PD-FEM-FVM efficient simulation analysis method and system for stress-seepage coupling of engineering rock masses

Abstract

The present invention proposes a PD-FEM-FVM efficient simulation and analysis method and system for engineering rock mass stress-seepage coupling, comprising: establishing corresponding size models for the solid layer and the fluid layer respectively according to actual engineering; applying initial boundary conditions to the entire established model; calculating the solid layer and the fluid layer respectively based on the applied initial boundary conditions, judging whether the bonds of the material points meet the failure conditions according to the displacement of the near-field dynamic material points in the solid layer, recording the local damage, and then describing the fracture of the rock mass; and obtaining the flow field distribution of the entire model according to the pressure of the FVM control body in the fluid layer, thereby performing efficient engineering-scale simulation of rock mass stress-seepage coupling.

Description

Technical Field

[0001] The present invention belongs to the technical field of numerical simulation of rock mass fluid-solid coupling, and in particular relates to an efficient simulation analysis method and system for engineering rock mass stress-seepage coupling using peridynamics (PD)-finite element method (FEM)-finite volume method (FVM). Background Art

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

[0003] In recent years, the construction of infrastructure such as railways, water conservancy and hydropower, and municipal infrastructure has flourished, ushering in unprecedented development opportunities for my country's transportation sector. The increasing saturation of highway traffic has significantly boosted the construction of underground projects, particularly tunnels. Due to the presence of groundwater, geological hazards in tunnels and underground projects are often caused by coupled stress and seepage fields. Scientific understanding of the evolution of hazards is the theoretical foundation and scientific basis for disaster prevention and control. With the rapid development of computer technology, numerical simulation, with its advantages of strong visualization, excellent repeatability, and time-saving and labor-saving, has become a major research tool.

[0004] The key to simulating the coupled stress-seepage of engineering rock masses lies in the continuous-discontinuous evolution process. Peridynamics (PD) is one of the most advanced numerical calculation methods currently used to solve discontinuous problems. It replaces the traditional differential model with an integral model of non-local action, does not have the problem of tip singularity, and is particularly suitable for simulating continuous-discontinuous problems. It is precisely because of the non-locality of peridynamics that the calculation is large in amount and the computational efficiency is low, which is not conducive to large-scale calculations at the engineering scale. In solid calculations and fluid-solid coupling calculations, coupling peridynamics with traditional continuum mechanics can simultaneously bring out the advantages of both and greatly improve the computational efficiency, which is of great significance for realizing engineering-scale fluid-solid coupling calculations of rock masses.

[0005] The inventors discovered that in current peridynamics and FVM coupling methods for fluid-structure interaction calculations, FVM is used for the fluid layer and PD is used for the solid layer, achieving coupling by establishing a transition layer between the two to transfer information. While this method improves the efficiency of fluid-structure interaction calculations to a certain extent, the solid layer still uses PD calculations entirely, resulting in low computational efficiency for the solid portion and a large amount of information exchange. This computational efficiency could be further improved. Summary of the Invention

[0006] To overcome the deficiencies of the above-mentioned prior art, the present invention provides an efficient PD-FEM-FVM simulation analysis method for stress-seepage coupling in engineering rock masses. The computational efficiency can be further improved to realize large-scale fluid-solid coupling calculations of engineering-scale rock masses.

[0007] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions:

[0008] First, a high-efficiency PD-FEM-FVM simulation analysis method for engineering rock mass stress-seepage coupling is disclosed, including:

[0009] According to actual engineering, corresponding size models are established for the solid layer and fluid layer respectively as rock mass calculation models;

[0010] Apply initial boundary conditions to the established rock mass calculation model;

[0011] Based on the initial boundary conditions, the solid layer and the fluid layer are calculated separately. The displacement of the peridynamic material point in the solid layer is used to determine whether the bond of the material point meets the failure condition, and the local damage is recorded to describe the fracture of the rock mass.

[0012] The flow field distribution of the entire model can be obtained based on the pressure of the FVM control volume in the fluid layer, thereby performing an efficient engineering-scale simulation of rock stress-seepage coupling.

[0013] As a further technical solution, the established solid part model is divided into three regions: the area where the rock mass may fracture is the peridynamic area, the area far away from the crack is the finite element area, and the part where the two areas connect is the coupling area;

[0014] The coupling zone is composed of connecting units;

[0015] The connection unit is a finite element unit embedded with peridynamic material points. The embedded material points can be used to transmit force and displacement, and also serve as a virtual boundary layer in the peridynamic zone. As the object of boundary conditions, it weakens the influence of boundary effects on the calculation results.

[0016] As a further technical solution, the size of the FVM control volume in the fluid layer is the same as the size of the PD material point in the solid layer, and one finite element unit in the solid layer corresponds to multiple FVM control volumes.

[0017] As a further technical solution, the actual environmental conditions of the rock mass are equivalent to physical quantities as initial boundary conditions. The physical quantities include stress, displacement and water pressure.

[0018] As a further technical solution, when calculating the solid layer:

[0019] The peridynamics region and the finite element region are connected by transferring forces and displacements in the coupling region. The forces and displacements in the coupling between the solid part PD and FEM are calculated as follows: the transferred forces and displacements are determined by shape function interpolation based on the relative positions of the embedded peridynamic material points and the connecting unit nodes.

[0020] As a further technical solution, the fluid layer is calculated using FVM. During the coupling process between the solid layer PD-FVM and the fluid layer FVM, the fluid pressure is transmitted in the following manner: the fluid pressure is transmitted to the solid layer. At this time, the transition layer is controlled by the solid layer PD-FEM, and the magnitude of the fluid pressure on the material points and finite element unit nodes is determined by the relative positions between the near-field dynamics material points, finite element units and fluid grid nodes.

[0021] The solid layer calculation uses an adaptive dynamic force relaxation algorithm to quickly balance the initial ground stress.

[0022] As a further technical solution, when calculating the fluid layer, Darcy's law is used to describe the flow field in saturated porous fractured media;

[0023] The pressure field of the entire area is obtained through matrix operations using the finite volume method.

[0024] As a further technical solution, when calculating the fluid layer:

[0025] Obtain the permeability coefficient of the solid layer, that is, the solid deformation is transferred to the fluid grid. At this time, the transition layer is controlled by the FVM grid nodes of the fluid part;

[0026] By determining the peridynamic material points and finite element units corresponding to the control volume of the fluid part grid node, the permeability coefficients of these material points and finite element unit nodes are used to transfer the solid deformation to the fluid grid.

[0027] Information such as solid deformation and fluid pressure can be obtained through the above solid layer calculation and fluid layer calculation.

[0028] Secondly, the PD-FEM-FVM high-efficiency simulation and analysis system for engineering rock mass stress-seepage coupling was disclosed, including:

[0029] The model building module is configured to: build corresponding size models for the solid layer and the fluid layer according to actual engineering;

[0030] The calculation module is configured to: impose initial boundary conditions on the entire established model;

[0031] Based on the initial boundary conditions, the solid layer and the fluid layer are calculated separately. The displacement of the peridynamic material point in the solid layer is used to determine whether the bond of the material point meets the failure condition, and the local damage is recorded to describe the fracture of the rock mass.

[0032] The simulation module is configured to obtain the flow field distribution of the entire model based on the pressure of the FVM control volume in the fluid layer, thereby performing efficient engineering-scale simulation of rock stress-seepage coupling.

[0033] One or more of the above technical solutions have the following beneficial effects:

[0034] (1) One or more embodiments of the present invention use the PD-FEM coupling method in the solid layer to divide the engineering-scale rock mass calculation model into a peridynamic zone, a finite element zone, and a coupling zone according to whether damage occurs. Compared with the pure peridynamic method, this method greatly reduces the number of material points and the computational workload.

[0035] (2) In one or more embodiments of the present invention, the fluid layer is calculated using the finite volume method, which not only improves the calculation efficiency but also ensures the accuracy of the calculation results.

[0036] (3) One or more embodiments of the present invention realize fluid-solid coupling calculation by locally establishing a transition layer, which reduces the amount of information interaction between the solid layer and the fluid layer, further improves the efficiency of fluid-solid coupling calculation, and thus can realize efficient fluid-solid coupling calculation of engineering rock masses.

[0037] Advantages of additional aspects of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0039] Figure 1 is a flow chart of embodiment 1 of the present invention;

[0040] Figure 2 It is the solid layer PD-FEM hybrid model of the first embodiment of the present invention;

[0041] Figure 3 (a)- Figure 3 (b) is a schematic diagram of the PD-FEM-FVM fluid-structure coupling method according to the first embodiment of the present invention;

[0042] Figure 4 Schematic diagram of the corresponding relationship between the FEM unit and the fluid grid in the first embodiment of the present invention;

[0043] Figure 5 It is a schematic diagram of the FEM unit subjected to water pressure according to the first embodiment of the present invention. DETAILED DESCRIPTION

[0044] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present invention belongs.

[0045] It should be noted that the terms used herein are for describing particular embodiments only and are not intended to limit the exemplary embodiments according to the present invention.

[0046] In the absence of conflict, the embodiments of the present invention and the features thereof may be combined with each other.

[0047] Example 1

[0048] This embodiment provides a PD-FEM-FVM numerical calculation method for stress-seepage coupling in engineering rock masses. First, the solid layer is modeled using peridynamics coupled with finite elements. Second, the fluid layer is modeled using the finite volume method. A transition layer is established between the peridynamic portion of the solid layer and the corresponding portion of the fluid layer. The transition layer stores the corresponding relationship between the solid and the fluid, thereby enabling information transmission between fluid pressure and solid deformation.

[0049] The method provided in this embodiment includes the following steps:

[0050] (1) According to the actual project, a corresponding rock mass calculation model is established, and the solid layer is divided into three regions. The area where fracture may occur is the peridynamic area, the area far away from the crack is the finite element area, and the part where the two areas connect is the coupling area, which is composed of connecting units.

[0051] The above-mentioned connection unit is a finite element unit embedded with peridynamic material points. The embedded material points can be used to transmit forces and displacements, and also serve as a virtual boundary layer in the peridynamic zone. As the object of boundary conditions, it weakens the influence of boundary effects on the calculation results.

[0052] The fluid layer is a finite volume grid. The size of the finite volume grid of the fluid layer is consistent with the PD material points in the solid layer and is smaller than the FEM unit size in the solid layer. The correspondence between the peridynamic material points, FEM nodes and the corresponding finite volume grid of the fluid layer is recorded according to the position coordinate relationship. When recording, the program retrieves the correspondence between the three according to the position coordinates.

[0053] For details, see the attached PD-FEM hybrid model. Figure 2 As shown in the figure. The PD-FEM-FVM fluid-structure coupling relationship is shown in the attached figure. Figure 3 (a)- Figure 3 (b) are schematic diagrams of the effect of fluid on solid and solid on fluid, respectively. The corresponding relationship diagram of FEM unit and fluid grid is shown in the attached Figure 4 As shown in the figure, the schematic diagram of FEM unit under water pressure is shown in the attached figure. Figure 5 shown.

[0054] The technical solution of the present invention improves the efficiency of fluid-solid coupling calculation by coupling calculation with traditional continuum mechanics methods to achieve large-scale calculation at an engineering scale.

[0055] (2) According to the actual engineering situation, stress and displacement boundary conditions are applied to the solid layer, and the adaptive dynamic relaxation method is used for iterative calculation.

[0056] In the solid layer, the area where the object may break is the peridynamic zone, and the area far away from the crack is the finite element zone, which is connected by the interface unit, that is, the mutual transmission of force and displacement.

[0057] The interface element is a finite element element embedded with peridynamic material points. The embedded material points can be used to transmit forces and displacements, and also serve as a virtual boundary layer in the peridynamic region. As the object of boundary conditions, the influence of boundary effects on the calculation results is weakened. The number of embedded material points is related to the size of the peridynamic neighborhood. Then, the short-range repulsive force is introduced in the peridynamics, so the coupling force expression is:

[0058]

[0059] Among them, f cp is the coupling force generated by all material points embedded in a certain interface unit, m is the number of material points in the interface unit, and f i p is the bond force on the embedded material point i, f i r is the short-range repulsive force on the embedded material point i, specifically:

[0060]

[0061] in,

[0062] d s =min{0.9|xx′|,1.35(r s +r s ′)}

[0063] Here, r s is the radius of the material point.

[0064] The coupling force is only distributed to the finite element nodes at the interface between the PD area and the FEM area. Therefore, for a two-dimensional problem, the coupling force distributed to the finite element nodes at the interface between the PD area and the FEM area is:

[0065] f I cp =∑N I (ξ,η)f cp I=1,2,3,4

[0066] Among them, N I is the shape function of the unit node I on the interface.

[0067] The displacements of the embedded peridynamic material points are obtained by interpolating the interface element node displacements through shape functions:

[0068]

[0069] In order to achieve efficient solution of static problems, by constructing the global matrix of the coupled system and adopting the adaptive dynamic relaxation method, the PD area and the FEM area are solved simultaneously under a unified framework, which accelerates the convergence speed and greatly improves the computational efficiency.

[0070] The discrete PD motion equation can be written as:

[0071]

[0072] Among them, U p is the displacement vector of the PD material point, and The displacement U p The second and first order derivatives of time are acceleration and velocity vectors; vector F p is the sum of the internal and external forces acting on the PD system; the superscript p indicates the variable related to the PD region; the single and double underscores indicate the variables located outside and inside the interface unit, respectively; c n represents the damping coefficient of the nth time step; D is a virtual diagonal density matrix whose diagonal elements are:

[0073]

[0074] In the formula is the stiffness matrix of the PD system.

[0075] Similarly, the finite element equation can be expressed as:

[0076]

[0077] Where the superscript f represents the variable related to the FEM region; M is the diagonal mass matrix. The mass matrix can be approximated as:

[0078]

[0079] Where I is the unit matrix. The mass vector for:

[0080]

[0081] Where A is the assembly operator. The weight is:

[0082]

[0083] Where, are the components of the element stiffness matrix.

[0084] is the unbalanced force vector of the finite element node at the nth time step, expressed as:

[0085]

[0086] in, is the external force vector of the FEM system at the nth time step; is the internal force vector, and the internal force on any finite element node I is:

[0087] Node I is in the conventional FEM area

[0088] Node I is at the interface between the PD area and the FEM area

[0089] Where, [·] I represents the finite element associated with node I, is the FEM element stiffness matrix, is the FEM unit displacement vector, f I cp is the coupling force acting on the finite element node at the interface between the PD area and the FEM area.

[0090] Finally, the equations for the coupled system are:

[0091]

[0092] in,

[0093] In the adaptive dynamic relaxation method, it is necessary to calculate the current optimal damping coefficient at each time step in order to speed up the convergence. The damping coefficient c of the nth time step is

[0094]

[0095] Among them, K t is the diagonal local stiffness matrix, which is expressed as:

[0096]

[0097] In this paper, the time step Δt is set to 1. In order to obtain the steady-state solution, the central difference explicit integration is used for calculation, and the recursive format is:

[0098]

[0099] When t=0, the iteration starts

[0100]

[0101] At the same time, in order to consider the interaction between solid deformation and fluid pressure, the finite element motion equation is modified according to the effective stress principle. The finite element motion equation based on the effective stress principle in saturated porous media is:

[0102]

[0103] Where U is the displacement vector of the finite element node, and are the second-order and first-order derivatives of displacement U with respect to time, i.e., acceleration and velocity vectors; P is the water pressure vector borne by the finite element node; c n represents the damping coefficient at the nth time step; α is the Biot coefficient; M is the diagonal mass matrix; and F is the force vector.

[0104] The basic equations of peridynamics in solid layers are modified. The relationship between the scalar force density state and the scalar effective force density state in peridynamics is:

[0105]

[0106] Among them, t total is the scalar force density state, t eff is the scalar effective force density state, α is the Biot coefficient, p is the pore pressure, m is the weighted volume scalar function, w is the influence function.

[0107] Therefore, the two-dimensional peridynamic equation of motion in saturated porous media based on the effective stress principle is:

[0108]

[0109] Where ρ is the material density, b is the body density, H x is the neighborhood of the material point x, Y is the deformation vector state, T is the force vector state.

[0110] At the same time, the solid layer peridynamics part is divided into the solid domain Ω s , transition domain Ω t and crack domain Ω f Three parts. Using the peridynamic damage field as the basis for division, two indicators are set to identify the three areas. The resulting linear indicator function is shown in the following formula:

[0111]

[0112]

[0113] Among them, c1 and c2 are two division indicators, c1 = 0.2, c2 = 0.4.

[0114] The solid permeability of the transition domain can be obtained by interpolating the permeabilities of the solid domain and the fracture domain using a linear index function:

[0115] k = x r k r +χ f k f

[0116] Among them, k r 、k f are the permeabilities of the solid domain and the fracture domain, respectively. The permeability of the fracture zone is calculated using the cubic law:

[0117]

[0118] Where: b is the crack opening.

[0119] During the iterative solution process, the bond of the material point in the peridynamic region is judged to see whether it meets the failure condition and the local damage is recorded. The failure condition is the judgment of the integrity of the material point bond expressed by the critical elongation:

[0120]

[0121] Where s0 is the elongation of a given material point bond, and s is the elongation of a material point bond, expressed as Where η is the relative displacement between any two material points, and ξ is the relative elongation between any two material points. In other words, when the tensile deformation s of the material point bond exceeds a given limit s0, the bond breaks, and the interaction relationship between the two interacting material points no longer exists.

[0122] Local damage is defined as the ratio of the number of intact bonds remaining to the initial number of bonds after the material point bonds are broken, expressed as:

[0123]

[0124] Among them, V ξ is the volume of material point i. Note that, Among them, 0 represents an intact state, and 1 represents a completely damaged state. The value between 0 and 1 is a quantitative representation of the degree of local damage.

[0125] The damage of the peridynamic part of the solid layer can be obtained based on the calculation above, and the permeability of the peridynamic part can be updated based on the breakage of the bonds between the material points. Since no rupture occurs in the FEM region, the permeability of the FVM control volume corresponding to the FEM region does not change and is the initial permeability.

[0126] (3) Apply the fluid pressure boundary condition, and according to the mutual correspondence between the fluid grid and the solid grid, transfer the permeability of the solid layer to the fluid grid node. In the finite element part of the solid layer, the permeability is directly transferred to the corresponding fluid layer FVM control volume. For the peridynamic part of the solid layer, the permeability is transferred according to the relative position relationship between the peridynamic material point and the fluid layer finite volume control volume.

[0127] Darcy's law is used to describe the flow field in saturated porous fractured media, which can be expressed as:

[0128]

[0129] Where: μ f is the fluid viscosity, K is the permeability tensor of the porous medium, and P is the fluid pressure. For a uniform isotropic body, K = kI.

[0130] Based on the relative position relationship, the water pressure on the peridynamic material point in the solid part is the water pressure at the corresponding fluid grid node. Each finite element in the solid part corresponds to multiple fluid grid nodes. The water pressure in each cell is obtained by averaging the water pressures on the fluid grid nodes within the cell, using the following formula:

[0131]

[0132] Among them, P e is the water pressure inside the solid part of the finite element unit, p i is the water pressure on the mesh nodes of the fluid part, and n is the number of fluid meshes contained in the finite element unit.

[0133] For a two-dimensional finite element with a certain thickness, the water load on each node in the element can be calculated using the following formula:

[0134]

[0135] Among them, P i is the water load borne by the unit node, l is the unit width, and h is the unit thickness.

[0136] Furthermore, the signs of the x and y water loads at each node can be determined based on the positions of the four nodes within the element. For example, the signs of the x and y water loads at nodes 1, 2, 3, and 4 are negative-negative, positive-negative, positive-positive, and negative-positive, respectively. For element nodes shared by multiple elements, the water loads on them are obtained by superposition.

[0137] When solid deformation and damage are transmitted to the fluid grid, this is primarily manifested as a change in the solid's permeability. The transition layer is controlled by the fluid grid nodes. Similar to the transmission of fluid pressure to the solid, solid deformation is transmitted to the fluid grid by determining the peridynamic material points and finite element nodes corresponding to the fluid grid nodes and utilizing the permeability coefficients of these material points and finite element nodes.

[0138] The above calculations can be used to obtain the solid deformation, damage and flow field characteristics of the fluid.

[0139] (4) Determine whether the specified time step has been reached. If so, the calculation ends; if not, the calculation proceeds to the next iteration.

[0140] The detailed calculation process of the technical solution of this embodiment is shown in the attached Figure 1 Specifically, the following are included:

[0141] 1) Initialize the basic variables and corresponding parameters;

[0142] 2) Determine the geometric dimensions and material parameters of the corresponding numerical calculation model based on the simulation object, divide the PD area and FEM area according to the expected failure mode, determine the finite element mesh, peridynamic material point size, and peridynamic neighborhood range, discretize each area and embed the corresponding number of material points in the interface unit, number the discrete finite element nodes and peridynamic material points, and determine the node composition of each finite element unit;

[0143] 3) Determine the total calculation time step and time step length. Since the solution strategy adopts the adaptive dynamic relaxation method, the time step is generally taken as 1;

[0144] 4) According to the relative position relationship, the correspondence between the solid material points and the finite element nodes and the fluid grid nodes;

[0145] 5) First, perform the solid part calculation. Determine the other material points in the neighborhood of each material point in the peridynamics, that is, determine the group membership of each material point and store them;

[0146] 6) Calculate the surface correction for each material point, that is, calculate the surface correction factor;

[0147] 7) Calculate the finite element global stiffness matrix, mass matrix, and peridynamic stability mass matrix, and assemble them to form the global mass matrix of the coupled system;

[0148] 8) Apply initial boundary conditions and load conditions to the discrete model and calculate the external force vector;

[0149] 9) Displacement transfer: The displacement of the embedded material point in the interface unit is obtained by interpolating the displacement of the finite element node on the interface unit in the previous time step. This displacement is used as the boundary condition of the peridynamic zone. The displacement of the finite element node on the interface unit in the initial time step is set to the initial value, that is, zero.

[0150] 10) Calculate the point force and short-range repulsive force of each material point according to the boundary conditions of the peridynamic zone;

[0151] 11) Force transfer: The sum of the point force and the short-range repulsive force on each material point in the interface unit, i.e., the coupling force, is distributed to the finite element nodes on the corresponding interface unit located at the interface between the two zones;

[0152] 12) Calculate the unbalanced forces in the finite element region and combine them with the point forces and short-range repulsive forces in the peridynamic region to form the overall force matrix of the coupled system;

[0153] 13) Solve the displacement of the coupled system according to the adaptive dynamic relaxation method;

[0154] 14) Calculate the elongation of the bond between the peridynamic material points. If it exceeds the critical elongation, the bond is judged to be broken. If it does not exceed the critical elongation, the bond is judged to be not broken.

[0155] 15) Determine whether the above steps have traversed all material points. If so, proceed to the next time step calculation; otherwise, return to step 14) to continue the calculation;

[0156] 16) Calculate the permeability of the finite element nodes and peridynamic material points at this time;

[0157] 17) transferring the permeability of the solid layer to the fluid grid according to the correspondence between the solid layer and the fluid grid established in step 4);

[0158] 18) Calculate the matrix coefficients corresponding to each fluid grid node respectively;

[0159] 19) Assemble the overall fluid calculation matrix to solve the fluid flow field distribution;

[0160] 20) Determine whether the calculation has reached the specified time step. If so, end the calculation and exit the program; if not, return to step 8) to continue the calculation.

[0161] Example 2

[0162] The purpose of this embodiment is to provide a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above method when executing the program.

[0163] Example 3

[0164] The purpose of this embodiment is to provide a computer-readable storage medium.

[0165] A computer-readable storage medium stores a computer program, which, when executed by a processor, performs the steps of the above method.

[0166] Example 4

[0167] The purpose of this embodiment is to provide an efficient PD-FEM-FVM simulation analysis system for engineering rock mass stress-seepage coupling, including:

[0168] The model building module is configured to: build corresponding size models for the solid layer and the fluid layer according to actual engineering;

[0169] The calculation module is configured to: impose initial boundary conditions on the entire established model;

[0170] Based on the initial boundary conditions, the solid layer and the fluid layer are calculated separately. The displacement of the peridynamic material point in the solid layer is used to determine whether the bond of the material point meets the failure condition, and the local damage is recorded to describe the fracture of the rock mass.

[0171] The simulation module is configured to obtain the flow field distribution of the entire model based on the pressure of the FVM control volume in the fluid layer, thereby performing efficient engineering-scale simulation of rock stress-seepage coupling.

[0172] The solid layer part mentioned above includes model establishment, area division, boundary condition application, calculation and analysis, etc. A calculation model of corresponding size is established according to the actual project, divided into peridynamic area, finite element area, and coupling area. Stress and displacement boundary conditions are applied according to the actual situation, and the adaptive dynamic relaxation method is used for calculation to obtain stress, displacement, and damage conditions.

[0173] Fluid layer: This includes model establishment, regional division, boundary condition application, and computational analysis. Darcy's law is used to describe the flow field in saturated porous and fractured media, and the finite volume method matrix operation is used to obtain the pressure field of the entire region.

[0174] The transition layer is where solid deformation and fluid pressure are transferred to each other. When solid deformation is transferred to the fluid grid, the transition layer is controlled by the fluid. By determining the PD material points and FEM nodes corresponding to the fluid FVM control volume, the solid deformation is transferred to the fluid grid using the permeability of the material points and FEM nodes. When fluid pressure is transferred to the solid layer, the transition layer is controlled by the solid layer (PD-FEM). Similarly, the relative positions of the PD material points, FEM nodes, and the fluid FVM control volume determine the magnitude of the fluid pressure on the solid.

[0175] The calculation results (stress, displacement, damage and pressure) of each iteration step are stored and displayed intuitively in the form of cloud maps.

[0176] The steps involved in the apparatuses of Examples 2, 3, and 4 above correspond to those of Method Example 1. For detailed implementations, please refer to the relevant description of Example 1. The term "computer-readable storage medium" should be understood to mean a single medium or multiple media containing one or more instruction sets; it should also be understood to include any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and causing the processor to perform any method of the present invention.

[0177] Those skilled in the art will appreciate that the modules or steps of the present invention described above can be implemented using a general-purpose computer device. Alternatively, they can be implemented using program code executable by a computing device, which can then be stored in a storage device and executed by the computing device. Alternatively, they can be fabricated into separate integrated circuit modules, or multiple modules or steps can be fabricated into a single integrated circuit module for implementation. The present invention is not limited to any specific combination of hardware and software.

[0178] Although the above describes the specific embodiments of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without any creative work are still within the scope of protection of the present invention.

Claims

1. The PD-FEM-FVM efficient simulation analysis method for engineering rock mass stress-seepage coupling is characterized by: include: Based on actual engineering, corresponding size models are established for the solid layer and fluid layer respectively as the rock mass calculation model; the established solid part model is divided into three regions: the area where the rock mass may break is the peridynamic region, the area away from the crack is the finite element region, and the part where the two regions connect is the coupling region; the coupling region is composed of connecting units; the connecting units are finite element units embedded with peridynamic material points. The embedded material points can be used to transmit force and displacement, and also serve as a virtual boundary layer in the peridynamic region. As the object of boundary condition application, the influence of boundary effect on the calculation results is weakened; Apply initial boundary conditions to the established rock mass calculation model; Based on the initial boundary conditions, the solid layer and the fluid layer are calculated separately. The displacement of the peridynamic material point in the solid layer is used to determine whether the bond of the material point meets the failure condition, and the local damage is recorded to describe the fracture of the rock mass. In solid layer calculations, when determining the transmitted force, the fluid pressure is transmitted to the solid layer. At this time, the transition layer is controlled by the solid layer PD-FEM. The magnitude of the fluid pressure on the material points and finite element nodes is determined by the relative positions between the peridynamic material points, finite element elements, and fluid grid nodes. One finite element unit in the solid layer corresponds to multiple FVM control volumes; The water pressure on the peridynamic material points in the solid part is the water pressure at the corresponding fluid mesh node. Each finite element in the solid part corresponds to multiple fluid mesh nodes. The water pressure in each element is obtained by averaging the water pressures on the fluid mesh nodes within the element, and is calculated using the following formula: Among them, P e is the water pressure inside the solid part of the finite element unit, p i is the water pressure on the mesh nodes of the fluid part, and n is the number of fluid meshes contained in the finite element unit. For a two-dimensional finite element unit with a certain thickness, the water load on each node in the unit is calculated using the following formula: Among them, P i is the water load borne by the unit node, l is the unit width, and h is the unit thickness; The flow field distribution of the entire model can be obtained based on the pressure of the FVM control volume in the fluid layer, thereby performing an efficient engineering-scale simulation of rock stress-seepage coupling.

2. The PD-FEM-FVM efficient simulation analysis method for engineering rock mass stress-seepage coupling according to claim 1 is characterized in that: The size of the FVM control volume in the fluid layer is the same as the size of the material point in the solid layer PD.

3. The PD-FEM-FVM efficient simulation analysis method for engineering rock mass stress-seepage coupling according to claim 1 is characterized in that: The actual environmental conditions of the rock mass are equivalent to physical quantities as initial boundary conditions. The physical quantities include stress, displacement and water pressure.

4. The PD-FEM-FVM efficient simulation analysis method for engineering rock mass stress-seepage coupling according to claim 1 is characterized in that: When calculating for a solid layer: The peridynamics region and the finite element region are connected by transferring forces and displacements through the coupling region. The magnitude of the transferred forces and displacements is determined by shape function interpolation based on the relative positions of the embedded peridynamic material points and the connecting element nodes.

5. The PD-FEM-FVM efficient simulation analysis method for engineering rock mass stress-seepage coupling according to claim 1 is characterized in that: When calculating the fluid layer, Darcy's law is used to describe the flow field in saturated porous fractured media; The pressure field of the entire area is obtained through matrix operations using the finite volume method; When calculating the fluid layer: Obtain the permeability coefficient of the solid layer, that is, the solid deformation is transferred to the fluid grid. At this time, the transition layer is controlled by the FVM grid nodes of the fluid part; By determining the peridynamic material points and finite element units corresponding to the control volume of the fluid part grid node, the permeability coefficients of these material points and finite element unit nodes are used to transfer the solid deformation to the fluid grid.

6. The PD-FEM-FVM high-efficiency simulation and analysis system for engineering rock mass stress-seepage coupling is characterized by including: The model building module is configured to: establish corresponding size models for the solid layer and fluid layer according to actual engineering; divide the established solid part model into three regions: the area where the rock mass may fracture is the peridynamic region, the area away from the crack is the finite element region, and the part where the two regions connect is the coupling region; the coupling region is composed of connecting units; the connecting units are finite element units embedded with peridynamic material points. The embedded material points can be used to transmit force and displacement and also serve as a virtual boundary layer in the peridynamic region. As the object of boundary conditions, the influence of boundary effects on the calculation results is weakened; The calculation module is configured to: impose initial boundary conditions on the entire established model; Based on the applied initial boundary conditions, the solid layer and the fluid layer are calculated separately. The displacement of the peridynamic material points in the solid layer is used to determine whether the bonds of the material points meet the failure conditions, record the local damage, and then describe the fracture of the rock mass. In the solid layer calculation, when determining the transmitted force, the fluid pressure is transmitted to the solid layer. At this time, the transition layer is controlled by the solid layer PD-FEM. The relative positions of the peridynamic material points, finite element units and fluid grid nodes determine the magnitude of the fluid pressure on the material points and finite element unit nodes. One finite element in the solid layer corresponds to multiple FVM control volumes. The water pressure on the peridynamic material points in the solid part is the water pressure at the corresponding fluid mesh node. Each finite element in the solid part corresponds to multiple fluid mesh nodes. The water pressure in each element is obtained by averaging the water pressures on the fluid mesh nodes within the element, and is calculated using the following formula: Among them, P e is the water pressure inside the solid part of the finite element unit, p i is the water pressure on the mesh nodes of the fluid part, and n is the number of fluid meshes contained in the finite element unit. For a two-dimensional finite element unit with a certain thickness, the water load on each node in the unit is calculated using the following formula: Among them, P i is the water load borne by the unit node, l is the unit width, and h is the unit thickness; The simulation module is configured to obtain the flow field distribution of the entire model based on the pressure of the FVM control volume in the fluid layer, thereby performing efficient engineering-scale simulation of rock stress-seepage coupling.

7. A computer device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, wherein: When the processor executes the program, the steps of the method described in any one of claims 1 to 5 are implemented.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method described in any one of claims 1 to 5 are executed.

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