Construction method, simulation method and system for fracture expansion behavior model in stratified rock mass

Abstract

The invention belongs to the technical field of geotechnical engineering, and provides a stratified rock mass fracture expansion behavior model construction method, a stratified rock mass fracture expansion behavior model simulation method and system. The construction method of the fracture expansion behavior model in the stratified rock mass comprises the following steps: constructing a stratified rock mass near-field dynamic stress solving model based on a near-field dynamic non-local differential operator; the near-field dynamics non-local force density is deduced according to small deformation assumption, a near-field dynamics non-local differential operator is combined, an expression of the near-field dynamics non-local force density is reestablished, a softening criterion based on the strain energy density theory is introduced, and a stratified rock mass strain energy density softening model is constructed; based on the material mechanical characteristics of the interface between different rock stratums, a material mechanical parameter calculation model of the interface junction of the stratified rock mass is constructed; and combining the stratified rock mass near-field dynamic stress solving model, the stratified rock mass strain energy density softening model and the stratified rock mass interface junction material mechanical parameter calculation model to obtain a stratified rock mass fracture expansion behavior model.

Description

Technical Field

[0001] The present invention belongs to the technical field of geotechnical engineering, and in particular relates to a method for constructing a crack extension behavior model in a layered rock mass, a simulation method and a system. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] In nature and under the action of external loads, cracks often appear in layered rock masses, especially in weak layers of rock masses. The formation and expansion of cracks show a specific spatial distribution law, which is called the interval fracture phenomenon. Studies have shown that the interval fracture phenomenon not only affects the mechanical properties of the rock mass, but may also pose a threat to the safety and performance of geotechnical engineering structures. Therefore, in-depth exploration of the formation mechanism of cracks in layered rock masses and their interval distribution characteristics is of great academic and engineering significance. Existing research methods mainly rely on classical finite element and other related theories, but these methods have certain limitations in dealing with complex crack propagation, such as the tip singularity during crack propagation. Therefore, a new model is urgently needed to more accurately simulate the crack propagation behavior in layered rock masses.

[0004] As an emerging numerical simulation technology, the peridynamic method uses displacement integral equations to establish interaction relationships. It has the advantages of avoiding tip singularities and not relying on external failure criteria, and has gradually attracted the attention of researchers. However, in the current classical bond-based peridynamic theory, due to the incomplete neighborhood of material points at the boundary, direct use of micromodulus for calculation will produce large deviations. The change in mechanical properties caused by damage at the crack is not considered in the calculation, and the distribution of stress and strain fields cannot be directly obtained. Summary of the invention

[0005] In order to solve the above technical problems, the present invention provides a method for constructing a model of crack propagation behavior in layered rock masses, a simulation method and a system, which can establish a more accurate near-field dynamic constitutive model for simulating the expansion of intermittent cracks in two-dimensional layered rock masses, so as to effectively reduce the calculation error at the boundary, and introduce the strain energy density theory to establish the relationship between the mechanical parameters of the medium at the crack and the residual strain energy.

[0006] In order to achieve the above object, the present invention adopts the following technical solution:

[0007] A first aspect of the present invention provides a method for constructing a fracture propagation behavior model in a layered rock mass.

[0008] In one or more embodiments, a method for constructing a fracture propagation behavior model in a layered rock mass is provided, comprising:

[0009] Based on the peridynamic nonlocal differential operator, a model for solving the peridynamic stress of layered rock mass is constructed.

[0010] Based on the small deformation assumption, the peridynamic nonlocal force density is derived, and the expression of peridynamic nonlocal force density is re-established by combining the peridynamic nonlocal differential operator. Then, the softening criterion based on the strain energy density theory is introduced to construct the strain energy density softening model of layered rock mass.

[0011] Based on the material mechanical properties of the interface between different rock layers, a calculation model for the material mechanical parameters at the interface of layered rock mass is constructed;

[0012] The crack propagation behavior model in layered rock mass is obtained by combining the near-field dynamic stress solution model of layered rock mass, the strain energy density softening model of layered rock mass and the material mechanical parameter calculation model at the interface of layered rock mass.

[0013] As an implementation of the first aspect of the present invention, the two-dimensional expression of the peridynamic non-local differential operator is:

[0014]

[0015] where x T =(x1,x2), ξ1 and ξ2 are the components of the relative position vector ξ, R(N,x) is an infinitesimal second-order residual; the function f(x) is a known quantity, and f(x+ξ)-f(x) is the change.

[0016] As an implementation of the first aspect of the present invention, the expression of the peridynamic nonlocal force density is derived based on the small deformation assumption as follows:

[0017]

[0018] where f(η,ξ) is the force density of classical peridynamics, y and y′ are the positions of x and x′ after deformation, η is the relative displacement of the material point after the shape change, ω is the micropotential energy at a point, c is the micromodulus of the model, s is the elongation of the bond, and ξ is the relative position vector.

[0019] As an implementation of the first aspect of the present invention, the expression of the peridynamic nonlocal force density is re-established as follows:

[0020]

[0021] Where δ is the neighborhood radius, h is the thickness, μ is the shear modulus; G(ξ) is the nonlocal function matrix; M(ξ) is the boundary neighborhood non-complete area; tr is the trace of the matrix, and I is the identity matrix.

[0022] As an implementation of the first aspect of the present invention, the strain energy density softening model of layered rock mass is:

[0023] When dW PD <dW rock(E) When the rock is in the initial elastic change stage, the rock is not damaged, and the effective elastic modulus is consistent with the initial modulus value: E n =E ini ;

[0024] Among them, dW PD , dW rock(E) 、E ini are the peridynamic strain energy density, elastic change critical strain energy density, and initial elastic modulus of each material point x; E n For each material point x at different residual strain energies W r The corresponding effective elastic modulus in the case, N is the total number of segments corresponding to different elastic moduli according to the change of strain energy;

[0025] When dW rock(E) <dW PD <dW rock(S) When dW rock(S) is the critical strain energy density of strain softening. This stage is in the hard-to-soft stage. The effective elastic modulus decreases with the gradual damage. According to the formula Calculation; where the reduction of effective elastic modulus will lead to a reduction of microelastic modulus, which in turn causes a change in non-local force; n is the current stage;

[0026] When dW rock(E) <dW PD When the residual modulus is reduced to E, it is the stage of softening residue, the crack development ends and the residual modulus is reduced to E n =0.05E ini .

[0027] As an implementation of the first aspect of the present invention, the material mechanical parameter calculation model at the interface of the layered rock mass is characterized by the average properties between material points of different rock layers;

[0028] When there are interfaces between different rock layers, the average properties between material points in different rock layers are used to calculate the non-local forces, and the average elastic modulus is The weighted expression is:

[0029]

[0030] Where E x With E x′ is the elastic modulus of different rock formations, d x With d x′They are respectively the lengths from the rock interface in the direction of the line connecting the material points.

[0031] A second aspect of the present invention provides a system for constructing a fracture propagation behavior model in a layered rock mass.

[0032] In one or more embodiments, a system for constructing a model of fracture propagation behavior in a layered rock mass includes:

[0033] Stress solution model building module, which is used to build a layered rock peridynamic stress solution model based on the peridynamic nonlocal differential operator;

[0034] The strain energy density softening model building module is used to derive the peridynamic nonlocal force density based on the small deformation assumption, combine the peridynamic nonlocal differential operator, re-establish the expression of peridynamic nonlocal force density, and then introduce the softening criterion based on the strain energy density theory to construct the strain energy density softening model of layered rock mass;

[0035] A module for calculating and constructing material mechanical parameters at the interface of a layered rock mass, which is used to construct a calculation model for material mechanical parameters at the interface of a layered rock mass based on the material mechanical properties of the interface between different rock layers;

[0036] The crack propagation behavior model construction module is used to combine the layered rock mass near-field dynamic stress solution model, the layered rock mass strain energy density softening model and the layered rock mass interface junction material mechanical parameter calculation model to obtain the crack propagation behavior model in the layered rock mass.

[0037] A third aspect of the present invention provides a method for simulating crack propagation behavior in a layered rock mass.

[0038] In one or more embodiments, a method for simulating fracture propagation behavior in a layered rock mass includes:

[0039] The crack propagation behavior model in the layered rock mass is constructed by using the method for constructing the crack propagation behavior model in the layered rock mass as described above;

[0040] Based on the crack propagation behavior model and initialization parameters in the layered rock mass, the near-field dynamic stress parameters of the layered rock mass, the strain energy density softening parameters of the layered rock mass and the material mechanics parameters at the interface of the layered rock mass are simulated;

[0041] Based on the simulation results, the crack propagation process of layered rock mass is visualized.

[0042] As an implementation of the third aspect of the present invention, the layered rock mass peridynamic stress parameters include the total non-local force, acceleration, displacement and stress of each material point;

[0043] The layered rock mass strain energy density softening parameters include the near-field dynamic strain energy density of each material point, the elastic change critical strain energy density and the initial elastic modulus, and the softening parameters are updated according to the residual strain energy of each point;

[0044] The material mechanical parameters at the interface of the layered rock mass include an average elastic modulus, which is used to calculate the non-local force; if the elongation is greater than the set critical failure elongation, the bond non-local force between the material points disappears.

[0045] A fourth aspect of the present invention provides a system for simulating crack propagation behavior in layered rock masses.

[0046] In one or more embodiments, a system for simulating fracture propagation behavior in a layered rock mass includes:

[0047] A model building module, which is used to build a fracture propagation behavior model in a layered rock mass by using the fracture propagation behavior model building method in a layered rock mass as described above;

[0048] A behavior simulation model, which is used to simulate the near-field dynamic stress parameters of the layered rock mass, the strain energy density softening parameters of the layered rock mass, and the material mechanics parameters at the interface of the layered rock mass based on the crack propagation behavior model in the layered rock mass and the initialization parameters;

[0049] The result visualization module is used to visualize the crack propagation process of layered rock mass based on the simulation results.

[0050] Compared with the prior art, the present invention has the following beneficial effects:

[0051] (1) The present invention introduces a nonlocal differential operator to establish a peridynamic stress analysis solution model, which solves the problem that stress-strain analysis cannot be performed in traditional models and provides an intuitive analysis method for simulating deformation and failure problems using the bond-based peridynamic method.

[0052] (2) The present invention re-derives the expression of the non-local force density of peridynamics, overcoming the computational error caused by the traditional method in dealing with the incomplete neighborhood of material points at the boundary, thereby improving the accuracy of the stress and strain fields, making the simulation results closer to the actual situation, and better reflecting the mechanical behavior of complex layered rock masses.

[0053] (3) The present invention combines the strain energy density theory to establish the relationship between the mechanical parameters of the medium at the crack and the residual strain energy, so that the influence of crack extension on the mechanical properties of the material can be more accurately considered during the simulation process, thereby improving the simulation reliability; and realizes the calculation of interface parameters between layered rock masses, taking the average properties between material points in different rock layers to calculate non-local forces. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0055] Figure 1 A schematic diagram of a peridynamic material point according to an embodiment of the present invention;

[0056] Figure 2 The meaning of each area of ​​strain energy;

[0057] Figure 3 is the variation of elastic modulus with strain energy in peridynamics, from E1 to E N ;

[0058] Figure 4 This is a flow chart of a layered rock simulation method based on peridynamics according to an embodiment of the present invention;

[0059] Figure 5 This is a calculation model diagram of the third embodiment of the present invention;

[0060] Figure 6 This is a diagram of the crack propagation process of a layered rock mass according to the third embodiment of the present invention;

[0061] Figure 7 This is a graph showing the variation of the average crack spacing with strain in Example 3 of the present invention. DETAILED DESCRIPTION

[0062] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0063] It should be noted that the following detailed descriptions are all illustrative and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0064] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0065] Embodiment 1

[0066] This embodiment provides a method for constructing a fracture propagation behavior model in a layered rock mass, which at least includes the following steps:

[0067] S101: Based on the peridynamic nonlocal differential operator, a model for solving the peridynamic stress in layered rock mass is constructed.

[0068] Among them, the two-dimensional expression of the peridynamic nonlocal differential operator is:

[0069]

[0070] where x T =(x1,x2), ξ1 and ξ2 are the components of the relative position vector ξ, R(N,x) is an infinitesimal second-order residual; the function f(x) is a known quantity, and f(x+ξ)-f(x) is the change.

[0071] like Figure 1 As shown in Figure 1, in peridynamics, the rock mass is discretized into a finite number of material points that carry information such as mass, volume, and density. At the same time, each material point interacts with other material points within a certain range. The interaction between material points is represented by the non-local force function f. According to Newton's second law, the motion equation followed by the material point at time t is:

[0072]

[0073] Where x′ is the neighborhood of x H x ={x′∈R,|x′-x|<δ}, the displacements of x and x′ at time t are u(x,t) and u(x′,t), respectively, and ρ is is the density and acceleration, b(x, t) is the body force, the relative position of x′ and x at the initial moment is x′-x=ξ, η is the relative displacement after the shape changes, so the position change is ξ+η, dV x′ is a spatial metric. For a two-dimensional problem, it represents the area element dA of each material point. x′ .

[0074] Construct the function at each material point according to the theory of nonlocal differential operators is a linear combination of polynomial basis functions:

[0075]

[0076] in etc. are unknown coefficients, and the weight coefficient is w(|ξ|)=exp(-(a|ξ| / δ) 2 ), δ is the neighborhood radius, and a is a specified constant. In addition, the function The following orthogonality is satisfied:

[0077]

[0078] Where n1,n2,p2,p2=0,1,2,δnp is the Kronecker symbol, dA x′ It is a two-dimensional space metric, which can be combined with the function Relationship with orthogonality to solve for the unknown coefficients:

[0079] Aa=b

[0080] Where A is a matrix of known shape, a is a matrix of unknown coefficients, and b is a matrix of known shape.

[0081]

[0082] The unknown coefficient matrix is ​​solved by inverting the matrix:

[0083] a=A -1 b

[0084] After solving the unknown coefficients, the corresponding differential of each material point function f(x) can be obtained:

[0085]

[0086] S102: Based on the small deformation assumption, the peridynamic nonlocal force density is derived. Combined with the peridynamic nonlocal differential operator, the expression of the peridynamic nonlocal force density is re-established. Then, the softening criterion based on the strain energy density theory is introduced to construct the strain energy density softening model of layered rock mass.

[0087] Using differential operators to represent the Navier equilibrium equation, the stress components can be constructed in two dimensions as:

[0088]

[0089] Where E and v are the elastic modulus and Poisson's ratio of the material, and u1 and u2 represent the displacement of each material point in the two coordinate directions respectively.

[0090] At this point, the construction of the peridynamic stress solution coefficients and solution equations is completed. And all vectors g(ξ) and matrices G(ξ) are stored as:

[0091]

[0092] The non-local force function f represents the constitutive force function related to the material properties. For elastic-brittle materials, its expression is:

[0093]

[0094] Where y and y′ are the positions of x and x′ after deformation, ω is the micro potential energy at a point, and c is the micro modulus of the model. In peridynamics, it is assumed that material points are connected by bonds, the direction of the nonlocal force f(η,ξ) is consistent with the direction of the connecting bond after deformation, and s is the elongation of the bond:

[0095]

[0096] s0 is the critical elongation of the connecting bond. When the elongation between material points exceeds the critical elongation, the bonds between material points break and the non-local interactions between material points disappear. The micromodulus corresponding to each bond is:

[0097]

[0098] Where δ is the neighborhood radius, h is the thickness, and μ is the shear modulus. At the same time, under the assumption of small deformation, the following relationship holds:

[0099]

[0100] n xx′ is the unit vector in the direction of the relative position of x and x′. The bond stretching due to small deformation can be further expressed as:

[0101]

[0102] The peridynamic nonlocal force density between x and x′ can be determined as:

[0103]

[0104] According to the vector equivalence relation The nonlocal force density between x and x′ is expressed as:

[0105]

[0106] According to the non-local differential operator, it can be expressed as follows under two-dimensional conditions:

[0107]

[0108] M(ξ)=(trG(ξ)I+2G(ξ)),

[0109] Furthermore, the non-local force density formula between x and x′ is obtained:

[0110]

[0111] Where δ is the neighborhood radius, h is the thickness, μ is the shear modulus; G(ξ) is the non-local function matrix; M(ξ) is the boundary neighborhood non-complete area; tr is the trace of the matrix, and I is the unit matrix. .

[0112] The non-complete area M(ξ) of the boundary neighborhood is not equal. In order to ensure that the forces calculated at material points x and x′ are equal to satisfy the conservation of angular momentum and linear momentum, the force density vector is expressed as:

[0113]

[0114] At this point, the construction of the calculation expression for the nonlocal force density of peridynamics has been completed.

[0115] The process of introducing the softening criterion based on strain energy density theory is as follows:

[0116] The effective elastic modulus of rock at the crack tip in different dissipation stages and the residual strain energy density are set up in a linear correspondence: Where E n For each material point x at different residual strain energies W r The corresponding effective elastic modulus in the case, N is the number of segments defined; n is the current stage. n With W r The changes go through the stages of damage initiation, effective modulus reduction, micromodulus weakening and damage evolution:

[0117] like Figure 2 and Figure 3 As shown in Figure 1, the iterative calculation of rock materials is accompanied by irreversible energy loss, which in turn causes strain softening and reduces the mechanical parameters at the failure point. If the AO unloading path will return to the original path in the elastic stage, if the loading continues to the post-peak point D, the area S OABDG is the absorbed strain energy W a At this time, the unloading returns along DE, and the shaded area S OABDE represents the dissipated strain energy W d , S DEG is the recoverable strain energy W e , S GDFCN is the residual strain energy W r ,S OABDFCN The total strain energy of the element W PD .

[0118] Specifically, Figure 2 and Figure 3 As shown in Figure 2, the strain energy density softening model of layered rock mass is:

[0119] When dW PD <dW rock(E) When the rock is in the initial elastic change stage, the rock is not damaged, and the effective elastic modulus is consistent with the initial modulus value: E n =E ini ;

[0120] Among them, dW PD , dW rock(E) 、E iniare the peridynamic strain energy density, elastic change critical strain energy density, and initial elastic modulus of each material point x; E n For each material point x at different residual strain energies W r The effective elastic modulus corresponding to the case, N is the total number of segments corresponding to different elastic moduli according to the change of strain energy; for example, if it is divided into 10 segments, then different strain energies correspond to 10 elastic moduli.

[0121] When dW rock(E) <dW PD <dW rock(S) When dW rock(S) is the critical strain energy density of strain softening. This stage is in the hard-to-soft stage. The effective elastic modulus decreases with the gradual damage. According to the formula Calculation; Among them, the reduction of effective elastic modulus will lead to the reduction of microelastic modulus, which in turn causes the change of non-local force; E1, E2, E3KE n is the effective elastic modulus at different stages, where N is the number of defined segments and n is the current stage.

[0122] When dW rock(E) <dW PD When the residual modulus is reduced to E, it is the stage of softening residue, the crack development ends and the residual modulus is reduced to E n =0.05E ini .

[0123] At this point, the relationship between the mechanical parameters of the medium at the crack and the residual strain energy is completed, and the softening iterative calculation method of the near-field dynamics strain energy density is realized.

[0124] S103: Based on the material mechanical properties of the interfaces between different rock layers, a material mechanical parameter calculation model at the interface of layered rock mass is constructed.

[0125] Among them, the calculation model of material mechanical parameters at the interface of layered rock mass is characterized by the average properties between material points in different rock layers;

[0126] When there are interfaces between different rock layers, the average properties between material points in different rock layers are used to calculate the non-local forces, and the average elastic modulus is The weighted expression is:

[0127]

[0128] Where E x With E x′ is the elastic modulus of different rock formations, d x With d x′ They are respectively the lengths from the rock interface in the direction of the line connecting the material points.

[0129] At this point, the calculation of interface parameters of different rock layers has been completed.

[0130] S104: combining a layered rock mass peridynamic stress solution model, a layered rock mass strain energy density softening model, and a layered rock mass interface interface material mechanical parameter calculation model to obtain a crack propagation behavior model in the layered rock mass.

[0131] Embodiment 2

[0132] This embodiment provides a system for constructing a fracture propagation behavior model in a layered rock mass, including:

[0133] Stress solution model building module, which is used to build a layered rock peridynamic stress solution model based on the peridynamic nonlocal differential operator;

[0134] The strain energy density softening model building module is used to derive the peridynamic nonlocal force density based on the small deformation assumption, combine the peridynamic nonlocal differential operator, re-establish the expression of peridynamic nonlocal force density, and then introduce the softening criterion based on the strain energy density theory to construct the strain energy density softening model of layered rock mass;

[0135] A module for calculating and constructing material mechanical parameters at the interface of a layered rock mass, which is used to construct a calculation model for material mechanical parameters at the interface of a layered rock mass based on the material mechanical properties of the interface between different rock layers;

[0136] The crack propagation behavior model construction module is used to combine the layered rock mass near-field dynamic stress solution model, the layered rock mass strain energy density softening model and the layered rock mass interface junction material mechanical parameter calculation model to obtain the crack propagation behavior model in the layered rock mass.

[0137] It should be noted here that the various modules in this embodiment correspond one-to-one to the various steps in Example 1, and the specific implementation process is the same, which will not be described in detail here.

[0138] Embodiment 3

[0139] like Figure 4 As shown, this embodiment provides a method for simulating crack propagation behavior in a layered rock mass, which at least includes the following steps:

[0140] A1: The method for constructing a crack propagation behavior model in a layered rock mass as described in the first embodiment above is used to construct a crack propagation behavior model in a layered rock mass.

[0141] Specifically, define the geometry of the layered rock mass, including the thickness W and length L of different rock layers for two-dimensional problems. Set the material properties of each rock layer, including the elastic modulus E, Poisson's ratio v, non-uniformity parameter m, and critical failure elongation s0 corresponding to each rock layer. If there are prefabricated cracks, define the initial position of the prefabricated cracks, the number of cracks n, and the crack spacing l parameters.

[0142] The prefabricated crack method is to pre-cut the connecting bonds on the prefabricated fracture path, so that the interaction between the material points disappears, thereby forming a crack.

[0143] To realize the inhomogeneous properties of rock, Weibull distribution or coefficient of variation can be used. If Weibull distribution is used, it is assumed that the critical failure elongation follows Weibull distribution:

[0144]

[0145] The smaller the shape parameter m, the wider the distribution, indicating that the rock is more heterogeneous, that is, the greater the difference in the critical failure elongation of the rock. The larger the shape parameter m, the narrower the distribution, indicating that the rock is less heterogeneous.

[0146] The coefficient of variation is a commonly used parameter to measure the degree of change in rock properties. If the coefficient of variation is used to describe rock heterogeneity, the critical failure elongation is randomly generated at each material point, and the ratio of its standard deviation σ to the mean μ is calculated:

[0147]

[0148] The smaller the coefficient of variation m, the more consistent the rock properties are and the smaller the heterogeneity is. The larger the coefficient of variation m, the greater the variation in rock properties, that is, the stronger the heterogeneity is.

[0149] A2: Based on the crack propagation behavior model and initialization parameters in the layered rock mass, the near-field dynamic stress parameters of the layered rock mass, the strain energy density softening parameters of the layered rock mass and the material mechanics parameters at the interface of the layered rock mass are simulated.

[0150] Specifically, the initialization parameters include:

[0151] Set the calculation parameters, including the total number of discrete material points M, neighborhood radius δ, boundary conditions, etc. Solve for the nonlocal differential operator coefficients at each material point Set the strain energy density parameters. Discrete the solution domain according to the calculation parameters, generate the material point coordinates, and determine the material points contained in each material point domain. Initialize the bond, non-local force, displacement field and other information of all material points in their near field, and calculate the interface parameters between different rock layers.

[0152] The boundary conditions are displacement boundary conditions or force density boundary conditions, and time-varying displacements or constant body force density are applied at the boundary material points.

[0153] The material points contained in each material point domain are searched according to the material point coordinates and the neighborhood radius δ. If they are within the radius, they are material points in the domain.

[0154] A3: Based on the simulation results, the crack propagation process of layered rock is visualized.

[0155] The peridynamic stress parameters of the layered rock mass include the total non-local force, acceleration, displacement and stress of each material point;

[0156] The layered rock mass strain energy density softening parameters include the near-field dynamic strain energy density of each material point, the elastic change critical strain energy density and the initial elastic modulus, and the softening parameters are updated according to the residual strain energy of each point;

[0157] The material mechanical parameters at the interface of the layered rock mass include an average elastic modulus, which is used to calculate the non-local force; if the elongation is greater than the set critical failure elongation, the bond non-local force between the material points disappears.

[0158] Determine the time step Δt, the number of time steps t, and start the loop calculation according to the input parameters. Calculate the non-local force f and acceleration of each material point based on the current information Displacement If the elongation is greater than the set critical failure elongation s0, the bond non-local force between material points disappears. The damage degree D(x) of each material point is calculated, and the softening parameters are updated according to the residual strain energy of each point.

[0159] The displacement calculation can be performed using Verlet-Velocity display difference:

[0160]

[0161] u n+1 = un +Δtu n+1 / 2

[0162]

[0163] In the peridynamic method, there is no need to introduce additional criteria to determine the failure. Instead, the damage at a point is defined by studying the failure of all the bonds connecting the point:

[0164]

[0165] The damage parameter D(x) ranges from 0 to 1, where 0 indicates that point x has not been damaged yet and 1 indicates complete damage.

[0166] The specific simulation results are given below:

[0167] like Figure 5 As shown in the figure, the geometry of the layered rock mass is defined, and three layers of rock mass are set, with the middle layer W f =30mm, upper and lower base W n =30mm, the total width of the model is W = 90mm, and the total length of the rock layer is L = 400mm. The elastic modulus of the middle layer is E f =50GPa, upper and lower base layers take E n =10Gpa, Poisson's ratio is v=0.3. The critical failure elongation follows the Weibull distribution, reflecting the inhomogeneous nature of the rock. The shape parameter of the middle layer is m=5, the shape parameter of the upper and lower base layers is m=10, and the critical elongation is set to s0=3.285×10 -3 , upper and lower base s1=4.927×10 -3 , there is no prefabricated crack in this example.

[0168] Through trial calculation, the particle size of the model is set to 400×90, the spacing between material points is Δx=1mm, the neighborhood radius δ=3.015Δx, and the horizontal tensile displacement boundary conditions that increase linearly with the time calculation step are applied at both ends of the rock layer, increasing by 1×10 -6 m. Solve for the coefficients of the nonlocal differential operator at each material point Set the strain energy density parameters, etc. Discrete the solution domain according to the calculation parameters, generate the material point coordinates, and determine the material points contained in each material point domain.

[0169] Determine the time step Δt = 1.4×10 -7 s, time step t = 1000, start loop calculation according to the input parameters. Calculate the non-local force f and acceleration of each material point according to the current information Displacement If the elongation is greater than the set critical failure elongation s0, the bond non-local force between material points disappears. The damage degree D(x) of each material point is calculated, and the softening parameters are updated according to the residual strain energy of each point. Figure 6 This is a diagram showing the crack propagation effect of layered rock under boundary conditions.

[0170] The simulation results were processed and analyzed. Under the displacement conditions on both sides of the rock formation, multiple cracks with basically the same spacing gradually emerged in the weak layer, which can be divided into three stages according to the damage form: the micro-crack extension stage, which is before the first macro-crack is initiated. With the application of boundary conditions, the micro-cracks in the weak layer are connected and connected; the interval crack generation stage, which is the stage where continuous loading after the micro-cracks are saturated will lead to the appearance of macro-cracks in the weak layer, the stress state between the cracks changes, and new cracks gradually appear between the old cracks; the equal-interval crack saturation stage, at this time, the number of cracks in the weak layer reaches the maximum, the cracks are basically in a compressive stress state, no new macro-cracks appear, and continuous loading will lead to interlayer interface peeling or base fracture. Figure 7 This is an analysis diagram of the change process of the average crack spacing.

[0171] Embodiment 4

[0172] This embodiment provides a simulation system for fracture propagation behavior in a layered rock mass, including:

[0173] A model building module, which is used to build a fracture propagation behavior model in a layered rock mass by using the fracture propagation behavior model building method in a layered rock mass as described above;

[0174] A behavior simulation model, which is used to simulate the near-field dynamic stress parameters of the layered rock mass, the strain energy density softening parameters of the layered rock mass, and the material mechanics parameters at the interface of the layered rock mass based on the crack propagation behavior model in the layered rock mass and the initialization parameters;

[0175] The result visualization module is used to visualize the crack propagation process of layered rock mass based on the simulation results.

[0176] It should be noted here that each module in this embodiment corresponds to each step in Example 3 one by one, and the specific implementation process is the same, which will not be described in detail here.

[0177] In particular, according to an embodiment of the present application, the process described above with reference to the flowchart can be implemented as a computer software program. For example, an embodiment of the present application includes a computer program product, which includes a computer program carried on a computer-readable medium, and the computer program contains a program code for executing the method of embodiment one or embodiment three. In such an embodiment, the computer program can be downloaded and installed from a network through a communication part, and / or installed from a removable medium. When the computer program is executed by a central processing unit, various functions defined in the device of the present application are executed.

[0178] The computer program instructions corresponding to the method of Embodiment 1 or Embodiment 3 may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory generate a product including an instruction device, which is implemented in the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0179] A person skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program, and the program can be stored in a computer-readable storage medium, and when the program is executed, it can include the processes of the embodiments of the above-mentioned methods. The storage medium can be a disk, an optical disk, a read-only memory (ROM) or a random access memory (RAM), etc.

[0180] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for constructing a fracture propagation behavior model in a layered rock mass, characterized in that: include: Based on the peridynamic nonlocal differential operator, a model for solving the peridynamic stress of layered rock mass is constructed. Based on the small deformation assumption, the peridynamic nonlocal force density is derived, and the expression of peridynamic nonlocal force density is re-established by combining the peridynamic nonlocal differential operator. Then, the softening criterion based on the strain energy density theory is introduced to construct the strain energy density softening model of layered rock mass. Based on the material mechanical properties of the interface between different rock layers, a calculation model for the material mechanical parameters at the interface of layered rock mass is constructed; The crack propagation behavior model in layered rock mass is obtained by combining the near-field dynamic stress solution model of layered rock mass, the strain energy density softening model of layered rock mass and the material mechanical parameter calculation model at the interface of layered rock mass.

2. The method for constructing a crack propagation behavior model in a layered rock mass according to claim 1, characterized in that: The two-dimensional expression of the peridynamic nonlocal differential operator is: where x T =(x1,x2), ξ1 and ξ2 are the components of the relative position vector ξ, R(N,x) is an infinitesimal second-order residual; the function f(x) is a known quantity, and f(x+ξ)-f(x) is the change.

3. The method for constructing a crack propagation behavior model in a layered rock mass according to claim 1, characterized in that: Based on the small deformation assumption, the expression of the peridynamic nonlocal force density is derived as follows: where f(η,ξ) is the force density of classical peridynamics, y and y′ are the positions of x and x′ after deformation, respectively, and η is the relative displacement of the material point after the shape change. ω is the micro potential energy at a point, c is the micro modulus of the model; s is the elongation of the bond; ξ is the relative position vector.

4. The method for constructing a crack propagation behavior model in a layered rock mass according to claim 3, characterized in that: The expression of the peridynamic nonlocal force density is re-established as: Where δ is the neighborhood radius, h is the thickness, μ is the shear modulus; G(ξ) is the nonlocal function matrix; M(ξ) is the boundary neighborhood non-complete area; tr is the trace of the matrix, and I is the identity matrix.

5. The method for constructing a crack propagation behavior model in a layered rock mass according to claim 1, characterized in that: The strain energy density softening model of layered rock mass is: When dW PD <dW rock(E) When the rock is in the initial elastic change stage, the rock is not damaged, and the effective elastic modulus is consistent with the initial modulus value: E n =E ini ; Among them, dW PD , dW rock(E) 、E ini are the peridynamic strain energy density, elastic change critical strain energy density, and initial elastic modulus of each material point x; E n For each material point x at different residual strain energies W r The corresponding effective elastic modulus in the case, N is the total number of segments corresponding to different elastic moduli according to the change of strain energy; When dW rock(E) <dW PD <dW rock(S) When dW rock(S) is the critical strain energy density of strain softening. This stage is in the hard-to-soft stage. The effective elastic modulus decreases with the gradual damage. According to the formula Calculation; where the reduction of effective elastic modulus will lead to a reduction of microelastic modulus, which in turn causes a change in non-local force; n is the current stage; When dW rock(E) <dW PD When the residual modulus is reduced to E, it is the stage of softening residue, the crack development ends and the residual modulus is reduced to E n =0.05E ini .

6. The method for constructing a crack propagation behavior model in a layered rock mass according to claim 1, characterized in that: The calculation model of material mechanical parameters at the interface of layered rock mass is characterized by the average properties between material points in different rock layers; When there are interfaces between different rock layers, the average properties between material points in different rock layers are used to calculate the non-local forces, and the average elastic modulus is The weighted expression is: Where E x With E x′ is the elastic modulus of different rock formations, d x With d x′ They are respectively the lengths from the rock interface in the direction of the line connecting the material points.

7. A system for constructing a fracture propagation behavior model in a layered rock mass, characterized in that: include: Stress solution model building module, which is used to build a layered rock peridynamic stress solution model based on the peridynamic nonlocal differential operator; The strain energy density softening model building module is used to derive the peridynamic nonlocal force density based on the small deformation assumption, combine the peridynamic nonlocal differential operator, re-establish the expression of peridynamic nonlocal force density, and then introduce the softening criterion based on the strain energy density theory to construct the strain energy density softening model of layered rock mass; A module for calculating and constructing material mechanical parameters at the interface of a layered rock mass, which is used to construct a calculation model for material mechanical parameters at the interface of a layered rock mass based on the material mechanical properties of the interface between different rock layers; The crack propagation behavior model construction module is used to combine the layered rock mass near-field dynamic stress solution model, the layered rock mass strain energy density softening model and the layered rock mass interface junction material mechanical parameter calculation model to obtain the crack propagation behavior model in the layered rock mass.

8. A method for simulating crack propagation behavior in a layered rock mass, characterized in that: include: The crack propagation behavior model in the layered rock mass is constructed by using the method for constructing the crack propagation behavior model in the layered rock mass according to any one of claims 1 to 6; Based on the crack propagation behavior model and initialization parameters in the layered rock mass, the near-field dynamic stress parameters of the layered rock mass, the strain energy density softening parameters of the layered rock mass and the material mechanics parameters at the interface of the layered rock mass are simulated; Based on the simulation results, the crack propagation process of layered rock mass is visualized.

9. The method for simulating crack propagation behavior in layered rock mass according to claim 8, characterized in that: The peridynamic stress parameters of the layered rock mass include the total non-local force, acceleration, displacement and stress of each material point; The layered rock mass strain energy density softening parameters include the near-field dynamic strain energy density of each material point, the elastic change critical strain energy density and the initial elastic modulus, and the softening parameters are updated according to the residual strain energy of each point; The material mechanical parameters at the interface of the layered rock mass include an average elastic modulus, which is used to calculate non-local forces; If the elongation is greater than the set critical failure elongation, the bond non-local forces between material points disappear.

10. A system for simulating crack propagation behavior in layered rock mass, characterized in that: include: A model building module, which is used to build a fracture propagation behavior model in a layered rock mass by using the fracture propagation behavior model building method in a layered rock mass according to any one of claims 1 to 6; A behavior simulation model, which is used to simulate the near-field dynamic stress parameters of the layered rock mass, the strain energy density softening parameters of the layered rock mass, and the material mechanics parameters at the interface of the layered rock mass based on the crack propagation behavior model in the layered rock mass and the initialization parameters; The result visualization module is used to visualize the crack propagation process of layered rock mass based on the simulation results.

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