Method for constructing fracture propagation behavior model in layered rock mass, simulation method and system

Abstract

The present application belongs to the technical field of geotechnical engineering, and provides a layered rock mass crack propagation behavior model construction method, simulation method and system. The layered rock mass crack propagation behavior model construction method comprises the following steps: constructing a layered rock mass near-field dynamics stress solving model based on a near-field dynamics non-local differential operator; deducing a near-field dynamics non-local force density according to a small deformation assumption, combining the near-field dynamics non-local differential operator to re-establish an expression of the near-field dynamics non-local force density, and then introducing a softening criterion based on a strain energy density theory to construct a layered rock mass strain energy density softening model; constructing a layered rock mass interface junction material mechanics parameter calculation model based on the material mechanics properties of the interface between different rock layers; and combining the layered rock mass near-field dynamics stress solving model, the layered rock mass strain energy density softening model and the layered rock mass interface junction material mechanics parameter calculation model to obtain a layered rock mass crack propagation behavior model.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of geotechnical engineering, and particularly relates to a layered rock mass crack propagation behavior model construction method, simulation method and system. BACKGROUND

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

[0003] Under the action of nature and external load, cracks often appear in layered rock mass, especially in soft rock mass, the formation and propagation of cracks show a specific spatial distribution rule, which is called interval cracking phenomenon. Research shows that interval cracking phenomenon not only affects the mechanical properties of rock mass, but also may pose a threat to the safety and use efficiency of geotechnical engineering structures. Therefore, it is of great academic and engineering significance to deeply explore the formation mechanism and interval distribution characteristics of cracks in layered rock mass. The 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 crack tip singularity and other problems. Therefore, there is an urgent need for a new model to more accurately simulate the crack propagation behavior in layered rock mass.

[0004] As a new numerical simulation technology, the near-field dynamics method uses displacement integral equation to establish the interaction relationship, has the advantages of avoiding crack tip singularity, not relying on external failure criterion, etc., and gradually attracts the attention of researchers. However, in the classical bond-based near-field dynamics theory, due to the incomplete neighborhood of the material points at the boundary, direct calculation using micro-modulus will produce large deviation. When calculating, the change of mechanical properties caused by damage at the crack is not considered and the distribution of stress field and strain field cannot be directly obtained. SUMMARY

[0005] In order to solve the above technical problems, the present application provides a layered rock mass crack propagation behavior model construction method, simulation method and system, which can establish a more accurate near-field dynamics constitutive model for simulating the interval crack propagation of two-dimensional layered rock mass, effectively reduce the calculation error at the boundary, and introduce the strain energy density theory to establish the correlation between the mechanical parameters of the medium at the crack and the residual strain energy.

[0006] In order to achieve the above purpose, the present application adopts the following technical solutions:

[0007] The first aspect of the present application provides a layered rock mass crack propagation behavior model construction method.

[0008] In one or more embodiments, a layered rock mass crack propagation behavior model construction method is provided, comprising:

[0009] Based on the non-local differential operator of near-field dynamics, a near-field dynamics stress solution model of layered rock mass is constructed;

[0010] According to the small deformation assumption, the non-local force density of near-field dynamics is derived, and the expression of the non-local force density of near-field dynamics is re-established in combination with the non-local differential operator of near-field dynamics, and a strain energy density softening model of layered rock mass is constructed by introducing a softening criterion based on the strain energy density theory;

[0011] Based on the material mechanics properties of the interface between different rock layers, a material mechanics parameter calculation model of the interface of layered rock mass is constructed;

[0012] The near-field dynamics stress solution model of layered rock mass, the strain energy density softening model of layered rock mass and the material mechanics parameter calculation model of the interface of layered rock mass are combined to obtain a crack propagation behavior model in layered rock mass.

[0013] As an embodiment of the first aspect of the application, the two-dimensional expression form of the non-local differential operator of near-field dynamics is:

[0014]

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

[0016] As an embodiment of the first aspect of the application, the expression of the non-local force density of near-field dynamics derived according to the small deformation assumption is:

[0017]

[0018] Wherein f(η,ξ) is the force density of classical near-field dynamics, y and y' are the positions after deformation of x and x', η is the relative displacement corresponding to the material point after 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.

[0019] As an embodiment of the first aspect of the application, the expression of the non-local force density of near-field dynamics is re-established as:

[0020]

[0021] Wherein 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 non-complete region of the boundary neighborhood; tr is the trace of the matrix, and I is the unit matrix.

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

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

[0024] Wherein, dW PD , dW rock(E) , E ini are the near-field kinetic strain energy density, the elastic change critical strain energy density, and the initial elastic modulus of each material point x respectively; E n is the effective elastic modulus corresponding to each material point x under different residual strain energies W r , and N is the total number of segments according to different elastic moduli corresponding to the strain energy change.

[0025] When dW rock(E) <dW PD <dW rock(S) , wherein dW rock(S) is the strain softening critical strain energy density, the stage is in the hard-softening stage, and the effective elastic modulus decreases with the gradual damage, and is calculated according to the formula ; wherein the decrease of the effective elastic modulus leads to the decrease of the micro-elastic modulus, and further causes the change of the non-local force; n is the current stage.

[0026] When dW rock(E) <dW PD , this is the softening residual stage, the fracture development is over, and the residual modulus is reduced: E n =0.05E ini .

[0027] As an embodiment of the first aspect of the application, the layered rock mass interface transition material mechanics parameter calculation model uses the average properties between different rock mass points to represent;

[0028] When there is an interface between different rock layers, the average properties between different rock mass points are taken to calculate the non-local force, and the average elastic modulus is weighted and expressed as:

[0029]

[0030] Wherein, E x and E x′ are the elastic moduli of different rock layers, d x and d x′Respectively, the length of the material point connecting line direction distance from the rock stratum interface.

[0031] The second aspect of the present application provides a layered rock mass crack propagation behavior model construction system.

[0032] In one or more embodiments, a layered rock mass crack propagation behavior model construction system comprises:

[0033] A stress solving model construction module is used to construct a layered rock mass near-field dynamics stress solving model based on a near-field dynamics non-local differential operator;

[0034] A strain energy density softening model construction module is used to derive a near-field dynamics non-local force density according to a small deformation assumption, combine the near-field dynamics non-local differential operator, re-establish the expression of the near-field dynamics non-local force density, and introduce a softening criterion based on the strain energy density theory to construct a layered rock mass strain energy density softening model;

[0035] An interface material mechanics parameter calculation construction module is used to construct a layered rock mass interface junction material mechanics parameter calculation model based on the material mechanics characteristics of the interface between different rock layers;

[0036] A crack propagation behavior model construction module is used to combine the layered rock mass near-field dynamics stress solving model, the layered rock mass strain energy density softening model and the layered rock mass interface junction material mechanics parameter calculation model to obtain a layered rock mass crack propagation behavior model.

[0037] The third aspect of the present application provides a layered rock mass crack propagation behavior simulation method.

[0038] In one or more embodiments, a layered rock mass crack propagation behavior simulation method comprises:

[0039] A layered rock mass crack propagation behavior model is constructed by using the layered rock mass crack propagation behavior model construction method described above;

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

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

[0042] As an embodiment of the third aspect of the present application, the layered rock mass near-field dynamics stress parameters comprise total non-local force, acceleration, displacement and stress of each material point.

[0043] The layered rock mass interface transition material mechanics parameter includes 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.

[0044] The layered rock mass interface transition material mechanics parameter includes 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] The fourth aspect of the present application provides a layered rock mass crack propagation behavior simulation system.

[0046] In one or more embodiments, a layered rock mass crack propagation behavior simulation system includes:

[0047] A model construction module is used to construct a layered rock mass crack propagation behavior model using the layered rock mass crack propagation behavior model construction method described above;

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

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

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

[0051] (1) The present application introduces a non-local differential operator to establish a near-field dynamic stress analysis solution model, solving the problem that the traditional model cannot perform stress and strain analysis, and providing an intuitive analysis means for the bond-based near-field dynamic method to simulate deformation and failure problems.

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

[0053] (3) The present application combines the strain energy density theory to establish the correlation between the mechanical parameters of the crack medium and the residual strain energy, so that the influence of crack propagation on the mechanical properties of the material can be more accurately considered during the simulation process, thereby improving the simulation reliability; and the interface parameter calculation between the layered rock mass is realized, and the average attribute between different rock mass material points is taken to calculate the non-local force. BRIEF DESCRIPTION OF DRAWINGS

[0054] The accompanying drawings, which form a part of this specification, are included to provide a further understanding of the application, and are incorporated in and constitute a part of this specification. The embodiments of the application, together with its

[0055] Figure 1 A schematic diagram of a near-field dynamic particle for an embodiment of the application;

[0056] Figure 2 A meaning represented by each part of the strain energy area;

[0057] Figure 3 A change of the elastic modulus with the strain energy in near-field dynamics, from E1 to E N ;

[0058] Figure 4 A flow chart of a near-field dynamic layered rock mass simulation method for an embodiment of the application;

[0059] Figure 5 A calculation model diagram for the third embodiment of the application;

[0060] Figure 6 A layered rock mass crack propagation process diagram for the third embodiment of the application;

[0061] Figure 7 A diagram of the average fracture spacing change with strain for the third embodiment of the application. DETAILED DESCRIPTION

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

[0063] It should be noted that the following detailed description is exemplary in nature and is intended to provide further description of the application. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

[0064] It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments in accordance with the application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and / or "comprising," when used in this specification, specify the presence of stated features, steps, operations, elements, components, and / or groups thereof, but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, and / or groups thereof.

[0065] Embodiment One

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

[0067] S101: Construct a layered rock mass near-field dynamics stress solution model based on a near-field dynamics non-local differential operator.

[0068] The two-dimensional expression form of the near-field dynamics non-local differential operator is:

[0069]

[0070] where x T =(x1,x2), ξ1 and ξ2 are 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 a change quantity.

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

[0072]

[0073] where x' is a material point within the neighborhood H x ={x'∈R,|x'-x|<δ} of x, u(x,t) and u(x',t) are the displacements corresponding to x and x' at time t, ρ and are the densities and accelerations, b(x,t) is the body force, the initial relative position of x and x' is x'-x=ξ, η is the corresponding relative displacement after shape change, so the position change is ξ+η, dV x′ is the spatial measure, and for a two-dimensional problem, dA x′ represents the area element of each material point.

[0074] According to the non-local differential operator theory, the function is constructed at each material point as a linear combination of polynomial basis functions:

[0075]

[0076] where are undetermined coefficients, and the weight coefficient is taken as w(|ξ|)=exp(-(a|ξ| / δ) 2 ), δ is the neighborhood radius, and a is a specified constant. In addition, the function satisfies the following orthogonality:

[0077]

[0078] where n1,n2,p2,p2=0,1,2, δnp for the Kronicker symbol, dA x′ for the two-dimensional space measure, can be combined with the function Solve the undetermined coefficients by the relationship of orthogonality:

[0079] Aa = b

[0080] where A is the known shape matrix, a is the unknown coefficient matrix, and b is the known shape matrix.

[0081]

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

[0083] a = A -1 b

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

[0085]

[0086] S102: According to the small deformation assumption, the non-local force density of near-field dynamics is derived, combined with the non-local differential operator of near-field dynamics, the expression of the non-local force density of near-field dynamics is re-established, and the softening criterion based on strain energy density theory is introduced to construct a strain energy density softening model of layered rock mass.

[0087] The Navier equilibrium equation is expressed by the differential operator, and in the two-dimensional case, the stress components can be constructed as:

[0088]

[0089] In the formula, 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 two coordinate directions.

[0090] At this point, the construction of the near-field dynamics stress solving coefficient and solving equation is completed. 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 properties of the material itself. For a brittle material, its expression is:

[0093]

[0094] where y and y' are the deformed positions of x and x', ω is the micro-potential energy at a point, c is the micro-modulus of the model. In near-field dynamics, it is assumed that the material points are connected by bonds, the direction of the non-local force f(η,ξ) is consistent with the direction of the deformed bond, and s is the elongation rate of the bond:

[0095]

[0096] s0 is the critical elongation of the bond, when the elongation between material points exceeds the critical elongation, the bond between material points breaks, and the non-local interaction between material points disappears. The micro modulus corresponding to each bond is:

[0097]

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

[0099]

[0100] n xx′ The bond stretching caused by small deformation can be further expressed as:

[0101]

[0102] The near-field dynamic non-local force density between x and x' can be determined as:

[0103]

[0104] According to the vector equivalence relationship The non-local force density expression between x and x' is:

[0105]

[0106] According to the non-local differential operator, it can be expressed as:

[0107]

[0108] M(ξ) = (trG(ξ)I + 2G(ξ)),

[0109] Further, the non-local force density expression between x and x' is obtained:

[0110]

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

[0112] wherein the boundary neighborhood non-complete region M(ξ) is not equal, in order to ensure that the forces calculated by material points x and x' are equal to meet the angular momentum and linear momentum conservation, the force density vector is expressed as:

[0113]

[0114] So far, the construction of the non-local force density expression of near-field dynamics is completed.

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

[0116] The effective elastic modulus of rock at the crack tip in different dissipation stages is set to be linearly related to the residual strain energy density: Where E n is the effective elastic modulus corresponding to each material point x in different residual strain energy W r , N is the defined number of segments; n is the current stage. E n Changes with W r in turn through the damage initiation, effective modulus reduction, micro modulus weakening and damage evolution stages:

[0117] As shown in Figure 2 and Figure 3 , the rock-like material is accompanied by irreversible energy loss during iterative calculation, which in turn leads to strain softening and reduction of mechanical parameters at the damage site. If the unloading path is folded back along the elastic stage AO, if the continuous loading is to the post-peak D point, the area S OABDG is the absorbed strain energy W a . At this time, the unloading is folded back 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 is the total strain energy W PD of the element.

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

[0119] When dW PD dW rock(E) , this stage is in the initial elastic change stage, the rock has no damage, and the effective elastic modulus is consistent with the initial modulus value: E n = E ini ;

[0120] Where, dW PD , dW rock(E) , E iniThe near-field dynamic strain energy density, the critical strain energy density of elastic change, and the initial elastic modulus of each material point x, respectively; E n The effective elastic modulus corresponding to each material point x at different residual strain energies W r , N is the total number of segments corresponding to different elastic moduli according to strain energy changes; for example, a total of 10 segments, then different strain energies correspond to 10 elastic moduli.

[0121] When dW rock(E) < dW PD , dW rock(S) , where dW rock(S) is the critical strain energy density of strain softening, which is in the hard-softening stage, and the effective elastic modulus decreases with the gradual damage, which is calculated according to the formula ; wherein the decrease of the effective elastic modulus will lead to the decrease of the micro-elastic modulus, and further cause the change of the non-local force; E1, E2, E3 KE n are the effective elastic moduli at different stages, where N is the defined number of segments, and n is the current stage.

[0122] When dW rock(E) < dW PD , this is the softening residual stage, and the fracture development is over, and the residual modulus is reduced: E n = 0.05E ini .

[0123] So far, the correlation between the mechanical parameters of the medium at the crack and the residual strain energy has been completed, and the near-field dynamic strain energy density softening iterative calculation method is realized.

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

[0125] Wherein, the layered rock mass interface junction material mechanics parameter calculation model uses the average properties between different rock layer material points to represent;

[0126] When there is an interface between different rock layers, the average properties between different rock layer material points are taken to calculate the non-local force, and the average elastic modulus is weighted and expressed as:

[0127]

[0128] Where E x and E x′ are the elastic moduli of different rock layers, d x and d x′ are the lengths of the material point connecting line direction distance from the rock layer interface.

[0129] So far, the interface parameter calculation of different rock layers is completed.

[0130] S104: Joint the layered rock mass near-field dynamics stress solution model, the layered rock mass strain energy density softening model and the layered rock mass interface transition material mechanics parameter calculation model to obtain the crack propagation behavior model in the layered rock mass.

[0131] Embodiment two

[0132] The embodiment provides a layered rock mass crack propagation behavior model construction system, which comprises:

[0133] The stress solution model construction module is used for constructing a layered rock mass near-field dynamics stress solution model based on a near-field dynamics non-local differential operator;

[0134] The strain energy density softening model construction module is used for deriving a near-field dynamics non-local force density according to a small deformation assumption, combining the near-field dynamics non-local differential operator, re-establishing the expression of the near-field dynamics non-local force density, and introducing a softening criterion based on the strain energy density theory to construct a layered rock mass strain energy density softening model;

[0135] The interface transition material mechanics parameter calculation construction module is used for constructing a layered rock mass interface transition material mechanics parameter calculation model based on the material mechanics characteristics of the interface between different rock layers;

[0136] The crack propagation behavior model construction module is used for jointing the layered rock mass near-field dynamics stress solution model, the layered rock mass strain energy density softening model and the layered rock mass interface transition material mechanics parameter calculation model to obtain the crack propagation behavior model in the layered rock mass.

[0137] It should be noted that each module in the embodiment corresponds to each step in the embodiment one, and the specific implementation process is the same, which will not be described here in detail.

[0138] Embodiment three

[0139] As shown in Figure 4 The embodiment provides a layered rock mass crack propagation behavior simulation method, which at least comprises the following steps:

[0140] A1: The layered rock mass crack propagation behavior model is constructed by using the layered rock mass crack propagation behavior model construction method in the above-mentioned embodiment one.

[0141] Specifically, the geometry of the layered rock mass is defined, including the thickness W and length L of different rock layers for a two-dimensional problem. The material properties of each rock layer are set, 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 pre-existing cracks, the initial position of the pre-existing cracks, the number of cracks n, and the crack spacing l parameters are defined.

[0142] where the pre-existing crack method is to pre-cut the connecting keys on the pre-existing crack path, and the interaction of the material points disappears, thereby forming a crack.

[0143] The non-uniform properties of the rock can be selected using Weibull distribution or coefficient of variation. If Weibull distribution is selected, 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 non-uniformity of the rock is greater, i.e., the difference in the critical failure elongation of the rock is greater. The larger the shape parameter m, the narrower the distribution, indicating that the non-uniformity of the rock is smaller.

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

[0147]

[0148] The smaller the coefficient of variation m, the more consistent the properties of the rock, and the smaller the non-uniformity. The larger the coefficient of variation m, the greater the variation in the properties of the rock, i.e., the stronger the non-uniformity.

[0149] A2: Based on the crack propagation behavior model and initialization parameters in the layered rock mass, 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 of the interface of the layered rock mass.

[0150] Specifically, the initialization parameters include:

[0151] Set the calculation parameters, including the total number of discrete material points M, the neighborhood radius δ, the boundary conditions, etc. Solve the non-local differential operator coefficient , set the strain energy density parameters. Discretize the solution domain according to the calculation parameters, generate the material point coordinates, and determine the material points contained in the field of each material point. Initialize the keys, non-local forces, displacement fields, etc. of all material points in their near-field fields, and calculate the interface parameters between different rock layers.

[0152] The boundary condition is displacement boundary condition or force density boundary condition, and a time-varying displacement or constant body force density is applied at the boundary material points.

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

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

[0155] The layered rock mass near-field dynamic stress parameters 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, elastic change critical strain energy density and initial elastic modulus of each material point, and the softening parameters are updated according to the residual strain energy of each point.

[0157] The layered rock mass interface transition material mechanics parameters include the 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] The time step Δt and the time step t are determined, and the loop calculation is started according to the input parameters. The non-local force f, acceleration Displacement of each material point are calculated according to the current information, and 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, and the softening parameters are updated according to the residual strain energy of each point.

[0159] The displacement calculation can use Verlet-Velocity explicit difference:

[0160]

[0161] u n+1 = un +Δtu n+1 / 2

[0162]

[0163] In the near-field dynamics method, no additional criterion is introduced to determine the damage, but the damage at the point is defined by studying the damage of all the bonds connected to the point:

[0164]

[0165] The damage parameter D(x) has a value range of 0 to 1, 0 indicating that the point x has not been damaged, and 1 indicating complete damage.

[0166] The specific simulation effect is shown below:

[0167] As shown in Figure 5 , the geometric shape of the layered rock mass is defined, three layers of rock mass are set, the middle layer W f = 30 mm, the upper and lower base layers W n = 30 mm, the total width of the model is W = 90 mm, and the total length of the rock layer is L = 400 mm. The elastic modulus of the middle layer is E f = 50 GPa, the elastic modulus of the upper and lower base layers is E n = 10 GPa, and the Poisson's ratio is v = 0.3. The critical damage elongation rate obeys the Weibull distribution, which reflects the non-uniform properties 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, the critical elongation rate of the middle layer is s0 = 3.285 x 10 -3 , and the critical elongation rate of the upper and lower base layers is s1 = 4.927 x 10 -3 . In this example, there is no pre-existing crack.

[0168] Through trial calculation, the particles of the model are set to 400 x 90, the spacing between the particles is Δx = 1 mm, the neighborhood radius δ = 3.015Δx, the horizontal tensile displacement boundary condition is applied at both ends of the rock layer, which increases linearly with time, and each step increases by 1 x 10 -6 m. The coefficients of the non-local differential operator at each particle are calculated , and the strain energy density parameters are set. According to the calculation parameters, the solution domain is discretized, the particle coordinates are generated, and the particles included in the field of each particle are determined.

[0169] The time step Δt = 1.4 x 10 -7 s is determined, the time step t = 1000 is determined, and the loop calculation is started according to the input parameters. According to the current information, the non-local force f, acceleration displacement and other parameters of each particle are calculated, and if the elongation rate is greater than the set critical damage elongation rate s0, the bond between the particles disappears. The damage degree D(x) of each particle is calculated, and the softening parameters are updated according to the residual strain energy of each point. Figure 6 The crack propagation effect diagram of the layered rock mass under the action of the boundary condition is shown in the following figure.

[0170] The simulation results are processed and analyzed. Under the displacement conditions of the two sides of the rock stratum, multiple cracks with the same interval gradually occur at the weak layer, which is divided into three stages according to the failure mode: a micro crack extension stage, which is before the first macro crack occurs, and the micro cracks in the weak layer are connected and penetrated with each other as the boundary conditions are applied; an interval crack generation stage, which is after the micro cracks are saturated, and the macro cracks in the weak layer appear as the continuous loading causes the stress state between the cracks to change, and new cracks gradually appear between the old cracks; and an equal interval crack saturation stage, at which the number of cracks in the weak layer reaches the maximum, the stress state between the cracks is basically compressive, no new macro crack appears, and continuous loading causes the interface between the layers to peel off or the base layer to break. Figure 7 FIG. 4 is a diagram of the change process of the average crack interval.

[0171] Embodiment Four

[0172] The embodiment provides a simulation system for crack propagation behavior in a layered rock mass, which comprises:

[0173] a model construction module configured to construct a crack propagation behavior model in a layered rock mass by using the layered rock mass crack propagation behavior model construction method described above;

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

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

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

[0177] In particular, according to the embodiments of the present application, the processes described above with reference to the flowcharts can be implemented as a computer software program. For example, the embodiments of the present application include a computer program product comprising a computer program carried on a computer readable medium, the computer program containing program code for executing the method of Embodiment One or Embodiment Three. In such embodiments, the computer program can be downloaded and installed from a network by a communication part, and / or installed from a detachable 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 of the method of the embodiment one or the embodiment three can also be stored in the computer readable storage medium which can direct the computer or other programmable data processing device to work in a specific way, so that the instructions stored in the computer readable storage medium produce the manufacture which includes the instruction device, and the instruction device realizes the functions specified in the flowcharts Figure 1 one flowchart or multiple flowcharts and / or blocks Figure 1 one block or multiple blocks.

[0179] A person of ordinary skill in the art can understand that all or part of the flowcharts in the above-mentioned embodiment methods can be completed by a computer program instructing related hardware, and the program can be stored in a computer readable storage medium. When the program is executed, it can include the flowcharts of the above-mentioned embodiment methods. The storage medium can be a magnetic disc, an optical disc, a read-only memory (ROM) or a random access memory (RAM), etc.

[0180] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for constructing a model of fracture propagation behavior in layered rock masses, characterized in that, include: Based on the nonlocal differential operator of peri-field dynamics, a peri-field dynamic stress solution model for layered rock masses is constructed. Based on the assumption of small deformation, the nonlocal force density of the peri-field dynamics is derived. Combined with the nonlocal differential operator of the peri-field dynamics, the expression of the nonlocal force density of the peri-field dynamics is re-established. Then, a softening criterion based on the strain energy density theory is introduced to construct a strain energy density softening model for layered rock masses. Based on the assumption of small deformation, the expression for the nonlocal force density of the near-field dynamics is derived as follows: in For the force density of classical peridynamics, , They are respectively , The position after deformation This represents the relative displacement of the material points after the shape change. Let the potential energy at a point be... The micromodulus of the model; Elongation of the bond; It is a relative position vector; The re-established expression for the nonlocal force density of the near-field dynamics is as follows: in The neighborhood radius, For thickness, Shear modulus; It is a nonlocal function matrix; For the boundary neighborhood, it is an incomplete region; The trace of the matrix, It is the identity matrix; Based on the material mechanical properties of the interfaces between different rock strata, a calculation model for the material mechanical parameters at the interface of layered rock masses is constructed. 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, a model of fracture propagation behavior in layered rock mass is obtained.

2. The method for constructing a fracture propagation behavior model in layered rock masses as described in claim 1, characterized in that, The two-dimensional expression of the nonlocal differential operator of near-field dynamics is as follows: in , and Relative position vector The amount, It is an infinitesimal second-order residual; function Given quantities - The variable is the amount of change.

3. The method for constructing a fracture propagation behavior model in layered rock masses as described in claim 1, characterized in that, The strain energy density softening model for layered rock masses is as follows: when At this stage, the rock is in the initial elastic change phase, no damage has occurred, and the effective elastic modulus is consistent with the initial modulus value. ; in, , , For each material point The near-field dynamic strain energy density, the critical strain energy density of elastic change, and the initial elastic modulus; For each material point Different residual strain energies The effective elastic modulus corresponding to the condition, This represents the total number of segments corresponding to different elastic moduli based on changes in strain energy. when At that time, among them This is the critical strain energy density for strain softening. This stage is the hardening-softening phase, where the effective elastic modulus decreases with the gradual occurrence of damage, according to the formula... Calculations show that a decrease in the effective elastic modulus leads to a decrease in the microelastic modulus, which in turn causes a change in the nonlocal forces. This refers to the current stage; when At this point, the residual material softens, fracture development ends, and the modulus decreases to the residual modulus. .

4. The method for constructing a fracture propagation behavior model in layered rock masses as described in claim 1, characterized in that, The calculation model for material mechanical parameters at the interface of layered rock masses uses the average properties between material points of different rock layers to characterize them; When there is an interface between different rock layers, the average properties of the material points in the different rock layers are used to calculate the nonlocal forces, and the average elastic modulus is used. The weighted representation is as follows: in and For different rock strata elastic moduli, and These represent the distances from the rock strata interface along the direction of the line connecting the material points.

5. A system for constructing a model of fracture propagation behavior in layered rock masses, characterized in that, include: The stress solution model construction module is used to construct a peri-field dynamic stress solution model for layered rock masses based on peri-field dynamic nonlocal differential operators. The strain energy density softening model construction module is used to derive the peri-field dynamic nonlocal force density based on the small deformation assumption, combine the peri-field dynamic nonlocal differential operator, re-establish the expression of the peri-field dynamic nonlocal force density, and then introduce the softening criterion based on strain energy density theory to construct the strain energy density softening model of layered rock mass. Based on the assumption of small deformation, the expression for the nonlocal force density of the near-field dynamics is derived as follows: in For the force density of classical peridynamics, , They are respectively , The position after deformation This represents the relative displacement of the material points after the shape change. Let the potential energy at a point be... The micromodulus of the model; Elongation of the bond; It is a relative position vector; The re-established expression for the nonlocal force density of the near-field dynamics is as follows: in The neighborhood radius, For thickness, Shear modulus; It is a nonlocal function matrix; For the boundary neighborhood, it is an incomplete region; The trace of the matrix, It is the identity matrix; The module for calculating and constructing material mechanical parameters at the interface is used to construct a model for calculating material mechanical parameters at the interface of layered rock masses based on the material mechanical properties of the interface between different rock layers. The fracture propagation behavior model construction module is used to combine 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 to obtain the fracture propagation behavior model in layered rock mass.

6. A method for simulating fracture propagation behavior in layered rock masses, characterized in that, include: The fracture propagation behavior model in layered rock masses is constructed using the method described in any one of claims 1-4. Based on the fracture propagation behavior model and initialization parameters in the layered rock mass, the near-field dynamic stress parameters, strain energy density softening parameters, and material mechanical parameters at the interface of the layered rock mass were simulated. Based on the simulation results, the crack propagation process of layered rock mass is visualized.

7. The simulation method for fracture propagation behavior in layered rock masses as described in claim 6, characterized in that, The near-field dynamic stress parameters of the layered rock mass include the total nonlocal force, acceleration, displacement, and stress at each material point; The layered rock mass strain energy density softening parameters include the near-field dynamic strain energy density, the critical strain energy density of elastic change, and the initial elastic modulus of each material point. The softening parameters are updated based on the residual strain energy of each point. The material mechanical parameters at the interface of the layered rock mass include the average elastic modulus, which is used to calculate nonlocal forces. If the elongation exceeds the set critical breaking elongation, the nonlocal forces between material points disappear.

8. A simulation system for fracture propagation behavior in layered rock masses, characterized in that, include: A model building module is used to build a model of fracture propagation behavior in layered rock masses using the model building method for fracture propagation behavior in layered rock masses as described in any one of claims 1-4. A behavioral simulation model is used to simulate the near-field dynamic stress parameters, strain energy density softening parameters, and material mechanical parameters at the interface of the layered rock mass based on the fracture propagation behavior model and initialization parameters in the layered rock mass. The results visualization module is used to visualize the crack propagation process in layered rock masses based on simulation results.

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