elastic deformation, which continuously increases. This indicates that elastic strain energy is the main state for storing and accumulating the input energy from the external environment and is the inherent driving force behind rock failure [15]. As shown in Fig. 13a, in the ideal state, rocks only store elastic strain energy during the elastic stage [50]. Thus, the areas of the three similar triangles formed by the yield point σs, peak point σp, and residual point σr, with the slope representing the elastic modulus E, respectively, represent the elastic strain energy dWe1 during the elastic stage, the total elastic strain energy dWe2 before failure, and the residual elastic strain energy dWe3 after failure.

Fig. 13
figure 13

Energy evolution during rock failure: (a) accumulation of elastic strain energy; the red dashed lines represent the values of L and M. (b) Different energy evolution process

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However, for rocks like shale that exhibits ductile failure characteristics, elastic strain energy is only a part of the driving force for failure. Shale has a laminated structure and is rich in small particles, and its failure mechanism involves complex plastic deformation. During the loading process, shale undergoes processes such as interlayer sliding, particle deformation, and microcrack propagation, which result in the storage and release of plastic strain energy in the rock. The stored plastic strain energy is released when the rock reaches its failure point, driving the continued development of failure [22]. According to the first law of thermodynamics, neglecting the heat exchange between rocks and the external environment, as well as the energy accumulation of confining pressure within the rock, the energy evolution during rock failure is illustrated in Fig. 13b. The area represented by the blue region indicates the energy dissipated dWd during the pre-peak stage, while the gray region represents the energy dWa input from the external environment to sustain further damage and failure during the post-peak stage. The area enclosed by the red border represents the energy consumed during the fracturing process, namely, the fracture energy dWf. Based on the energy conversion relationship during the post-peak stage, the following can be deduced:

$$dW_{\text{f}} = dW_{\text{a}} + (dW_{{\text{e2}}} - dW_{{\text{e3}}} )$$
(14)

Combining the analysis of the stress–strain curves of layered shale under different conditions in Sect. 2, the influences of bedding angle, moisture content, and confining pressure on the energy evolution process can be understood. As shown in Fig. 10, the anisotropy of shale bedding planes does not significantly affect the overall trend of the stress–strain curve. Hence, the variation of shale anisotropy is consistent with the total elastic strain energy dWe2 before failure, exhibiting a "U-shaped" trend with increasing bedding angle.

The increase in moisture content primarily affects the curves of shale stress–strain in terms of slowing down and prolonging the elastic stage, plastic yielding stage, and post-peak failure stage. This corresponds to a decrease in the proportions of dWe1, dWe2, and dWe3, and an increase in the proportions of dWd and dWa during the energy evolution process, indicating a weakening in rock strength and brittleness.

The presence of confining pressure mainly affects the linearity of the curves, as seen in the decrease in slope during the pre-peak stage, dramatic increase in strength, prolonged post-peak stage, and increased residual stress. This corresponds to an overall increase in energy input from the external environment, with noticeable increases in the proportions of dissipative energies such as dWd. This suggests an overall increase in rock strength, reduced brittleness, and enhanced plasticity.

Based on the above analysis, it is evident that factors such as bedding angle, moisture content, and confining pressure influence various stages of energy evolution in shale. Therefore, the mechanical performance of shale under the influence of environmental factors can be described by the energy evolution process. However, it is important to consider the combined effects of these factors on the input, accumulation, dissipation, and release of energy during the process.

Understanding the energy evolution process provides valuable insights into the mechanical behavior and response of shale under different conditions. It aids in the assessment and prediction of shale's stability, deformation characteristics, and failure modes. Such an analysis helps in formulating effective engineering strategies and mitigating potential risks in various applications involving shale formations.

5.2 Energy-based evaluation index and analysis for shale condition assessment

The analysis of rock mechanics is typically employed in practical engineering to provide theoretical guidance for on-site safety and production efficiency. In the case of shale as an oil and gas reservoir, the stability of the wellbore and the formation of artificial fractures are key applications of shale characteristic analysis [53]. Therefore, based on the analysis of mechanical results from laboratory experiments and considering the energy evolution during rock failure, the influences of shale bedding, moisture content, and confining pressure are integrated to derive mechanical indices that can be applied in engineering practice and validate their rationality [43].

On-site assessments of wellbore stability often rely on the ultimate compressive strength or yield strength of the rock as the criteria. However, as analyzed in Sect. 3, the impact of external factors on shale performance is multifaceted. Relying solely on strength parameters may not accurately reflect the stability characteristics of shale. Combining the analysis in Fig. 13, when the peak strength σp and elastic modulus E of the rock are constant, a higher yield strength σs indicates a better compressive capacity, implying that a higher elastic strain energy storage dWe1 corresponds to greater stability of the rock, given a constant total energy received before failure (dWe2 + dWd).

Furthermore, in practical engineering, it is crucial to consider the prevention of unforeseen circumstances where the wellbore is subject to abrupt increases in external forces, resulting in rock failure. Even during the energy release process, it is necessary to ensure the safety and stability of the wellbore. For instance, when the unloading elastic energy required during the rock failure process (dWe2-dWe3) is constant, a larger external energy input dWa indicates that the rock requires more time for complete failure. This additional time can be devoted to implementing emergency response measures.

Therefore, an index, denoted as SIr, is obtained to characterize the stability of shale:

$$SI_{\text{r}} = \left( {\frac{{dW_{{\text{e1}}} }}{{dW_{{\text{e2}}} + dW_{\text{d}} }} + k\frac{{dW_{\text{a}} }}{{dW_{{\text{e2}}} - dW_{{\text{e3}}} }}} \right) \cdot \sigma_{\text{p}}$$
(15)

where SIr represents the index for characterizing the stability of shale, and k = L/M, L represents the stiffness of the loading system in compression experiments, while M represents the post-peak modulus [37]. The specific meaning is represented by the dashed line in Fig. 13.

Regarding the formation of artificial fractures, it is primarily controlled by the brittle characteristics of the rock. Research conducted by Chen et al. has shown that even when the rock has the same elastic modulus E, peak strength σp, and yield strength σs, the extent of energy dissipation during the plastic yielding stage and the fracture energy required during the post-peak stage may vary. This can result in different plastic yielding characteristics and brittleness of the rock under the influence of environmental factors such as bedding and moisture content. Thus, the energy dissipated during the pre-peak stage (dWd), and the fracture energy consumed during the post-peak fracture process (dWf) can be used to describe the brittleness characteristics of the rock when considering the effects of the environment, bedding, and moisture content.

When the elastic strain energy accumulated during the yielding stage (dWe2 + dWe1) remains constant, a smaller change in the plastic yielding stage corresponds to a smaller energy dissipated during the pre-peak stage (dWd), indicating a higher brittleness of the shale. Similarly, when the unloading elastic energy during the post-peak stage (dWe2-dWe3) remains constant, a smaller fracture energy required for post-peak rock fracture expansion (dWf) signifies a higher brittleness of the shale. This brittleness suggests that the rock is more likely to generate stable artificial fractures [13], leading to higher production capacity in the field.

Based on the above considerations, a brittleness index for shale fracturing, denoted as BIr, can be summarized:

$$BI_{\text{r}} = \frac{{dW_{\text{d}} \cdot dW_{\text{f}} }}{{\left( {dW_{{\text{e2}}} + dW_{{\text{e1}}} } \right)\left( {dW_{{\text{e2}}} - dW_{{\text{e3}}} } \right)}}$$
(16)

Based on the analysis above, it is evident that the stronger the stability of the shale, the larger the stability index SIr, which indicates a safer wellbore. Similarly, a stronger brittleness of the shale results in a BIr closer to 0, whereas a stronger plasticity leads to a larger BIr. In this study, the stability and brittleness of the layered shale specimens were evaluated using the aforementioned indices. Considering that the fitted stress–strain curve can more comprehensively describe the complete loading and failure process of shale, the energy values (dWi) can be obtained by integrating the fitted stress–strain curve using MATLAB software. Due to limitations in space, only partial results are presented in Table 2.

Table 2 Partial results of stability and brittleness evaluation for layered shale specimens
Full size table

Analyzing Table 2 reveals that the evaluation patterns of the two indices align with the engineering conditions and mechanical characteristics of the shale. The stability index SIr shows a slight variation in relation to its strength characteristics. It exhibits lower values for inclination angles (θ) in the range of 30° and 45° and higher values for θ in the range of 75° and 90°. The influence of moisture content and confining pressure on stability is similar to the mechanical properties of shale. Increasing moisture content reduces stability, while higher confining pressure enhances stability. Therefore, during shale drilling operations, it is advisable to avoid inclination angles in the range of 30° and 45°, use oil-based drilling fluids, and prevent prolonged exposure and erosion of the wellbore by aqueous solutions. Special attention should be given to the stability of the shale wellbore at the borehole entrance [48].

The evaluation patterns presented in Table 2 align with the characteristics and engineering conditions of shale. These findings have practical implications for shale drilling and can guide decision-making in designing safe and efficient drilling operations. However, a comprehensive analysis using complete datasets and further considerations may be required to optimize drilling strategies and ensure wellbore stability in specific geological contexts.

The brittleness index (BIr) of shale exhibits the following variations with respect to bedding angle, moisture content, and confining pressure:

  1. (1)

    As the inclination angle increases, the change in brittleness index is not significant in the range of 0° and 30°, indicating that variations in bedding angle have a minimal impact on shale brittleness within this range. However, for angles between 30° and 90°, the brittleness index shows a distinct inverted "U-shaped" trend, with an initial increase followed by a decrease. At an inclination angle (θ) of 60°, the brittleness index reaches its maximum value, indicating that shale exhibits its weakest brittleness and may even display plastic behavior at this angle. While the brittleness index decreases noticeably at θ = 90°, it remains higher than that at θ = 0°, suggesting that shale is less brittle when loaded to parallel bedding compared to perpendicular loading.

  2. (2)

    The brittleness of shale is significantly influenced by moisture content. With an increasing moisture content, the brittleness index gradually increases, indicating a decreasing brittleness of the shale. This suggests that higher moisture content in practical engineering is unfavorable for the formation of artificial fractures in shale. Therefore, when necessary, mineral oil can be used as a dispersing medium in fracturing fluids to ensure stable development of artificial fractures.

  3. (3)

    The brittleness index of shale increases notably with increasing confining pressure, indicating a strong correlation between shale brittleness and confining pressure. In deeper shale development operations, more energy within the shale is consumed by plastic deformation, impairing the formation of fracture networks. This also leads to easier closure of fractures and higher demands for proppants, which directly impact the productivity and efficiency of underground resource extraction.

The analysis demonstrates that the brittleness index is highly sensitive to the bedding angle, moisture content, and confining pressure in shale. These findings have implications for optimizing hydraulic fracturing operations, assessing reservoir productivity, and enhancing the efficiency of resource extraction in shale formations.

6 Conclusions

In this study, triaxial compression tests were conducted on layered shale specimens under different moisture content conditions to analyze the effects of bedding angle, moisture content, confining pressure, and their coupling on shale mechanical properties. Based on the theory of energy evolution, an assessment index combining field conditions was proposed. The following conclusions were drawn:

  1. (1)

    The bedding angle, moisture content, and confining pressure all have significant effects on the mechanical properties of shale. As the bedding angle increases, shale exhibits distinct anisotropic mechanical characteristics and deformation features. The increase in moisture content weakens the mechanical properties of shale, and the coupling effect of orientation and moisture content further diminishes shale's anisotropic behavior. Confining pressure has a certain limiting effect on the anisotropy of shale strength, but due to the restricted lateral deformation, the anisotropy of shale's elastic modulus actually increases with increasing confining pressure. Additionally, the failure modes of shale also demonstrate explicit anisotropy. Under uniaxial loading, shale can fail in four ways: tensile splitting along the bedding planes, shear failure along the bedding planes, shear failure across the bedding planes, and various compound failures. Under triaxial compression conditions, the predominant failure types of shale are shear failure across the bedding planes and shear failure along the bedding planes. Moreover, the increase in moisture content leads to the failure of shale bedding planes, consequently significantly reducing the stability of shale wellbore due to the coupling effect of anisotropy and hydration.

  2. (2)

    Based on the energy evolution process during shale failure under the influence of multiple factors (bedding angle, moisture content, and confining pressure), stability and brittleness indices were established. The evaluation results indicate that, during drilling, maintaining a drilling angle parallel to the bedding plane (θ = 90°), using oil-based drilling fluids, and avoiding prolonged exposure and erosion of the wellbore by aqueous solutions, can effectively ensure shale wellbore stability and production safety. In hydraulic fracturing, selecting a fracturing direction parallel to the shale fracture angle (θ = 30°), using mineral oil as a dispersing medium in fracturing fluids, and choosing shallow depth formations facilitate the expansion of shale fracture networks and improve production efficiency.