Method, device and equipment for simulating shear failure and friction fracture of rock material

Abstract

The invention provides a rock material shear failure and friction fracture simulation method, device and equipment, and the rock material shear failure and friction fracture simulation method comprises the steps: determining a fourth-order tensor matrix corresponding to the stress tensor of a rock material according to a friction fracture phase field model; establishing a crack surface local coordinate system, correcting a traditional degradation function to obtain a target degradation function, and introducing the target degradation function and a crack density function; in the friction fracture phase field model, historical field variables are set, and a friction fracture phase field control equation is determined; and based on the friction fracture phase field control equation, obtaining a stress field, a phase field finite element weak form, a residual error and a stiffness matrix. According to the invention, the traditional phase field model is optimized, the calculation precision of the phase field model is improved, and the simulation result is more reliable.

Description

Technical Field

[0001] The present invention relates to the technical field of geological disaster prevention and control, and particularly relates to a method, device and equipment for simulating shear failure and frictional fracture of rock materials. Background Technique

[0002] The propagation and evolution of internal cracks in rocks are one of the reasons for the continuous deterioration of the macroscopic mechanical parameters of rocks, and also the fundamental reasons for rock engineering and geological disasters. To explain the phenomenon of rock crack propagation and solve the problems such as the instability of crack propagation in rock engineering, scholars at home and abroad have conducted in-depth research on this. Indoor experimental research was first used to study the problem of crack propagation, and remarkable achievements have been made in theoretical research and numerical simulation, etc.

[0003] The existing theories on rock damage and fracture mainly include strength theory, fracture theory, damage theory, etc. Among them, the rock strength theory is the most widely used in scientific research and engineering problems. The most widely applied strength theory is the Mohr-Coulomb strength criterion. In addition, there are such as the Drucker-Prager criterion, Griffith strength theory, and Hoek-Brown criterion. These criteria are widely used in engineering practice and numerical simulation, and remarkable effects have been achieved.

[0004] For complex geotechnical engineering problems, the failure process of rocks mostly needs to be solved by numerical simulation. From the current calculation methods, they are roughly divided into two types according to the characteristics of the methods. One is the continuous method, including the gradient damage method, viscous regularization method, and phase field method; the other is the discrete method, such as the extended finite element method, discrete element method, discontinuous deformation analysis method, and cohesive element method. Among the continuous methods, the phase field method has received extensive attention. Compared with other methods, the advantage of the phase field method is that it disperses sharp cracks into continuous damage values, eliminates the discontinuous problem of the displacement field, and can automatically capture the initiation, nucleation, merging, and branching of cracks. However, the existing simulation evolution methods are not sensitive to the phase field characteristic length, the calculation accuracy is not good, and the reliability of the simulation results is relatively low.

[0005] Regarding the problem of poor calculation accuracy of the existing simulation evolution methods, no effective solution has been proposed yet. Summary of the Invention

[0006] The present invention provides a method, device and equipment for simulating shear failure and frictional fracture of rock materials to solve the defect of poor calculation accuracy of the existing simulation evolution methods.

[0007] In the first aspect, the present invention provides a method for simulating shear failure and frictional fracture of rock materials, including: Determine the fourth-order tensor matrix corresponding to the stress tensor of the rock material according to the frictional fracture phase field model; Establish a local coordinate system for the crack surface, correct the traditional degradation function to obtain the target degradation function, and introduce the target degradation function and the crack density function; In the frictional fracture phase field model, set the historical field variables and determine the frictional fracture phase field control equation; Based on the frictional fracture phase field control equation, obtain the finite element weak forms of the stress field and the phase field, as well as the residual and stiffness matrices.

[0008] According to a method for simulating shear failure and frictional fracture of rock materials provided by the present invention, according to the frictional fracture phase field model, determine the fourth-order tensor matrix corresponding to the stress tensor of the rock material, including: Introduce a local coordinate system, and determine the normal strain and normal stress of the rock material according to the strain tensor and the normal vector; Determine the current state of the crack surface of the rock material according to the normal strain or normal stress of the rock material; Based on the current state of the crack surface of the rock material, generate the fourth-order tensor matrix.

[0009] According to a method for simulating shear failure and frictional fracture of rock materials provided by the present invention, determine the current state of the crack surface of the rock material according to the normal strain of the rock material, including: If the normal strain of the rock material is greater than zero, the crack surface of the rock material is in an open state; If the normal strain of the rock material is less than or equal to zero, the crack surface of the rock material is in a contact state.

[0010] According to a method for simulating shear failure and frictional fracture of rock materials provided by the present invention, when the crack surface of the rock material is in an open state, determine the stress tensor of the rock material according to damage attenuation; When the crack surface of the rock material is in a contact state, introduce a friction function, determine whether the crack surface of the rock material is in a bonded state or a sliding state, and determine the corresponding stress tensor.

[0011] According to a method for simulating shear failure and frictional fracture of rock materials provided by the present invention, introduce a friction function to determine whether the crack surface of the rock material is in a bonded state or a sliding state, including: If the friction function value is less than zero, the crack surface of the rock material is in a bonded state and there is no relative movement between the crack surfaces; If the friction function value is greater than or equal to zero, the crack surface of the rock material is in a sliding state and there is friction between the crack surfaces.

[0012] According to a method for simulating shear failure and frictional fracture of rock materials provided by the present invention, establish a local coordinate system for the crack surface, including: Determine the normal and tangential directions of the crack surface of the rock material; Generate a local coordinate system of the crack surface based on the normal and tangential directions of the crack surface of the rock material.

[0013] According to a method for simulating shear failure and frictional fracture of rock materials provided by the present invention, determining the normal and tangential directions of the crack surface of the rock material includes: Determine the angle between the principal stress and the shear plane when the shear stress of the rock material is maximized; Determine the normal vector and tangential vector of the crack surface of the rock material according to the angle.

[0014] According to a method for simulating shear failure and frictional fracture of rock materials provided by the present invention, in the frictional fracture phase field model, set the historical field variable and determine the frictional fracture phase field control equation, including: At the initial stage of the evolution of the frictional fracture phase field model, assign an initial value to the historical field variable; In the loading stage of the frictional fracture phase field model, update the value of the historical field variable according to the state of the integration point, and determine the frictional fracture phase field control equation according to the historical field variable.

[0015] In a second aspect, the present invention also provides a device for simulating shear failure and frictional fracture of rock materials, including: A determination module, configured to determine a fourth-order tensor matrix corresponding to the stress tensor of the rock material according to the frictional fracture phase field model; A correction module, configured to establish a local coordinate system of the crack surface, correct the traditional degradation function to obtain a target degradation function, and introduce the target degradation function and the crack density function; An evolution module, configured to set a historical field variable in the frictional fracture phase field model and determine the frictional fracture phase field control equation; A generation module, configured to obtain the finite element weak forms of the stress field and the phase field, as well as the residual and stiffness matrices based on the frictional fracture phase field control equation.

[0016] In a third aspect, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, it implements the method for simulating shear failure and frictional fracture of rock materials as described in the first aspect above.

[0017] In a fourth aspect, the present invention also provides a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the method for simulating shear failure and frictional fracture of rock materials as described in the first aspect above.

[0018] Fifthly, the present invention also provides a computer program product, including a computer program which, when executed by a processor, implements the method for simulating shear failure and frictional fracture of rock materials as described in the first aspect above.

[0019] Compared with the prior art, the present invention has the following beneficial effects: The method for simulating shear failure and frictional fracture of rock materials provided by the present invention takes into account the problem that the traditional model is insensitive to the phase field characteristic length. By introducing a new degradation function and crack density function, the traditional phase field model is optimized, the calculation accuracy of the phase field model is improved, and the simulation results are more reliable. In addition, the above process can all be programmed, which is convenient for operation and programming. The simulation of shear failure and frictional fracture of rock materials based on the phase field method is realized by a computer, greatly reducing the amount of manual calculation. Description of the Drawings

[0020] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0021] Figure 1 is a flowchart of the method for simulating shear failure and frictional fracture of rock materials provided by the present invention; Figure 2 is a schematic diagram of the geometric dimensions and boundary conditions of a square plate with a prefabricated crack in the embodiment of the present invention; Figure 3 is a phase field distribution diagram with different characteristic lengths in the embodiment of the present invention; Figure 4 is a contour map of the displacement distribution in the horizontal direction with different characteristic lengths in the embodiment of the present invention; Figure 5 is a contour map of the displacement distribution in the vertical direction with different characteristic lengths in the embodiment of the present invention; Figure 6 is a contact normal stress curve diagram in the embodiment of the present invention; Figure 7 is a contact tangential stress curve diagram in the embodiment of the present invention; Figure 8 is a schematic diagram of the geometric dimensions and boundary conditions of a biaxial compression numerical model in the embodiment of the present invention; Figure 9 is a force-displacement curve diagram of the loading process in the embodiment of the present invention; Figure 10 is in the embodiment of the present invention Schematic diagram of the evolution process of the phase field of the biaxial compression model at [[ID=]] = 100 KPa; Figure 11 In the embodiment of the present invention Schematic diagram of the evolution process of the vertical displacement field at [[ID=]] = 100 KPa; Figure 12 Schematic diagram of the geometric dimensions and displacement boundary conditions of the slope in the embodiment of the present invention; Figure 13 Displacement evolution nephogram of the slope in the embodiment of the present invention; Figure 14 Phase field evolution nephogram of the slope in the embodiment of the present invention; Figure 15 Structural block diagram of the shear failure and frictional fracture simulation device for rock materials provided by the present invention; Figure 16 Structural schematic diagram of the electronic device provided by the present invention. Specific embodiments

[0022] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions in the present invention will be clearly and completely described below with reference to the accompanying drawings in the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0023] The present invention provides a method for simulating shear failure and frictional fracture of rock materials, Figure 1 It is a flowchart of the method for simulating shear failure and frictional fracture of rock materials provided by the present invention, as Figure 1 shown, and the method includes the following steps: Step S101, according to the frictional fracture phase field model, determine the fourth-order tensor matrix corresponding to the stress tensor of the rock material; Step S102, establish a local coordinate system of the crack surface, correct the traditional degradation function to obtain a target degradation function, and introduce the target degradation function and the crack density function; Step S103, in the frictional fracture phase field model, set the historical field variables and determine the frictional fracture phase field control equation; Step S104, based on the frictional fracture phase field control equation, obtain the finite element weak forms of the stress field and the phase field, as well as the residual and stiffness matrices.

[0024] In this method, the frictional fracture phase field model is reproduced, and the fourth-order tensor matrix corresponding to the stress tensor of the rock material is determined according to the frictional fracture phase field model. Then, a local coordinate system of the crack surface is constructed, and due to the coarsely corrected target degradation function and the crack density function, the traditional frictional fracture phase field model is optimized. Then, in the frictional fracture phase field model, historical field variables are set, and the frictional fracture phase field control equation is determined. Finally, according to the frictional fracture phase field control equation, the finite element weak forms of the stress field and the phase field are derived, and their residuals and stiffness matrices are obtained. In the above process, considering the problem that the traditional model is insensitive to the phase field characteristic length, the traditional phase field model is optimized by introducing new degradation functions and crack density functions, improving the calculation accuracy of the phase field model and making the simulation results more reliable. In addition, the above process can all be programmed, which is convenient for operation and programming, and realizes the simulation of shear failure and frictional fracture of rock materials based on the phase field method through a computer, greatly reducing the amount of manual calculation.

[0025] In some of these embodiments, step S101 of determining the fourth-order tensor matrix corresponding to the stress tensor of the rock material according to the frictional fracture phase field model includes: introducing a local coordinate system, and determining the normal strain and normal stress of the rock material according to the strain tensor and the normal vector; determining the current state of the crack surface of the rock material according to the normal strain or normal stress of the rock material; and generating a fourth-order tensor matrix based on the current state of the crack surface of the rock material.

[0026] Specifically, determining the current state of the crack surface of the rock material according to the normal strain of the rock material includes: if the normal strain of the rock material is greater than zero, the crack surface of the rock material is in an open state; if the normal strain of the rock material is less than or equal to zero, the crack surface of the rock material is in a contact state.

[0027] More specifically, when the crack surface of the rock material is in an open state, the stress tensor of the rock material is determined according to damage attenuation; when the crack surface of the rock material is in a contact state, a friction function is introduced to determine whether the crack surface of the rock material is in a bonded state or a sliding state, and the corresponding stress tensor is determined.

[0028] Introducing a friction function to determine whether the crack surface of the rock material is in a bonded state or a sliding state includes: if the friction function value is less than zero, the crack surface of the rock material is in a bonded state and there is no relative movement between the crack surfaces; if the friction function value is greater than or equal to zero, the crack surface of the rock material is in a sliding state and there is friction between the crack surfaces.

[0029] Exemplarily, introducing a local coordinate system, the crack surface normal vector is , and the tangential vector is , assuming that the normal direction of the crack surface is the Y-axis and the tangential direction of the crack surface is the X-axis. Given the known interface normal vector, the strain in the normal direction is calculated based on the strain tensor and the normal vector, and its expression is:

[0030] Among them, represents the normal strain, represents the strain tensor. The corresponding normal stress can be expressed as:

[0031] Among them, and are Lame constants. The normal strain or normal stress can distinguish whether the crack surface is in a contact state or an open state. When , it indicates that the crack surface is open and there is no frictional contact. There is no contact stress on the crack surface. Therefore, , represents the contact stress on the crack surface, and the stress tensor can be directly determined according to the damage attenuation:

[0032] Among them, represents the stress tensor, g ( d ) represents the damage function of the crack surface, is the stress tensor when the rock material is intact, , represents the elastic coefficient matrix.

[0033] On the contrary, when , the crack surface is in a contact state. There are two states of crack contact, namely the bonding state and the sliding state. A friction function needs to be introduced, and its expression is:

[0034] Among them, f represents the friction function value. When , the contact surface begins to slide. When , the crack surface is in the bonding state, represents the shear yield strength of the rock material, represents the shear stress along the crack surface, and its calculation expression is as follows:

[0035] Among them, G represents the shear modulus, is the tensor obtained from the normal vector and the tangential vector, .

[0036] When the crack surfaces are in a bonded state, there is no relative movement between the crack surfaces. Assuming that the material matrix is the same as the intact material matrix, the stress tensor of the crack surfaces when they are in a bonded state can be expressed as:

[0037] When the crack surfaces are in a sliding state, there is friction between the crack surfaces, and the shear modulus needs to be attenuated along the shear direction during the sliding process. Its expression is:

[0038] Among them, is a fourth-order tensor, which can be calculated from the normal vector, , is the shear modulus, and C bulk represents the bulk modulus of the material, is the frictional stress tensor, and its expression is as follows:

[0039] Among them, p n represents the normal stress of the crack surface, represents the residual friction angle. Combining the above formulas, the expression form of the stress tensor can be obtained as follows:

[0040] Correspondingly, the fourth-order tensor matrix of the stress tensor can be expressed as:

[0041] During the derivation of the fourth-order tensor matrix, the frictional force is regarded as an external force and does not participate in the calculation of the fourth-order tensor.

[0042] In some of these embodiments, in step S102, a local coordinate system of the crack surface is established, including: determining the normal and tangential directions of the crack surface of the rock material; generating a local coordinate system of the crack surface based on the normal and tangential directions of the crack surface of the rock material.

[0043] The direction in which shear occurs is the direction with the maximum energy dissipation, which is equivalent to the direction with the maximum shear stress. Therefore, in this embodiment, determining the normal and tangential directions of the crack surface of the rock material includes: determining the angle between the principal stress and the shear plane when the shear stress of the rock material is maximized; determining the normal vector and tangential vector of the crack surface of the rock material according to the angle.

[0044] Exemplarily, use to represent the angle between the principal stress and the shear plane, and the expression is as follows:

[0045] wherein, is the residual shear stress, assuming , p N represents the normal stress on the crack surface, and its expression is:

[0046] The peak shear strength of the Mohr–Coulomb strength criterion is:

[0047] wherein, is the cohesion, is the friction angle. The yield strengths of the intact rock material and the damaged rock material are inconsistent. Assume that the yield strength is related to the phase field:

[0048] wherein, d represents the phase field. Express , , as the first principal stress, the intermediate principal stress, and the minimum principal stress in the compression state. The slip plane is constructed by and . On this plane, and can be expressed as:

[0049]

[0050] Combining the above formulas, we can obtain:

[0051] Taking the derivative of the above formula, we can obtain the angle between the principal stress and the shear plane when the shear stress of the rock material is maximized:

[0052] Assume , and are the unit direction vectors corresponding to the principal stresses. Given the known angle, the normal vector and the tangential vector of the crack surface can be expressed as:

[0053]

[0054] During the numerical simulation process, when damage occurs, the normal vector at this time will be recorded and the tangential vector , and the direction vector of this integration point will no longer change at subsequent time steps.

[0055] Introduce new degradation functions and crack density functions to ensure that the phase field model is insensitive to the characteristic length. The general form of the crack density function is written as:

[0056] where represents the local energy density function, is the local dissipated energy density function, and its expression is , and this density function will make the phase field sensitive to the characteristic length , so it is necessary to eliminate this influence to ensure that the material properties are reflected during shearing. Select .

[0057] Because the density function of the phase field has changed and its first derivative will have a constant term, it is necessary to correct its degradation function. The expression of the degradation function is:

[0058] In the above formula, the polynomial expression is:

[0059] To ensure that the phase field evolution is insensitive to the phase field characteristic length , the parameters of the degradation function are corrected. Take = 2, , and is derived to obtain:

[0060] where represents the energy release rate, is the energy threshold to ensure that the phase field does not evolve in the initial state, and its expression is:

[0061] where c represents the cohesive force, G represents the shear modulus. The first derivative of the degradation function can be expressed as:

[0062] where m represents the coefficient after derivation and simplification.

[0063] In some of these embodiments, in step S103, in the frictional fracture phase field model, historical field variables are set and the frictional fracture phase field control equation is determined, including: in the initial stage of the evolution of the frictional fracture phase field model, initial values are assigned to the historical field variables; in the loading stage of the frictional fracture phase field model, the values of the historical field variables are updated according to the status of the integration points, and the frictional fracture phase field control equation is determined based on the historical field variables.

[0064] In this embodiment, in order to ensure the irreversibility of crack propagation, it is necessary to set historical field variables , in the frictional fracture phase field model, its historical field variables have inconsistent expression forms in different states. In the initial stage of calculation, it is necessary to assign initial values to the historical field variables:

[0065] Among them, H t represents the initial value of the historical field variable. When the model is gradually loaded, the states of different integration points are different, and the evolution of the historical field variables is inconsistent, which can be expressed as:

[0066] Among them, t n represents the time step, is the shear strain between adjacent time steps, which can be expressed as: . After obtaining the historical field variable , the frictional fracture phase field control equation can be obtained:

[0067]

[0068] Among them, represents the gradient operator, represents the stress tensor, represents the surface force, and b represents the body force. Based on the control equation, the weak forms of the stress field and the phase field finite element can be obtained, and their residuals and stiffness matrices are derived. The residual of the phase field can be expressed as:

[0069] Among them, R d represents the residual of the phase field, N d represents the shape function matrix, B d represents the strain matrix, represents the integration domain. After obtaining the residual equation of the phase field, the stiffness matrix of the phase field can be established:

[0070] Among them, represents the stiffness matrix of the phase field, represents the strain function matrix of the i-th node, represents the strain function matrix of the j-th node, represents the shape function matrix of the i-th node, represents the shape function matrix of the j-th node, is the second derivative of the degradation function, which can be expressed as:

[0071] Among them, is the second derivative of the degradation function.

[0072] In summary, under the action of tectonic stress, cracks are widespread in rock masses. During the crack propagation process, most of them are mainly shear fractures, and tensile failures are less. Aiming at the common shear failure phenomenon in rock masses, the shear elastic energy is decomposed along the crack surface, a phase field model of shear failure is developed, and a cohesive force model is introduced at the same time, making the model insensitive to the phase field characteristic length; the basic control equations of the frictional fracture phase field are derived, and this model is used to simulate the frictional fracture problems of rock-like materials. In addition, all calculation processes can be programmed, which is convenient for operation and programming. The shear failure and frictional fracture simulation of rock materials based on the phase field method are realized by computer, greatly reducing the artificial calculation amount. Therefore, the advantages of this method are: considering that the model is insensitive to the phase field characteristic length, improving the calculation accuracy, and making the simulation results more reliable.

[0073] To verify the effectiveness of the above method, the following simulation experiments were carried out: 1. Simulation of a square plate with a prefabricated internal crack A square plate contains a prefabricated crack. The square plate is subjected to compression, and its geometric dimensions and boundary conditions are as Figure 2 shown, Figure 2 is a schematic diagram of the geometric dimensions and boundary conditions of the square plate with a prefabricated crack in the embodiment of the present invention. The model is 1 m wide, and the starting and ending coordinates of the prefabricated crack are (0.3, 0.33) m and (0.7, 0.68) m respectively. The elastic modulus of the model = 1 GPa, Poisson's ratio = 0.3, the friction angle and the residual friction angle are both 5.71° ( = 0.1), the cohesive force = 10 MPa, the energy release rate = 30 N / m. A vertical displacement load is applied downward to the top of the model, with a total of 0.1 mm applied in 10 steps. To study the influence of the characteristic length on the numerical calculation results, the characteristic length Three values are set, which are 0.002m, 0.004m and 0.006m respectively. The model is discretized using quadrilateral elements, and the total number of elements is 155,848. The minimum element size = 0.0004m. Therefore, the ratios of the characteristic length to the element size are 5, 10 and 15 respectively, and the ratios are sufficient to meet the accuracy requirements.

[0074] Figure 3 is the phase field distribution diagram of different characteristic lengths in the embodiment of the present invention. From Figure 3 it can be seen that as the characteristic length increases, the dispersion width of the prefabricated crack also gradually increases. Figure 4 is the displacement distribution nephogram in the horizontal direction of different characteristic lengths in the embodiment of the present invention. Figure 5 is the displacement distribution nephogram in the vertical direction of different characteristic lengths in the embodiment of the present invention. From Figure 4 and Figure 5 it can be seen that under different characteristic lengths the numerical simulation results are basically consistent.

[0075] Figure 6 is the contact normal stress curve diagram in the embodiment of the present invention. Figure 7 is the contact shear stress curve diagram in the embodiment of the present invention. From Figure 6 and Figure 7 it can be seen that the calculation results of different characteristic lengths are basically the same. As the characteristic length decreases, the peak strength of the stress is higher, indicating that the characteristic length makes the dispersion width of the phase field smaller, and the calculation results are closer to the crack discontinuity of the actual situation, and the convergence effect is better. The smaller the value of the characteristic length , the finer the mesh needs to be divided, and the calculation amount is larger. Therefore, the value of the characteristic length is kept at ≥ 5 to meet the accuracy requirements.

[0076] 2. Biaxial compression experiment simulation This simulation is to subject the test containing defects to shear failure under biaxial compression and explore the influence of different confining pressures on the shear peak strength and residual strength of the specimen. The geometric dimensions and boundary conditions of the model are as Figure 8 shown. Figure 8 is the schematic diagram of the geometric dimensions and boundary conditions of the biaxial compression numerical model in the embodiment of the present invention. Confining pressures are applied to both the left and right sides of the model , the displacement in the Y direction is constrained at the bottom, and a vertical downward displacement load is applied at the top. The displacement at the middle point of the top is fixed in the horizontal direction to prevent the occurrence of non-convergence in the calculation due to rigid body displacement during the simulation. The shear modulus of the model = 26 MPa, Poisson's ratio = 0.3, cohesion = 40 KPa. It is assumed that the friction angle is equal to the residual friction angle, = 15°, energy release rate = 20 N / m, characteristic length of the phase field = 1 mm. The model is discretized using quadrilateral elements, and the minimum element size = 0.2 mm. The total number of elements is 60222. Three different confining pressures are set, which are 50 KPa, 100 KPa, and 200 KPa respectively, and the loading rate is 0.001 mm per step.

[0077] The confining pressure is applied to the model first, and then the displacement load is applied. Figure 9 is the force-displacement curve diagram during the loading process in the embodiment of the present invention. It can be seen from Figure 9 that the shear strength of the phase field model of frictional fracture will change with the stress distribution, and the peak shear strength and residual shear strength of the material can be predicted. Moreover, as the displacement load increases, the curve gradually becomes stable, indicating that the shear crack has penetrated. The latter part of the curve is the residual shear strength of the material under the current stress state. Figure 10 is in the embodiment of the present invention = 100 KPa, a schematic diagram of the evolution process of the phase field of the biaxial compression model, Figure 11 is in the embodiment of the present invention = 100 KPa, a schematic diagram of the evolution process of the vertical displacement field. It can be seen from Figure 9 that before = -1.2 mm, the value of the shear phase field does not completely equal 1, and the model is in the shear strength softening stage, rapidly decreasing from the peak strength. As the displacement load increases, the shear crack gradually penetrates, and the latter part of the curve also gradually remains unchanged.

[0078] 3. Simulation of soil slope instability Landslides are one of the most common natural disasters, causing significant economic and human losses. Progressive cracks are the root causes of slope instability. Frictional sliding is the main mechanism for the cracking and instability of many slopes. In this section, the proposed phase field model of frictional fracture is applied to slope instability analysis. According to previous studies, the simplified slope is as shown in Figure 12 , Figure 12It is a schematic diagram of the geometric dimensions and displacement boundary conditions of the slope in the embodiment of the present invention. The slope is 20 m wide and 10 m high. The slope is unstable and damaged due to the loading at the top of the slope. It is assumed that the loading object is a rigid body with a width of 4 m, and the displacement increment applied at each time step is =-4×10 -4 m. The displacement at the bottom of the slope is fixed, and the displacement in the horizontal direction is restricted on the right side. The elastic modulus of the slope =8.4 MPa, Poisson's ratio =0.4, soil density =2.04×103 kg / m 3 , cohesion =40 KPa, friction angle =16.7°, residual friction angle =10°, energy release rate =10 kN / m, phase field characteristic length =0.1 m. The model is discretized using quadrilateral elements, and the minimum size of the elements =0.02 m.

[0079] The simulation first performs in-situ stress balance and then applies displacement load until the slope fails. Although the in-situ stress balance at the beginning does not seem to have any effect on the slope, the existence of the initial in-situ stress will give the slope an initial shear strength, and after the slope fails, the initial in-situ stress field promotes the slope to slide downward. Figure 13 It is the displacement evolution nephogram of the slope in the embodiment of the present invention, Figure 14 It is the phase field evolution nephogram of the slope in the embodiment of the present invention. From Figure 13 and Figure 14 it can be seen that the rupture surface of the landslide first occurs on the left side of the rigid body loading and then gradually develops downward in an arc shape until it develops into a through rupture surface.

[0080] The present invention also provides a simulation device for shear failure and frictional fracture of rock materials. The simulation device for shear failure and frictional fracture of rock materials provided by the present invention will be described below. The simulation device for shear failure and frictional fracture of rock materials described below can be mutually corresponded and referred to with the simulation method for shear failure and frictional fracture of rock materials described above. Figure 15 It is the structural block diagram of the simulation device for shear failure and frictional fracture of rock materials provided by the present invention. As Figure 15 shown, the device includes: A determination module 1501, configured to determine a fourth-order tensor matrix corresponding to the stress tensor of the rock material according to the frictional fracture phase field model; A correction module 1502, configured to establish a local coordinate system of the crack surface, correct the traditional degradation function to obtain a target degradation function, and introduce the target degradation function and the crack density function; An evolution module 1503 for setting historical field variables and determining the governing equations of the frictional fracture phase field model in the frictional fracture phase field model; A generation module 1504 for obtaining the finite element weak forms of the stress field and the phase field, as well as the residual and stiffness matrices based on the governing equations of the frictional fracture phase field.

[0081] When the device is in use, the determination module 1501 replicates the frictional fracture phase field model and determines the fourth-order tensor matrix corresponding to the stress tensor of the rock material according to the frictional fracture phase field model. Then, the correction module 1502 constructs a local coordinate system of the crack surface, due to the coarsely corrected target degradation function and the crack density function, thereby optimizing the traditional frictional fracture phase field model. Then, the evolution module 1503 sets historical field variables in the frictional fracture phase field model and determines the governing equations of the frictional fracture phase field. Finally, the generation module 1504 derives the finite element weak forms of the stress field and the phase field according to the governing equations of the frictional fracture phase field and obtains its residual and stiffness matrices. In the above process, considering the problem that the traditional model is insensitive to the characteristic length of the phase field, by introducing a new degradation function and a crack density function, the traditional phase field model is optimized, the calculation accuracy of the phase field model is improved, and the simulation results are made more reliable. In addition, the above process can all be programmed, which is convenient for operation and programming. Through a computer, the shear failure and frictional fracture simulation of rock materials based on the phase field method are realized, greatly reducing the artificial calculation amount. Figure 16 An example of the physical structure diagram of an electronic device is shown as Figure 16 As shown, the electronic device may include: a processor 1601, a communication interface 1602, a memory 1603, and a communication bus 1604. Among them, the processor 1601, the communication interface 1602, and the memory 1603 complete mutual communication through the communication bus 1604. The processor 1601 can call the logical instructions in the memory 1603 to execute the method for simulating the shear failure and frictional fracture of rock materials, and the method includes: Determining the fourth-order tensor matrix corresponding to the stress tensor of the rock material according to the frictional fracture phase field model; Establishing a local coordinate system of the crack surface, correcting the traditional degradation function to obtain a target degradation function, and introducing the target degradation function and the crack density function; Setting historical field variables in the frictional fracture phase field model and determining the governing equations of the frictional fracture phase field; Obtaining the finite element weak forms of the stress field and the phase field, as well as the residual and stiffness matrices based on the governing equations of the frictional fracture phase field.

[0082] In addition, when the logical instructions in the above-mentioned memory 1603 are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods according to the various embodiments of the present invention. The aforementioned storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs that can store program codes.

[0083] On the other hand, the present invention also provides a computer program product. The computer program product includes a computer program. The computer program can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the rock material shear failure and friction fracture simulation method provided by the above-mentioned various methods. The method includes: According to the friction fracture phase field model, determine the fourth-order tensor matrix corresponding to the stress tensor of the rock material; Establish a local coordinate system of the crack surface, correct the traditional degradation function to obtain a target degradation function, and introduce the target degradation function and the crack density function; In the friction fracture phase field model, set historical field variables and determine the friction fracture phase field control equation; Based on the friction fracture phase field control equation, obtain the finite element weak forms of the stress field and the phase field, as well as the residual and stiffness matrices.

[0084] On another aspect, the present invention also provides a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it is implemented to execute the rock material shear failure and friction fracture simulation method provided by the above-mentioned various methods. The method includes: According to the friction fracture phase field model, determine the fourth-order tensor matrix corresponding to the stress tensor of the rock material; Establish a local coordinate system of the crack surface, correct the traditional degradation function to obtain a target degradation function, and introduce the target degradation function and the crack density function; In the friction fracture phase field model, set historical field variables and determine the friction fracture phase field control equation; Based on the friction fracture phase field control equation, obtain the finite element weak forms of the stress field and the phase field, as well as the residual and stiffness matrices.

[0085] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed to multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment. A person of ordinary skill in the art can understand and implement it without creative labor.

[0086] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on such an understanding, the essence of the above technical solution, or the part that contributes to the prior art, can be embodied in the form of a software product. The computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0087] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments or perform equivalent replacements for some of the technical features. And these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for simulating shear failure and friction fracture of rock materials, characterized in that: include: According to the friction fracture phase field model, the fourth-order tensor matrix corresponding to the stress tensor of the rock material is determined; A local coordinate system of the crack surface is established, the traditional degradation function is modified to obtain a target degradation function, and the target degradation function and crack density function are introduced; In the friction fracture phase field model, setting the history field variables and determining the friction fracture phase field control equations; Based on the friction fracture phase field governing equations, the stress field and phase field finite element weak forms, as well as the residual and stiffness matrices are obtained.

2. The rock material shear failure and friction fracture simulation method according to claim 1, characterized in that: According to the friction fracture phase field model, the fourth-order tensor matrix corresponding to the stress tensor of the rock material is determined, including: A local coordinate system is introduced to determine the normal strain and normal stress of the rock material according to the strain tensor and the normal vector; Determining a current state of a crack surface of the rock material according to a normal strain or a normal stress of the rock material; The fourth-order tensor matrix is ​​generated based on the current state of the crack surface of the rock material.

3. The rock material shear failure and friction fracture simulation method according to claim 2, characterized in that: Determining a current state of a crack surface of the rock material according to the normal strain of the rock material includes: If the normal strain of the rock material is greater than zero, the crack surface of the rock material is in an open state; If the normal strain of the rock material is less than or equal to zero, the crack surfaces of the rock material are in a contact state.

4. The rock material shear failure and friction fracture simulation method according to claim 3, characterized in that: When the crack surface of the rock material is in an open state, determining the stress tensor of the rock material according to damage attenuation; When the crack surface of the rock material is in a contact state, a friction function is introduced to determine whether the crack surface of the rock material is in a bonding state or a sliding state, and the corresponding stress tensor is determined.

5. The rock material shear failure and friction fracture simulation method according to claim 4, characterized in that: Introducing a friction function to determine whether the crack surface of the rock material is in a bonding state or a sliding state includes: If the friction function value is less than zero, the crack surfaces of the rock material are in a bonded state, and there is no relative movement between the crack surfaces; If the friction function value is greater than or equal to zero, the crack surfaces of the rock material are in a sliding state, and friction exists between the crack surfaces.

6. The rock material shear failure and friction fracture simulation method according to claim 1, characterized in that: Establish the local coordinate system of the crack surface, including: determining normal and tangential directions of a crack surface of the rock material; The crack surface local coordinate system is generated based on the normal and tangential directions of the crack surface of the rock material.

7. The rock material shear failure and friction fracture simulation method according to claim 6, characterized in that: Determining the normal and tangential directions of the crack surface of the rock material includes: Determining the angle between the principal stress and the shear plane when the shear stress of the rock material is maximized; The normal vector and the tangential vector of the crack surface of the rock material are determined according to the angle.

8. The rock material shear failure and friction fracture simulation method according to claim 1, characterized in that: In the friction fracture phase field model, the historical field variables are set and the friction fracture phase field control equations are determined, including: In the initial stage of the evolution of the friction fracture phase field model, initial values ​​are assigned to the historical field variables; In the loading stage of the friction fracture phase field model, the value of the historical field variable is updated according to the state of the integration point, and the friction fracture phase field control equation is determined according to the historical field variable.

9. A rock material shear failure and friction fracture simulation device, characterized in that: include: A determination module, used for determining a fourth-order tensor matrix corresponding to the stress tensor of the rock material according to a friction fracture phase field model; A correction module is used to establish a local coordinate system of the crack surface, correct the traditional degradation function, obtain the target degradation function, and introduce the target degradation function and crack density function; An evolution module, used for setting historical field variables and determining friction fracture phase field control equations in the friction fracture phase field model; A generation module is used to obtain the stress field and phase field finite element weak form, as well as the residual and stiffness matrices based on the friction fracture phase field governing equation.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the rock material shear failure and friction fracture simulation method as described in any one of claims 1 to 8 is implemented.

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