Realistic shear fracture calculation method of anisotropic rock based on brazilian disc experiment consideration

Abstract

The application discloses a calculation method of real shear fracture of anisotropic rock based on Brazilian disc experiment consideration, and specifically relates to the following steps: collecting physical and mechanical parameters, engineering geological environment parameters and bilateral notch Brazilian disc geometric parameters of deep anisotropic reservoir rock; drawing a rock mass calculation domain simulating real shear fracture of rock mass with different bedding angles according to the geometric parameters; adding multiple physical fields such as solid mechanics field, historical strain field and phase field to the calculation domain, establishing an anisotropic real shear phase field model which is mutually coupled, and solving the coupling by using an interleaving scheme, keeping the displacement loading rate unchanged, repeating the above steps until the rock is completely sheared and fractured. The method fully considers the anisotropic characteristics of the rock and the engineering geological environment characteristics, quantitatively represents the real shear fracture mode of the anisotropic rock, and provides an important reference for evaluating the mechanical parameters of the rock in the construction process of deep underground engineering.

Description

Technical Field

[0001] This invention belongs to the field of geotechnical engineering technology, specifically relating to a method for calculating the real shear fracture of anisotropic rocks based on the Brazilian disk experiment. Background Technology

[0002] With continuous economic development, underground engineering construction is gradually expanding to greater depths. The engineering geological environment under high confining pressure makes reservoir rocks more susceptible to shear failure. For example, during unconventional oil and gas drilling and deep tunnel excavation, the surrounding rock near the wellbore and cavern is prone to shear failure and instability due to stress release. Simultaneously, because most strata are layered structures composed of rocks of different lithologies, reservoir rocks generally exhibit anisotropic characteristics, resulting in complex shear fracture propagation behavior. Therefore, understanding the shear fracture mechanism of anisotropic rocks is crucial for the effective development of underground energy and the safety of underground rock engineering.

[0003] Extensive literature indicates that the shear fracture mechanism of anisotropic rocks remains largely unexplored, primarily due to the difficulty in conducting shear-based fracture tests. Existing standard laboratory shear crack propagation tests typically observe crack kinks at a certain angle, the formation of which is driven by tensile stress. Therefore, most experiments fail to accurately reveal the true shear fracture mechanism of rocks. Although through-shear (PTS) and shear box tests have been reported to capture the true shear fracture morphology of rocks, their complex setups and additional requirements limit the acquisition of experimental data. Therefore, given the stringent conditions of laboratory testing, numerical simulations of the true shear fracture propagation in anisotropic rocks are necessary.

[0004] Radial compression of bilaterally notched Brazilian disks (DNBDs) is an emerging method for testing true shear fracture. It is simple to operate and can determine the true shear fracture toughness in any direction relative to anisotropic directions. However, current shear fracture propagation models based on bilaterally notched Brazilian disks do not consider the influence of rock anisotropy and deep engineering geological environments on the true shear crack propagation of rocks, thus having certain limitations. Summary of the Invention

[0005] The purpose of this invention is to provide a method for calculating the true shear fracture of anisotropic rocks based on the Brazilian disk experiment. This method comprehensively considers the engineering environment characteristics of deep anisotropic reservoir rocks, thereby accurately predicting the true shear fracture morphology of the rocks.

[0006] The technical solution adopted in this invention is a method for calculating the real shear fracture of anisotropic rocks based on the Brazilian disk experiment, specifically implemented according to the following steps:

[0007] Step 1: Collect physical and mechanical parameters of deep anisotropic reservoir rocks, underground engineering geological environment parameters, and geometric parameters of the bilateral notch Brazilian disk;

[0008] Step 2: Based on the shear fracture toughness obtained from the physical and mechanical parameters under different principal directions, calculate the critical energy release rate G of pure shear fracture of rock under different bedding angles. c The formulas are shown in equations (1) and (2):

[0009] K IIc =K IIc,1 sin 2 α1+K IIc,2 cos 2 α1 (1);

[0010]

[0011] In the formula, K IIc,1 Shear fracture toughness perpendicular to the bedding direction; K IIc,2 E1 is the shear fracture toughness along the bedding direction; E2 is the elastic modulus perpendicular to the bedding direction; ζ = E1 / E2, where E2 is the elastic modulus along the bedding direction; α1 is the bedding angle; v 12 and v 23 These are Poisson's ratios along the bedding plane and perpendicular to the bedding plane, respectively.

[0012] Step 3: Use COMSOL software to draw the geometric calculation domain of the Brazilian disk with double notches, and use the built-in basis coordinate system of COMSOL to characterize the transverse isotropic characteristics of the rock under different bedding angles;

[0013] Step 4: Add solid mechanical field, historical strain field and phase field to the computational domain respectively, establish the coupling relationship between them, and thus obtain an anisotropic real shear phase field model;

[0014] Step 5: Solve the anisotropic real shear phase field model independently on a decoupled solver using an interleaved scheme;

[0015] Step 6: Keep the displacement loading rate constant and repeat step 5 until the rock is completely fractured and the calculation is stopped. This will give you the true shear fracture morphology of the rock at different bedding angles.

[0016] The invention is further characterized in that,

[0017] In step 1, the physical and mechanical parameters include: the elastic modulus, shear modulus, Poisson's ratio, shear fracture toughness, and Biot coefficient of the rock along and perpendicular to the bedding direction; the engineering geological environment parameters include: the confining pressure, pore pressure, and in-situ stress of the rock; the geometric parameters of the double-notched Brazilian disk include: the radius of the disk, the size of the prefabricated notch, and the loading angle.

[0018] In step 3, the specific steps for drawing the geometric calculation domain of the Brazilian disk with double notches are as follows: First, generate a circle with a radius of 37.5mm and a rectangle of 94mm×1.8mm with the origin of the coordinate system as the center. Then, establish two interpolation curves in coordinate form to determine the length of the prefabricated notch. After all geometric objects are combined by Boolean set, delete the prefabricated notch areas on both sides. Finally, obtain the calculation domain of the Brazilian disk model with double notches.

[0019] Establish a built-in basis vector coordinate system, as shown in equation (3):

[0020]

[0021] In the formula, x and y represent the x-axis and y-axis directions of the global coordinate system, respectively; x′ and y′ represent the direction perpendicular to the bedding plane and the direction along the bedding plane, respectively; α represents the angle between the direction along the bedding plane and the y-axis direction. Five different bedding angles α = 0°, 22.5°, 45°, 67.5° and 90° are selected for real shear simulation analysis.

[0022] In step 4, the anisotropic real shear phase field model includes solid mechanics equations, phase field control equations, and history strain equations.

[0023] The solid mechanics equation is shown in equation (4):

[0024]

[0025] In the formula, σ=[(1-κ)(1-φ) 2 +κ]￡:ε, 0<κ≤1 is used to avoid singularities in the numerical model, φ is the phase field for crack initiation and propagation, ￡ is the non-degenerate fourth-order stiffness tensor, and ε is the strain tensor; f b and f s These represent the body forces and surface forces of the rock, respectively; n is the direction vector; ▽ is the gradient operator;

[0026] The phase field control equation is shown in equation (5):

[0027]

[0028] In the formula, l0 is the length dimension parameter; G c B is the critical energy release rate; B is the anisotropic gradient; the tensile portion of the elastic strain energy.

[0029] in, ε ii For linear strain, ε ij (i≠j) represents shear strain; i = 1, 2, 3, j = 1, 2, 3;

[0030] ▽φ represents the phase field gradient; C l The Voight notation for the non-degenerate fourth-order stiffness tensor ε is expressed as follows:

[0031]

[0032] In the formula, For the stiffness component, its different expressions are as follows:

[0033]

[0034]

[0035] In the formula, E i (i = 1, 2, 3) represents the elastic modulus (e1, e2, e3) along the three principal material directions; G ij (i = 1, 2, 3, j = 1, 2, 3) are derived from e i and e j The shear modulus in the defined orthogonal plane; v ij =v ji E i / E j Poisson's ratio in the orthogonal plane;

[0036] The historical strain equation is shown in equation (6):

[0037]

[0038] In the formula, t is time; x is the position vector of any point in the two-dimensional domain; and σ0 is the initial stress tensor.

[0039] Step 5 specifically involves:

[0040] Substitute the physical and mechanical parameters of the deep anisotropic reservoir rock and the underground engineering geological environment parameters from step 1 into the anisotropic real shear phase field model. Based on the different bedding angles given in step 3, set the upper part of the disk computational domain as a specified displacement boundary to simulate the fracturing process, set the lower part as a roller support, and the rest as free boundaries. Input the displacement increment Δu = 0.05 mm / min at the specified displacement boundary. Perform separate coupled transient calculations in the order of displacement field - historical strain field - phase field to obtain the stress, strain and phase field distributions respectively.

[0041] The beneficial effects of this invention are as follows: Addressing the issue of rocks being prone to shear failure in deep underground engineering geological environments, an anisotropic pure solid phase-field model is established, providing a calculation method for predicting the actual shear fracture of rocks. Because this method fully considers the anisotropic characteristics of rocks and the characteristics of the engineering geological environment, it can accurately predict the actual shear fracture morphology of rocks and quantitatively assess the differences in morphological parameters of the shear fracture surface. The calculation results not only provide an important reference for evaluating the mechanical parameters of rocks during deep underground engineering construction, but also have significant implications for accurately selecting fracture surfaces and studying the strength and deformation under different working conditions. Attached Figure Description

[0042] Figure 1 This is a flowchart of the method for calculating the real shear fracture of anisotropic rocks based on the Brazilian disk experiment.

[0043] Figure 2 This is a schematic diagram of the computational domain and boundary conditions of the double-notch Brazilian disk in the method of the present invention;

[0044] Figure 3 This is a diagram illustrating the multiphysics coupling mechanism in the anisotropic pure solid phase field model of this invention.

[0045] Figure 4 This is a comparison diagram of shear crack shapes under different bedding angles and experimental results in the embodiments of the present invention;

[0046] Figure 5 This is a comparison chart of the numerical results and experimental results of the maximum principal strain in the embodiments of the present invention. Detailed Implementation

[0047] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0048] Example 1

[0049] This invention relates to a method for calculating the true shear fracture of anisotropic rocks based on the Brazilian disk experiment. Specifically, the method involves: collecting physical and mechanical parameters, engineering geological environment parameters, and geometric parameters of the double-notched Brazilian disk from deep anisotropic reservoir rocks; drawing a calculation domain for the rock mass simulating true shear fracture at different bedding angles based on the geometric parameters; adding multiple physical fields, such as a solid mechanical field, a historical strain field, and a phase field, to the calculation domain to establish a coupled anisotropic true shear phase field model; solving the coupled system using an alternating scheme, updating the phase field through historical strain energy to drive crack initiation and propagation; and repeating the above steps while keeping the displacement loading rate constant until the rock completely shears fractures.

[0050] The method of this invention fully considers the anisotropic characteristics of rocks and the characteristics of engineering geological environment, and quantitatively characterizes the real shear fracture mode of anisotropic rocks. It not only provides an important reference for evaluating the mechanical parameters of rocks during the construction of deep underground engineering, but also has important significance for accurately selecting fracture surfaces to study the strength and deformation under different working conditions.

[0051] Example 2

[0052] This invention is based on a method for calculating the real shear fracture of anisotropic rocks considering the Brazilian disk experiment, such as... Figure 1 As shown, please follow these steps:

[0053] Step 1: Collect physical and mechanical parameters of deep anisotropic reservoir rocks, underground engineering geological environment parameters, and geometric parameters of the bilateral notch Brazilian disk;

[0054] The physical and mechanical parameters include: the elastic modulus, shear modulus, Poisson's ratio, shear fracture toughness, and Biot coefficient of the rock in the two principal directions (along the bedding direction and perpendicular to the bedding direction);

[0055] Engineering geological environmental parameters include: confining pressure on the rock, pore pressure, and in-situ stress;

[0056] The geometric parameters of the double-notch Brazilian disc include: the radius of the disc, the size of the prefabricated notch, and the loading angle;

[0057] Step 2: Based on the shear fracture toughness obtained from the physical and mechanical parameters under different principal directions, calculate the critical energy release rate G of pure shear fracture of rock under different bedding angles. c The formulas are shown in equations (1) and (2):

[0058] K IIc =K IIc,1 sin 2 α1+K IIc,2 cos 2 α1 (1);

[0059]

[0060] In the formula, K IIc,1 Shear fracture toughness perpendicular to the bedding direction; K IIc,2 E1 is the shear fracture toughness along the bedding direction; E2 is the elastic modulus perpendicular to the bedding direction; ζ = E1 / E2, where E2 is the elastic modulus along the bedding direction; α1 is the bedding angle; v 12 and v 23 These are Poisson's ratios along the bedding plane and perpendicular to the bedding plane, respectively.

[0061] Step 3: Based on the geometric parameters, use COMSOL software to draw the geometric calculation domain of the double-notched Brazilian disk, and use the built-in basis coordinate system of COMSOL to characterize the transverse isotropic characteristics of the rock under different bedding angles.

[0062] The specific steps for drawing the geometric computational domain of the Brazilian disk with double notches are as follows: First, generate a circle with a radius R of 37.5mm and a rectangle of 94mm × 1.8mm centered on the origin. Then, establish two interpolation curves in coordinate form to determine the length of the prefabricated notch. After merging all geometric objects through a Boolean union set, delete the prefabricated notch areas on both sides. Finally, obtain the computational domain of the Brazilian disk model with double notches, as shown below. Figure 2 As shown.

[0063] Establish a built-in basis vector coordinate system, as shown in equation (3):

[0064]

[0065] In the formula, x and y represent the x-axis and y-axis directions of the global coordinate system, respectively; x′ and y′ represent the direction perpendicular to the bedding plane and the direction along the bedding plane, respectively; α represents the angle between the direction along the bedding plane and the y-axis direction. Five different bedding angles α = 0°, 22.5°, 45°, 67.5° and 90° are selected for real shear simulation analysis.

[0066] Step 4: Add multiple physical fields, such as solid mechanical field, historical strain field, and phase field, to the computational domain, and establish their coupling relationships to obtain an anisotropic true shear phase field model, such as... Figure 3 As shown;

[0067] A phase-field model of anisotropic rock shear fracture was constructed using the solid mechanics equations, history-strain equations, and phase-field equations in COMSOL. First, the tensile elastic energy density was extracted from the solid mechanics field. Stored in a variable list. Then, the tensile elastic energy density is retrieved via the historical strain field. The local history strain field H is then updated. The updated H is used to solve for the phase field, which is then used to modify the stiffness matrix in the solid mechanical field. By using the history field H, it can be ensured that the phase field monotonically increases during compression or unloading, thereby preventing crack healing.

[0068] An anisotropic real shear phase field model includes solid mechanics equations, phase field control equations, and history strain equations;

[0069] The solid mechanics equation is shown in equation (4):

[0070]

[0071] In the formula, 0 < κ ≤ 1 is used to avoid singularities in the numerical model, φ is the phase field for crack initiation and propagation, ε is the non-degenerate fourth-order stiffness tensor, and ε is the strain tensor; f b and f s These represent the body forces and surface forces of the rock, respectively; n is the direction vector; ▽ is the gradient operator;

[0072] The phase field control equation is shown in equation (5):

[0073]

[0074] In the formula, l0 is the length dimension parameter; G c B is the critical energy release rate; B is the anisotropic gradient; the tensile portion of the elastic strain energy.

[0075] in, ε ii For linear strain, ε ij (i≠j) represents shear strain; i = 1, 2, 3, j = 1, 2, 3;

[0076] ▽φ represents the phase field gradient; C l The Voight notation for the non-degenerate fourth-order stiffness tensor ε is expressed as follows:

[0077]

[0078] In the formula, For the stiffness component, its different expressions are as follows:

[0079]

[0080]

[0081] In the formula, E i (i = 1, 2, 3) represents the elastic modulus (e1, e2, e3) along the three principal material directions; G ij (i = 1, 2, 3, j = 1, 2, 3) are derived from e i and e j The shear modulus in the defined orthogonal plane; v ij =v ji E i / E j is Poisson's ratio in the orthogonal plane.

[0082] Historical strain equation:

[0083] In order to realistically simulate the underground engineering geological environment, the effects of confining pressure, pore pressure and in-situ stress on the rock must be fully considered. The corresponding historical strain equation is shown in equation (6):

[0084]

[0085] In the formula, t is time; x is the position vector of any point in the two-dimensional domain; and σ0 is the initial stress tensor.

[0086] Step 5: Solve the anisotropic real shear phase field model independently on a decoupled solver using an interleaved scheme;

[0087] Specifically, the physical and mechanical parameters of the deep anisotropic reservoir rock and the underground engineering geological environment parameters from step 1 are substituted into the anisotropic real shear phase field model. Based on the different bedding angles given in step 3 (i.e., α = 0°, 22.5°, 45°, 67.5° and 90°), the upper part of the disk computational domain is set as a specified displacement boundary to simulate the fracturing process, the lower part is set as a roller support, and the rest are free boundaries. The displacement increment Δu = 0.05 mm / min is input for the specified displacement boundary. Separate coupling transient calculations are performed in the order of displacement field - historical strain field - phase field to obtain the stress, strain and phase field distributions respectively.

[0088] Step 6: Keep the displacement loading rate constant and repeat step 5 until the rock is completely fractured and the calculation is stopped. This will give you the true shear fracture morphology of the rock at different bedding angles.

[0089] Example 3

[0090] Taking a double-notched Brazilian disk (DNBD) experiment as an example, the experimental parameters of the anisotropic granite shown in Table 1 were used to simulate the actual shear fracture morphology of the rock. The simulation calculations were carried out according to the steps above, and the actual shear fracture morphology of the rock was finally obtained. Subsequently, the simulation results were compared with the experimental results, as shown below. Figure 4 As shown in the figure, the numerical calculation results agree well with the experimental results. Furthermore, the numerical results for the maximum principal strain are also compared with the experimental results, as shown in the figure. Figure 5 As shown, this is in excellent agreement with the experimental results. Based on the above comparison of the failure modes and maximum principal strain of granite, it is demonstrated that the proposed calculation method is effective in simulating real shear fracture.

[0091] Table 1. Experimental parameters of an anisotropic granite.

[0092]

[0093]

[0094] (Note: In the reservoir coefficient, "1" and "2" represent along the bedding direction and perpendicular to the bedding direction, respectively; "12" and "23" represent anisotropic plane and isotropic plane, respectively.)

[0095] This invention addresses the issue of rock's susceptibility to shear failure in deep underground engineering geological environments by establishing an anisotropic pure solid phase-field model and providing a computational method for predicting the true shear fracture of rocks. Because this method fully considers the anisotropic characteristics of rocks and the features of the engineering geological environment, it can accurately predict the true shear fracture morphology of rocks and quantitatively characterize the true shear fracture modes of anisotropic rocks. The calculation results not only provide important references for evaluating the mechanical parameters of rocks during deep underground engineering construction but also have significant implications for accurately selecting fracture surfaces and studying strength and deformation under different working conditions.

Claims

1. A method for calculating the true shear fracture of anisotropic rocks based on the Brazilian disk experiment, characterized in that, The specific steps are as follows: Step 1: Collect physical and mechanical parameters of deep anisotropic reservoir rocks, underground engineering geological environment parameters, and geometric parameters of the bilateral notch Brazilian disk; Step 2: Based on the shear fracture toughness obtained from the physical and mechanical parameters under different principal directions, calculate the critical energy release rate of pure shear fracture of rock under different bedding angles. The formulas are shown in equations (1) and (2): （1）； （2）； In the formula, Shear fracture toughness perpendicular to the bedding direction; Shear fracture toughness along the bedding direction; The elastic modulus is perpendicular to the bedding direction; , The elastic modulus along the bedding direction; From the perspective of stratification; and These are Poisson's ratios along the bedding plane and perpendicular to the bedding plane, respectively. Step 3: Based on the geometric parameters, draw the calculation domain of the rock mass simulating real shear fracture at different bedding angles. Use COMSOL software to draw the geometric calculation domain of the double-notch Brazilian disk, and use the built-in basis vector coordinate system of COMSOL to characterize the transverse isotropic characteristics of the rock at different bedding angles. Step 4: Add solid mechanical field, historical strain field and phase field to the computational domain respectively, establish the coupling relationship between them, and thus obtain an anisotropic real shear phase field model; An anisotropic real shear phase field model includes solid mechanics equations, phase field control equations, and history strain equations; The solid mechanics equation is shown in equation (4): （4）； In the formula, , To avoid singularities in numerical models, The phase field for crack initiation and propagation. For the non-degenerate fourth-order stiffness tensor, For strain tensor; and These are the body forces and surface forces of the rock, respectively. It is a direction vector; For gradient operators; The phase field control equation is shown in equation (5): （5）； In the formula, For length dimensions; The critical energy release rate; Anisotropic gradient; tensile portion of elastic strain energy ; in, ; For linear strain, For shear strain, ; i =1,2,3、 j =1,2,3; The phase field gradient; For the non-degenerate fourth-order stiffness tensor The Voight notation is as follows: In the formula, For the stiffness component, its different expressions are: In the formula, Represents the elastic modulus along the three principal material directions. , i =1,2,3; It is by and Shear modulus in the defined orthogonal plane i =1,2,3、 j =1,2,3; Poisson's ratio in the orthogonal plane; The historical strain equation is given by equation (6): （6）； In the formula, t For time; x Let the position vector be any point in the two-dimensional domain; This is the initial stress tensor; Step 5: Solve the anisotropic true shear phase field model independently on a decoupled solver using an interleaved scheme; specifically: Substituting the physical and mechanical parameters of the deep anisotropic reservoir rock and the underground engineering geological environment parameters from Step 1 into the anisotropic true shear phase field model, and based on the different bedding angles given in Step 3, the upper part of the disk computational domain is set as a specified displacement boundary to simulate the fracturing process, the lower part is set as a roller support, and the rest are free boundaries. The specified displacement boundary is input with displacement increment Δ. u =0.05mm / min, and perform separate coupled transient calculations in the order of displacement field-historical strain field-phase field to obtain stress, strain and phase field distribution respectively; Step 6: Keep the displacement loading rate constant and repeat step 5 until the rock is completely fractured and the calculation is stopped. This will give you the true shear fracture morphology of the rock at different bedding angles.

2. The method for calculating the true shear fracture of anisotropic rocks based on the Brazilian disk experiment as described in claim 1, characterized in that, In step 1, the physical and mechanical parameters include: the elastic modulus, shear modulus, Poisson's ratio, shear fracture toughness, and Biot coefficient of the rock along and perpendicular to the bedding direction; the engineering geological environment parameters include: the confining pressure, pore pressure, and in-situ stress of the rock; the geometric parameters of the double-notched Brazilian disk include: the radius of the disk, the size of the prefabricated notch, and the loading angle.

3. The method for calculating the true shear fracture of anisotropic rocks based on the Brazilian disk experiment as described in claim 1, characterized in that, In step 3, the specific steps for drawing the geometric calculation domain of the Brazilian disk with double notches are as follows: First, a circle with a radius of 37.5mm and a rectangle of 94mm×1.8mm are generated with the origin of the coordinate system as the center. Then, two interpolation curves are established in coordinate form to determine the length of the prefabricated notch. All geometric objects are merged through Boolean set and then the prefabricated notch areas on both sides are deleted. Finally, the calculation domain of the Brazilian disk model with double notches is obtained. Establish a built-in basis vector coordinate system, as shown in equation (3): （3）； In the formula, x and y Representing the global coordinate system x Axial direction and y Axial direction; x and y ´ represent perpendicular to the bedding direction and along the bedding direction, respectively; α Indicates the direction along the bedding plane and y The included angle along the axial direction was selected from five different bedding angles. α =0°, 22.5°, 45°, 67.5° and 90° are used for realistic shear simulation analysis.

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