Characterization of the Fine-Scale Evolution of Damage in Shale under the Influence of Two-Way Stress Differences Based on CT Images and Fractal Theory—The Example of the Anba Dyke in the Wufeng–Longmaxi Formation

Abstract

To better understand the influence of different levels of two-way stress differences on the development of damage in Anchang diametral laminar shale in the northern Qianbei area, a numerical model of laminar shale with a representative fine-scale structure was established by using RFPA3D-CT. A triaxial compression test was conducted; a three-dimensional mesoscale fracture box dimension algorithm based on digital images was generated by using MATLAB R2020b; and the fractal characteristics were quantitatively analyzed. The results showed that under the influence of the horizontal stress ratio and two-way stress, the greater the two-way stress is, the more notable the plastic characteristics of specimen damage are, and the higher the residual strength is. The specimens with lower two-way stress exhibited obvious brittle damage characteristics. The difficulty degree of complex fracture network formation increased with the increase in the horizontal tension ratio, and the degree of increase in the fracture network complexity gradually decreased. At a horizontal stress ratio of 1.25, the fractal dimension was the highest, which indicates that the cracks were the most pronounced. Fracture formation after specimen damage was the most common phenomenon. Under the condition of a lower horizontal stress ratio, a large number of fracture structures could be generated in shale specimens after damage, promoting the expansion of natural fractures.

1. Introduction

As the Chinese economy continues to develop at a rapid pace, the supply and demand for oil and natural gas resources are notably increasing [1,2,3,4,5]; thus, there is a pressing need to strengthen national endeavors in oil and gas exploration and development. Shale gas, classified as an unconventional energy source [6,7,8], exhibits tremendous potential as a feasible substitute for traditional oil and gas resources. As a result, it has attracted considerable interest from scholars both domestically and internationally [9,10,11,12]. China possesses abundant supplies of shale gas, and many other nations have intensified their research on and use of shale gas in recent years [13,14,15]. China’s recoverable shale gas volume ranges from about 11.5 × 10¹² to 36.1 × 10¹² m³ and is among the largest worldwide [16].

Zou [17] et al. noted that hydraulic fractures can intersect natural fractures at high levels of differential stress. Rickman et al. [18] postulated that the presence of a substantial clay mineral content impedes the development of intricate fracture networks, which are more prone to forming in brittle shale characterized by a high mineral content. Olsen et al. [19] demonstrated that shale formations exhibiting low Poisson’s ratios and extremely low permeability are more prone to undergoing complex fracturing. Hou et al. [20] and collaborators further revealed, via comprehensive laboratory experiments, that rocks enriched with a substantial quantity of brittle minerals demonstrate an increased predisposition to the formation of intricate fracture networks in comparison to other rock types. This rock type not only contains discontinuous surfaces that can be activated and connected into a complex fracture network but also provides the large fracture lengths required for notable reservoir transformations [21,22].

However, most of the above studies have focused on shale samples, as well as shale outcrops containing a small number of discontinuities, which do not suitably represent actual layered shale reservoirs. The extension geometry of shallow shale fractures, rather than that of deep shale horizons, has been investigated in several shale outcrop experiments; the latter structures are widely found in the northern part of the Qianbei region. Deep shale horizons are located above 3500 m, and they exhibit different geomechanical properties from shallow shale horizons. These rocks have higher horizontal stress and temperatures above 110 °C [23], and in such deep shale horizons, the confluence of elevated fracture pressure, high density, and diminished brittleness culminates in restricted fracture width, constrained fracture propagation, sand accumulation, and diminished flow conductivity, thus challenging reservoir modification, making it difficult to implement fracturing treatments, and potentially leading to a decrease in shale gas production. To date, there has been a dearth of research investigating approaches to estimating and regulating fracture extension and reservoir remodeling volume in deep formations with elevated stress concentration levels. Therefore, delving into the mechanisms governing fracture extension in deep shale formations is imperative for the precise estimation of and enhancement in reservoir transformation volume. Numerical simulation helps to identify crack extension paths. However, current two-dimensional numerical simulation methods are flawed and inaccurate in assessing reservoir volume modification. Through the simplification of the complex network of fractures within a three-dimensional domain to multiple fractures projected onto a two-dimensional horizontal plane, these methodologies concentrate exclusively on fracture extension at a designated elevation, neglecting the interplay between fractures and structural discontinuities [24].

Presently, a deficiency persists in the utilization of three-dimensional (3D) numerical models incorporating CT scanning within extant simulation investigations aimed at scrutinizing the intricate internal composition of laminated shale formations. Consequently, this investigation employs cutting-edge CT scanning, advanced imaging technology, and the state-of-the-art RFPA3D-CT finite element computation method, thereby facilitating the construction of a sophisticated three-dimensional numerical model to aptly capture the intricacies of weak lamination surfaces. As a result, a comprehensive and accurate 3D numerical model specifically tailored to laminated shale formations in the Zheng’an region is successfully formulated. In order to examine the damage evolution, damage morphology, and mechanical characteristics of laminated shale specimens sourced from the Zheng’an region, a rigorous true triaxial compression test was executed. The primary aim of this experiment was to evaluate the influence of biaxial stress differentials on the mechanical attributes, damage morphology, and fracture intricacies of shale formations.

The utilization of the fractal dimension, serving as an index of fracture network effects, permits the identification of optimal fracturing conditions for the adjustment of fracture networks within hydraulic fracturing operations in shale oil reservoirs. This investigation has the potential to provide a theoretical framework for hydraulic fracturing endeavors within deep, high-stress shale formations manifesting diverse disparities.

2. Geological and Tectonic Background of the Study Area

The Anchang syncline is located in the Wuling depression between the southeastern edge of the Middle and Upper Yangzi Massifs and the Xuefeng Mountain basement detachment orogenic belt (Figure 1), which is the western side of the Sichuan eastern compartmentalized trough fold belt. Tectonically, it is located north of Guizhou Province and is part of the northeastern tectonic deformation area of the Yangzi quasi-platform, Qianbei Plateau, convex Zunyi fault, and Fenggang north-northeast tectonic deformation zone. The northern region of Guizhou Province exhibits notable structural features characterized by prominently developed synclines and fault structures. These folds predominantly exhibit a consistent northeastern to north-northeastern orientation, and they are mainly divided trough folds, with narrow and tightly closed, steeply dipping troughs and banded distributions on the surface. The backslopes are wide and gradually sloping in the form of a box and often exhibit the characteristics of compound structures, while internal extrusion tectonics, such as lenticular bodies, rubbing folds, compressive faults, and slip tectonics, are very well developed. The fold axis is generally an NNE–NE arc-like curve. Fractures in the fold belt are extremely common, with the main strike occurring in the NE–NNE direction, mostly in the core and wings of the dorsal slope, and the fractures are mostly retrograde in nature, with a small number of positive fractures also present. The Anchang dorsal slope is located in the weak–medium deformation zone in northern Yunnan–Guizhou, which is a negative tectonic unit formed against the geotectonic background of the Early Paleozoic era, whereas the positive tectonic attributes of the southern neighboring East Yunnan–Guizhou–China uplift are exactly the opposite, but the formation and development processes of these two structures are complementary and closely related. Deformational tectonics in the deformation area were mainly formed during the Yanshan main fold orogeny in the Early Cretaceous period, and the typical tectonic type is the syncline fold-and-rupture combination with folds, which is a straight torsion tectonic type.

3. Introduction to RFPA3D

Rockfall Process Analysis in Three Dimensions (RFPA3D), an extension of Rockfall Process Analysis in Two Dimensions (RFPA2D) [25,26], is a simulation tool tailored for modeling fracture and damage phenomena in quasi-brittle materials such as rock. RFPA3D adopts the finite element method (FEM) incorporating eight-node isoparametric elements for stress analysis, enabling the depiction of the nonhomogeneous nature of rock materials and intricate characterization of rock mechanical parameter distributions. Furthermore, RFPA3D employs an elastic–brittle intrinsic model to accurately portray the nonlinear damage-phase behavior exhibited by rock.

Equation (1) in RFPA3D is frequently employed to quantitatively assess the maximum tensile strain threshold, which serves as a criterion for identifying the initiation of fracture generation and the occurrence of tensile failure. Furthermore, Equation (2) is employed as the secondary damage threshold, supplying valuable information regarding the occurrence of shear mode damage in a given element [27,28].

$${\epsilon }_3\le \frac{{\sigma }_{t0}}{E}$$

(1)

$$F={\sigma }_1-{\epsilon }_3\frac{1+\sin \phi }{1-\sin \phi }\ge {\sigma }_{c0}$$

(2)

An elastic–brittle damage constitutive model is used to describe the stress–strain relationship and consider its residual strength. Each unit is considered elastic, and before reaching the damage threshold, the stress–strain curve of each unit is considered linear elastic. The determination of damage thresholds in RFPA3D relies on the utilization of both the maximum compressive stress (or strain) criterion and the Mohr–Coulomb criterion. Upon reaching the prescribed strength criterion, the onset of damage accumulation ensues within the element, ultimately resulting in the stepwise degradation of the element’s elastic modulus as the damage process advances. The constitutive relationship of damaged components can be expressed as follows:

$$\sigma =E\epsilon =E_0\left(1-D\right)\epsilon$$

(3)

where E is the modulus of elasticity of the unit after damage has occurred, E₀ is the initial modulus of elasticity of the unit, and D is the damage parameter. With D = 0, the unit exhibits no damage; with D = 1, the unit exhibits a complete damage state; and with 0 < D < 1, the unit exhibits damage. Notably, according to Equation (3), the modulus of elasticity is E = 0 if damage parameter D = 1, which does not correspond to the actual damage to the rock specimen. For this reason, a relatively small E value of 1.0 × 10⁻⁵ is specified in the tests, where E, E₀, and D are scalar quantities, because RFPA3D assumes that the unit and damage are isotropic.

Figure 2 elucidates the ontological interconnection between the maximum compressive stress (or strain) criterion and microscopic cells during the triaxial compression process, and the corresponding damage variables are given as follows [29,30,31]:

$$D=\{\begin{array}{cc}0& \epsilon >{\epsilon }_{t0}\\ 1-\frac{{\sigma }_{tr}}{\epsilon E_0}& {\epsilon }_{t0}\ge \epsilon \ge {\epsilon }_{tu}\\ 1& \epsilon <{\epsilon }_{tu}\end{array}$$

(4)

In Equation (4), σ_tr is the residual compressive strength of the unit; σ_t0 is the ultimate compressive strength of the unit; σ_rt = λσ_t0; λ is the residual compressive strength coefficient, and 0 < λ < 1. Moreover, ε_t0 is the compressive strain of the unit at the elastic limit, which is the strain threshold for compression damage, and ε_tu is the ultimate compressive strain of the unit when it is completely destroyed. Finally, ε_tu = ηε_t0, where η is the ultimate compressive strain coefficient.

In multiaxial stress scenarios, the influence of the supplementary principal stresses on the maximum or minimum principal strain is duly considered. As the compressive strain surpasses the specified damage strain threshold (ε_t0), the substitution of the equivalent strain for the compressive strain (ε) in Equation (4) becomes appropriate. The equivalent strain can be expressed as follows:

$$\overline{\epsilon }=-\sqrt{{\langle {\epsilon }_1\rangle }^2+{\langle {\epsilon }_2\rangle }^2+{\langle {\epsilon }_3\rangle }^2}$$

(5)

where ε₁, ε₂, and ε₃ are the principal strains along the three directions. The angle brackets are functions defined as follows:

$$\langle {\epsilon }_i\rangle =\{\begin{array}{cc}{\epsilon }_i& ({\epsilon }_i\le 0,i=1,2,3)\\ 0& ({\epsilon }_i>0,i=1,2,3)\end{array}$$

(6)

The stress–strain relationship derived in terms of elastic damage theory can be expressed as follows:

$${\sigma }_{ij}=\{\begin{array}{cc}2G{\epsilon }_{ij}+\lambda {\delta }_{ij}{\epsilon }_{kk}& \overline{\epsilon }>{\epsilon }_{t0}\\ \frac{{\sigma }_{rt}}{\overline{\epsilon }{E}_0}\left(2G{\epsilon }_{ij}+\lambda {\delta }_{ij}{\epsilon }_{kk}\right)=\frac{{\sigma }_{rt}}{\overline{\epsilon }}\left(\frac{{\epsilon }_{ij}}{1+\upsilon }+\frac{{\delta }_{ij}{\epsilon }_{kk}}{\left(1+\upsilon \right)\left(1-2\upsilon \right)}\right)& {\epsilon }_{t0}\ge \overline{\epsilon }\ge {\epsilon }_{tu}\\ 0& \overline{\epsilon }<{\epsilon }_{tu}\end{array}$$

(7)

where G is the shear modulus of the material, with $G=\frac{E_0}{2(1+v)}$; η is the Poisson’s ratio of the material; λ is the residual coefficient, with $\lambda =\frac{E_{0}v}{(1+v)(1-2v)}$; and when i = j, σ_ij = 1. Otherwise, σ_ij = 0.

4. CT Scanning Experiments and Numerical Image Characterization

4.1. CT Scanning Process

The shale specimens are transformed into digital images utilizing CT scanning and digital image processing techniques. Grayscale and color data are used to differentiate the geometric and spatial distributions of mesoscopic components. Through the application of a predefined threshold to partition each medium, an image is generated, portraying the heterogeneous nature of the material distribution [32]. As shown in Figure 3a, the scanning test apparatus used was an X-ray 3D microscope-equipped nanoVoxel-4000 system. The primary mechanism of CT scanning is the interaction of radiation with matter. An item scatters a high percentage of input photons as a ray travels through it. This attenuates the intensity of the ray, which is then translated by imaging tools into a CT image (Figure 3b). To obtain the scanned slice shown in Figure 3d, the specimen was scanned every 0.1 mm from top to bottom (Figure 3c). The image has a resolution of 1000 × 1000 pixels and measures 100 mm × 100 mm. Different rock types are represented by various shades of gray. The high-density rock areas, mostly comprising quartz, appear lighter. In contrast, the low-density areas, mainly consisting of laminar structures, appear black. The shale matrix, which has a density between the two, appears gray. The image in Figure 3d was imported into ImageJ2 software for the purpose of segmentation, facilitating the measurement of grayscale values associated with individual pixels along a designated cut line. This segmentation allowed for the creation of a two-dimensional bar distribution of grayscale values, as shown in Figure 3e. The thresholds for binarization were determined as 85 and 100.

The digital representation in Figure 3f illustrates the nonuniformity of the fine-scale structure of the shale specimen after image processing. The experiment employs high-resolution CT scan images to improve the detection of color features occurring at the intersections of multiple material types. This enables more accurate material zoning and parameter assignment in the digital image characterization process.

4.2. Numerical Modeling

The images were numbered sequentially and converted into model data. The data were then stacked along the z-axis and imported into RFPA3D to reconstruct a 3D structural model. A cubic volume unit was used to measure finite quantities. To characterize the different fine-grained materials in the shale specimen, the image was converted into multiple finite element cubes. Given the nonuniformity of the material, it is proposed that the mechanical properties of the fine-grained cells follow the Weibull distribution, expressed as Equation (8) [27].

$$f\left(x\right)=\frac{m}{\beta }\cdot {\left(\frac{x}{\beta }\right)}^{m-1}\cdot e^{-{\left(\frac{x}{\beta }\right)}^m},x\ge 0$$

(8)

where the variable x denotes the mechanical property parameter associated with the fine-scale rock unit, encompassing characteristics such as modulus of elasticity, strength, Poisson’s ratio, and others. The parameter β represents the average value of each mechanical property parameter for the fine-scale unit, while the coefficient m quantifies the material’s homogeneity, reflecting its degree of uniformity.

The Monte Carlo method was utilized to assign values to the material components based on color and to input the corresponding nonuniformity coefficients according to the mechanical parameters listed in

Table 1. Material parameters of rock samples [33,34].

Material	Elastic Modulus/GPa	Compressive Strength/MPa	Poisson’s Ratio	Compression-Tension Ratio	Internal Friction Angle/(°)
Black shale	51.6	145	0.22	14	35
Bedding	30.9	116	0.31	13	30
Quartz	96.0	375	0.08	15	60

. Figure 3b shows the numerical model that incorporates the actual fine-scale structure of the material. To ensure consistency, each sample was processed through digital image processing to maintain the same scale. The specimens used in the simulation were 100 mm × 100 mm × 100 mm in size, and a total of five specimens were numerically simulated. Considering the disparity between the tensile strength and compressive strength of brittle materials, RFPA3D-Basic software incorporates a tailored Mohr–Coulomb criterion as the unit damage strength criterion. The loading process involves gradually applying the load up to the predetermined perimeter pressure value, followed by the application of axial displacement once the system perimeter pressure has stabilized. The initial displacement was set to 0.001 mm, with subsequent increments of 0.0005 mm per step. Loading continued until the specimen reached a damaged state, as shown in Figure 4.

The analysis of stress distribution in the Zheng’an shale gas reservoirs of the Anchang slant region, aimed at real shale gas extraction, entailed the investigation of five distinct regional well groups. In order to guarantee precise simulation, five sets of two-dimensional stress loading values were defined, and the corresponding experimental parameters are reported in

Table 2. Surrounding pressure settings.

Material	Group 1	Group 2	Group 3	Group 4	Group 5
Maximum horizontal stress (MPa)	45.84	64.96	71.39	80.84	54.66
Minimum horizontal stress (MPa)	36.82	47.95	55.82	63.08	41.07

.

5. Experimental Results and Discussion

5.1. Mechanical Characterization

In the course of triaxial compaction, the stress–strain curves of shale samples manifested three distinct phases, as illustrated in Figure 5: During the elastic stage, the stress–strain relationship demonstrates linearity with a consistent slope, alongside the gradual advancement of microscopic ruptures. In the nonlinear deformation stage, the slope of the curve decreases as the loading level exceeds approximately 70–80% of the peak strength, indicating that the stress continues to cause specimen damage and decrease the force. The elastic potential energy stored is released, resulting in irreversible deformation, which in turn causes the compaction of some cracks. The stress in the shale specimens of Groups 1, 2, and 5 sharply decreases after the peak phase; the internal microscopic cracks expand through the specimens and form macroscopic main cracks; and the specimens are destabilized and damaged. Similarly, as the post-peak curves decrease almost perpendicularly, irreversible plastic distortion occurs, and the load carrying capacity gradually decreases to 0. The specimens of Groups 3 and 4 still provide a certain load-bearing capacity after failure. Cracks do not penetrate all the way through the specimens at peak stress. When the loading process is continued, new cracks are formed and continue to branch out; the time when the main fracture emerges and when the specimen emits the loudest sounds, therefore, lags behind the ultimate load.

5.2. Analysis of the Rupture Process

The damage to the cells during specimen loading is shown in Figure 6a, where the red color indicates the damaged cells. The isotropic stress slightly affects the specimen, and little major damage occurs during the elastic phase. In nonlinear deformation, fine-scale damage begins to occur at two sites, one corresponding to particle cementation of the laminated surface and one corresponding to the shale matrix, and the number of units associated with internal damage continues to increase. Surface cracks are developed in some of the damaged elements.

In Figure 6d, individual circles symbolize acoustic emission events, with the circle’s diameter correlating with the magnitude of the emitted acoustic emission energy. Each circle’s center demarcates the position of the damaged unit, distinguishing tensile damage in blue and shear damage in red. During the elastic phase, localized tensile stress concentrations arise at the ends of the joints, accompanied by an evenly distributed pressure load across the laminae, which is manifested as scattered micropoint fractures. This indicates that the laminae are fragile and can be easily damaged. As loading proceeds, the energy gradually accumulates, and when the accumulated energy reaches a certain extent, a plethora of sizable red acoustic emission circles are identified within the specimen, indicating the presence of compressive damage within the macroscopic crack. The fracture zone within the high-stress region notably plays a substantial role in the energy release process during specimen fracturing, as illustrated in Figure 6b, and the dominant damage type near the interface between the sample and platen is shear damage. Compressive damage of the fine-grained shale unit leads to the initiation and expansion of fine-grained holes and cracks because the laminar part of the shale specimen cannot withstand high compressive stresses, and the compressive stresses first reach the compressive strength.

In the post-peak phase, the lamellae exhibit the formation of extensive and relatively shallow damage zones, accompanied by interconnected damage among particles. As the number of fine-scale damage points through the joints surpasses a predetermined threshold, the macroscopic damage becomes irreversibly established. The laminae represent the most vulnerable locations, with the most severe damage to the members at the junctions and cracks at the joints. The sequence of damage development in the specimen progresses from the inside to the outside and finally to the surface of the sample.

Under high peripheral pressure, a number of crack zones is generated due to shear damage, and the crack zones extend beyond the region of localized deformation in the direction of the applied load, as depicted in Figure 6c. Under controlled tensile stress, tilted monoplane tensile cracks begin to appear inside the specimen along the nodal direction and extend along the weak surface, and elongation occurs approximately parallel to the maximum principal stress.

6. Fractal Characterization of Shale Fracture Structures

6.1. Calculation of the Fractal Dimension of a Three-Dimensional Fracture Structure

The fractal dimension provides a quantitative measure to assess the intricacy and structural characteristics of shale fractures [35,36]. Different research objects exhibit fractal characteristics within different scale ranges, so different methods can be used to calculate the fractal dimension in a targeted manner [37]. Lopes and Betrouni classified these methods into three categories, one of which includes the box dimension method [38,39]. Because the algorithm for determining the box dimension value is simple, is more suitable for analyzing digital images, and has a clearer physical interpretation, it is commonly utilized in the analysis of crack morphology [40,41,42].

In the model constructed in RPFA3D, since the shale specimen comprises multiple cubic units of the same size, each pixel has a corresponding grayscale value [43,44]. In space, cubes of size m×n×h pixel points are divided (as shown in Figure 7). Therefore, a cubic box can be selected to cover the crack model in three dimensions. The bisection method is chosen to determine the side lengths of the small cubes.

$$\begin{array}{c}{\delta }_k=\frac{1}{C^{k-1}}\left|0<k\le \frac{\ln \min (m,n,h)}{\ln \mathrm{c}}\right|+1\\ \mathrm{k}=0,1,2,3\dots \end{array}$$

(9)

In RPFA3D, the fracture distribution map of each slice can be generated and exported. The spatial arrangement of cracks in the image was analyzed using the principles of 3D reconstruction to assess their shapes. In Figure 8, the cracks in the postprocessed slices obtained with RFPA3D are generated via a custom procedure to determine the coordinates of the pixels with cracks.

The size of the cube directly impacts the number of small cubes (N_k) required to encompass the crack space. Following image preprocessing procedures, a binary representation of the crack image is produced. The total number of cubes necessary to fully cover the entire crack space is calculated by multiplying it by the constant C. For any value of c, a series of data (1/c^k−1, N_k) can be obtained. In the double logarithmic coordinate system, the straight line represented by (1/c^k−1, N_k) reflects the fractal characteristics. In the model constructed by RPFA3D, since the shale specimen comprises multiple cubic units of the same size, a cubic box is selected to cover the three-dimensional fracture model.

$$\begin{array}{l}\lg c^{k-1}=\lg (k)\\ \end{array}$$

(10)

$$D=-\underset{r\to 0}{\lim }\frac{\lg N(k)}{\lg (k)}$$

(11)

6.2. Effect of the Horizontal Stress Ratio

According to the definition of the cube coverage method, an increase in the complexity of cracks in shale specimens leads to a higher fractal dimension [45,46]. From the fracture network morphology and the fractal dimensions of the shale specimens under each horizontal stress difference condition (Figure 9), the fractal dimensions of the fractal networks based on the cube coverage method range from about 2.339 to 2.517. By analyzing the fractal dimensions of the damaged fracture networks under varying horizontal stresses, it can be determined that within the same specimen, there is significant variation in the fractal size of the cracks after failure under the different horizontal stress levels. For horizontal stress ratios below 1.282, an incremental growth in the horizontal stress ratio is associated with a gradual reduction in the rate of change in the fractal dimension. Within the range of 1.278 to 1.331 for the horizontal stress ratio, a notable decline in the rate of change in the fractal dimension is observed. This observation implies that elevating the horizontal stress ratio within this interval hinders the evolution of a sophisticated fracture network, leading to a gradual decline in the intricacy of the fracture network. At a horizontal stress ratio of 1.25, the fractal dimension is the highest, and most cracks are formed after the specimens are damaged. At lower horizontal stress ratios, a large number of fracture structures are formed after shale sample damage, and further expansion of natural fractures is promoted.

Compared with the results for a horizontal tension of 1.25, the fractal dimension for a horizontal tension of 1.282 is lower, and relatively few cracks are formed after specimen damage. However, there are cracks along the direction of the laminar surface, which is favorable for achieving connectivity with natural fractures and promotes the formation of a single crack (Figure 10). At a high horizontal stress ratio, no single crack produces fine crack branches, except for the main crack, and the fractures do not extend along the laminar surface. Thus, with the increase in the horizontal stress ratio, the fractal dimension of the crack decreases. At tension levels of 1.331 and 1.355 in the horizontal direction, the manipulation of crack orientation poses a notable challenge. At this time, it is more difficult for the cracks to become connected and for them to communicate with more natural cracks and to induce the expansion of the natural cracks. Moreover, the final reconstructed crack network showed that the main fractures perpendicular to the minimal horizontal main tension are more likely to be formed at this time. In other words, when the horizontal tension is relatively low, shale damage is more prone to forming a complex network of fractures, while an excessive horizontal stress ratio promotes the creation of a single giant crack after damage, which is unfavorable for the development of a complex fracture network.

7. Conclusions

Through shale true triaxial compression simulation experiments, fractal theory and 3D CT reconstruction technology were utilized to study the fracture network complexity, and the conclusions below were drawn.

(1) The macrofracture pattern is consistent with the cumulative development of microfractures. The damage to the specimen spreads from the interior to the exterior and eventually extends to the surface. Influenced by the horizontal stress ratio and two-way stress, the higher the two-way stress is, the more notable the plastic characteristics are, and the higher the residual stress of the sample is after damage. Moreover, all the specimens with lower two-way stress exhibit obvious brittle damage characteristics.

(2) Compared with the structure obtained with the 2D numerical simulation, a 3D structure provides a more intuitive and precise depiction of the internal fracture morphology and cell behavior throughout deformation and damage mechanisms.

(3) Fine-scale nonhomogeneity and laminar defects exert a substantial influence on molding the stress distribution, crack propagation trajectory, damage mechanism, and overarching fracturing progression. The strength of shale material exhibits obvious nonuniformity and statistical characteristics, i.e., the initial defects, such as gaps and other areas of low strength, are destroyed first, followed by high-strength regions.

As the horizontal tensile stress ratio increases, the complexity of developing intricate crack networks also escalates, and the extent of the increase in the fracture network complexity gradually decreases. At a horizontal stress ratio of 1.25, the highest fractal dimension is observed, which suggests that the cracks produced after specimen damage are the most well developed. Under a reduced horizontal stress ratio, shale specimens display abundant fracture patterns after damage, thereby promoting the propagation of pre-existing natural fractures.