Rock material shear failure and frictional failure simulation method, device and equipment

Abstract

The application provides a rock material shear failure and frictional failure simulation method, device and equipment, and the rock material shear failure and frictional failure simulation method comprises the following steps: according to a frictional failure phase field model, a four-order tensor matrix corresponding to a stress tensor of a rock material is determined; a local coordinate system of a crack surface is established, a traditional degradation function is modified to obtain a target degradation function, and the target degradation function and a crack density function are introduced; in the frictional failure phase field model, a history field variable is set, and a frictional failure phase field control equation is determined; based on the frictional failure phase field control equation, a stress field and a phase field finite element weak form are obtained, and a residual error and a stiffness matrix are obtained. Through the application, the traditional phase field model is optimized, the calculation accuracy of the phase field model is improved, and the simulation result is more reliable.

Description

TECHNICAL FIELD

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

[0002] The crack propagation evolution in rock is one of the reasons for the continuous deterioration of the macroscopic mechanical parameters of rock, and is also the fundamental cause of rock engineering and geological disasters. In order to explain the crack propagation phenomenon of rock and solve the crack propagation instability problem of rock engineering, domestic and foreign scholars have conducted in-depth research. Laboratory test research is first used to study crack propagation problems, and significant achievements have been made in theoretical research and numerical simulation.

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

[0004] For complex geotechnical engineering problems, the damage process of rock mostly needs to rely on numerical simulation to solve. From the current calculation method, it is roughly divided into two kinds according to the characteristics of the method. One is the continuous method, including gradient damage method, viscosity regularization method and phase field method. The second is the discrete method, such as extended finite element method, discrete element method, discontinuous deformation analysis method and cohesive force element method. In the continuous method, the phase field method has received widespread attention. Compared with other methods, the phase field method has the advantages of dispersing sharp cracks into continuous damage values, eliminating the discontinuity problem of the displacement field, and automatically capturing the crack initiation, nucleation, merging and branching. However, the existing simulation evolution method is not sensitive to the phase field characteristic length, the calculation precision is not good, and the reliability of the simulation result is low.

[0005] At present, there is no effective solution to the problem of poor calculation precision of the existing simulation evolution method. SUMMARY

[0006] The present application provides a rock material shear failure and frictional fracture simulation method, device and equipment to solve the defect of poor calculation precision of the existing simulation evolution method.

[0007] In a first aspect, the present application provides a rock material shear failure and frictional fracture simulation method, comprising:

[0008] According to the frictional fracture phase field model, a fourth-order tensor matrix corresponding to the stress tensor of the rock material is determined;

[0009] A local coordinate system of a crack surface is established, a traditional degradation function is modified to obtain a target degradation function, and the target degradation function and a crack density function are introduced;

[0010] In the frictional fracture phase field model, a history field variable is set, and a frictional fracture phase field control equation is determined;

[0011] Based on the frictional fracture phase field control equation, a stress field and a phase field finite element weak form are obtained, and a residual and a stiffness matrix are obtained.

[0012] According to the rock material shear failure and frictional fracture simulation method provided by the application, according to the frictional fracture phase field model, the fourth-order tensor matrix corresponding to the stress tensor of the rock material is determined, including:

[0013] A local coordinate system is introduced, and the normal strain and the normal stress of the rock material are determined according to the strain tensor and the normal vector;

[0014] The current state of the crack surface of the rock material is determined according to the normal strain or the normal stress of the rock material;

[0015] Based on the current state of the crack surface of the rock material, the fourth-order tensor matrix is generated.

[0016] According to the rock material shear failure and frictional fracture simulation method provided by the application, the current state of the crack surface of the rock material is determined according to the normal strain of the rock material, including:

[0017] If the normal strain of the rock material is greater than zero, the crack surface of the rock material is in an open state;

[0018] If the normal strain of the rock material is less than or equal to zero, the crack surface of the rock material is in a contact state.

[0019] According to the rock material shear failure and frictional fracture simulation method provided by the application, when the crack surface of the rock material is in an open state, the stress tensor of the rock material is determined according to damage attenuation;

[0020] When the crack surface of the rock material is in a contact state, a friction function is introduced, the crack surface of the rock material is determined to be in a bonded state or a sliding state, and the corresponding stress tensor is determined.

[0021] According to the rock material shear failure and frictional fracture simulation method provided by the application, a friction function is introduced to determine that the crack surface of the rock material is in a bonded state or a sliding state, including:

[0022] If the friction function value is less than zero, the crack surface of the rock material is in a bonded state, and there is no relative movement between the crack surfaces.

[0023] If the friction function value is greater than or equal to zero, the crack surface of the rock material is in a sliding state, and there is friction between the crack surfaces.

[0024] According to the rock material shear failure and frictional fracture simulation method provided by the application, a crack surface local coordinate system is established, comprising:

[0025] Determining the normal and tangential directions of the crack surface of the rock material;

[0026] Generating the crack surface local coordinate system based on the normal and tangential directions of the crack surface of the rock material.

[0027] According to the rock material shear failure and frictional fracture simulation method provided by the application, the normal and tangential directions of the crack surface of the rock material are determined, comprising:

[0028] Determining the included angle between the principal stress and the shear plane when the shear stress of the rock material is maximized;

[0029] According to the included angle, the normal vector and the tangential vector of the crack surface of the rock material are determined.

[0030] According to the rock material shear failure and frictional fracture simulation method provided by the application, in the frictional fracture phase field model, a history field variable is set, and a frictional fracture phase field control equation is determined, comprising:

[0031] In the initial stage of evolution of the frictional fracture phase field model, the history field variable is given an initial value;

[0032] In the loading stage of the frictional fracture phase field model, the value of the history field variable is updated according to the state of the integral point, and the frictional fracture phase field control equation is determined according to the history field variable.

[0033] In a second aspect, the application further provides a rock material shear failure and frictional fracture simulation device, comprising:

[0034] A determination module is configured to determine a fourth-order tensor matrix corresponding to a stress tensor of a rock material according to a frictional fracture phase field model;

[0035] A correction module is configured to establish a crack surface local coordinate system, correct a traditional degradation function to obtain a target degradation function, and introduce the target degradation function and a crack density function;

[0036] An evolution module is configured to set a history field variable in the frictional fracture phase field model and determine a frictional fracture phase field control equation.

[0037] A generating module is configured to obtain a stress field and a phase field finite element weak form, and a residual and a stiffness matrix based on the frictional cracking phase field control equation.

[0038] In a third aspect, the present application 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 shear failure and frictional cracking simulation method of the first aspect.

[0039] In a fourth aspect, the present application 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 shear failure and frictional cracking simulation method of the first aspect.

[0040] In a fifth aspect, the present application provides a computer program product, comprising a computer program, wherein the computer program is executable on a processor to implement the rock material shear failure and frictional cracking simulation method of the first aspect.

[0041] Compared with the prior art, the present application has the following beneficial effects:

[0042] The rock material shear failure and frictional cracking simulation method provided by the present application considers the problem that the traditional model is not sensitive to the phase field characteristic length, optimizes the traditional phase field model by introducing new degradation functions and crack density functions, improves the calculation accuracy of the phase field model, and makes the simulation result more reliable. In addition, the above process can be programmed, which is convenient for operation and programming. The rock material shear failure and frictional cracking simulation based on the phase field method is realized by a computer, which greatly reduces the amount of human calculation. BRIEF DESCRIPTION OF DRAWINGS

[0043] In order to more clearly illustrate the technical solutions in the present application or the prior art, the following will briefly introduce the drawings needed in the embodiments or prior art description. Obviously, the drawings in the following description are some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor.

[0044] Figure 1 is a flow chart of the rock material shear failure and frictional cracking simulation method provided by the present application;

[0045] Figure 2 is a schematic diagram of the geometric size and boundary conditions of a square plate containing prefabricated cracks in the embodiment of the present application;

[0046] Figure 3 is a phase field distribution diagram of different characteristic lengths in the embodiment of the present application;

[0047] Figure 4 These are horizontal displacement distribution cloud maps of different feature lengths in embodiments of the present invention;

[0048] Figure 5 This is a vertical displacement distribution cloud map of different feature lengths in an embodiment of the present invention;

[0049] Figure 6 This is a contact normal stress curve diagram in an embodiment of the present invention;

[0050] Figure 7 This is a contact tangential stress curve diagram in an embodiment of the present invention;

[0051] Figure 8 This is a schematic diagram of the geometric dimensions and boundary conditions of the biaxial compression numerical model in an embodiment of the present invention;

[0052] Figure 9 This is a force-displacement curve diagram of the loading process in an embodiment of the present invention;

[0053] Figure 10 This is an embodiment of the present invention. A schematic diagram of the phase field evolution process of the biaxial compression model at 100 kPa;

[0054] Figure 11 This is an embodiment of the present invention. A schematic diagram illustrating the evolution of the vertical displacement field at 100 kPa.

[0055] Figure 12 This is a schematic diagram of the slope geometry and displacement boundary conditions in an embodiment of the present invention;

[0056] Figure 13 This is a displacement evolution cloud map of the slope in an embodiment of the present invention;

[0057] Figure 14 This is a phase field evolution cloud map of the slope in an embodiment of the present invention;

[0058] Figure 15 This is a structural block diagram of the rock material shear failure and frictional fracture simulation device provided by the present invention;

[0059] Figure 16 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0060] In order to make the objects, technical solutions and advantages of the present application clearer, the following will clearly and completely describe the technical solutions in the present application with reference to the drawings in the present application. Obviously, the described embodiments are only some but not all of the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0061] The present application provides a rock material shear failure and frictional failure simulation method, Figure 1 The present application provides a flow chart of the rock material shear failure and frictional failure simulation method, as shown in Figure 1 The method comprises the following steps:

[0062] In step S101, according to the frictional failure phase field model, a fourth-order tensor matrix corresponding to the stress tensor of the rock material is determined;

[0063] In step S102, a local coordinate system of the crack surface is established, a traditional degradation function is modified to obtain a target degradation function, and the target degradation function and a crack density function are introduced;

[0064] In step S103, in the frictional failure phase field model, a history field variable is set, and a frictional failure phase field control equation is determined;

[0065] In step S104, based on the frictional failure phase field control equation, a stress field and a phase field finite element weak form are obtained, as well as a residual error and a stiffness matrix.

[0066] In the method, the frictional failure phase field model is reproduced, and the fourth-order tensor matrix corresponding to the stress tensor of the rock material is determined according to the frictional failure phase field model. Then, the local coordinate system of the crack surface is constructed, and the target degradation function after rough correction and the crack density function are introduced, so that the traditional frictional failure phase field model is optimized. Then, in the frictional failure phase field model, the history field variable is set, and the frictional failure phase field control equation is determined. Finally, according to the frictional failure phase field control equation, the stress field and the phase field finite element weak form are derived, and the residual error and the stiffness matrix are obtained. In the above process, the problem that the traditional model is not sensitive to the characteristic length of the phase field is considered, the traditional phase field model is optimized by introducing the new degradation function and the crack density function, the calculation accuracy of the phase field model is improved, and the simulation result is more reliable. In addition, all the above processes can be programmed, which is convenient for operation and programming. The rock material shear failure and frictional failure simulation based on the phase field method is realized by computer, and the amount of human calculation is greatly reduced.

[0067] In some embodiments, the step S101 comprises: introducing a local coordinate system, determining normal strain and normal stress of the rock material according to the strain tensor and the normal vector; determining the current state of the crack surface of the rock material according to the normal strain or the normal stress of the rock material; generating the fourth-order tensor matrix based on the current state of the crack surface of the rock material.

[0068] Specifically, the current state of the crack surface of the rock material is determined according to the normal strain of the rock material, comprising: if the normal strain of the rock material is greater than zero, the crack surface of the rock material is in an open state; if the normal strain of the rock material is less than or equal to zero, the crack surface of the rock material is in a contact state.

[0069] More specifically, when the crack surface of the rock material is in the open state, the stress tensor of the rock material is determined according to the damage attenuation; when the crack surface of the rock material is in the contact state, a friction function is introduced to determine whether the crack surface of the rock material is in a bonded state or a sliding state, and to determine the corresponding stress tensor.

[0070] The crack surface of the rock material is determined to be in the bonded state or the sliding state by introducing the friction function, comprising: if the value of the friction function is less than zero, the crack surface of the rock material is in the bonded state, and there is no relative movement between the crack surfaces; if the value of the friction function is greater than or equal to zero, the crack surface of the rock material is in the sliding state, and there is friction between the crack surfaces.

[0071] For example, the local coordinate system is introduced, the crack surface normal vector is , the tangential vector is , it is assumed that the crack surface normal is the Y axis and the crack surface tangential is the X axis, and the strain in the normal direction is calculated according to the strain tensor and the normal vector under the condition that the interface normal vector is known, and the expression is:

[0072]

[0073] wherein, represents the normal strain, represents the strain tensor. The corresponding normal stress can be represented as:

[0074]

[0075] wherein, and are Lame constants. The normal strain or the normal stress can distinguish whether the crack surface is in the contact state or the open state, when , it indicates that the crack surface is open, there is no friction contact, and there is no contact stress on the crack surface, so , The contact stress on the crack surface can be directly determined according to the damage attenuation and the stress tensor:

[0076]

[0077] wherein, represents the stress tensor, g d represents the damage function of the crack surface, is the stress tensor of the rock material when it is intact, , represents the elastic coefficient matrix.

[0078] On the contrary, when , the crack surface is in a contact state, and the crack contact exists in two states, namely, a bonding state and a sliding state, and a friction function needs to be introduced, and the expression thereof is as follows:

[0079]

[0080] wherein, f represents the value of the friction function, when , the contact surface starts to slide, when , the crack surface is in a bonding state, represents the shear yield strength of the rock material, represents the shear stress along the crack surface, and the calculation expression thereof is as follows:

[0081]

[0082] wherein, G represents the shear modulus, is a tensor obtained according to the normal vector and the tangent vector, .

[0083] When the crack surface is in a bonding state, there is no relative movement between the crack surfaces, it is assumed that the material matrix is consistent with the intact material matrix, and the stress tensor of the crack surface when the crack surface is in a bonding state can be expressed as:

[0084]

[0085] When the crack surface is in a sliding state, there is a friction force between the crack surfaces, and the shear modulus needs to be attenuated along the shear direction during the sliding process, and the expression thereof is as follows:

[0086]

[0087] wherein, is a fourth-order tensor, which can be calculated from the normal vector, , is the shear modulus, C bulk ​denotes the bulk modulus of the material, is the friction stress tensor, which is expressed as follows:

[0088]

[0089] wherein, p n denotes the normal stress of the crack surface, denotes the residual friction angle. In combination with the above formula, the expression of the stress tensor can be obtained as follows:

[0090]

[0091] Correspondingly, the fourth-order tensor matrix of the stress tensor can be expressed as:

[0092]

[0093] In the derivation process of the fourth-order tensor matrix, the friction force is regarded as an external force and does not participate in the calculation of the fourth-order tensor.

[0094] In some embodiments of the method, the step S102 of establishing the local coordinate system of the crack surface comprises: determining the normal and tangential directions of the crack surface of the rock material; and generating the local coordinate system of the crack surface based on the normal and tangential directions of the crack surface of the rock material.

[0095] The direction in which the shear occurs is the direction in which the energy dissipation is the largest, which is equivalent to the direction in which the shear stress is the largest. Therefore, in the present embodiment, the determination of the normal and tangential directions of the crack surface of the rock material comprises: determining the angle between the principal stress and the shear plane when the shear stress of the rock material is maximized; and determining the normal vector and the tangential vector of the crack surface of the rock material according to the angle.

[0096] Exemplarily, the angle between the principal stress and the shear plane is denoted as , and the expression is as follows:

[0097]

[0098] wherein, is the residual shear stress, and it is assumed that , p N denotes the normal stress of the crack surface, and the expression is as follows:

[0099]

[0100] The peak shear strength of the Mohr-Coulomb strength criterion is:

[0101]

[0102] wherein, is the cohesion, is the friction angle. The yield strength of intact rock material and damaged rock material is not consistent, assuming that the yield strength is related to the phase field:

[0103]

[0104] where d represents the phase field. The , , is expressed as the first principal stress, the intermediate principal stress and the minimum principal stress in the compression state, and the sliding plane is constructed by and On this plane, and can be expressed as:

[0105]

[0106]

[0107] Combining the above formulas, we can get:

[0108]

[0109] Taking the derivative of the above formula, we can get the angle between the principal stress and the shear plane when the shear stress of the rock material is maximized:

[0110]

[0111] Assuming , and are the unit direction vectors corresponding to the principal stress, in the case of known angle, the crack surface normal vector and the tangent vector can be expressed as:

[0112]

[0113]

[0114] In the process of numerical simulation, when damage occurs, the normal vector and the tangent vector at this time will be recorded, and the direction vector of this integration point will not change in the subsequent time step.

[0115] A new degradation function and crack density function are introduced to ensure that the phase field model is not sensitive to the characteristic length. The general form of the crack density function is written as:

[0116]

[0117] wherein, represents a local energy density function, is a local dissipation energy density function, and its expression is The density function will make the phase field sensitive to the characteristic length , so it is necessary to eliminate this effect and ensure that the material properties are reflected in the shear process. The .

[0118] Because the density function of the phase field has changed, the first derivative will have a constant term, so the degenerate function needs to be modified. The expression of the degenerate function is:

[0119]

[0120] In the above formula, the polynomial expression is:

[0121]

[0122] In order to ensure that the phase field evolution is not sensitive to the characteristic length of the phase field, the parameters of the degenerate function are modified, and = 2, , the is derived, and the result is:

[0123]

[0124] wherein, represents the energy release rate, is the energy threshold, which ensures that the phase field does not evolve in the initial state, and its expression is:

[0125]

[0126] wherein, c represents the cohesive force, G represents the shear modulus. The first derivative of the degenerate function can be expressed as:

[0127]

[0128] wherein, m represents the coefficient after derivation and simplification.

[0129] In some embodiments, step S103, in the frictional fracture phase field model, a history field variable is set, and a frictional fracture phase field control equation is determined, including: in the initial stage of evolution of the frictional fracture phase field model, the initial value is given to the history field variable; in the loading stage of the frictional fracture phase field model, the value of the history field variable is updated according to the state of the integration point, and the frictional fracture phase field control equation is determined according to the history field variable.

[0130] In this embodiment, in order to ensure the irreversibility of crack propagation, it is necessary to set the history field variable In the frictional fracture phase field model, the history field variable The expression form is inconsistent in different states, and in the initial calculation stage, the history field variable is assigned an initial value:

[0131]

[0132] wherein, H t The initial value of the history field variable is represented, and when the model is gradually loaded, the state of different integral points is different, and the history field variable evolution is inconsistent, which can be represented as:

[0133]

[0134] wherein, t n The time step is represented, is the shear strain of the adjacent time step, which can be represented as: The history field variable can be obtained, and then the frictional fracture phase field control equation can be obtained:

[0135]

[0136]

[0137] wherein, The gradient operator is represented, The stress tensor is represented, The surface force is represented, and b represents the body force. Based on the control equation, the stress field and the phase field finite element weak form can be obtained, and the residual and stiffness matrix thereof are derived, and the residual of the phase field can be represented as:

[0138]

[0139] wherein, R d The residual of the phase field is represented, N d The shape function matrix is represented, B d The strain matrix is represented, The integral domain is represented. After obtaining the residual equation of the phase field, the stiffness matrix of the phase field can be established:

[0140]

[0141] wherein, The stiffness matrix of the phase field is represented, The strain function matrix of i node is represented, a strain function matrix representing the j node, a shape function matrix representing the i node, a shape function matrix representing the j node, The second derivative of the degenerate function can be expressed as:

[0142]

[0143] wherein, The second derivative of the degenerate function.

[0144] In summary, under the action of stress, cracks are generally present in the rock mass, and during the crack propagation process, most of them are mainly shear fracture, and tensile failure is less. In view of the shear failure phenomenon generally existing in the rock mass, the shear elastic energy is decomposed along the crack surface, the phase field model of shear failure is developed, and the cohesion model is introduced, so that the model is not sensitive to the characteristic length of the phase field; The basic control equation of frictional fracture phase field is derived, and the model is used to simulate the frictional fracture problem of rock-like materials. In addition, all the calculation processes can be programmed, which is convenient for operation and programming, and the shear failure and frictional fracture simulation of rock materials based on the phase field method is realized by computer, which greatly reduces the amount of human calculation. Therefore, the advantages of the method are: considering that the model is not sensitive to the characteristic length of the phase field, improving the calculation accuracy, and the simulation result is more reliable.

[0145] In order to verify the effectiveness of the above method, the following simulation experiments are carried out:

[0146] 1. Simulation of square plate with pre-existing internal crack

[0147] A square plate contains a pre-existing crack, and the square plate is subjected to compression, and the geometric size and boundary conditions are as shown in Figure 2 Figure 2 It is the geometric size and boundary condition diagram of the square plate containing a pre-existing crack in the embodiment of the application. The model is 1m wide, the starting point and the end point coordinates of the pre-existing crack are (0.3, 0.33)m and (0.7, 0.68)m respectively, the elastic modulus of the model is =1GPa, the Poisson's ratio is =0.3, the friction angle and the residual friction angle are both 5.71° =0.1), the cohesion is =10MPa, the energy release rate is =30N / m, the vertical displacement load is applied to the top of the model, a total of 0.1mm, in 10 steps. In order to study the influence of characteristic length on numerical calculation result, the characteristic length ​Three values ​​were set: 0.002m, 0.004m, and 0.006m. The model was discretized using quadrilateral elements, with a total of 155,848 elements. The minimum element size was... =0.0004m, therefore the ratio of characteristic length to element size is The ratios are 5, 10, and 15, respectively, and all of these ratios are sufficient to meet the accuracy requirements.

[0148] Figure 3 These are phase field distribution diagrams with different feature lengths in embodiments of the present invention, derived from... Figure 3 It can be seen that, with the feature length As the number of pre-fabricated cracks increases, the width of the pre-fabricated cracks also gradually increases. Figure 4 These are horizontal displacement distribution cloud maps of different feature lengths in embodiments of the present invention. Figure 5 This is a vertical displacement distribution cloud map of different feature lengths in an embodiment of the present invention, derived from... Figure 4 and Figure 5 It can be seen that the feature length Under different conditions, the results of numerical simulations remain basically consistent.

[0149] Figure 6 This is a contact normal stress curve diagram from an embodiment of the present invention. Figure 7 This is a contact tangential stress curve diagram from an embodiment of the present invention. Figure 6 and Figure 7 It can be seen from this that different feature lengths The calculation results are basically consistent, with the feature length increasing. The decrease in the characteristic length leads to a higher peak stress intensity, indicating a longer characteristic length. The smaller the dispersion width of the phase field, the closer the calculation results are to the actual crack discontinuity, the better the convergence effect, and the better the characteristic length. The smaller the value, the finer the mesh needs to be, resulting in a larger computational load. Therefore, the feature length... The value remains A value of ≥5 is sufficient to meet the accuracy requirements.

[0150] 2. Simulation of biaxial compression experiment

[0151] This simulation subjects a defective specimen to shear failure under biaxial compression and investigates the effects of different confining pressures on the peak shear strength and residual strength of the specimen. The model's geometry and boundary conditions are as follows: Figure 8 As shown, Figure 8 This is a schematic diagram of the geometric dimensions and boundary conditions of the biaxial compression numerical model in this embodiment of the invention, with confining pressures applied to both the left and right sides of the model. , the bottom constraint Y direction displacement, the top of the vertical downward displacement load, the top of the middle point displacement fixed horizontal direction displacement, prevent rigid body displacement occurs during simulation caused by calculation does not converge phenomenon occurs. The shear modulus of the model = 26MPa, Poisson's ratio = 0.3, cohesion = 40KPa, the friction angle is equal to the residual friction angle, = 15°, energy release rate = 20N / m, the characteristic length of the phase field = 1mm, the model is discretized by four-sided element, the minimum element size = 0.2mm, the total number of elements is 60222, set three different confining pressures , respectively, 50KPa, 100KPa and 200KPa, the loading rate is 0.001mm per step.

[0152] The model first applies confining pressure, and then applies displacement load. Figure 9 is the force-displacement curve of the loading process in the embodiment of the application, from Figure 9 It can be seen that the shear strength of the frictional fracture phase field model changes with the change of stress distribution, which can predict the peak shear strength and residual shear strength of the material, and with the increase of displacement load, the curve gradually tends to be stable, representing that the shear crack has been penetrated, and the latter part of the curve is the residual shear strength of the material under the current stress state. Figure 10 is the evolution process diagram of the phase field of the biaxial compression model when = 100KPa, Figure 11 is the evolution process diagram of the vertical displacement field when = 100KPa, Figure 9 It can be seen that before = -1.2mm, the value of the shear phase field is not equal to 1, the model is in the shear strength softening stage, and the peak strength decreases rapidly, and with the increase of displacement load, the shear crack gradually penetrates, and the latter part of the curve also gradually remains unchanged.

[0153] 3, soil slope instability simulation

[0154] Landslide is one of the most common natural disasters, causing significant economic and personnel losses. Progressive cracking is the root cause of slope instability. Frictional sliding is the main mechanism of many slope cracking and instability. The frictional fracture phase field model proposed in this section is applied to slope instability analysis. According to previous research, the simplified slope is shown in Figure 12 Figure 12 ​is a schematic diagram of the slope geometry and displacement boundary condition in the embodiment of the present application. The slope is 20 m wide and 10 m high. The slope top is subjected to loading, which leads to slope instability and failure. It is assumed that the loading object is a rigid body. The rigid body is 4 m wide. The displacement increment is applied at each time step =-4×10 -4 m. The slope bottom is fixed in displacement. The right side is constrained in horizontal displacement. The slope elastic modulus =8.4 MPa. The Poisson's ratio =0.4. The soil density =2.04×103 kg / m 3 . The cohesive force =40 KPa. The friction angle =16.7°. The residual friction angle =10°. The energy release rate =10 KN / m. The phase field characteristic length =0.1 m. The model is discretized using quadrilateral elements. The minimum element size =0.02 m.

[0155] The simulation is first performed to balance the ground stress, and then the displacement load is applied until the slope fails. Although the initial ground stress balancing is performed, it does not have any effect on the slope. However, the initial ground stress provides the initial shear strength of the slope. After the slope fails, the initial ground stress field promotes the downward sliding of the slope. Figure 13 is the displacement evolution cloud chart of the slope in the embodiment of the present application, Figure 14 is the phase field evolution cloud chart of the slope in the embodiment of the present application. From Figure 13 and Figure 14 it can be seen that the failure surface of the landslide first occurs from the left side of the rigid body loading, and then gradually develops in a circular arc shape downward until it develops into a through failure surface.

[0156] The present application also provides a rock material shear failure and frictional rupture simulation device. The rock material shear failure and frictional rupture simulation device provided by the present application is described below. The rock material shear failure and frictional rupture simulation device described below can be correspondingly referred to the rock material shear failure and frictional rupture simulation method described above. Figure 15 is a structural block diagram of the rock material shear failure and frictional rupture simulation device provided by the present application, as Figure 15 indicated, the device comprises:

[0157] A determination module 1501 is configured to determine a fourth-order tensor matrix corresponding to a stress tensor of a rock material according to a frictional rupture phase field model.

[0158] The correction module 1502 is configured to establish a local coordinate system of a crack surface, correct a traditional degradation function, obtain a target degradation function, and introduce the target degradation function and a crack density function.

[0159] The evolution module 1503 is configured to set a history field variable in the frictional and cracked phase field model, and determine a frictional and cracked phase field control equation.

[0160] The generation module 1504 is configured to obtain a stress field and a phase field finite element weak form, and a residual and a stiffness matrix based on the frictional and cracked phase field control equation.

[0161] In use, the determination module 1501 reproduces the frictional and cracked phase field model, and determines a fourth-order tensor matrix corresponding to a stress tensor of the rock material according to the frictional and cracked phase field model. Then, the correction module 1502 establishes a local coordinate system of a crack surface, and corrects a traditional degradation function to obtain a target degradation function and a crack density function, thereby optimizing the traditional frictional and cracked phase field model. Then, the evolution module 1503 sets a history field variable in the frictional and cracked phase field model, and determines a frictional and cracked phase field control equation. Finally, the generation module 1504 derives a stress field and a phase field finite element weak form according to the frictional and cracked phase field control equation, and obtains a residual and a stiffness matrix thereof. In the above process, the problem that the traditional model is not sensitive to the characteristic length of the phase field is considered, the traditional phase field model is optimized by introducing a new degradation function and a crack density function, the calculation accuracy of the phase field model is improved, and the simulation result is more reliable. In addition, all the above processes can be programmed, which is convenient for operation and programming, and the rock material shear failure and frictional and cracked simulation based on the phase field method can be realized by a computer, thereby greatly reducing the amount of human calculation

[0162] Figure 16 An example of a schematic diagram of a physical structure of an electronic device is shown in Figure 16 The electronic device can include a processor 1601, a communications interface 1602, a memory 1603, and a communications bus 1604, wherein the processor 1601, the communications interface 1602, and the memory 1603 complete mutual communication through the communications bus 1604. The processor 1601 can invoke a logical instruction in the memory 1603 to execute a rock material shear failure and frictional and cracked simulation method, which includes:

[0163] According to the frictional and cracked phase field model, a fourth-order tensor matrix corresponding to a stress tensor of the rock material is determined;

[0164] A local coordinate system of a crack surface is established, a traditional degradation function is corrected, a target degradation function is obtained, and a target degradation function and a crack density function are introduced;

[0165] In the frictional crack phase field model, a history field variable is set, and a frictional crack phase field control equation is determined;

[0166] Based on the frictional crack phase field control equation, stress field and phase field finite element weak forms, and residual and stiffness matrices are obtained.

[0167] In addition, the logical instructions in the memory 1603 described above can be implemented 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 parts that contribute to the prior art or parts 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 a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the 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.

[0168] On the other hand, the present application also provides a computer program product, which comprises 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, and the computer can execute the rock material shear failure and frictional crack simulation method provided by the above-mentioned method, the method comprises:

[0169] According to the frictional crack phase field model, a fourth-order tensor matrix corresponding to the stress tensor of the rock material is determined;

[0170] A local coordinate system of the crack surface is established, a traditional degradation function is modified to obtain a target degradation function, and the target degradation function and a crack density function are introduced;

[0171] In the frictional crack phase field model, a history field variable is set, and a frictional crack phase field control equation is determined;

[0172] Based on the frictional crack phase field control equation, stress field and phase field finite element weak forms, and residual and stiffness matrices are obtained.

[0173] In another aspect, the present application also provides a non-transitory computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to implement the rock material shear failure and frictional crack simulation method provided by the above-mentioned method, the method comprises:

[0174] According to the frictional rupture phase field model, a four-order tensor matrix corresponding to the stress tensor of the rock material is determined;

[0175] A local coordinate system of the crack surface is established, the traditional degradation function is modified to obtain a target degradation function, and the target degradation function and a crack density function are introduced;

[0176] In the frictional rupture phase field model, a history field variable is set, and a frictional rupture phase field control equation is determined;

[0177] Based on the frictional rupture phase field control equation, a stress field and a phase field finite element weak form are obtained, as well as a residual and a stiffness matrix.

[0178] The device embodiments described above are only illustrative, wherein the units illustrated as separate components can or can not be physically separated, and the components illustrated 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 to achieve the purpose of the embodiment scheme according to actual needs. Those skilled in the art can understand and implement without creative labor.

[0179] Through the description of the above embodiments, those skilled in the art can clearly understand that the embodiments can be realized by means of software and the necessary general hardware platform, and of course, they can also be realized by hardware. Based on such understanding, the above technical solutions can be embodied in the form of a software product, which can be stored in a computer readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes a plurality of instructions to make a computer device (which can be a personal computer, server, or network device, etc.) execute the methods described in each embodiment or some parts of the embodiments.

[0180] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to 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 they can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for some technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method of simulating shear failure and frictional slip of a rock material, characterized by, The method comprises the following steps: determining a fourth-order tensor matrix corresponding to a stress tensor of a rock material according to a frictional crack phase field model; establishing a local coordinate system of a crack surface, modifying a traditional degradation function to obtain a target degradation function, and introducing the target degradation function and a crack density function; in the frictional crack phase field model, setting a history field variable and determining a frictional crack phase field control equation; based on the frictional crack phase field control equation, obtaining a stress field and a phase field finite element weak form, and a residual and a stiffness matrix; the crack density function is: wherein represents a local energy density function, is a local dissipated energy density function, expressed as ; selecting ; the degradation function is: wherein , ; represents the energy release rate, is an energy threshold, and ; c represents the cohesion, G represents the shear modulus; history field variable assign initial value: where, H t denotes the initial value of the history field variable, when the model is gradually loaded, the state of different integration points is different, the history field variable evolution is inconsistent, which can be expressed as: where, t n denotes the time step, is the shear strain of the adjacent time step, denoted as: ; the history field variable After that, the frictional rupture phase field control equation can be obtained: wherein, denotes the gradient operator, denotes the stress tensor, denotes the surface force, b denotes the body force; based on the control equation, the stress field and the phase field finite element weak form are obtained, and the residual and stiffness matrix thereof are derived, and the residual of the phase field can be expressed as: where R d represents the phase field residual, N d represents the shape function matrix, B d represents the strain matrix, represents the integration domain.

2. The rock material shear failure and frictional breakdown simulation method according to claim 1, characterized in that, determining a fourth-order tensor matrix corresponding to a stress tensor of a rock material according to a frictional crack phase field model, comprising: introducing a local coordinate system, and determining normal strain and normal stress of the rock material according to a strain tensor and a normal vector; determining a current state of a crack surface of the rock material according to the normal strain or the normal stress of the rock material; generating the fourth-order tensor matrix based on the current state of the crack surface of the rock material.

3. The rock material shear failure and frictional breakdown simulation method according to claim 2, characterized in that, determining the current state of the crack surface of the rock material according to the normal strain of the rock material, comprising: if the normal strain of the rock material is greater than zero, the crack surface of the rock material is in an open state; if the normal strain of the rock material is less than or equal to zero, the crack surface of the rock material is in a contact state.

4. The rock material shear failure and frictional breakdown simulation method according to claim 3, characterized in that, when the crack surface of the rock material is in the open state, determining the stress tensor of the rock material according to damage attenuation; when the crack surface of the rock material is in the contact state, introducing a friction function to determine that the crack surface of the rock material is in a bonded state or a sliding state, and determining a corresponding stress tensor.

5. The rock material shear failure and frictional breakdown simulation method according to claim 4, characterized in that, introducing a friction function to determine that the crack surface of the rock material is in a bonded state or a sliding state, comprising: if the value of the friction function is less than zero, the crack surface of the rock material is in a bonded state, and there is no relative movement between the crack surfaces; if the value of the friction function is greater than or equal to zero, the crack surface of the rock material is in a sliding state, and there is a friction force between the crack surfaces.

6. The method of claim 1, wherein, establishing a local coordinate system of a crack surface, comprising: determining a normal direction and a tangential direction of the crack surface of the rock material; generating the local coordinate system of the crack surface based on the normal direction and the tangential direction of the crack surface of the rock material.

7. The rock material shear failure and frictional breakdown simulation method according to claim 6, characterized in that, determining the normal direction and the tangential direction of the crack surface of the rock material, comprising: determining an included angle between a principal stress and a shear plane when the shear stress of the rock material is maximized; determining a normal vector and a tangential vector of the crack surface of the rock material according to the included angle.

8. The method of claim 1, wherein, in the frictional crack phase field model, setting a history field variable and determining a frictional crack phase field control equation, comprising: in an initial stage of evolution of the frictional crack phase field model, assigning an initial value to the history field variable; in a loading stage of the frictional crack phase field model, updating a value of the history field variable according to a state of an integration point, and determining the frictional crack phase field control equation according to the history field variable.

9. A rock material shear failure and frictional breakdown simulation apparatus for implementing the rock material shear failure and frictional breakdown simulation method according to any one of claims 1 to 8, characterized by, The method comprises the following steps: a determination module is configured to determine a fourth-order tensor matrix corresponding to a stress tensor of a rock material according to a frictional crack phase field model; The correction module is configured to establish a local coordinate system of a crack surface, correct a traditional degradation function, obtain a target degradation function, and introduce the target degradation function and a crack density function. The evolution module is configured to set a history field variable in the frictional crack phase field model and determine a frictional crack phase field control equation. The generation module is configured to obtain a stress field and a phase field finite element weak form, and a residual and a stiffness matrix based on the frictional crack phase field control equation.

10. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor implements the rock material shear failure and frictional crack simulation method according to any one of claims 1 to 8 when executing the program.

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