Rock material tension-shear failure simulation method and equipment based on dynamic two-phase field model

Abstract

The invention discloses a rock material tension-shear failure simulation method and equipment based on a dynamic dual-phase field model. The method comprises the following steps: establishing a stress tensor physical model corresponding to a rock material constitutive relationship; respectively introducing a tension phase field and a shear phase field, and establishing a dynamic double-phase field model corresponding to the rock tension-shear failure physical process; deducing an energy functional of the dynamic double-phase field model; establishing a crack surface local coordinate system, and judging a crack contact state according to a frictional contact phase field theory; switching a stress tensor decomposition mode according to the contact state, and calculating a phase field evolution driving force; rock material tension-shear failure simulation based on the dynamic two-phase field model is achieved, and rock fracture form evolution data are output and used for evaluating rock slope stability.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of geological disaster prevention and control, and particularly relates to a rock material tensile-shear failure simulation technical scheme based on a dynamic two-phase field model. BACKGROUND

[0002] In rock mass engineering, after a long geological process, complex structures such as cracks, joints, weak interlayers, crack cementation, etc. are formed inside the rock mass, and these structure surfaces have a controlling effect on the stability of the slope under seismic load. The expansion and evolution of cracks inside 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 materials is a hot issue in 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 of studying rock damage, and numerical solutions are obtained through iteration to analyze the rock failure mechanism. From the current numerical simulation method, the simulation method is divided into two kinds through accurate characterization or dispersion characterization of 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 element method.

[0004] Rock materials and rock-like materials usually fail in a quasi-brittle manner, that is, the material strength gradually softens after the peak value, and many micro-cracks grow and evolve during the softening process. In addition, there are some other important characteristics of rock and rock-like material cracking behavior, first, when these materials fail under compressive stress, they usually have a complex composite fracture composed of tensile fracture and shear fracture due to the previous geometric defects of the material; second, under the action of compressive stress, sliding fracture occurs on the crack surface, which produces obvious friction, and the existence of friction plays a very important role in fracture kinematics and propagation dynamics; most importantly, the shear fracture energy of rock is generally much larger than its tensile fracture energy. Therefore, in order to correctly simulate the cracking process of rock in rock mass, all the above factors must be considered.

[0005] In actual engineering, rock mass will be subjected to a large tectonic stress, and due to the existence of joints, cracks and other geometric defects, the rock will mostly fail in a tensile-shear mixed manner. SUMMARY

[0006] The present application aims at the defects of the prior art, and provides a rock material tensile-shear failure simulation scheme based on a dynamic double-phase field model, wherein two kinds of phase fields are introduced to simulate tensile cracks and shear cracks of the rock respectively, so that tensile-shear composite failure of the rock material under dynamic load can be simulated, and intelligent evaluation of slope stability under seismic load can be supported.

[0007] The technical scheme provided by the present application is a rock material tensile-shear failure simulation method based on a dynamic double-phase field model, comprising the following processes, establishing a stress tensor physical model corresponding to a rock material constitutive relationship; introducing tensile phase field and shear phase field respectively, and establishing a dynamic double-phase field model corresponding to a rock tensile-shear failure physical process; deriving an energy functional of the dynamic double-phase field model; establishing a crack surface local coordinate system; judging a crack contact state according to a friction contact phase field theory; switching a stress tensor decomposition mode according to the contact state, and calculating a phase field evolution driving force; realizing rock material tensile-shear failure simulation based on the dynamic double-phase field model, and outputting rock failure morphology evolution data for evaluating rock slope stability.

[0008] Moreover, when the dynamic double-phase field model is established, the tensile phase field and the shear phase field are both modeled by using a cohesive fracture energy density function, and a degradation function is applied, so that the dynamic double-phase field model is not sensitive to the phase field characteristic length. Moreover, the derivation of the energy functional of the dynamic double-phase field model comprises decomposing the total energy of the system into strain energy, friction internal energy, phase field fracture energy, system kinetic energy and external force work; the strain energy is further decomposed into tensile strain energy, shear strain energy and compression strain energy, wherein the tensile strain energy and the shear strain energy are used to simulate tensile cracks and shear cracks respectively, and the compression strain energy does not participate in the phase field evolution.

[0009] Moreover, the normal direction of the crack surface local coordinate system is set as the Y axis to indicate the crack surface opening direction, and the tangential direction is set as the X axis to indicate the crack surface slip direction; according to the maximum shear stress rule, the angle between the crack normal direction and the main direction of the slip surface is found, which makes the derivative of the driving force maximum; the derivative of the driving force is a function of the phase field driving force of the tensile crack and the shear crack.

[0010] Moreover, when judging the crack contact state, if the normal strain is a positive value, it is judged that the crack surface is in an opening state, otherwise, the crack surface is in a closed state; a judgment function is further introduced to distinguish between the bonded state and the sliding state.

[0011] Moreover, for the complete region, the tensile failure threshold energy and the shear failure threshold energy are defined as the crack driving force under the peak tensile strength and the peak shear strength respectively.

[0012] Moreover, in the open state, the crack surface normal stress exceeding the material tensile strength drives the tensile phase field evolution; in the sliding state, the crack surface shear stress exceeding the peak strength drives the shear phase field evolution.

[0013] In another aspect, the present application also provides an electronic device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor implements the rock material tensile-shear failure simulation method based on the dynamic double phase field model as described above when executing the program.

[0014] In another aspect, the present application also provides a non-transitory computer readable storage medium having a computer program stored thereon, wherein the computer program is executable on a processor to implement the rock material tensile-shear failure simulation method based on the dynamic double phase field model as described above.

[0015] In another aspect, the present application also provides a computer program product comprising a computer program, wherein the computer program is executable on a processor to implement the rock material tensile-shear failure simulation method based on the dynamic double phase field model as described above.

[0016] The present application introduces two phase fields to represent tensile fracture and shear fracture respectively, decomposes the stress tensor, judges the contact state of the integral point, derives the driving force of the two phase fields respectively, develops a dynamic double phase field model for simulating tensile-shear composite cracks, completes the simulation of tensile-shear composite cracks under dynamic load, realizes the evaluation of the stability of the slope under the action of the seismic load, and thus provides early warning support.

[0017] The simulation of the shear failure and frictional fracture of the rock material based on the phase field method is realized automatically, which greatly reduces the calculation amount of human beings, improves the calculation accuracy due to the consideration of the insensitivity of the model to the phase field characteristic length, and the simulation result is more reliable.

[0018] The present application introduces two phase fields to simulate the cohesive tensile crack and the frictional shear crack in the composite fracture process of the rock, simultaneously introduces a dynamic factor in the energy functional, and completes the simulation of the composite crack of the rock under the action of the dynamic load. Through the uniaxial compression example of the pre-prepared single crack, the simultaneous identification of the tensile crack and the shear crack is successfully realized, and finally four crack morphologies, i.e., the wing crack, the anti-wing crack, the horse tail crack and the quasi-co-planar secondary crack, are successfully simulated, which are consistent with the simulation results of the BB-PD. Through the uniaxial compression example of the pre-prepared co-planar double crack, the identification of the tensile crack and the shear crack is also realized, and finally the crack evolution morphology is consistent with the simulation results of the XFEM and the GPD. Through the calculation and comparison of the two examples, the correctness of the dynamic phase field model considering the frictional contact proposed in the present application is verified. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1Geometric size and boundary condition of uniaxial compression test of single prefabricated crack for example 1; Figure 2 Phase field evolution diagram of uniaxial compression test of single prefabricated crack at different time for example 1, wherein (a) is , (b) is , (c) is , (d) is , (e) is , (f) is Phase field evolution diagram of corresponding test at time t = 0.1 s; Figure 3 Comparison diagram of simulation effects of different numerical methods of uniaxial compression test of single prefabricated crack for example 1, (a) is dynamic double phase field method, (b) is BB-PD method; Figure 4 Geometric size and boundary condition of uniaxial compression of coplanar double-hole for example 2; Figure 5 Phase field evolution diagram of uniaxial compression model of double-hole at different time for example 2, wherein (a) is , (b) is , (c) is Phase field evolution diagram of corresponding test at time t = 0.1 s; Figure 6 Comparison diagram of simulation effects of different numerical methods of uniaxial compression test of double prefabricated cracks for example 2, (a) is PFM method, (b) is XFEM method, (c) is GPD method.

[0020] Figure 7 Flow chart of example. DETAILED DESCRIPTION

[0021] The application will be further described below in combination with the drawings and examples: The application discloses a rock material tensile-shear failure simulation technology based on a dynamic double phase field model, which comprises the following steps: according to a rock material constitutive relation, an expression form of a stress tensor is derived; crack density functions and corresponding degradation functions suitable for both tensile phase fields and shear phase fields are introduced, and a dynamic double phase field model is established; an energy functional of the dynamic double phase field model is derived; strong and weak forms of displacement field and phase field control equations are derived; a local coordinate system of a crack surface is established; according to a friction contact phase field theory, a crack surface contact state is judged, stress tensor decomposition modes and phase field evolution driving force calculation formulas in different states are determined; finally, the weak form of the control equation is derived, and computer process automatic operation is supported to realize the rock material tensile-shear failure simulation based on the dynamic double phase field model.

[0022] Referring to Figure 7The embodiment provides a rock material tensile-shear failure simulation method based on a dynamic two-phase field model, two kinds of phase fields are introduced to simulate tensile cracks and shear cracks of the rock respectively, so that tensile-shear composite failure of the rock material under dynamic load can be simulated, and the specific implementation steps are as follows: Step 1, establishing a stress tensor physical model corresponding to a rock material constitutive relationship: according to the rock material constitutive relationship, the expression form of the stress tensor is derived; the fourth-order tensor matrix corresponding to the stress tensor and the strain tensor is represented; In step 1, according to the constitutive relationship of the rock material, the specific expression form of the stress tensor is derived, and in the application, the elastic constitutive relationship is adopted, that is, when the strain is The stress tensor is The calculation formula is: (1.1) In the formula, is the fourth-order elastic modulus of the complete rock material, and the calculation formula is: (1.2) In the formula, and are the Lame constants, is a second-order identity tensor, is a fourth-order symmetric identity tensor.

[0023] After the fourth-order matrix of the stress tensor and the strain tensor is calculated through the above formula, the stress of the complete rock can be attenuated according to the damage condition, and the crack surface state can be judged through the normal strain.

[0024] Step 2, establishing a two-phase field model corresponding to the physical process of rock tensile-shear failure, the crack density function suitable for the tensile phase field and the shear phase field and the corresponding degradation function are introduced, and the dynamic two-phase field model is established; The embodiment introduces two kinds of phase fields and , wherein represents a tensile crack, represents a shear crack, , the phase field value of 0 represents a complete (undamaged) area of the corresponding fracture mode, the phase field value of 1 represents a completely damaged (discontinuous) area, both kinds of phase fields follow an energy density function, the cohesive fracture energy density function is used for phase field modeling, and the energy density function is taken as: (1.3) (1.4) , wherein and The tensile phase field gradient and the shear phase field gradient are, The phase field characteristic length is.

[0025] The cohesive fracture energy density function is used to ensure that the dynamic two-phase field model is not sensitive to the characteristic length, and the correct calculation of the tensile and shear composite cracks is ensured. In order to adapt to the cohesive fracture energy density function, the degradation function is introduced : (1.5) (1.6) In the formula, and are the degradation functions corresponding to the tensile crack and the shear crack, and are coefficients related to material properties, and represent the tensile failure threshold energy and the shear failure threshold energy, is the phase field characteristic length, is the energy release rate of the type, is the energy release rate of the type, and are independent parameters, and the degradation function of the embodiment of the application adopts a standard format, and .

[0026] Step 3, derive the dynamic two-phase field model energy functional; derive the strong and weak forms of the displacement field and the phase field control equation; establish a local coordinate system of the crack surface; according to the friction contact phase field theory, judge the contact state of the crack surface, and determine the stress tensor decomposition mode and the phase field evolution driving force calculation formula under different states; The application proposes to switch the stress tensor decomposition mode according to the contact state, and calculate the phase field evolution driving force.

[0027] In step 3 of the embodiment, the system total energy mainly has strain energy , friction internal energy , phase field fracture energy , system kinetic energy and external work , that is, the system energy functional is: (1.7) In the formula, is the strain energy, is the friction internal energy, is the phase field dissipation energy, is the system kinetic energy, is the external force work.

[0028] (1) Strain energy

[0029] From the numerical point of view, the change of strain energy drives the evolution of phase field. In order to model the two phase fields, a new form of strain energy is derived to satisfy the evolution of two phase fields respectively. Firstly, when the material has not been damaged, the strain energy is: (1.8) where: is the double dot product symbol, is the infinitesimal strain tensor, is the stress-strain tangent tensor of the material when it has not been damaged (at this time, it is assumed that the material satisfies isotropy and linear elasticity), the calculation formula of is: (1.9) where, is the shear modulus, is the bulk modulus, is the second-order identity tensor, is the fourth-order symmetric identity tensor.

[0030] In order to simulate mixed fracture, the strain energy is decomposed into three parts: tensile strain energy (to simulate tensile cracks), shear strain energy (to simulate shear cracks) and compressive strain energy (not involved in the evolution of phase field), that is: (1.10) The derivative of strain energy with respect to strain can obtain the stress tensor when the damage has not occurred: (1.11) where, is the tensile stress, is the shear stress, is the compressive stress.

[0031] Next, the specific formula of , and needs to be derived, because the tensile stress only exists in the crack surface in the opening state and the shear stress only exists in the crack surface in the closed state, therefore, the normal strain and the judging function are used to judge the state of the crack surface.

[0032] The calculation formula of normal strain is: (1.12) where, is the system strain, is the crack surface normal vector.

[0033] When the normal strain , the crack surface is in an open state; when the normal strain , the crack surface is in a closed state, which is further divided into stick and slip states, and a judging function is introduced to determine whether the crack surface is stick or slip: (1.13) where, is the complete region shear stress, is the complete region shear stress magnitude, is the material yield strength, when the material is intact ( ), ; when the material is damaged ( ), , is the material cohesive strength, is the normal stress, is the material internal friction angle. When , the crack surface slips, i.e., in a slip state; when , the crack surface is only in a closed state but does not slip, i.e., in a stick state.

[0034] According to the state determination, the tensile stress , shear stress are calculated as follows: (1.14) (1.15) where, is the crack surface normal stress, and are the crack surface normal and tangential vectors, is the tensor related to the crack surface, is the one-dimensional constraint modulus, is the Lame's first constant, is the shear stress of the undamaged region, . Regardless of the contact condition, the compression stress is calculated as follows: (1.16) where, is the undamaged stress, is the tensile stress, for the shear stress.

[0035] After obtaining the computational formulae of , and , the real stress tensor considering the damage can be obtained as follows: (1.17) where , are the degradation functions of the tensile and shear stresses, respectively, and only cause the degradation of the corresponding stress. After obtaining the specific computational formula of the stress tensor considering the damage, the strain energy density can be written in the rate form as follows: (1.18) where is the strain rate.

[0036] (2) Friction internal energy

[0037] The crack is frictionless in the opening state, but a large friction force will be generated in the sliding crack, so the friction internal energy also needs to be considered in the total energy of the system.

[0038] The friction stress does not exist in the opening and bonding states, and is provided by the residual shear stress in the sliding process. The friction stress tensor is calculated as follows: (1.19) where is the tensor related to the crack surface, is the residual strength. Then, the rate form of the friction internal energy density function is: (1.20) where is the shear strain rate.

[0039] (3) Fracture energy

[0040] Since there are two phase fields, the phase field fracture energy is also decomposed into two parts: (1.21) where and are the fracture energies corresponding to mode I and mode II, respectively, and the fracture energies of the two modes are: (1.22) In the formula, The phase field characteristic length, and The energy release rates are for Mode I and Mode II.

[0041] (4) Kinetic energy

[0042] The system's kinetic energy is independent of the contact state at the crack surface; therefore, the system's kinetic energy is: (1.23) In the formula, For the quality of the integration point, The velocity is the velocity at the integration point.

[0043] (5) Work done by external forces

[0044] The work done by the external force is: (1.24) In the formula, For external force, It is a displacement vector.

[0045] After obtaining the expression for the total system energy, the governing equations for the displacement field and phase field can be obtained by taking variational results with respect to the total system energy and the displacement field and phase field: (1.25) (1.26) In the formula, and Let be the first derivatives of the tensile crack degradation function and the shear crack degradation function. For the gradient operator, in the displacement field governing equation The driving force of the tensile crack phase field in the phase field control equation and shear crack phase field driving force Different forms of decomposition and calculation are required depending on the different contact states. The phase field characteristic length, For the computational domain, For the time domain.

[0046] After obtaining the governing equations, it is necessary to derive the calculation formulas for the local coordinate system and the phase field driving force. To identify the contact state, a coordinate system is introduced relative to the normal and tangential directions of the crack surface, where the unit vector of the normal direction is... Indicates the direction of crack opening; unit vector in the tangential direction. 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. For phase-field modeling of mixed fracture, it is necessary to avoid situations where tensile and shear failures occur simultaneously at a single integration point; therefore, it is necessary to determine the crack driving force at each integration point. and Therefore, based on The criterion (maximum shear stress criterion) will Defined as the angle between the crack normal direction and the principal direction of the slip surface, it is necessary to find the derivative of the driving force. The largest value, The principle is stated as follows: (1.27) In the formula, and For the phase field driving force of tension cracks and shear cracks, The system strain is given by the derivative of the driving force, which is a function of the phase-field driving force for tension and shear cracks.

[0047] Assumption , 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: (1.28) (1.29) In the formula, The angle between the crack normal direction and the principal direction of the slip surface.

[0048] Based on potential energy and Based on the criteria, the crack driving forces are now derived for four cases: intact region (region without cracks), open, bonded, and sliding. and The calculation formula is as follows: In the open state, the tensile phase field evolution is driven when the normal stress on the crack surface exceeds the tensile strength of the material; in the sliding state, the shear stress on the crack surface evolution is driven when it exceeds the peak strength.

[0049] For the intact region, the driving force is taken as the threshold energy to ensure that the phase field does not evolve. The tensile failure threshold energy... and shear failure threshold energy Defined as the crack driving force at peak tensile strength and peak shear strength: (1.30) (1.31) where, is the tensile crack history variable, is the tensile stress, is the one-dimensional constraint modulus, is the tensile strength of the rock material, is the crack face normal stress, is the shear modulus of the rock material, is the peak shear stress, is the residual shear stress, is the material cohesion strength, is the normal stress, is the material internal friction angle.

[0050] Substituting equation (1.17) into equation (1.18) when the crack face is in the opening state, the strain energy in the opening state is derived as Equation: (1.32) where, is the compressive stress, is the strain, is the tensile crack history variable, is the tensile stress, is the time of the previous step of calculation of the tensile crack, is the shear crack history variable, is the shear stress, is the time of the previous step of calculation of the shear crack, is the current calculation time.

[0051] Substituting equations (1.14), (1.15) and (1.16) into equation (1.32), the specific form of the strain energy is obtained as (1.33) where, , , is the normal stress and normal strain, , is the shear stress and shear strain, substituting equation (1.33) can obtain the final form of the strain energy : (1.34) According to the definition, and need to be multiplied by and , so as to represent the strength of the residual material after damage occurs. Therefore, from the above equation, the tensile fracture threshold energy and the shear fracture threshold energy (1.35) (1.36) where, is the normal stress on the crack surface, is the shear stress on the crack surface.

[0052] Substituting equations (1.35) and (1.36) into (1.27), we get the derivative of the driving force (1.37) According to the principal strain and equations (1.14), (1.15), equation (1.37) can be rewritten as: (1.38) where, and are the maximum and minimum principal strains. In order to find the value of that maximizes we take the derivative of the driving force derivative with respect to (1.39) It can be seen that when , which means that in the opening condition, the crack growth direction is the same as the direction of the principal stress, and there is no shear stress on the crack surface, i.e., the shear crack driving force only exists, and the tensile driving force When the normal tensile stress exceeds the material tensile strength (i.e., the driving force breaks through the tensile threshold energy), the phase field begins to evolve, so the driving force calculation formula in the tensile state is: (1.40) When the crack surface is in a bonded state, neither of the two modes of failure occurs at this time, and the driving force is 0: (1.41) When the crack surface is in a sliding state, the tensile driving force does not exist, and the shear driving force is provided by the shear strain energy, i.e.: (1.42) where, is the peak shear stress, is the residual shear stress, ​​​This represents the peak shear strain. For shear strain. At this time, when At that time, the derivative of the driving force Take the maximum value. It is the internal friction angle.

[0053] In order to ensure stable convergence during numerical simulation, the normal vector corresponding to the current time step is stored after damage occurs. tangent vector The direction vector of the integration point remains unchanged in subsequent calculations.

[0054] Finally, to ensure that the phase field does not undergo reverse evolution, the driving force must also satisfy a condition that is greater than or equal to the historical field variables. In summary, the driving force behind the destruction in both modes is: (1.43) (1.44) In the formula, For a moment Normal stress on the crack surface , For the time period The historical maximum field variables of tension and shear. This represents the increment of shear strain energy.

[0055] Step 4: Implement the simulation of tensile-shear failure of rock materials based on the dynamic two-phase field model, and output the rock fracture morphology evolution data for evaluating the stability of rock slopes.

[0056] In step 4 of the embodiment, the strong and weak forms of the phase field and displacement field are derived. In specific implementation, a computer program can be developed to realize the automatic operation of the simulation of tensile-shear failure of rock materials based on the dynamic dual-phase field model.

[0057] 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.

[0058] Variational analysis is performed on the strong forms of the governing equations of formulas (1.25) and (1.26) to obtain the corresponding weak forms. In practice, those skilled in the art can use computer software technology to achieve automatic operation.

[0059] 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: (1.45) In the formula, It is an empty set.

[0060] The boundary conditions can then be specified as follows: (1.46) 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.

[0061] To achieve finite element method implementation, the solution variables (displacement) and phase field The trace space of a ) is defined as: (1.47) (1.48) In the formula, , For the displacement and phase field solution variable trace space, 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.

[0062] The corresponding test function space is: (1.49) (1.50) In the formula, This is a displacement field test function. For phase field testing functions, , For the displacement and phase field solution variables, test function space. Represents a first-order Sobolev space. is the initial condition of the displacement field test function. In order to avoid stress oscillation in the solution of the cohesive force fracture model, the second-order interpolation function is used when solving the displacement field, and the linear interpolation function is used when solving the phase field.

[0063] is the weak form of the displacement field control equation: (1.51) is the weak form of the phase field control equation: (1.52) wherein, is the displacement field control equation, is the phase field control equation, is the phase field driving force, represents the volume integral of the system, is the energy release rate, is the stress of the system, , is the surface force boundary and the volume force boundary, is the acceleration of the system, is the mass of the integral point.

[0064] For the control equation of the phase field, there is a principle in the variational problem to reduce the order of the parameter as much as possible, so the Laplace operator term in equation (1.52) is reduced by using partial integration and Gauss transformation, and the final weak form of the phase field control equation is: (1.53) (1.54) wherein, , is the weak form of the tension phase field and shear phase field control equation, is the characteristic length of the phase field, and is the first-order derivative of the tension crack degradation function and the first-order derivative of the shear crack degradation function, , is the phase field gradient term of the tension phase field and the shear phase field.

[0065] Based on the method flow provided in the above embodiment, the following specific application embodiments are further provided: Embodiment 1: Uniaxial compression test simulation of single pre-prepared crack This embodiment is a uniaxial compression numerical simulation of a single opening, simulating the shear and tensile failure of a specimen with a pre-prepared crack during axial compression. The geometric size and boundary conditions are shown in Figure 1 . The material parameters of the model are: the elastic modulus of the model , density , Poisson's ratio , tensile strength , cohesive strength , the internal friction angle is assumed to be equal to the angle of internal friction, i.e. , mode I fracture energy , mode II fracture energy , the time step is taken , the phase field characteristic length is taken as 0.5 mm, the triangular element is used for discretization, and the total number of elements is 93754. The bottom of the model is constrained in the horizontal and vertical directions, the top is constrained in the horizontal direction, and a downward dynamic stress load is applied.

[0066] Figure 2 The distribution of the phase field is shown, and it can be seen that, when , the rock sample first appears a tensile crack (wing crack), which is caused by the low tensile strength of the rock; when , a shear crack (quasi-coplanar secondary crack) begins to appear, at which time the specimen has two types of cracks; when , the shear crack (quasi-coplanar secondary crack) further evolves; when , the rock appears a horsetail crack on the basis of the original shear crack (quasi-coplanar secondary crack) and further extends and evolves; when , the rock also appears an anti-wing crack (anti-wing crack), the direction of the anti-wing crack (anti-wing crack) is opposite to that of the wing crack, and it roughly evolves upward to cut the rock, thus the entire rock has four types of cracks.

[0067] Figure 3 The uniaxial compression test of the single pre-prepared crack is shown in the comparison chart of the simulation effects of different numerical methods, the new BB-PD (BB-PD) is used to study the crack propagation and coalescence behavior in the rock sample containing pre-existing open defects, and a similar crack diagram is obtained, which is very consistent with the calculation effect of the dynamic two-phase field model in this paper.

[0068] Example 2: Geometric size and boundary conditions of coplanar double-hole uniaxial compression Figure 4 The geometric size and boundary conditions of the coplanar double-hole uniaxial compression are shown, the uniaxial compression numerical simulation of the double-hole is carried out, the shear and tensile failure of the specimen with two coplanar pre-prepared cracks in the axial process is simulated, the geometric size and boundary conditions are shown in Figure 4 , and the material parameters are: elastic model , Poisson's ratio material density tensile strength cohesion Assume that the internal friction angle is equal to the internal friction angle participating, that is, Mode I fracture energy Mode II fracture energy The time step is taken The phase field characteristic length is taken as 1mm, triangular elements are used for discretization, and the total number of elements is 67304. The bottom of the model is constrained in the horizontal and vertical directions, the top is constrained in the horizontal direction, and the top is subjected to a downward dynamic load.

[0069] Figure 5 The phase field evolution diagram of the double-hole uniaxial compression model can be seen in the figure (a), the two ends of the crack of the two holes appear tensile cracks first, and the evolution direction of the crack is basically perpendicular to the single-hole direction; in figure (b), the connection of the defects occurs through the connection of the internal quasi-co-planar secondary cracks, which is due to the geometric influence of the double-hole co-planar, which is consistent with the simulation results of Wang et al; in figure (c), the growth length of the inner wing crack is inhibited by the quasi-co-planar secondary crack, so the wing crack initiated by the inner wing crack tip is shorter than the wing crack initiated by the outer wing crack tip.

[0070] Figure 6 The comparison diagram of the simulation effects of different numerical methods of the uniaxial compression test of the double-precracked fracture can be seen, the crack effect calculated by the dynamic double-phase field model proposed in the present application is basically consistent with the calculation effect of XFEM and GPD, which proves the correctness of the model proposed in the present application. At the same time, it can be seen from the comparison that the model proposed in the present application can more intuitively display the crack evolution in the uniaxial compression process of the double-hole.

[0071] In specific implementation, the method proposed in the technical scheme of the present application can be automatically run by a computer software technology, and the system device of the method, such as a computer readable storage medium storing the corresponding computer program of the technical scheme of the present application and a computer device including a computer program running device, should also be within the protection scope of the present application.

[0072] The following examples describe the electronic device provided by the present application, and the electronic device described below can be correspondingly referred to the rock material tensile-shear failure simulation method based on the dynamic double-phase field model described above.

[0073] The electronic device can include a processor, a communications interface, a memory, and a communications bus, wherein the processor, the communications interface, and the memory complete mutual communication through the communications bus. The processor can invoke a logic instruction in the memory to execute the rock material tension-shear failure simulation method based on the dynamic two-phase field model, mainly including the software processing part in the above steps.

[0074] In addition, the logic instruction in the memory described above can be realized in the form of a software function unit and sold or used as an independent product, and can be stored in a computer-readable storage medium. Based on such understanding, the technical solutions of the present application essentially or the part that contributes to the prior art or part of the technical solutions can be embodied in the form of a software product. The computer software product is stored in a storage medium, and includes several instructions to make a computer device (which can be a personal computer, a server, or a network device, etc.) execute all or part of the steps of the methods described in the various embodiments of the present application. The aforementioned storage medium includes: a U disk, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a magnetic disk or an optical disk, and various media that can store program codes.

[0075] On the other hand, the embodiments of the present application also provide a computer program product, which includes a computer program, the computer program can be stored on a non-transitory computer readable storage medium, and the computer program is executed by a processor, so that the computer can execute the software processing part in the rock material tension-shear failure simulation method based on the dynamic two-phase field model provided by the above-mentioned methods.

[0076] In another aspect, the embodiments of the present application also provide a non-transitory computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to implement the software processing part in the rock material tension-shear failure simulation method based on the dynamic two-phase field model provided by the above-mentioned methods.

[0077] The device embodiments described above are only schematic, wherein the units described as separate components can or can not be physically separated, and the components displayed as units can or can not be physical units, i.e., they can be located in one place, or distributed on multiple network units. Part or all of the modules can be selected according to actual needs to achieve the purpose of the present embodiment scheme. Those skilled in the art can understand and implement without creative labor.

[0078] Those skilled in the art can clearly understand the technical solutions of the various embodiments from the above description of the embodiments, and the various embodiments can be implemented by means of software with the necessary general hardware platforms, and of course, can also be implemented by hardware. Based on such understanding, the above technical solutions, essentially or in other words, the part of the prior art that makes a contribution, can be embodied in the form of a software product, which can be stored in a computer readable storage medium, such as a ROM / RAM, a magnetic disk, an optical disk, and the like, and includes a number of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0079] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, rather than limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for some technical features therein; 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 application.

Claims

1. A method for simulating tensile-shear failure of rock materials based on a dynamic two-phase field model, characterized in that, Includes the following processes, Establish a physical model of the stress tensor corresponding to the constitutive relation of rock materials; By introducing tension phase field and shear phase field respectively, a dynamic two-phase field model corresponding to the physical process of rock tension-shear failure is established. The energy functional of the dynamic two-phase field model is derived; a local coordinate system of the crack surface is established, and the crack contact state is determined according to the friction contact phase field theory; the stress tensor decomposition mode is switched according to the contact state, and the driving force of phase field evolution is calculated. A simulation of tensile-shear failure of rock materials based on a dynamic two-phase field model is realized, and data on the evolution of rock fracture morphology are output for evaluating the stability of rock slopes.

2. The method for simulating tensile-shear failure of rock materials based on a dynamic two-phase field model according to claim 1, characterized in that: When establishing the dynamic two-phase field model, both the tension phase field and the shear phase field are modeled using the cohesive fracture energy density function, and a degradation function is applied to make the dynamic two-phase field model insensitive to the characteristic length of the phase field.

3. The method for simulating tensile-shear failure of rock materials based on a dynamic two-phase field model according to claim 1, characterized in that: The derived energy functional of the dynamic two-phase field model includes decomposing the total energy of the system into strain energy, frictional internal energy, phase field fracture energy, system kinetic energy, and work done by external forces; strain energy is further decomposed into tensile strain energy, shear strain energy, and compressive strain energy, wherein tensile strain energy and shear strain energy are used to simulate tensile cracks and shear cracks, respectively, and compressive strain energy does not participate in the phase field evolution.

4. The method for simulating tensile-shear failure of rock materials based on a dynamic two-phase field model according to claim 1, characterized in that: The local coordinate system of the crack surface is set with the normal direction as the Y-axis to indicate the crack opening direction and the tangential direction as the X-axis to indicate the crack slip direction. Based on the maximum shear stress, the angle between the crack normal direction and the principal direction of the slip surface that maximizes the derivative of the driving force is found. The derivative of the driving force is a function of the phase field driving force of tension cracks and shear cracks.

5. The method for simulating tensile-shear failure of rock materials based on a dynamic two-phase field model according to claim 1, characterized in that: When determining the contact state of a crack, if the normal strain is positive, the crack surface is considered to be in an open state; otherwise, the crack surface is considered to be in a closed state. A judgment function is introduced to further distinguish between the bonded and sliding states.

6. The method for simulating tensile-shear failure of rock materials based on a dynamic two-phase field model according to claim 1, characterized in that: For the complete region, the tensile failure threshold energy and the shear failure threshold energy are defined as the crack driving forces at the peak tensile strength and peak shear strength, respectively.

7. The method for simulating tensile-shear failure of rock materials based on a dynamic two-phase field model according to claim 1, characterized in that: In the open state, the tensile phase field evolution is driven when the normal stress on the crack surface exceeds the tensile strength of the material; in the sliding state, the shear stress on the crack surface evolution is driven when it exceeds the peak strength.

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 the method for simulating tensile-shear failure of rock materials based on a dynamic two-phase field model 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 the method for simulating tensile-shear failure of rock materials based on a dynamic two-phase field model 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 the method for simulating tensile-shear failure of rock materials based on a dynamic two-phase field model as described in any one of claims 1 to 7.

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