Damage assessment method for simulating shear failure of rock material based on near-field dynamic constitutive model

Abstract

The invention discloses a damage assessment method for simulating shear failure of a rock material based on a near-field dynamics constitutive model, and the method comprises the steps: constructing an initial simulation model based on rock information, and initializing the initial simulation model to obtain a rock mass simulation model; a plurality of substance points are formed based on the rock mass simulation model and the near-field dynamics, and a near-field dynamics stress solving model is constructed according to a near-field dynamics non-local differential operator theory; using small deformation assumption to obtain near-field dynamic non-local force density, and updating the near-field dynamic non-local force density; on the basis of the non-local force density, a non-linear rock material constitutive force function is introduced, and rock material non-linear constitutive force is obtained; constructing a near-field dynamics rock discrimination criterion based on compressive strength, tensile strength and Mohr-Coulomb; and monitoring the non-local force density of the near-field dynamics, calculating the nonlinear constitutive force of the rock material when a judgment criterion is met, and evaluating the compression-pull and shear damage of a key between material points based on the nonlinear constitutive force of the rock material.

Description

Technical Field

[0001] The present invention relates to the field of rock mechanics and material science and technology, and in particular to a damage assessment method for simulating shear failure of rock materials based on a peridynamic constitutive model. Background Art

[0002] Rock, as a brittle material, often contains various forms of microcracks within it. Under specific loading conditions, these microcracks may expand and eventually form macrocracks, resulting in a reduction in rock mass strength. The mechanisms of rock crack initiation, propagation, and penetration have long been the focus of research by scholars at home and abroad. However, traditional theoretical approaches often require significant simplifications when exploring crack propagation mechanisms, and the experimental cycles are long, costly, and the experimental conditions difficult to control. Therefore, with the rapid development of computer technology, numerical simulation has gradually become an important tool for studying rock failure. Currently, numerical simulation methods such as the finite element method, discrete element method, and molecular dynamics have achieved certain results in rock failure research. However, the finite element method faces the problem of tip singularities when simulating crack propagation, the discrete element method cannot effectively reflect the continuously changing properties of the material during simulation, and molecular dynamics has difficulty processing large-scale rock materials. Therefore, a new method is urgently needed to overcome the shortcomings of these traditional methods.

[0003] The peridynamic method, which uses non-local effects to describe the mechanical properties of materials, establishes equilibrium relationships through integral equations. The absence of displacement differential forms can effectively avoid problems encountered in the method, such as the difficulty in handling crack tips. Currently, bond-based peridynamics does not involve numerical differentiation concepts such as stress and strain, and the effect of non-local forces and elongation is linear. In addition, in this theory, following the critical elongation criterion cannot effectively distinguish between tensile, compressive and shear failures, and the elastic modulus is the only relevant material parameter. Under the condition of vertical principal stress, classical theory has certain difficulties in numerically simulating the damage evolution process of complete specimens without prefabricated macroscopic cracks. Summary of the Invention

[0004] To solve the above problems, the present invention proposes a damage assessment method for simulating shear failure of rock materials based on a peridynamic constitutive model. The method specifically includes:

[0005] Step S1, setting simulated material properties and rock mass crack information based on the geometric shape of the shear-damaged rock mass, and constructing an initial simulation model based on the simulated material properties and the rock mass crack information;

[0006] Step S2: Initializing the parameters of the initial simulation model to obtain a rock mass simulation model;

[0007] Step S3: generating a plurality of material points based on the rock mass simulation model and peridynamics, and constructing a peridynamic stress solution model at each material point according to the peridynamic nonlocal differential operator theory;

[0008] Step S4: obtaining the peridynamic nonlocal force density using the small deformation assumption, and updating the peridynamic nonlocal force density using the peridynamic nonlocal differential operator theory;

[0009] Step S5: Based on the updated peridynamic nonlocal force density, a nonlinear rock material constitutive force function is introduced to obtain a nonlinear constitutive force of the rock material;

[0010] Step S6: constructing a peridynamic rock discrimination criterion based on compressive strength, tensile strength and Mohr-Coulomb;

[0011] Step S7: Using the peridynamic stress solution model to monitor the peridynamic nonlocal force density, when the discrimination criterion is met, the nonlinear constitutive force of the rock material is calculated, and based on the nonlinear constitutive force of the rock material, the compression, tension, and shear damage of the bonds between the material points are evaluated, thereby completing the damage assessment of the shear failure of the rock material simulated based on the peridynamic constitutive model.

[0012] Optionally, the geometry of the rock mass includes the width and length of the rock mass; and the simulated material properties include elastic modulus, Poisson's ratio, inhomogeneous parameter, compressive strength, tensile strength, cohesion, internal friction angle, crack location, number of cracks, crack angle and crack spacing.

[0013] Optionally, in step S3, the two-dimensional expression of the peridynamic nonlocal differential operator theory is:

[0014]

[0015] Where f(x+ξ) represents the function value at the material point x+ξ, f(x) represents the function value at x, ξ1 and ξ2 represent the component values of ξ in two directions, respectively, and R(N,x) represents the residual value.

[0016] Optionally, in step S3, the content of the peridynamic stress solution model specifically includes:

[0017] Using differential operators to represent the Navier equilibrium equation, the stress components in two-dimensional cases are expressed as:

[0018]

[0019] Among them, E and v represent the elastic modulus and Poisson's ratio of the material respectively, u1 and u2 represent the displacement in the two coordinate directions respectively, represents the differential operator coefficient, Ax' Represents a two-dimensional spatial metric.

[0020] Optionally, in step S4, the content of obtaining the peridynamic nonlocal force density using the small deformation assumption includes:

[0021] Based on the small deformation assumption, the bonds of the material points are stretched, and the bond stretching model is obtained:

[0022] The classical peridynamic density is calculated based on the bond stretching model to obtain the peridynamic nonlocal force density.

[0023] Optionally, in step S4, the process of updating the peridynamic nonlocal force density using the peridynamic nonlocal differential operator theory specifically includes:

[0024] Based on a vector equivalence relation, the peridynamic nonlocal force density is vector-substituted, and the force density vector is calculated using the replaced peridynamic nonlocal force density.

[0025] Optionally, in step S5, the calculation process of the nonlinear constitutive force of rock materials specifically includes:

[0026] f(η,ξ)=(1-Re(s))·μ·M(ξ)·η

[0027] Where Re(s) represents the weakening coefficient of elongation, μ represents the shear modulus, M(ξ) represents the incomplete area of the boundary neighborhood, and η represents the relative displacement of the material point after the shape change.

[0028] Optionally, in step S6, the compressive strength, tensile strength and Mohr-Coulomb peridynamic rock discrimination criteria are specifically expressed as:

[0029]

[0030] Among them, σ1 and σ2 represent the maximum and minimum principal stresses at the same point, coh represents the micromodulus of the model, represents the peak elongation, Indicates the elongation at failure.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] (1) The present invention establishes a peridynamic stress analysis solution model by introducing nonlocal differential operators, which solves the problem that stress and 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.

[0033] (2) The expression for the nonlocal force density in peridynamics is re-derived, overcoming the computational errors caused by the incomplete neighborhood of material points at the boundary in traditional methods. Considering the relationship between the peak elongation in tension and compression and the rock strength, an elongation weakening coefficient is introduced to describe the nonlinear deformation of rock materials.

[0034] (3) During the damage assessment process, compressive strength, tensile strength and Mohr-Coulomb criterion are used to evaluate the compression, tension and shear damage of the bonds between material points, and a nonlinear peridynamic damage model is established. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0036] Figure 1 This is a principle diagram of a peridynamic material point according to an embodiment of the present invention;

[0037] Figure 2 Schematic diagram of nonlinear nonlocal forces in peridynamics according to an embodiment of the present invention;

[0038] Figure 3 Schematic diagram of the Mohr-Coulomb criterion of peridynamics according to an embodiment of the present invention;

[0039] Figure 4 This is a flow chart of rock shear fracture simulation based on peridynamics according to an embodiment of the present invention;

[0040] Figure 5 This is a calculation model diagram of Example 4 of the present invention;

[0041] Figure 6 This is a diagram of the rock crack propagation process in Example 4 of the present invention;

[0042] Figure 7 This is the stress-strain curve of the rock mass in Example 4 of the present invention. DETAILED DESCRIPTION

[0043] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0044] Example 1

[0045] A damage assessment method based on peridynamic constitutive model to simulate shear failure of rock materials, such as Figure 4 As shown, the method includes:

[0046] Step S1: setting simulated material properties and rock mass crack information based on the geometric shape of the shear-damaged rock mass, and constructing an initial simulation model based on the simulated material properties and the rock mass crack information.

[0047] The geometry of the rock mass includes the width and length of the rock mass; and the simulated material properties include elastic modulus, Poisson's ratio, inhomogeneity parameter, compressive strength, tensile strength, cohesion, internal friction angle, crack location, crack number, crack angle, and crack spacing.

[0048] Step S2: Initialize the parameters of the initial simulation model to obtain a rock mass simulation model.

[0049] Step S3: generating a plurality of material points based on the rock mass simulation model and peridynamics, and constructing a peridynamic stress solution model at each material point according to the peridynamic nonlocal differential operator theory.

[0050] The two-dimensional expression of the peridynamic nonlocal differential operator is:

[0051]

[0052] Where f(x+ξ) represents the function value at the material point x+ξ, f(x) represents the function value at x, ξ1 and ξ2 represent the component values of ξ in two directions, respectively, and R(N,x) represents the residual value.

[0053] The three-dimensional expression is:

[0054]

[0055] For the two-dimensional problem x T =(x1,x2), three-dimensional problem x T =(x1,x2,x3), ξ1, ξ2 and ξ3 are the components of the relative position vector ξ, and R(N,x) is an infinitesimal second-order residual. The function f(x) is a known quantity, and f(x+ξ)-f(x) represents the change. For two-dimensional problems, for each term, multiply it by the non-local function Where p1 and p2 are the corresponding orders, considering that R(N,x) can be ignored in the interaction neighborhood H x The inner integral can be obtained:

[0056]

[0057] where dA x′ is the two-dimensional spatial measure of the neighborhood, usually the unit area. For three-dimensional problems, for multiplication by non-local functions Among them, p1, p2 and p3 are the corresponding three-dimensional orders. Also, under the condition that R(N,x) can be ignored, in the three-dimensional interaction neighborhood Hx The inner integral can be obtained:

[0058]

[0059] where dV x′ is the three-dimensional spatial metric of the neighborhood, generally the unit volume. Furthermore, for the two-dimensional non-local function The following orthogonality is satisfied:

[0060]

[0061] Where n1, n2, p1, p2 = 0, 1, 2, δ np is the Kronecker symbol, dA x′ It is a two-dimensional space metric, generally a unit area. The differential corresponding to the function f(x) can be expressed as:

[0062]

[0063] The gradient and Laplace operator of function f(x) are expressed as:

[0064]

[0065] The vector g(ξ) and the matrix G(ξ) are:

[0066]

[0067] For three-dimensional nonlocal functions The following orthogonality is satisfied:

[0068]

[0069] Where n1, n2, n3, p1, p2, p3 = 0, 1, 2, and the differential corresponding to the function f(x) can be expressed as:

[0070]

[0071] The gradient and Laplace operator of f(x) are expressed as:

[0072]

[0073] The vector g(ξ) and the matrix G(ξ) are:

[0074]

[0075] Furthermore, for the two-dimensional problem non-local function It can be constructed as a linear combination of polynomial basis functions:

[0076]

[0077] in etc. are unknown coefficients, w 00 (|ξ|), w 10 (|ξ|) and others are weight coefficients. The same weight coefficient can be used for the same power in the calculation. The unknown coefficients can be solved by combining (5) and (15):

[0078] Aa=b (16)

[0079] Where A is a known shape matrix, a is an unknown coefficient matrix, and b is a known shape matrix. For three-dimensional problems, non-local functions Can be constructed as:

[0080]

[0081] The solution of the unknown coefficients and weight coefficients is similar to that of the two-dimensional case.

[0082] The peridynamic stress solution model uses differential operators to represent the Navier equilibrium equation. In the two-dimensional case, the stress components can be constructed as:

[0083]

[0084] Where E and v are the elastic modulus and Poisson's ratio of the material, u1 and u2 represent the displacement in the two coordinate directions respectively. and represents the differential operator coefficient, A x' represents a two-dimensional metric. The three-dimensional equation is solved in a similar way to the two-dimensional one.

[0085] Based on the small deformation assumption, the peridynamic nonlocal force density can be expressed as:

[0086]

[0087] where f(η,ξ) is the force density in 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, and c is the micromodulus of the model. In peridynamics, it is assumed that the material points are connected by bonds. The direction of f(η,ξ) is consistent with the direction of the connecting bond after deformation, and s is the elongation of the bond:

[0088]

[0089] Where δ is the neighborhood radius, h is the thickness, and μ is the shear modulus. Under the assumption of small deformation, the following relationship holds:

[0090]

[0091] n xx′ is a unit vector in the relative position direction, and the bond stretching due to small deformation can be further expressed as:

[0092]

[0093] The peridynamic nonlocal force density can be determined by combining (21) and (24):

[0094]

[0095] Step S4: Obtain the peridynamic nonlocal force density using the small deformation assumption, and update the peridynamic nonlocal force density using the peridynamic nonlocal differential operator theory.

[0096] The process of re-establishing the nonlocal force density based on the differential operator is as follows:

[0097] By vector equivalence relation The nonlocal force density in S13 can be expressed as:

[0098]

[0099] in According to the nonlocal differential operator in S11, it can be expressed as:

[0100]

[0101]

[0102] Where M(ξ) and n xx′ They are:

[0103] M(ξ)=(trG(ξ)I+2G(ξ)) (31)

[0104]

[0105] The nonlocal force density is further expressed as:

[0106]

[0107] The non-holonomic region M(ξ) of the boundary neighborhood is not equal. In order to ensure that the forces calculated at the material points x and x′ are equal to satisfy the conservation of angular momentum and linear momentum, the force density vector is expressed as:

[0108]

[0109] Step S5: Based on the updated peridynamic nonlocal force density, a nonlinear rock material constitutive force function is introduced to obtain a nonlinear constitutive force of the rock material.

[0110] In the classical bond-based peridynamics theory, the nonlocal force varies linearly with the elongation, which is difficult to describe the nonlinear deformation and failure of rock materials. Referring to the stress-strain relationship of rock, the elongation weakening coefficient Re(s) is introduced and expressed in different stages as:

[0111]

[0112] in Represent the elongation corresponding to the bond tension and compression peaks, Represents the elongation at failure, and α and β represent the adjustment coefficients of tension and compression. Taking the two-dimensional problem as an example, the nonlinear constitutive force of rock materials after considering the weakening function is:

[0113] f(η,ξ)=(1-Re(s))·μ·M(ξ)·η (35)

[0114] Step S6: constructing a peridynamic rock discrimination criterion based on compressive strength, tensile strength and Mohr-Coulomb.

[0115] Step S7: Using the peridynamic stress solution model to monitor the peridynamic nonlocal force density, when the discrimination criterion is met, the nonlinear constitutive force of the rock material is calculated, and based on the nonlinear constitutive force of the rock material, the compression, tension, and shear damage of the bonds between the material points are evaluated, thereby completing the damage assessment of the shear failure of the rock material simulated based on the peridynamic constitutive model.

[0116] Using the peridynamic stress solver model, we take a two-dimensional problem as an example and solve the maximum and minimum principal stresses at x and x′ respectively:

[0117]

[0118] Since the maximum and minimum principal stresses at x and x′ are different, the average value of the two points is taken when using the Mohr-Coulomb strength criterion:

[0119]

[0120] Combined with the rock shear mechanics indicators cohesion coh and internal friction angle φ, shear failure occurs when the average maximum and minimum principal stresses between x and x′ meet the following conditions:

[0121]

[0122] When the stress circle between material points is tangent to the line determined by cohesion and internal friction angle, the nonlocal force disappears. The peridynamic rock identification criterion based on compressive strength, tensile strength and Mohr-Coulomb can be expressed as:

[0123]

[0124] Among them, σ1 and σ2 represent the maximum and minimum principal stresses at a point, coh represents the cohesion, represents the peak elongation, Indicates the elongation at failure.

[0125] The peak tensile and compressive elongations of the connecting bond are related to the rock strength. The corresponding relationship with intensity is:

[0126]

[0127] where f t and f c Represents the tensile strength and compressive strength of rock materials respectively. Peak elongation and failure elongation The connection between them is defined as:

[0128]

[0129] where m t and m c Represents the microscopic parameters in the constitutive model of rock materials and can be fine-tuned to keep consistent with the rock fracture energy. Rock shear strength parameters such as cohesion and internal friction angle have a significant impact on the failure mode. Based on the Mohr-Coulomb strength criterion, the shear failure of the connecting bond is determined.

[0130] Example 2

[0131] 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. Each material point interacts with other material points within a certain range. The interactions between material points are represented by the nonlocal force function f. According to Newton's second law, the equation of motion followed by the material point at time t is:

[0132]

[0133] 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, and for two-dimensional problems, it represents the area element dA of each material point. x′ .

[0134] According to the theory of nonlocal differential operators, construct the function at each material point is a linear combination of polynomial basis functions:

[0135]

[0136] 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:

[0137]

[0138] Where n1, n2, p2, p2=0, 1, 2, δ np is the Kronecker symbol, dA x′ It is a two-dimensional space metric, which can be combined with the function Solve for the unknown coefficients based on the relationship with orthogonality:

[0139] Aa=b (47)

[0140] Where A is a matrix of known shape, a is a matrix of unknown coefficients, and b is a matrix of known shape.

[0141]

[0142]

[0143] Furthermore, the unknown coefficient matrix is solved by inverse matrix:

[0144] a=A -1 b (50)

[0145] After solving the unknown coefficients, the corresponding differential of the function f(x) at each material point can be obtained:

[0146]

[0147] Furthermore, by using differential operators to represent the Navier equilibrium equation, the stress components can be constructed in two dimensions as:

[0148]

[0149] Where E and v are the elastic modulus and Poisson's ratio of the material, respectively, and u1 and u2 represent the displacement of each material point in the two coordinate directions.

[0150] At this point, the construction of the peridynamic stress coefficients and solution equations is completed. All vectors g(ξ) and matrices G(ξ) are stored as:

[0151]

[0152] Furthermore, the non-local force function f represents the constitutive force function related to the material properties. For elastic-brittle materials, its expression is:

[0153]

[0154] Where y and y′ are the positions of x and x′ after deformation, ω is the micropotential energy at a point, and c is the micromodulus 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:

[0155]

[0156] s0 is the critical elongation of the connecting bond. When the elongation between material points exceeds the critical elongation, the bond between the material points breaks and the non-local interaction between the material points disappears. The micromodulus corresponding to each bond is:

[0157]

[0158] Where δ is the neighborhood radius, h is the thickness, and μ is the shear modulus. Under the assumption of small deformation, the following relationship holds:

[0159]

[0160] n xx′ is the unit vector in the relative position direction of x and x′. The bond stretching due to small deformation can be further expressed as:

[0161]

[0162] Furthermore, the peridynamic nonlocal force density between x and x′ can be determined as:

[0163]

[0164] According to the vector equivalence relation The nonlocal force density between x and x′ is expressed as:

[0165]

[0166] According to the nonlocal differential operator, it can be expressed as follows under two-dimensional conditions:

[0167]

[0168] Furthermore, the non-local force density formula between x and x′ is obtained:

[0169]

[0170] The non-holonomic region M(ξ) of the boundary neighborhood is not equal. In order to ensure that the forces calculated at the material points x and x′ are equal to satisfy the conservation of angular momentum and linear momentum, the force density vector is expressed as:

[0171]

[0172] At this point, the construction of the calculation expression for the nonlocal force density of peridynamics has been completed.

[0173] like Figure 2 As shown in the classical bond-based peridynamics theory, the nonlocal force varies linearly with the elongation, which is difficult to describe the nonlinear deformation and failure of rock materials. Referring to the stress-strain relationship of rock, the elongation weakening coefficient Re(s) is introduced and expressed as:

[0174]

[0175] in Represent the elongation corresponding to the bond tension and compression peaks, Represents the elongation at failure, and α and β represent the adjustment coefficients of tension and compression. After considering the weakening function, the nonlinear constitutive force of rock materials is:

[0176] f(η,ξ)=(1-Re(s))·μ·M(ξ)·η (68)

[0177] At this point, the construction of the nonlinear force density expression of peridynamics is completed.

[0178] Furthermore, the peak tensile and compressive elongations of the connecting bonds are related to the rock strength. The corresponding relationship with intensity is:

[0179]

[0180] where f t and f c Represents the tensile strength and compressive strength of rock materials respectively. Peak elongation and failure elongation The connections between them are:

[0181]

[0182] where m t and m c is the microscopic parameter in the constitutive model of the rock material. The maximum and minimum principal stresses at x and x′ are further solved, and the shear failure of the connecting bond is determined using the Mohr-Coulomb strength criterion:

[0183]

[0184] Since the maximum and minimum principal stresses are different, the average value of x and x′ is taken in the calculation:

[0185]

[0186] like Figure 3 As shown in Figure 2, the cohesion and internal friction angle of the rock mass are coh and φ respectively. Shear failure occurs when the average maximum and minimum principal stresses between x and x′ meet the following conditions:

[0187]

[0188]

[0189] At this point, the peridynamic rock identification criteria based on compressive strength, tensile strength and Mohr-Coulomb have been completed.

[0190] Example 3

[0191] This embodiment also provides a rock shear fracture simulation method based on peridynamics, comprising the following steps:

[0192] A1 model construction, defining the geometry of the rock mass, including its width W and length L. Setting material properties, including elastic modulus E, Poisson's ratio v, inhomogeneity parameter m, and compressive strength f c , tensile strength f t , cohesion coh, internal friction angle φ, etc. If there are prefabricated cracks, the initial position of the prefabricated cracks, the number of cracks n, the crack angle, the crack spacing l, etc. are defined.

[0193] The prefabricated crack method involves pre-cutting the connecting bonds on the prefabricated crack path, so that the interaction between the material points disappears, thereby forming cracks.

[0194] To realize the heterogeneous properties of rock, Weibull distribution, coefficient of variation or fractal theory can be used. If Weibull distribution is used, it is assumed that the rock compressive strength f c , tensile strength f t , cohesion coh or internal friction angle φ, one or more of them obeys Weibull distribution:

[0195]

[0196] The smaller the shape parameter m, the wider the distribution, which means the greater the rock heterogeneity, that is, the rock tensile strength f t The greater the difference, the larger the shape parameter m is, and the narrower the distribution is, indicating that the rock has less heterogeneity.

[0197] 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 tensile strength f is randomly generated at each material point. t , and calculate the ratio of its standard deviation σ to its mean μ:

[0198]

[0199] The smaller the coefficient of variation m, the more consistent the rock properties are and the less heterogeneous they are. The larger the coefficient of variation m, the greater the variation in rock properties, that is, the stronger the heterogeneity.

[0200] If fractal theory is used, it is believed that the structure of rock cracks, pore distribution and so on has self-similarity and can be quantified by fractal dimension and characterized by box counting method:

[0201] N(λ)~λ -D (78)

[0202] Where N(λ) is the number of identifiable fractures in the rock sample at scale λ, and D is the fractal dimension, typically 1 ≤ D ≤ 3. A higher fractal dimension indicates a more complex fracture structure and greater heterogeneity in the rock, while a lower fractal dimension indicates less heterogeneity.

[0203] A2 parameter initialization, set the calculation parameters, including the total number of discrete material points M, neighborhood radius δ, boundary conditions, etc. Solve the non-local differential operator coefficients at each material point Set the microscopic parameters in the rock material constitutive model. Discretize the solution domain based on the calculated parameters, generate material point coordinates, and determine the material points contained in each material point domain. Initialize the bonds, nonlocal forces, displacement fields, and other information for all material points in their near-field domain, and set boundary conditions.

[0204] The boundary conditions are displacement boundary conditions or force density boundary conditions, which impose time-varying displacement or constant body force density at the boundary material points.

[0205] The material points contained in the domain of each material point are searched according to the material point coordinates and the neighborhood radius δ. If the material point is within the radius, it is considered a material point in the domain.

[0206] A3 runs the simulation, determines the time step Δt, the number of time steps t, and starts the loop calculation based on the input parameters. Based on the current information, the non-local force f and acceleration of each material point are calculated. If the displacement u and other parameters meet one of the conditions in the peridynamic rock judgment criteria based on compressive strength, tensile strength and Mohr-Coulomb, the bond nonlocal force between material points disappears, and the damage degree D(x) of each material point is calculated. The judgment condition is:

[0207]

[0208] The discrete equation for the interaction between the material point x and its neighborhood at the nth time step is:

[0209]

[0210] Calculate the acceleration at the material point x at time t based on the explicit central difference method speed With displacement u:

[0211]

[0212] In the peridynamics method, the damage level at a material point is defined by the breaking of the bond at that point:

[0213]

[0214] The damage parameter D(x) ranges from 0 to 1, where 0 indicates no damage at point x and 1 indicates complete damage.

[0215] The main contents of A4 result analysis are: outputting calculation results, visualizing the rock crack propagation process, and analyzing the results.

[0216] Example 4

[0217] The specific implementation steps of the calculation effect include:

[0218] A1 model construction, such as Figure 5 As shown, the geometric shape of the rock mass is defined as width W = 50 mm and length L = 100 mm. The elastic modulus of the rock mass is E f =4.22GPa, Poisson's ratio v=0.3, density ρ=2060kg / m 3 , the tensile strength is f t =2.01MPa, tensile strength is f t =2.01MPa, compressive strength is f c =32.4MPa, cohesion is coh=2.01MPa, internal friction angle is φ=72°, Weibull distribution is used to describe heterogeneity, shape parameter m=10, and there is no prefabricated crack.

[0219] A2 parameter initialization, through trial calculation, the model particles are set to 200×100, the spacing between material points is Δx=0.5mm, the neighborhood radius δ=3.015Δx, and vertical compression boundary conditions that increase linearly with the time calculation step are applied at the upper and lower ends of the rock layer to solve the non-local differential operator coefficient at each material point Configure the nonlocal differential operator and the microscopic parameters in the rock material constitutive model. Discrete the solution domain according to the calculation parameters, generate the coordinates of the material points, and determine the material points contained in each material point domain.

[0220] A3 runs the simulation and determines the time step Δt = 2.4×10 -7 s, time step t = 4000, 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 If the elongation is greater than the set critical failure elongation s0, the bond non-local force between the material points disappears. The damage degree D(x) of each material point is calculated. Figure 6 This is a diagram showing the crack propagation effect of rock mass under boundary conditions.

[0221] A4 Result Analysis: Process and analyze the simulation results. Figure 7 To simulate the stress-strain curve corresponding to the rock mass, the results show that the entire process can be divided into four stages: compaction, elasticity, pre-peak yield, and post-peak. During the initial loading phase, the rock's compaction curve shows a slight upward depression, followed by the elastic phase, where the stress-strain relationship is linear. Yield occurs during the pre-peak and post-peak phases, and the post-peak failure phase exhibits typical strain-softening characteristics, with the stress-strain curve rapidly decreasing with increasing strain, ultimately reaching residual strength.

[0222] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by persons skilled in the art should fall within the scope of protection defined by the claims of the present invention.

Claims

1. A damage assessment method for simulating shear failure of rock materials based on a peridynamic constitutive model, characterized in that: The method comprises: Step S1, setting simulated material properties and rock mass crack information based on the geometric shape of the shear-damaged rock mass, and constructing an initial simulation model based on the simulated material properties and the rock mass crack information; Step S2: Initializing the parameters of the initial simulation model to obtain a rock mass simulation model; Step S3: generating a plurality of material points based on the rock mass simulation model and peridynamics, and constructing a peridynamic stress solution model at each material point according to the peridynamic nonlocal differential operator theory; Step S4: obtaining the peridynamic nonlocal force density using the small deformation assumption, and updating the peridynamic nonlocal force density using the peridynamic nonlocal differential operator theory; Step S5: Based on the updated peridynamic nonlocal force density, a nonlinear rock material constitutive force function is introduced to obtain a nonlinear constitutive force of the rock material; Step S6: constructing a peridynamic rock discrimination criterion based on compressive strength, tensile strength and Mohr-Coulomb; Step S7: Using the peridynamic stress solution model to monitor the peridynamic nonlocal force density, when the discrimination criterion is met, the nonlinear constitutive force of the rock material is calculated, and based on the nonlinear constitutive force of the rock material, the compression, tension, and shear damage of the bonds between the material points are evaluated, thereby completing the damage assessment of the shear failure of the rock material simulated based on the peridynamic constitutive model.

2. The damage assessment method for simulating shear failure of rock materials based on a peridynamic constitutive model according to claim 1, characterized in that: The geometry of the rock mass includes the width and length of the rock mass; the simulated material properties include elastic modulus, Poisson's ratio, inhomogeneity parameter, compressive strength, tensile strength, cohesion, internal friction angle, crack location, crack number, crack angle and crack spacing.

3. The damage assessment method for simulating shear failure of rock materials based on a peridynamic constitutive model according to claim 1, characterized in that: In step S3, the two-dimensional expression of the peridynamic non-local differential operator theory is: Where f(x+ξ) represents the function value at the material point x+ξ, f(x) represents the function value at x, ξ1 and ξ2 represent the component values of ξ in two directions, respectively, and R(N,x) represents the residual value.

4. The damage assessment method for simulating shear failure of rock materials based on a peridynamic constitutive model according to claim 3, characterized in that: In step S3, the content of the peridynamic stress solution model specifically includes: Using differential operators to represent the Navier equilibrium equation, the stress components in two-dimensional cases are expressed as: Among them, E and v represent the elastic modulus and Poisson's ratio of the material respectively, u1 and u2 represent the displacement in the two coordinate directions respectively, represents the differential operator coefficient, A x' Represents a two-dimensional spatial metric.

5. The damage assessment method for simulating shear failure of rock materials based on a peridynamic constitutive model according to claim 1, characterized in that: In step S4, the content of obtaining the peridynamic nonlocal force density using the small deformation assumption includes: Based on the small deformation assumption, the bonds of the material points are stretched, and the bond stretching model is obtained: The classical peridynamic density is calculated based on the bond stretching model to obtain the peridynamic nonlocal force density.

6. The damage assessment method for simulating shear failure of rock materials based on a peridynamic constitutive model according to claim 5, characterized in that: In step S4, the process of updating the peridynamic nonlocal force density using the peridynamic nonlocal differential operator theory specifically includes: Based on a vector equivalence relation, the peridynamic nonlocal force density is vector-substituted, and the force density vector is calculated using the replaced peridynamic nonlocal force density.

7. The damage assessment method for simulating shear failure of rock materials based on a peridynamic constitutive model according to claim 1, characterized in that: In step S5, the calculation process of the nonlinear constitutive force of rock materials specifically includes: f(η,ξ)=(1-Re(s))·μ·M(ξ)·η Where Re(s) represents the weakening coefficient of elongation, μ represents the shear modulus, M(ξ) represents the incomplete area of the boundary neighborhood, and η represents the relative displacement of the material point after the shape change.

8. The damage assessment method for simulating shear failure of rock materials based on a peridynamic constitutive model according to claim 1, characterized in that: In step S6, the compressive strength, tensile strength and Mohr-Coulomb peridynamic rock discrimination criteria are specifically expressed as follows: Among them, σ1 and σ2 represent the maximum and minimum principal stresses at the same point, coh represents the micromodulus of the model, represents the peak elongation, Indicates the elongation at failure.

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