Direct tensile damage process of calcite vein shale based on 3D CT reconstruction

From core observations of shales of the Niutitang formation in the northern part of Guizhou Province, China, calcite was often found to act as a natural fracture filler and affect the extension of fractures in hydraulic fracturing. Therefore, it is crucial to understand the tensile mechanical behavior of shales by calcite veins. In this paper, by computed tomography scanning of shales containing calcite veins of different dip angles from the Niutitang formation, a three‐dimensional numerical model reflecting the internal fine structure of the shale was constructed. Direct tensile numerical simulations were carried out to investigate the effect of calcite veins at different angles on the fine‐scale damage process and mechanical properties of shale. The experimental results show that the tensile capacity of the shale increases with the increase in calcite veins. Depending on the dip angle of the calcite vein, the damage pattern of the shale is divided into three types of damage: pull‐off damage along the calcite vein, jagged damage, and horizontal damage perpendicular to the loading method. At high dip angles, the shale damage is more intense and the fracture network more complex. The temporal and spatial characteristics of the acoustic emissions provide a good indication of the microscopic behavior of the shale specimens during the damage process. The box dimension method was used to calculate the fractal dimension of the shale specimens at the final damage, and it was found that the damage was more intense and the fracture network was more complex at high dip angles, and there was an angular threshold.

4][5] In recent years, many countries in the world have increased the exploration and development of shale gas.China is rich in shale gas resources, and according to the evaluation results of the Ministry of Land and Resources of China, the U.S. Information and Energy Administration, and other agencies, China's recoverable shale gas is 11.5 × 10 12 -36.1 × 10 12 m 3 , ranking among the top in the world. 6hale is a typical brittle rock with a weak resistance to tensile deformation.As an important parameter of hydraulic fracturing, tensile strength plays a controlling role in fracture extension in shale reservoirs.Therefore, many scholars have conducted a lot of research on the tensile strength of shale for a long time.He et al. combined physical experiments and numerical simulations, investigated the effects of laminar weak surfaces and interlaminar cohesion on tensile strength and damage modes in Brazilian tests.Wang et al. conducted  Brazilian tests on Longmaxi formation shales with different laminar dip angles, analyzed the effect of laminar dip angle on fracture toughness, and derived a functional relationship between laminar dip angle and fracture toughness.Li et al. conducted Brazilian splitting and direct shear tests on shales containing different mineral flakes and found that calcite flakes affect the tensile fracture pattern of the shale.
These studies on the mechanical properties of shale mainly focus on the laminae surface, but none of them consider the influence of mineral particles in shale on the mechanical properties of shale in terms of microstructure, let alone the controlling effect of calcite flakes at different angles on the tensile properties of shale.As a nonhomogeneous material, shale contains a large amount of minerals that fill within it, and calcite often forms a complete cut through the shale reservoir, which greatly affects the mechanical properties of the shale as well as fracture extension. 4,7n fact, the Brazilian test, as an indirect test method, obtains tensile strength parameters that are often greater than the true values of the rock material, and the stress-strain curve of the rock under tensile stress cannot be obtained, and the tensile deformation damage characteristics of the rock cannot be obtained. 8,9lthough many scholars have performed direct tensile tests on rock specimens, 8,10 the accuracy of the experiments is difficult to guarantee.This is due to the difficulty in clamping the specimen and the difficulty in overcoming the stress concentration at the end of the rock specimen and the eccentric force during direct tension. 11Numerical simulations can obtain the progressive damage process inside the rock.In direct tensile experiments, numerical simulations can avoid the influence of various factors such as stress concentration and eccentric force in physical experiments, and therefore can effectively reduce the error.
Wu et al. conducted numerical simulations of uniaxial compression experiments on shales containing calcite veins. 12The variation of the damage pattern of shale with the azimuth of calcite veins under twodimensional loading conditions was investigated, and the damage characteristics of shale were effectively characterized by the fractal dimension.Song et al. used twodimensional rock damage process analysis (RFPA 2D ) to numerically simulate uniaxial tension in shales containing calcite veins and found that calcite veins inhibit fracture extension in hydraulic fracturing. 13However, the actual rock fracture process occurs in three dimensions, and the two-dimensional images lose much of the three-dimensional (3D) spatial information, making it difficult for the researcher to reproduce the complete structure and changes within the specimen, which greatly limits the validity of the simulation results and their conformity to real conditions. 14,15omputed tomography (CT) microscopic imaging is a nondestructive testing method that uses the penetrating ability of X-rays to analyze the interior of an object to obtain information such as internal images of rocks, minerals, and pore distribution. 16,17Since 2003, CT scanning has been applied to quantitative characterization of coal rock fractures. 18Ding et al. used CT scan to study the development pattern of fracture structure in coal rock under different loading methods and analyzed the extension direction, development degree, and connectivity of major fractures in coal under different loading conditions from a microscopic perspective. 19Li et al. obtained a progressive damage model for shale specimens loaded using CT scanning as well as 3D reconstruction techniques for real-time scanning of shale specimens during loading. 20n the existing numerical simulation studies, few 3D numerical models have been constructed using CT scanning means to study the internal fine structure of calcite vein-bearing shale as the object.In this paper, we use CT scanning technology, digital image processing technology, and the three-dimensional rock damage process analysis (RFPA 3D ) finite element calculation method to construct a 3D numerical model that can characterize the calcite veins in different angles inside the shale.Numerical experimental studies on the direct tension of calcite vein-bearing shale specimens were conducted to analyze the damage process, damage mode and tensile mechanical properties of calcite vein-bearing shale specimens, and to discuss the effect of calcite vein dip angle on the tensile mechanical properties of shale.This work will provide an important basis for the mechanism of fracture initiation and the prediction of fracture expansion during hydraulic fracturing.

| Geological and tectonic background of the study area
The study area is located in the northern region of Guizhou Province, China.The northern part of Guizhou is geotectonically located in the Upper Yangzi Platform area, which is consistent with the regional tectonic evolution of the Yangzi Platform.The Yangzi platform has been influenced by multiple tectonic movements of the Xuefeng, Early-Middle Garidon, Late Garidon, Haixi, Yinzhi, Yanshan, and Xishan movements, resulting in a complex tectonic pattern. 13Figure 1 shows the tectonic map of the northern part of Guizhou.As shown in Figure 1, 21,22 the folds and fracture structures are very developed in the northern part of Guizhou Province, and the folds are mainly north-east oriented on the whole, while north-south, east-west, and north-west folds and fractures are also developed.Fold types are mainly septal groove folds, which are narrow and tightly closed in a groove shape toward the slope, and wide and soothing in a box shape on the back slope, but septal folds can also be seen.The fractures in the northern part of Guizhou are formed by multiple striking fractures cutting, uniting and interfering with each other.4][25] The faults are mainly northeast and north-northeast oriented extrusiontorsional faults, with multiple strike faults cutting and overlapping each other.The north-south tectonic zone is the earliest, followed by the north-northeast tectonic zone, and finally, the northeast tectonic zone is formed.Generally, faults can control the complexity of fracture development, and the density of fracture development is higher on compression-torsion faults. 24

| Shale core observation of the Niutitang formation
Core sampling was conducted from the Fengcan 1 well (FC-1) at a depth of 2447.93-2516.72m.By observing the fractures in the drill core of FC-1, it is found that the natural fractures in the shales of the Niutitang formation are more developed and mainly dominated by tectonic fractures.The core observation diagram is shown in Tectonic map of the northern part of Guizhou Province. 21,22igure 2. Tectonic cracks are divided into tension cracks, tectonic cracks, and sutures formed by piezo-soluble effect.The tension cracks are usually filled with calcite veins and pyrite, the fracture surface is irregular, and the length and width of the cracks vary greatly (Figure 2A).The kneading action generally does not affect the width of the crack, but bending cracks can be formed (Figure 2B).The core develops high-angle shear fractures with flat fracture surfaces and is filled with calcite veins (Figure 2C).The piezo-soluble action forms suture parallel to the laminae (Figure 2D).Interlayer joints are developed parallel to the laminae surface, are more numerous, and are mostly filled by calcite veins (Figure 2E).The number of fibrous developed calcite veins is high and they are distributed in a geese column pattern (Figure 2F).Therefore, it is necessary to study the damage mode and mechanical properties of calcitebearing shale under direct tension.This has significant implications for the tensile damage behavior of shale during hydraulic fracturing.

| INTRODUCTION TO RFPA D
7][28] It can simulate the fracture and damage process of quasi-brittle materials such as rocks. 29,30RFPA 2D has been successfully applied to two-dimensional modeling of tunnel slope damage, hydraulic fracturing, etc.In RFPA 3D , the finite element method is used as the basic stress analysis tool, where eight-node homogeneous cells are used as the basic cells in the finite element mesh.The model can represent the nonhomogeneity of the rock material and embody the distribution of the mechanical parameters of the rock at a fine scale.In addition, RFPA 3D uses an elastic-brittle intrinsic model to represent the nonlinear damage phase behavior of the rock.

| Inhomogeneous characterization of rocks
In the RFPA 3D software, the Weibull distribution is invoked to determine the mechanical parameters (elastic modulus, Poisson's ratio, etc.) of each fine-scale unit of the shale model. 12,27 where x denotes each mechanical property parameter (modulus of elasticity, strength, Poisson's ratio, etc.) of the fine unit of the rock medium.β indicates the average value of the mechanical property parameters of each fine unit; m is the homogeneity coefficient of the material, reflecting the degree of homogeneity of the material, generally the larger the homogeneity coefficient m the more homogeneous the material is.f(x) is the statistical distribution density.The Monte-Carlo method was used to satisfy the requirements of randomness and nonuniformity of the mechanical parameters of the fine view units.

| Constitutive relationships for unit damage in tension
In RFPA 3D , the stress-strain relationship is described using an elastic-brittle damage intrinsic model and its residual strength is considered.Each cell is considered elastic and the stress-strain curve for each cell is considered linearly elastic until the damage threshold is reached.The maximum tensile stress (or strain) criterion and the Mohr-Coulomb criterion were chosen as the damage thresholds.When the tensile stress (or strain) satisfies the strength criterion, the unit begins to accumulate damage and the modulus of elasticity of the unit gradually decreases as the damage progresses.
The intrinsic structural relationship of the damaged element is expressed as follows 27,31 : where E is the elastic modulus of the unit after damage; E 0 is the initial elastic modulus of the unit; and D is the damage variable.When D = 0, the unit is in a damagefree state; when D = 1, it corresponds to the complete damage state of the unit; 0 < D < 1, which indicates different degrees of damage of the unit.It is worth noting that according to Equation ( 2), the elastic modulus E = 0 when the damage variable D = 1, which is inconsistent with the actual damage evolution process of the rock unit.Therefore, a relatively small E of 1.0 × 10 −5 is specified in the test.E, E 0 , and D are all scalars, as RFPA 3D assumes the cell and damage to be isotropic.The intrinsic relationship for the maximum tensile stress (strain) criterion of the microscopic cell in the uniaxial tensile state is shown in Figure 3, and the corresponding damage variable is given by the following equation 27,31 : where σ tr is the residual tensile strength of the unit, σ t0 is the ultimate tensile strength of the unit, σ rt = λσ t0 , λ is the residual tensile strength coefficient and 0 <λ < 1. ε t0 is the tensile strain corresponding to the unit at its elastic limit, which is the strain threshold for tensile damage; ε tu is the ultimate tensile strain of the unit, at which point the unit is completely destroyed.ε tu = ηε t0 , η is the ultimate tensile strain coefficient.Under multi-axial stress conditions, taking into account the influence of the other two principal stresses on the maximum principal strain or the minimum principal strain.When the tensile strain increases above the damage strain threshold ε t0 , the equivalent effect variationε ¯can be used to replace the tensile strain ε in Equation ( 3).The equivalent effect variation ε ¯is expressed as follows 31 : where ε 1 , ε 2 , and ε 3 are the principal strains in the three directions.The angle brackets are the functions defined as follows 31 : The stress-strain relationship derived from elastic damage theory is as follows 31 : where G is the shear modulus of the material; η is the Poisson's ratio of the material; λ is the residual coefficient

| CT scan processing
To obtain a clear picture of the internal structure of the shale containing calcite veins, the shale containing calcite veins at different angles was made into a cylindrical specimen of 50 mm radius and 100 mm height.Calcitebearing shale specimens were scanned using a nanoVoxel-3502E series X-ray micro-CT system from Tianjin Sanying Precision Instruments.The system can distinguish fissures and pores at the micron level.The shale specimens were scanned in the height direction from top to bottom in 5000 layers with a scan interval of 50 μm per layer, an imaging size of 1275 × 1246 pixels, and a scan cell size of 19.12 × 19.12 μm.The images obtained by CT scan are shown in Figure 4. Figure 4A shows a CT scan of a section in which calcite veins and laminae structures are clearly visible.Figure 4B shows a magnified fine view image of one of the areas, which is capable of fine characterization of the mineral distribution within the embodied shale.

| 3D model reconstruction and direct tensile test scheme
To build a 3D numerical model, the information in the picture first needs to be converted into the vectorized data required for modeling.Digital images are made up of square pixel dots.In 3D space, the images will be considered to have a certain thickness, then each image can be considered as a finite element mesh. 15,19Arrange the images in the order they were scanned and overlay them.When the defined thickness t of each picture is small enough, the error in the 3D model it constitutes and the actual rock mass is negligible.Convert the corner coordinates of each pixel point to the corresponding vector space physical position (where each pixel point has a thickness of 1 and an edge length of 1).To keep the model structure consistent with the real specimen, the dimensions of the constructed model were kept consistent with the real rock specimen, that is 50 mm in diameter, 100 mm in height, and 0.5 mm × 0.5 mm × 0.5 mm in cell size.The image overlay and vectorization conversion are shown in Figure 5.
The color and brightness of the shale matrix and the calcite and quartz minerals that fill it are distinctly different, so that different colors and gray levels characterize the microstructure of the shale specimens.I is the gray value, and the hue-saturation-intensity color space (0-255) is selected to threshold the image segmentation.The I value reflects the brightness of different minerals, and the larger the I value, the stronger the corresponding mineral brightness. 12,15igure 6 is a graph of the variation of the grayscale values of the shale CT scan image on the scan line.From the graph of gray values, it can be found that the gray value limit is 115 for shale matrix and calcite veins, and 160 for quartz and calcite.Therefore, based on the threshold values obtained from the gray value graphs, fracture units with gray values of 0-40 are considered as voids, units from 40 to 115 are assigned as shale matrix, units from 115 to 160 are assigned as calcite, and units above 160 are assigned as quartz.In fact, a clear distribution of laminae can be obtained in the CT scan image shown in Figure 4, but this paper focuses on the effect of the angle of calcite veins on the tensile properties of shale without considering the laminae effect.Therefore, the weaker laminae are also considered as shale matrix in the process of assigning values.
The material parameters of the shale matrix, calcite, and quartz are shown in Table 1. 12,24o study the effects of calcite veins at different angles on shale microscale crack evolution and fracture patterns as well as tensile capacity during uniaxial compression, shale models with calcite veins at seven azimuths of 0°, 15°, 30°, 45°, 60°, 75°, and 90°were constructed.A schematic diagram of core sampling is shown in Figure 7. From the 5000 CT images derived from the top-down scans, 200 CT images were selected at the same interval for modeling and scaled to 100 × 100 pixels.Taking 75°a s an example, the numerical model constructed is shown in Figure 8.The number of cells per model is about 1,571,000.Among them, Figure 8A shows the numerical model of calcite veins reconstructed by CT scan at an inclination angle of 75°, Figure 8B shows the elastic modulus model after assigning the material parameters of different units according to the gray value interval, and Figure 8C shows the calcite vein morphology and the mineral distribution of quartz and calcite separately.The uniaxial tension is loaded as shown in Figure 8D, where the bottom of the model is fixed and an axial displacement load parallel to the coordinate axis direction is applied to the model surface.When the load is applied parallel to the Y-axis direction, the center point of the XOZ surface (bottom surface) is fixed in the horizontal and vertical directions, and the load is applied to the XOZ surface (upper surface).In the uniaxial tensile experiment, the initial step of displacement load is −0.0002 mm, and the displacement increment of each step is −0.0002 mm.At the same time, during the loading process, data such as stress, strain, acoustic emission energy, and real-time pictures characterizing the shale damage evolution are continuously collected.

| Uniaxial tensile test results analysis
According to classical elastic mechanics, the uniaxial tensile strength of a specimen is calculated by the following equation: where P is the maximum tensile load during the loading of the specimen, and A is the cross-sectional area of the specimen.Figure 9 shows the full stress-strain diagram of the uniaxial tensile test of shale specimens with different calcite vein inclination angles.As can be seen from Figure 9, the damage characteristics of the specimens with different calcite vein inclination angles are different.At the initial stage of uniaxial stretching, with the elevation of tensile stress, the shale specimens all underwent only elastic deformation, producing little damage before the tensile strength reached its peak.The damage curve of the shale specimens did not produce an obvious yielding phase when the calcite vein inclination angle was 0°, 15°, 30°, and 45°, and the tensile strength fell precipitously after reaching the peak, showing significant damage characteristics of direct tensile breakage, and the shale specimens had extremely low residual strength after direct tensile damage and lost almost all tensile capacity.At the calcite vein inclination angles of 60°, 75°, and 90°, after the linear elastic deformation phase of the shale specimen ends, the shale specimen enters the yielding phase, the maintenance time of this phase is elevated with the elevation of the angle, the tensile strength at the damage phase is stepped down, the degree of fall is relatively slow, and the curve is characterized by a certain ductility.
The values of ultimate tensile strength and elastic modulus of shale specimens at different calcite vein inclination angles are given in Table 2. Figure 10 shows the trend of ultimate tensile strength and elastic modulus for seven sets of tests at different calcite vein inclination angles.
It can be seen from Figure 10 that the tensile strength and elastic modulus of shale show obvious anisotropy under the influence of calcite veins, and the tensile strength of shale gradually increases with the increase of calcite dip angle, and the maximum is 4.48 MPa when the dip angle of calcite veins is 90°, and the minimum is 3.01 MPa when the dip angle of calcite veins is 0°, with a difference of 1.47 MPa.The ultimate tensile strength at 90°is 48.8% stronger than that at 0°.The modulus of elasticity also tends to increase with calcite vein inclination.The lower tensile strength of shale when the dip of calcite veins is small, which is due to the weak degree of cementation of calcite veins as weak structural surfaces and the lower tensile strength of calcite veins than shale, so that the ultimate tensile strength and elastic modulus of shale in direct tension depend mainly on the mechanical properties of calcite veins.The higher tensile strength and modulus of elasticity of the shale at higher calcite vein inclination, this is due to the fact that the ability of the shale to resist tensile loading comes primarily from the shale matrix.

| Rupture pattern analysis
Figure 11 shows the final damage pattern of shale specimens with different calcite vein dip angles.
From Figure 11, it can be found that when the calcite vein inclination angle is 0°−45°, the damage patterns of shale specimens are all tensile fracture damage along the calcite veins.When the calcite veins are inclined at 60°, multiple fracture surfaces are formed, and secondary cracks connecting the fracture surfaces together are produced on the calcite veins, forming a jagged damage pattern.When the calcite vein inclination angle is 75°a nd 90°, the shale specimens show chain damage at the same horizontal height, dominated by 1-3 damage surfaces, forming a tensile damage perpendicular to the loading direction.
Numerical simulations can obtain a complete process map of crack emergence, extension, connectivity, and destruction in shale specimens.Shale specimens with large differences in damage states were selected for detailed analysis of the progressive damage process.Figures 12-14 show the progressive damage process of shale specimens with calcite vein inclination angles of 0°, 60°, and 90°, respectively.
As shown in Figure 12, when the dip angle of the calcite vein is 0°, the initial crack is first produced on the edge of calcite vein, and with the loading, the end crack expands along the calcite vein to the other end under the tensile stress, and finally forms the tensile crack damage along the calcite vein.When the inclination angle of calcite veins is 60°, it can be found from Figure 12 that the initially formed microcracks are all concentrated on the calcite veins at different horizontal heights, and under the continuous action of tensile stress, the stress concentration phenomenon appears at the ends of these cracks, and the cracks expand around along the horizontal direction to form a larger rupture surface.It is noteworthy that after the rupture surface reaches a certain width, these rupture surfaces almost stop expanding in the horizontal direction due to more horizontal rupture surfaces at different heights and smaller spacing, and they are connected under the shear action, which is spatially manifested as mutual meshing and overlapping, forming a jagged rupture pattern along the calcite veins.
When the calcite vein inclination is 90°, the profile and surface view in Figure 13 show that cracks start to sprout along the horizontal direction from the calcite vein through the shale specimen and continue to load, the shale particles around the calcite vein start to sprout horizontal cracks under the tension-induced effect, producing multiple larger horizontal rupture surfaces, and these rupture surfaces expand steadily under tension  and eventually penetrate the shale matrix, forming multiple macroscopic rupture surfaces perpendicular to the loading direction.Lee and Pietruszczak proposed a damage criterion for uniaxial stretching of rock masses containing a single weak face based on Jaeger's theory of single weak face damage in laminated rock masses. 32Assuming that each physical surface except the weak surface has the same tensile strength, the tensile equivalent model of a single weak surface is established.Since the tensile strength of the weak face is usually much lower than that of the intact rock material, tensile fracture may occur along the weak face if its inclination is less than the critical value.
The critical angle θ* is determined by the following equation 32 : where θ is the angle of inclination of the weak surface, the angle between the normal direction of the weak surface and the loading direction; T 0 is the tensile strength of the specimen with a weak surface inclination of 0°, the tensile strength of the weak surface material; T90 is the tensile strength of the specimen with a weak surface inclination of 90°, the tensile strength of the matrix material.The critical weak surface dip angle of calcite vein-bearing shale obtained from Equation ( 8) is 35.95°, and the critical weak surface dip angle derived from this experiment is between 45°and 60°, which is due to the strong anisotropy of the shale and the fact that when the thickness of the calcite vein reaches a certain level (4 mm), the cohesion between the calcite vein and the shale is greater and is not a very weak surface. 33igure 15 shows a schematic diagram of the direct tensile damage mode of calcite-bearing shale.
When the dip angle of the lamina surface is 0°, the damage pattern of the laminated rock specimen is shown in Figure 15A.With the increase of axial tensile load, when the tensile strength reaches the tensile strength of calcite, the calcite will be damaged and the rupture surface is perpendicular to the loading direction.At this time, the tensile strength of shale can be considered equal to the tensile strength of calcite veins.It is expressed as When the dip angle of calcite veins is between 0°and the critical angle, the damage mode is shown in Figure 15B.For the rock sample subjected to axial load only, the normal stress of calcite veins is σ n = σ 1 cos 2 θ.When the normal stress on calcite veins reaches the tensile strength limit of calcite veins, σ n = T 0 , tensile damage will occur, at which time the tensile strength of shale is σ t = σ 1 = T 0 /cos 2 θ.This shows that the tensile strength of shale increases with the increase of calcite vein dip angle before the critical angle. 32he damage pattern of mutual engagement presented after the calcite vein inclination is the critical angle as shown in Figure 15C.In fact, influenced by the thickness of calcite veins, the calcite veins at different heights take the lead in breaking as multiple tiny planes under the axial load, and the shale is not only subjected to tensile stress in the axial direction but also to shear stress due to shear misalignment.
When the dip angle of the lamina is 90°, the damage pattern of the shale specimen is shown in Figure 15D.Unlike the 0°specimen, the cross-section of the specimen consists of the shale matrix and calcite, and the load-bearing capacity of the specimen is borne by the shale matrix after the damage of calcite occurs first, and the tensile strength is basically not affected.As the axial tensile load continues to increase and reaches the tensile strength of the shale matrix, the shale only starts to expand horizontally along the middle of the cross-section and the damage surface is perpendicular to the loading direction, and the tensile strength of the shale at this time is σ t = σ 1 = T 90 .In summary, calcite veins have a significant effect on the anisotropy of the shale.Under the influence of calcite veins, the direct tensile damage mode of the shale is in three types, tensile damage along the calcite veins at 0°-45°, jagged damage with horizontal fractures and fractures on calcite veins penetrating each other at 60°, and damage perpendicular to the loading direction at 75°a nd 90°.Therefore, the angle of calcite veins below 60°d uring hydraulic fracturing, when the shale undergoes damage mainly due to tensile stress, may cause fractures to unfold mainly along the calcite veins, inhibiting the formation of a complex hydraulic fracture network in the shale and leading to a substantial reduction in the volume of the modified reservoir.At the same time, hydraulic fracturing is easily induced by the weaker calcite veins to turn, resulting in a decrease in fracture height for hydraulic fracturing. 34On the contrary, the angle of calcite veins higher than 60°promotes the creation of complex fractures in shales and optimizes the spatial distribution of fractures, thus increasing the production of shale gas.

| Spatial and temporal characterization of acoustic emission energy during damage evolution
During axial stretching, the shale specimens produce significant deformation of the form, which is also accompanied by a large amount of acoustic emission signal emission.When microfracture of the rock occurs under load, a portion of the energy is released and transient elastic waves are generated.The signal of acoustic emission carries the information of the evolution of microfractures inside the rock, therefore, the effective use of acoustic emission information can explore the change of the internal structure of the specimen in the process of damage at a deeper level.In the constructed model, a microrupture of a cell is an acoustic emission (AE) event and the accumulative acoustic emission (AAE) count is the sum of the acoustic emission events.Figure 16 shows the evolution of the spatial distribution of acoustic emission energy at different calcite vein inclination angles.
As can be seen in Figure 16, the macroscopic damage pattern of the shale specimen during uniaxial tension is precisely a combination of damage units for each tensile damage.At the beginning of loading, calcite veins in the shale specimen, as well as the weaker shale matrix, are the first to undergo tensile damage, and acoustic emission energy is disordered and released.Continued loading, as the shale specimen is subjected to tensile stress in the lead hammer direction only, calcite veins belong to the structurally weak surface with lower tensile   It can be learned from Figure 17 that during the loading process, the shale specimens with calcite vein inclination of 0°-45°have increasing acoustic emission energy and increasing rate during the elastic phase, and there is almost no yielding phase.Unlike at low inclination angles, calcite veins with inclination angles of 60°−90°enter the yielding phase at the end of the elastic deformation phase, during which the acoustic emission energy changes from accelerated growth during the elastic phase to slow growth, when horizontal cracks expand rapidly at different heights of the shale specimens with increasing number and size.During the damage phase, accompanied by a large release of acoustic emission energy, at this time the fracture extends substantially up the shale matrix along the horizontal damage surface, and the specimen gradually loses its loadbearing capacity, eventually forming a huge macroscopic rupture pattern.

| Fractal characteristics of shale damage
Fractal theory is a tool that can quantitatively describe irregular and complex objects in nature and also includes the fractal behavior of rock damage. 12,24,35To quantify the effect of calcite vein inclination on the tensile fracture network complexity of shale specimens, the fractal dimension was used to assess the fracture network complexity of shale specimens after damage.
In RFPA 3D , the destruction of a cell is considered as a microrupture.The development and concatenation of microruptures form large-scale cracks.Therefore, the degree of damage to the rock specimen can be reflected by the number and location distribution of damage units.The damage of each cell in the numerical model corresponds to an acoustic emission event, and the acoustic emission model characterizes the number of damaged cells and their location distribution， therefore, the acoustic emission model has fractal characteristics.In RFPA 3D , the shale specimens are divided into equal-sized square units, so a box of squares is used to cover the shale specimens.The calculation of the capacity dimension becomes a count of the damage events falling into square boxes of different sizes.Varying the dimensions of the box r, different numbers of boxes N(r) can be obtained, and a series of r-N(r) data are obtained after several variations.The scatter plot of r-N(r) is made using double logarithmic coordinates, and the fitted curve is obtained by the least squares method, whose slope is the capacity dimension, and the expression is where D is the capacity dimension, r is the side length of the square box, and N(r) is the number of boxes needed to cover the damaged area.The relationships between different stress levels, calcite vein inclination and fractal dimension, and cumulative acoustic emission energy are given in Table 3.
Figures 18 and 19 show the fractal dimension and cumulative acoustic emission energy plots of the shale specimens at different calcite vein inclination angles  and at different stress level stages, respectively.From Figures 18 and 19, it is found that the higher the dip angle of calcite veins, the higher the fractal dimension and the more the accumulated acoustic emission energy.Under the action of tensile stress, the greater the calcite vein inclination angle, the higher the complexity of the fracture network and the better the fracturing effect, which is macroscopically manifested as a change from direct pull-off at low angles to a more complex nonuniform damage mode, and the most complex fracture network is formed when the calcite vein inclination angle is 90°.It is noteworthy that the increase in fractal dimension and cumulative acoustic emission energy is greater as the calcite vein dip angle changes from 45°to 60°, which is a boundary between damage being almost exclusively present on the calcite veins and damage beginning to appear on the shale matrix.

| CONCLUSION
In this paper, a model of shale containing calcite veins at different angles was established, and the effect of calcite vein inclination angle on the tensile strength of shale and the fracture mode under tensile stress was studied, and the following conclusions were drawn: 1. Calcite veins have a significant effect on the tensile strength of shale.The tensile strength of shale specimens gradually increased with the increase of calcite vein inclination angle, and the maximum was 4.48 MPa when loaded along the calcite veins; the minimum was 3.01 MPa when loaded perpendicular to the calcite veins, and the ratio of tensile strength at 90°-0°was 1.48.2. The damage patterns of shale specimens at different calcite vein inclination angles can be roughly divided into three types: at 0°−45°, the damage pattern is tensile damage along the calcite vein; at 60°, it presents jagged damage with horizontal fractures and fractures on the calcite vein penetrating each other; at 75°and 90°, multiple horizontal fracture surfaces perpendicular to the loading direction appear.Calcite, as a structurally weak surface, is more likely to crack along calcite veins under the action of tensile stress.When damage due to tensile stress occurs mainly in shale, if the angle of calcite veins is lower than 60°, it can lead to fracture unfolding mainly along calcite veins and inhibit the formation of complex hydraulic fracture network in shale, resulting in a significant reduction in the volume of the reformed reservoir.Meanwhile, hydraulic fracture is easily induced to turn by weaker calcite veins, resulting in a decrease in the fracture height of hydraulic fracture.3. Acoustic emission shows well the evolution of microscopic damage inside the shale.Independent of the dip angle, the appearance of microdamage is always concentrated on calcite veins.At low angles, there is almost no yielding phase in the shale, and microdamage on the calcite veins penetrates very easily, creating macroscopic damage along the calcite veins and causing the shale to lose its full tensile capacity directly.At high angles, there is a clear yielding phase during loading of the shale, and the growth rate of acoustic emission energy slows down, when the number and scale of horizontal cracks are elevated.4. The fractal dimension can quantify the effect of calcite vein dip angle on the fracture complexity.Under the action of tensile stress, the greater the calcite vein inclination angle, the higher the complexity of the fracture network, and the most complex fracture network is formed at the calcite vein inclination angle of 90°.There is a jump in cumulative acoustic emission energy and fractal dimension around the calcite vein dip angle of 60°, which is a critical angle at which the damage starts to appear on the shale matrix from being almost exclusively on the calcite veins to the damage.

F I G U R E 2
Observation diagram of the core of FC-1 Niutitang formation.(A) Tension fractures.(B) Tension fractures formed by kneading action.(C) High-angle shear fractures.(D) Sutures formed by piezo-soluble action solution.(E) Interlamellar joints developed parallel to the laminae surface and filled by calcite veins.(F) Calcite veins developed in fibrous form.
Images of shale obtained by computed tomography scan and microstructural features.(A)CTscan slice image.(B) Magnified image of a region after slicing.

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Schematic diagram of image superposition and vectorization conversion.F I G U R E 6 Scan line and gray value change curve on the scan line.(A) Position of the scan line.(B) Gray value change on the scan line with two thresholds to distinguish calcite, quartz, and shale.T A B L E 1 Material parameters of rock samples.Core sampling schematic.F I G U R E 8 Constructed numerical model of calcite vein dip angle 75°.(A) Three-dimensional model obtained from computed tomography scan reconstruction.(B) Elastic modulus diagram of the model after assigning different material parameters according to the gray value interval.(C) Morphology of calcite veins in the model with scattered quartz and calcite mineral distribution.(D) Loading method of uniaxial tensile test.

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I G U R E 9 Stress-strain diagram of shale at different calcite vein dip angles.T A B L E 2 Modulus of elasticity and uniaxial tensile strength of shale with different calcite vein dip angles.

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I G U R E 10 Ultimate tensile strength and elastic modulus of shale at different calcite vein dip angles.

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I G U R E 12 Progressive damage process of shale specimens with calcite vein inclination of 0°.(A) Failure mode diagram.(B) Internal cutaway view.
strength and are the first to form a tensile stress concentration zone, regardless of the angle of calcite veins, tensile damage units are the first to concentrate on the calcite veins, and these unit damages soon gather together to form cracks.Eventually, different damage patterns are presented under different stress distributions.The spatial distribution characteristics of acoustic emission can well represent the microscopic damage evolution inside the shale specimen, and at the same time better reflect the influence of calcite veins with different dip angles on the macroscopic damage pattern.Eventually, different damage patterns are presented under different stress distributions.The spatial distribution characteristics of acoustic emission can well represent the microscopic damage evolution inside the shale specimen, and at the same time better reflect the influence of calcite veins with different dip angles on the macroscopic damage pattern.

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I G U R E 13 Progressive damage process of shale specimens with calcite vein inclination of 60°.(A) Failure mode diagram.(B) Internal cutaway view.F I G U R E 14 Progressive damage process of shale specimens with calcite vein inclination of 90°.(A) Failure mode diagram.(B) Internal cutaway view.F I G U R E 15 Schematic diagram of direct tensile damage mode of shale containing calcite veins.(A) 0°.(B) 0~45°.(C)45~90°.(D) 90°.

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Figure17shows the trend of stress, AE energy, and accumulative AE energy with displacement for different calcite vein inclination angles.It can be learned from Figure17that during the loading process, the shale specimens with calcite vein inclination of 0°-45°have increasing acoustic emission energy and increasing rate during the elastic phase, and there is almost no yielding phase.Unlike at low inclination angles, calcite veins with inclination angles of 60°−90°enter the yielding phase at the end of the elastic deformation phase, during which the acoustic emission energy changes from accelerated growth during the elastic phase to slow growth, when horizontal cracks expand rapidly at different heights of the shale specimens with increasing number and size.During the damage phase, accompanied by a large release of acoustic emission energy, at this time the fracture extends substantially up the shale matrix along the horizontal damage surface, and the specimen gradually loses its loadbearing capacity, eventually forming a huge macroscopic rupture pattern.

F I G U R E 18
Fractal dimension of shale specimens under different calcite vein dips and stress levels.

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I G U R E 19 AAE energy plots of shale specimens at different calcite vein inclination angles and stress levels.AAE, accumulative acoustic emission.
T A B L E 3 AAE energy and fractal dimension at different calcite vein inclination and stress levels.