Rock dynamic shear failure simulation method and equipment considering frictional contact

Abstract

The invention provides a rock dynamic shear failure simulation method and equipment considering frictional contact. The method comprises the following steps: calculating a stress tensor and a four-order elastic modulus matrix according to an elastic constitutive relation of a rock material; establishing a crack surface local coordinate system based on a maximum shear stress criterion, and determining normal and tangential unit vectors; introducing a crack density function and a corresponding degradation function of the cohesion phase field model, and configuring to eliminate the influence of the phase field characteristic length; deducing an energy functional of a dynamic shear phase field model, judging a contact state according to normal strain of a crack surface, and deducing strong forms of a displacement field control equation and a phase field control equation; variational processing is conducted on the strong forms of the displacement field control equation and the phase field control equation, corresponding weak forms are obtained, rock dynamic shear failure simulation considering frictional contact is achieved based on the weak forms, and rock mass stability evaluation in geological disaster prevention and control is supported. The model is insensitive to the phase field characteristic length, and the simulation result is more reliable.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of geological disaster prevention and control, and particularly relates to a simulation technology for dynamic shear failure of rock material considering frictional contact. BACKGROUND

[0002] In rock mass engineering, complex structures such as cracks, joints, weak interlayers, crack cementation, etc. are formed in the rock mass after a long geological process, and these structure surfaces have a controlling influence on the stability of rock slope under seismic load. The expansion and evolution of cracks in the rock mass lead to continuous deterioration of the mechanical properties of the rock mass, which is the main reason for large-scale rock mass engineering instability and engineering geological disasters. Nowadays, the problem of crack propagation in rock material is a hot issue in current geotechnical engineering, and many experts and scholars have researched and achieved a large number of research results from the experimental or numerical simulation point of view.

[0003] However, due to the complexity of geotechnical engineering, it is generally difficult to obtain an analytical solution for the rock failure process, so numerical simulation has become an important means for studying rock damage, and the numerical solution is obtained by iteration to analyze the rock failure mechanism. From the current numerical simulation method, the simulation method is divided into two kinds by accurately characterizing or dispersively characterizing the crack surface, one is the continuous method, such as gradient damage method, viscosity regularization method and phase field method; the other is the discrete method, such as extended finite element method, discrete element method, discontinuous deformation analysis method and cohesive force element method. The expansion and evolution of cracks in the rock mass will continuously deteriorate the mechanical properties, but the existing numerical simulation method cannot accurately capture the dynamic shear failure process, especially the simulation error of frictional contact behavior (such as crack surface closure, bonding and sliding) is high. SUMMARY

[0004] The technical problem to be solved by the present application is to provide a rock dynamic shear failure simulation method considering frictional contact, which is used to solve the stability prediction problem of fractured rock mass under seismic load.

[0005] The technical solution provided by the present application is a rock dynamic shear failure simulation method considering frictional contact, which comprises the following processes: According to the elastic constitutive relation of rock material, the stress tensor and the fourth-order elastic modulus matrix are calculated; Based on the maximum shear stress criterion, a local coordinate system of the crack surface is established to determine the normal and tangential unit vectors; the crack density function and the corresponding degradation function of the cohesive force phase field model are introduced, and the crack density function and the degradation function are configured to eliminate the influence of the phase field characteristic length; The energy functional of the dynamic shear phase field model is derived, the contact state is judged according to the normal strain of the crack surface, and the strong form of the displacement field control equation and the phase field control equation is derived; The strong forms of the displacement field control equation and the phase field control equation are subjected to variational processing to obtain the corresponding weak forms. Based on the weak forms, dynamic shear failure simulation of rocks considering frictional contact is realized, which supports rock mass stability assessment in geological disaster prevention and control.

[0006] Furthermore, the establishment of a local coordinate system for the crack surface based on the maximum shear stress criterion includes taking the direction of maximum shear stress as the crack propagation direction, and then determining the normal and tangential unit vectors of the crack surface.

[0007] When configuring the crack density function, the influence of the phase field characteristic length is eliminated by setting the local dissipated energy density function to the appropriate form that correctly simulates the material shear parameters.

[0008] Moreover, when configuring the degradation function, the parameter values ​​are adjusted to ensure that the phase field evolution is insensitive to the phase field feature length.

[0009] Moreover, the energy functional includes strain energy, frictional internal energy, fracture energy, system kinetic energy, and work done by external forces.

[0010] Moreover, the strong forms of the displacement field control equation and the phase field control equation are obtained based on the balance between the energy input to the system by external forces and the energy consumed within the system.

[0011] Furthermore, the stress divergence term in the displacement field control equation and the phase field driving force term in the phase field control equation are calculated by differential decomposition based on the contact state of the crack surface; the contact state includes the opening state, the bonding state, and the sliding state.

[0012] On the other hand, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the rock dynamic shear failure simulation method considering frictional contact as described above.

[0013] On the other hand, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the rock dynamic shear failure simulation method considering frictional contact as described above.

[0014] On the other hand, the present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the rock dynamic shear failure simulation method considering frictional contact as described above.

[0015] This invention overcomes the challenges of physical simulation in rock engineering. Through the design of physical rules such as establishing a local coordinate system, correcting material constitutive relations (degeneracy functions), and constructing state-specific energy functionals, it ultimately outputs the rock mass failure prediction data required for engineering projects. Under tectonic stress and various dynamic loads, cracks are prevalent in rock masses, which primarily exhibit shear failure. This invention addresses the common shear failure phenomenon in rock masses by establishing a local coordinate system along the crack surface, decomposing the shear elastic energy along the crack surface, developing a dynamic shear phase field model considering frictional contact, and introducing the crack density function and degradation function from the cohesion model, making the model insensitive to the characteristic length of the phase field. The strong and weak forms of the displacement field and phase field governing equations are derived, completing the simulation of frictional shear failure of rock materials, and enabling the assessment of rock slope stability under seismic loads, thereby providing early warning support.

[0016] By automating the simulation of shear failure of rock materials under dynamic loads, the amount of manual calculation is greatly reduced.

[0017] Compared with existing technologies, the modeling method for the physical process of rock frictional contact proposed in this invention has been improved in the following aspects: (a) Establish a local coordinate system and define the contact state based on the maximum shear stress criterion; (b) Introduce specific crack density functions and degradation functions to eliminate characteristic length sensitivity; (c) An energy functional including the internal energy of friction was established, and an automatic generation scheme for stress tensor and phase field driving force was set according to the contact state (opening, bonding, sliding).

[0018] In summary, this invention overcomes the dependence of traditional phase-field methods on characteristic length when simulating rock shear failure, and can more accurately simulate the frictional contact behavior of crack surfaces (including normal closure, adhesion, and sliding) and their influence on energy dissipation and failure processes, thereby improving the accuracy and reliability of dynamic shear failure simulation.

[0019] This invention can be applied to safety control in geotechnical engineering, enabling stability monitoring of rock slopes, predicting instability risks and reducing accident rates by simulating dynamic shear failure; or supporting the design of underground engineering support, optimizing support schemes and extending the service life of projects by combining biaxial compression results. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the geometric dimensions and boundary conditions of the square plate with prefabricated internal cracks in Example 1; Figure 2 The figures show the stress diagrams of a square plate with pre-fabricated internal cracks at different times in Example 1, where (a) is... (b) is (c) is (d) is (e) is (f) is (g) is ; (h is) Stress diagram of the corresponding square plate at time t; Figure 3 For Example 1, prefabricated internal cracks Contact normal stress curve at 0.002m; Figure 4 For Example 1, prefabricated internal cracks Contact tangential stress curve at 0.002m; Figure 5 This is a schematic diagram of the geometry and boundary conditions of the direct shear test in Example 2; Figure 6 The figures are force-displacement curves at different shear rates in the direct shear test simulation of Example 2, where (a) is the curve at low shear rate (0.02 mm / s), (b) is the curve at medium shear rate (0.04 mm / s), and (c) is the curve at high shear rate (0.06 mm / s). Figure 7 The graphs show the shear strength-loading rate curves in the direct shear test simulation of Example 2, where (a) is the peak shear strength-loading rate curve and (b) is the residual shear strength-loading rate curve. Figure 8 This is a schematic diagram of the phase field evolution process in Example 2 when the shear rate is 0.06 mm / s and the normal stress is 150 kPa, where (a) is the horizontal displacement. =0.651 mm, (b) Horizontal displacement =0.681 mm, (c) horizontal displacement =0.723 mm, (d) horizontal displacement =0.783 mm; Figure 9 This is a schematic diagram of the displacement evolution process under a shear rate of 0.06 mm / s and a normal stress of 150 kPa in Example 2, where (a) is the horizontal displacement. =0.651 mm, (b) Horizontal displacement =0.681 mm, (c) horizontal displacement =0.723 mm, (d) horizontal displacement =0.783 mm; Figure 10 This is a schematic diagram of the geometry and boundary conditions for the biaxial compression test in Example 3; Figure 11This is a force-displacement curve diagram for biaxial compression under different confining pressures in Example 3, where (a) loading speed (b) Loading speed (c) Loading speed ; Figure 12 The graphs are shear strength-loading speed curves in the biaxial compression test simulation of Example 3. (a) is the peak strength-loading speed curve, and (b) is the residual strength-loading speed curve. Figure 13 For Example 3, the loading speed was 0.02 mm / s and the confining pressure was... The phase field evolution diagrams are shown, where (a) is the phase field distribution when the vertical displacement is 0.5 mm, (b) is the phase field distribution when the vertical displacement is 1.0 mm, and (c) is the phase field distribution when the vertical displacement is 1.5 mm. Figure 14 For Example 3, the loading speed was 0.02 mm / s and the confining pressure was... The vertical displacement evolution diagrams are shown, where (a) is the displacement diagram when the vertical displacement is 0.5 mm, (b) is the displacement diagram when the vertical displacement is 1.0 mm, and (c) is the displacement diagram when the vertical displacement is 1.5 mm.

[0021] Figure 15 The flowchart is for an example. Detailed Implementation

[0022] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0023] In practical engineering, rock masses often fail primarily due to shear failure. To study the crack propagation mechanism in rock masses under dynamic loading, this invention establishes a dynamic shear phase-field model considering frictional contact, introducing new density and degradation functions to optimize the traditional phase-field method. A square plate model with pre-existing internal cracks verifies that the model accurately reflects dynamic factors, and the results are compared with those calculated using the XFEM method, confirming the model's correctness. Direct shear tests are used to investigate the effects of normal stress and shear rate on shear strength. A biaxial compression model is used to study the effects of confining pressure and loading rate on peak shear strength and residual shear strength at shear failure, verifying the model's correctness.

[0024] See Figure 15 This invention provides a method for simulating dynamic shear failure of rock considering frictional contact. It simulates the frictional contact phenomenon and shear failure of rock materials under dynamic compressive loads. The method includes, after determining the expression forms of the stress and strain tensors based on the constitutive relations of the rock material, establishing a local coordinate system for the crack surface, introducing new crack surface density and degradation functions, deriving the strong and weak forms of the governing equations for the displacement and phase fields, and implementing them on a finite element platform. The specific implementation steps of this embodiment are as follows: Step 1: Based on the constitutive relation of rock materials, derive the expression forms of stress tensor and strain tensor; express the fourth-order tensor matrices of stress tensor and strain tensor; In step 1 of the embodiment, based on the constitutive relation of the rock material, the specific expression of the stress tensor is derived. In this invention, the elastic constitutive relation is used, that is, when the strain is... When, stress tensor The calculation formula is: (1.1) In the formula, The fourth elastic modulus of intact rock material is calculated using the following formula: (1.2) In the formula, and Let Lamé constant be . It is a second-order identity tensor. It is a fourth-order symmetric identity tensor.

[0025] After calculating the fourth-order matrices of the stress tensor and strain tensor using the above formula, the stress of intact rock can be attenuated according to the damage condition, and the crack surface state can be judged by normal strain, etc.

[0026] Step 2: Establish a local coordinate system for the crack surface based on the F criterion (maximum shear stress criterion); introduce the crack density function and corresponding degradation function of the cohesive phase field model; This invention proposes that, in step 2, a local coordinate system for the crack surface needs to be established, and a new crack surface density function and degradation function are introduced. The local coordinate system for the crack surface is established based on the maximum shear stress criterion, where the unit vectors in the normal and tangential directions are calculated using the principal stress directions. The crack density function and corresponding degradation function of the cohesive phase field model are introduced, wherein the crack density function and degradation function are configured to eliminate the influence of the phase field characteristic length.

[0027] To identify the contact state, a coordinate system is introduced relative to the normal and tangent directions of the crack surface, where the unit vector of the normal direction is... Indicates the direction of crack opening, tangential direction unit vector This indicates the direction of crack surface slip. Assume the crack surface normal is the Y-axis and the crack surface tangential is the X-axis. To determine the crack surface normal and tangential directions, the direction of maximum shear stress is taken as the crack propagation direction. This represents the angle between the principal stress and the shear failure surface. The angle that maximizes the shear stress is the desired angle, i.e.: (1.3) In the formula, For the complete region of shear stress, Residual stress (normal stress is) Its calculation and shear angle (For ease of description, all subsequent references will be abbreviated as follows) and Its expression is: (1.4) (1.5) In equation (1.5) It is the residual friction angle. For vectors with vector The dyadic vector is calculated using the following formula: If the strength criterion adopts the Mohr-Coulomb criterion, then the peak shear stress is... for: (1.6) In the formula, The cohesive strength of the material. It is the internal friction angle of the material.

[0028] Yield strength of material It will reflect the mechanical properties of the material; the yield strength of intact rock and damaged rock will differ when using phase field analysis. When used to represent damage, the yield strength of the rock can be... Represented as: (1.7) Assumption , , The sliding plane is defined by the first principal stress, intermediate principal stress, and minimum principal stress under triaxial compression. and Constructed on this plane, and It can be represented as: (1.8) Substituting equation (1.8) into equation (1.3), we obtain the formula for calculating the included angle: (1.9) By analyzing equation (1.9), we can obtain that letting the function , The value and Relevant, therefore it is necessary to find out Maximum angle value Through the Differentiate and solve outposts: The angle is: (1.10) After solving for the angle, assume , and It is the unit direction vector corresponding to the principal stress, and using the Rodriguez vector rotation formula, the crack surface normal vector. and tangential vector It can be represented as: (1.11) (1.12) To make the model calculation insensitive to characteristic length, a crack density function and a degradation function from the cohesive phase field model are introduced. The crack density function is: (1.13) In the above formula, Let be the local dissipation energy density function, and the traditional expression for the phase field density function is: , For phase field value, This represents the phase field gradient value. This is the normalization constant.

[0029] This density function will cause the phase field to be symmetrical about the characteristic length. While sensitive, this length sensitivity is unreasonable for cohesive phase-field models because the peak intensity of the viscous region should be a constant, related to the material's inherent properties, and should not be affected by the characteristic length. To eliminate this influence, the local dissipation energy density function is taken as... This allows it to accurately simulate material shear parameters. The new density function is then: (1.14) In the formula, The characteristic length of the phase field.

[0030] To match the new density function, a degenerate function is used. as follows: (1.15) In the formula, For the parameters of the degenerate function, the polynomial The expression is: (1.16) To ensure that the phase field evolution affects the phase field characteristic length Insensitive, the parameter values ​​of the degradation function have been modified, taking... =2, , The calculation formula is: (1.17) In the above formula, It is a type II energy release rate. This is the energy threshold, ensuring that the phase field does not evolve in its initial state. Only when the energy exceeds a certain threshold can the phase field evolve. The expression is: (1.18) In the formula, The cohesive strength of the material. This refers to the material's shear strength.

[0031] Then the first derivative of the new degenerate function for: (1.19) (1.20) In the formula, for Type of energy release rate, It is a coefficient related to material parameters.

[0032] Step 3: Derive the energy functional of the dynamic shear phase field model; based on the frictional contact phase field theory, determine the contact state of the crack surface and derive the strong form of the displacement field and phase field control equations; In step 3 of the embodiment, the energy functional of the dynamic shear phase field model is derived. The energy functional includes elastic strain energy, frictional internal energy, fracture energy, kinetic energy, and external force work. Based on the frictional contact phase field theory, the contact state of the crack surface is determined, and the displacement field and phase field control equations are derived.

[0033] The derivation of the governing equations first requires determining the overall energy functional of the system. In the dynamic shear phase-field model, the system's energy functional... for: (1.21) In the formula, For strain energy, For frictional internal energy, For fracture energy, As the system's kinetic energy, The formula for calculating the work done by an external force is: (1.22) in, For elastic strain, For shear strain, for Type of energy release rate, For the system displacement, For system speed, For the physical force received by the system, , To account for stress and friction after damage attenuation.

[0034] Variationalizing equation (1.21) yields: (1.23) In the formula, Work done by external forces on the system For the system's internal energy, For the largest historical field variable, For the physical force received by the system, For the surface forces acting on the system, For the variation of the system's total energy, For the variation of the phase field, For the variation of displacement, For the computational domain, For the volume integral of the computational domain, To calculate the normal vector of the domain boundary, For the computational domain boundary, To compute the area integral at the domain boundary, For stress divergence, For density.

[0035] According to the principle of conservation of energy, the energy input into the system by work done by an external force is... Energy consumed within the system Maintaining a balance between them, that is: (1.24) The governing equations for the phase field and displacement field are: (1.25) In the formula, For the gradient operator, in the displacement field governing equation Phase field driving force in the phase field control equation Different forms of decomposition and calculation are required depending on the different contact states.

[0036] The crack surface condition can be determined based on the normal strain. To make a judgment: (1.26) In the formula, For elastic strain, This is the normal vector of the crack surface.

[0037] When normal strain At that time, the crack surface is in an open state; when the normal strain... At this point, the crack surface is in a closed state, which is further divided into two states: stick and slip. A judgment function is then introduced. To determine whether a crack surface is bonded or slipped: (1.27) In the formula, For the complete region of shear stress, The yield strength of the rock. For the magnitude of the shear stress in the complete region, when At this time, the crack surface undergoes relative sliding, that is, it is in a sliding state; when At this time, the crack surface is only in a closed state but does not slide relative to each other, that is, it is in a bonded state.

[0038] This step mainly considers compressive-shear failure, therefore it primarily focuses on stress tensor decomposition under bonded and sliding conditions.

[0039] For the displacement field control equations : When the cracks are in the open state, there is no mutual intrusion between the crack surfaces, and the cracks are in a fully damaged state. The stress tensor is attenuated directly based on the degradation function. (1.28) When in a bonded state, the material does not break down, assuming that the material parameters are the same as those of the intact material, i.e.: (1.29) When in a sliding state, it is necessary to reduce the shear modulus of the material while ensuring that crack surfaces do not interpenetrate. In addition, the frictional forces generated during the sliding process must also be considered. (1.30) In the formula, The elastic modulus decreases along the direction of shear stress. For frictional stress, It is a fourth-order stress-strain shear tensor. In response to the situation.

[0040] For the calculation of friction, since friction only exists during the sliding process, the calculation formula is: (1.31) In the formula, This is the residual friction angle.

[0041] Ultimately, the stress tensor can be obtained. The calculation formula is as follows: (1.32) Phase field driving force in the phase field control equation : The calculation of the driving force in the phase field governing equations also needs to be performed separately according to the crack surface state, and the maximum historical field variable is still used as the driving force for phase field evolution. Since this step considers frictional shear cracks, only the phase field driving force under bonding and sliding conditions is considered for the time being.

[0042] When in a bonded state, for historical field variables Set a threshold to ensure that the material is not damaged in the bonded state: (1.33) In the formula, The threshold energy is calculated using the formula shown in (1.18).

[0043] When the crack surface is in a sliding state, the shear strain energy along the crack surface direction serves as the driving force for phase field evolution. Historical field variables. It can be represented as: (1.34) In the formula, This represents the shear strain at adjacent time steps. , For the current step of response, In response to the previous time step, This represents the increment of shear strain energy under sliding conditions.

[0044] Step 4: Implement a dynamic shear failure phase field model that considers frictional contact to support rock mass stability assessment in geological disaster prevention and control.

[0045] In step 4 of the embodiment, the weak forms of the displacement field and phase field governing equations were derived. In specific implementation, those skilled in the art can use computer programs to realize the automatic simulation of dynamic shear failure of rock materials considering frictional contact. By constructing an energy functional system that is insensitive to characteristic length and combining it with stress decomposition rules driven by contact state, high-precision simulation of dynamic shear failure of rock can be achieved on a finite element platform, and stress-displacement evolution data for rock mass stability assessment can be output.

[0046] The basic method for transforming a partial differential equation into a variational problem is to multiply the partial differential equation by a function. Integrating over the domain yields the equation, and integrating some terms using the second derivative. The function multiplied by the partial differential equation... The test function is the function to be approximated. It is called the trial function.

[0047] Variational analysis is performed on the strong form of the governing equation (1.25) to obtain the corresponding weak form, and the corresponding program is written.

[0048] The derivation of the variational formula begins with specifying boundary conditions, defining the domain of the model under study as... The Dirichlet boundary condition in the finite element boundary conditions is defined as follows: The Neumann boundary is defined as Then the boundary conditions of the domain satisfy: (1.35) In the formula, It is an empty set.

[0049] The boundary conditions can then be specified as follows: (1.36) In the formula, Domain boundary Outward normal unit vector, , These are the initial boundary values ​​of displacement and initial boundary values ​​of stress given on the corresponding boundaries. It is system stress.

[0050] To achieve finite element method implementation, the solution variables (displacement) and phase field The trace space of is defined as: (1.37) (1.38) in, These are the initial boundary conditions for the displacement field. and It is the function space of displacement field and phase field. It is the computational domain of the model. It is a second-order Sobolev space. It is a first-order Sobolev space.

[0051] Test function (displacement) and phase field The corresponding test function space is: (1.39) (1.40) In the formula, Represents a first-order Sobolev space. These are the initial conditions for the displacement field test function. To avoid stress oscillations during the solution of the cohesive fracture model, a second-order interpolation function is used for the displacement field solution, and a linear interpolation function is used for the phase field solution.

[0052] It is the weak form of the displacement field governing equations: (1.41) It is the weak form of the phase field governing equations: (1.42) In the formula, Represents the system volume fraction. These are the control equations for the displacement field. These are the phase field control equations. It is the energy release rate.

[0053] For the governing equations of the phase field, in variational problems, there is a principle to minimize the order of the parameters. Therefore, by using integration by parts and Gaussian transform, the order of the Laplace operator term in equation (1.42) is reduced, resulting in the final weak form of the phase field governing equations: (1.43) Based on the method flow provided in the above embodiments, the following specific application embodiments are further provided: Example 1: Simulation of a square plate with pre-fabricated internal cracks A square plate contains a pre-fabricated crack, and its geometry and boundary conditions are as follows: Figure 1 As shown. The model is 1m wide, and the coordinates of the initiation and termination points of the pre-fabricated crack are (0.3 m, 0.3 m) and (0.7 m, 0.7 m) respectively. The elastic modulus of the model is... =1 GPa, Poisson's ratio =0.3, the friction angle and the residual friction angle are both 5.71° ( =0.1), cohesion =10MPa, energy release rate =30N / m. A square slab is fixed horizontally, with the bottom fixed both horizontally and vertically, and a dynamic load applied to the top. In the formula , Figure 2 The stress diagrams of a square plate with precast internal cracks at different times are shown. When a dynamic load is applied, an expansion wave is generated and propagates from the top down in a layered manner. The presence of cracks will affect the propagation of stress waves, and the stress profile at the tip will be affected. Normal stress redistribution occurs. As the stress wave propagates to the bottom, the obvious dynamic response basically disappears. At this time, the stress at the tips on both sides of the precast crack is very concentrated.

[0054] Figure 3 , Figure 4 It is a graph of contact normal pressure and tangential stress, from Figure 3 , Figure 4As can be seen, both the contact normal stress curve and the normal tangential stress curve of the crack show a trend of being larger in the middle and smaller on both sides.

[0055] Example 2: Simulation of Direct Shear Test Numerical simulations of direct shear tests under different normal stresses primarily verify whether the dynamic shear phase field can correctly account for frictional contact and simulate shear cracks. This example simulates the shear failure of a specimen with initial defects under horizontal loading and explores the effects of different shear rates and peak strengths on the specimen's peak shear strength and residual strength.

[0056] The model's geometry and boundary conditions are as follows: Figure 5 As shown, the bottom of the specimen is fixed horizontally and vertically. A normal stress is first applied vertically to the top, followed by a horizontal dynamic displacement load. The material parameters of the model are: shear modulus of the model... Poisson's ratio Cohesion Assuming the friction angle and the residual friction angle are equal, Energy release rate Phase field eigenvalues The simulation uses triangular elements, with a total of 22,600 elements and a density of [missing information]. The normal stresses are taken as 50 kPa, 100 kPa and 150 kPa.

[0057] Figure 6 To simulate the force-displacement curves at different shear rates in a direct shear test, from... Figure 6 It can be seen that the dynamic phase field model considering frictional contact can correctly reflect the softening process of shear strength. That is, the shear strength will increase continuously with the increase of shear displacement. After the shear displacement increases to a certain value, the shear strength will drop sharply and remain unchanged at a certain value. At this time, the shear strength is borne by the frictional force of the crack surface.

[0058] Figure 7 This is a graph showing the shear strength versus loading rate in a direct shear test simulation. Figure 7 (a) It can be seen that under the same normal stress, the peak stress increases with the increase of shear rate, and the shear properties of the material are enhanced. Figure 7 (b) It can be seen that the residual strength hardly changes with the loading rate. The residual strength of the material under the same normal stress but different loading rates remains basically unchanged. This is because in the direct shear test, when the material is completely destroyed, the residual strength of the material is provided by the friction on the shear surface. Therefore, it is only related to the normal stress and not to the shear rate.

[0059] Figure 8 , Figure 9This describes the evolution of the phase field and displacement field during a direct shear test at a shear rate of 0.06 mm / s and a normal stress of 150 kPa, before the shear displacement reaches... Previously, the crack continued to evolve horizontally to the right, resulting in a large displacement in the upper part of the model, corresponding to Figure 6 The shear strength rises during the intermediate stage; when the shear displacement reaches... At that time, the crack tip had reached the right boundary of the model, and the crack was about to penetrate. The upper part of the model as a whole underwent significant deformation. Figure 6 In the descending segment, a shear strength softening effect occurs, and the peak strength decreases rapidly; when the shear displacement is greater than... Afterwards, the crack had completely penetrated the surface, and the upper part of the model shifted to the right, corresponding to... Figure 6 The moderate section in the model represents the point where the shear test has been completed, and the shear strength in the model is provided by the residual strength of the material.

[0060] Example 3: Simulation of Biaxial Compression Test Numerical simulations of biaxial compression under different confining pressures were conducted to verify whether the dynamic shear phase field could correctly account for frictional contact, prevent relative intrusion between crack surfaces, and simulate shear cracks. The simulation involved subjecting defective specimens to shear failure under biaxial compression and investigating the effects of different confining pressures on the specimens' peak shear strength and residual strength.

[0061] The model's geometry and boundary conditions are as follows: Figure 10 As shown, confining pressures are applied to the left and right sides of the model, the bottom is constrained by displacement in the Y direction, and the displacement of the top midpoint is fixed in the horizontal direction to prevent rigid body displacement during the simulation from causing non-convergence. A vertically downward dynamic displacement load is applied to the top. The material parameters of the model are: shear modulus Poisson's ratio Cohesion ,density Assuming the friction angle is equal to the residual friction angle, Energy release rate Characteristic length of phase field Using triangular elements for simulation, the smallest discrete element size is determined. The total number of units is 32000, and the time step is... Three different confining pressures were set. The values ​​are 50 kPa, 80 kPa and 100 kPa, respectively.

[0062] Figure 11The figure shows the force-displacement curves under different confining pressures during biaxial compression. As can be seen from the figure, the force-displacement curves can be divided into three main stages: the first stage is a linear increase stage, where the material has not yet failed, and the shear force is provided by the material's shear strength; the second stage is a decrease stage, where the material has undergone some damage (cracks appear but are not yet penetrating), and the load-bearing capacity decreases, but it is not completely destroyed; the third stage is a plateau stage, where the material has completely failed, the cracks have penetrated, and the residual shear stress is balanced by the frictional force at the contact surface, serving as the main load-bearing capacity. Furthermore, the figure shows that with increasing confining pressure, both the peak strength and residual strength of the material increase. Therefore, it can be concluded that confining pressure can improve the shear strength of the material.

[0063] Figure 12 This is a graph showing the shear strength-loading rate in a biaxial compression test simulation. From... Figure 12 As can be seen, under the same confining pressure, the higher the shear rate, the higher the peak strength and residual strength of the material. This conclusion is consistent with the results of many experiments and simulations.

[0064] Figure 13 , Figure 14 For a loading speed of 0.02 mm / s and a confining pressure The evolution diagrams of the phase field and displacement field are shown. It can be seen that when the loading displacement is 0.5 mm, the energy has not reached the shear energy threshold, and the phase field does not evolve; this is a pure finite element problem. When the loading displacement is 1.0 mm, the energy accumulates at the initial crack and exceeds the shear energy threshold. The phase field near the initial crack begins to evolve, and it moves along a path roughly perpendicular to the vertical direction. The angle extends and evolves to both sides, and the evolution of the phase field leads to a significant crack-directing effect in the vertical displacement. When the loading displacement is 1.5 mm, the crack has completely penetrated, and the specimen has been completely sheared and destroyed. At this time, the directions of displacement of the upper and lower parts of the crack are also significantly different.

[0065] In specific implementation, the method proposed in the technical solution of this invention can be automatically executed by those skilled in the art using computer software technology. System devices for implementing the method, such as computer-readable storage media storing the corresponding computer program of the technical solution of this invention and computer equipment including the computer program running the corresponding computer program, should also be within the protection scope of this invention.

[0066] The following embodiments describe the electronic device provided by the present invention. The electronic device described below can be referred to in correspondence with the rock dynamic shear failure simulation method considering frictional contact described above.

[0067] The electronic device may include a processor, a communications interface, memory, and a communication bus. The processor, communications interface, and memory communicate with each other via the communication bus. The processor can call logical instructions from the memory to execute a simulation method for dynamic shear failure of rock considering frictional contact, mainly including the software processing portion described above.

[0068] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and sold or used as independent products, and can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, 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. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0069] On the other hand, embodiments of the present invention also provide a computer program product, the computer program product including a computer program, the computer program being stored on a non-transitory computer-readable storage medium, and when the computer program is executed by a processor, the computer is able to execute the software processing portion of the rock dynamic shear failure simulation method considering frictional contact provided by the above methods.

[0070] In another aspect, embodiments of the present invention also provide a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to perform the software processing portion of the rock dynamic shear failure simulation method considering frictional contact provided by the above methods.

[0071] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0072] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This 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 cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0073] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for simulating dynamic shear failure of rock considering frictional contact, characterized in that, Includes the following processes: Calculate the stress tensor and fourth-order elastic modulus matrix based on the elastic constitutive relation of rock material; A local coordinate system for the crack surface is established based on the maximum shear stress criterion, and the normal and tangential unit vectors are determined. The crack density function and corresponding degradation function of the cohesive phase field model are introduced, and the crack density function and degradation function are configured to eliminate the influence of the phase field characteristic length. The energy functional of the dynamic shear phase field model is derived, the contact state is determined based on the normal strain of the crack surface, and the strong form of the displacement field control equation and the phase field control equation is derived. The strong forms of the displacement field control equation and the phase field control equation are subjected to variational processing to obtain the corresponding weak forms. Based on the weak forms, dynamic shear failure simulation of rocks considering frictional contact is realized, which supports rock mass stability assessment in geological disaster prevention and control.

2. The method for simulating dynamic shear failure of rock considering frictional contact according to claim 1, characterized in that: The establishment of a local coordinate system for the crack surface based on the maximum shear stress criterion includes taking the direction of maximum shear stress as the crack propagation direction, and then determining the normal and tangential unit vectors of the crack surface.

3. The method for simulating dynamic shear failure of rock considering frictional contact according to claim 1, characterized in that: When configuring the crack density function, the influence of the phase field characteristic length is eliminated by setting the local dissipated energy density function to the appropriate form that correctly simulates the material shear parameters.

4. The method for simulating dynamic shear failure of rock considering frictional contact according to claim 1, characterized in that: When configuring the degradation function, the parameter values ​​are adjusted to ensure that the phase field evolution is insensitive to the phase field characteristic length.

5. The method for simulating dynamic shear failure of rock considering frictional contact according to claim 1, characterized in that: The energy functional includes strain energy, frictional internal energy, fracture energy, system kinetic energy, and work done by external forces.

6. The method for simulating dynamic shear failure of rock considering frictional contact according to claim 1, characterized in that: The strong forms of the displacement field control equation and the phase field control equation are obtained based on the balance between the energy input to the system by external forces and the energy consumed within the system.

7. The method for simulating dynamic shear failure of rock considering frictional contact according to claim 1, characterized in that: The stress divergence term in the displacement field control equation and the phase field driving force term in the phase field control equation are calculated by differential decomposition based on the contact state of the crack surface; the contact state includes the opening state, the bonding state, and the sliding state.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, it implements a method for simulating dynamic shear failure of rock considering frictional contact as described in any one of claims 1 to 7.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by the processor, it implements a method for simulating dynamic shear failure of rock considering frictional contact as described in any one of claims 1 to 7.

10. A computer program product, comprising a computer program, characterized in that: When the computer program is executed by the processor, it implements a method for simulating dynamic shear failure of rock considering frictional contact as described in any one of claims 1 to 7.

Images