Finite element-near field dynamics tunnel large deformation calculation method considering creep

Abstract

The invention discloses a finite element-near field dynamics tunnel large deformation calculation method considering creep deformation, and relates to the field of tunnel deformation calculation.The method comprises the steps that meshing is conducted on a research area of tunnel surrounding rock, and a finite element analysis area and a near field dynamics analysis area are determined; an overlapping region exists between the finite element analysis region and the near-field dynamics analysis region; determining near-field dynamic mass points according to the grids in the near-field dynamic area; performing finite element analysis on the complete finite element analysis area to obtain a tunnel surrounding rock deformation condition in the complete finite element analysis area; carrying out finite element analysis and near-field dynamics analysis on the overlapping region to obtain a tunnel surrounding rock deformation condition in the overlapping region; and performing near-field dynamics analysis considering a surrounding rock material creep phenomenon on the complete near-field dynamics analysis region to obtain a tunnel surrounding rock deformation condition in the complete near-field dynamics analysis region. The efficiency and accuracy of tunnel deformation calculation can be improved.

Description

Technical Field

[0001] The present application relates to the field of tunnel deformation calculation, and in particular to a finite element-peridynamic tunnel large deformation calculation method considering creep. Background Art

[0002] In existing large deformation calculations of tunnels, the finite element method or finite difference method is usually used, based on the continuous medium assumption. However, in large deformation calculations of tunnels, the mesh deformation is usually too large, and the use of the continuous medium assumption will produce large errors and affect the calculation efficiency. In addition, in the problem of large deformation of tunnels, there is usually a creep phenomenon, that is, the deformation of the tunnel has a certain correlation with time, but the creep phenomenon has not been considered in the existing large deformation calculations of tunnels. Summary of the invention

[0003] The purpose of this application is to provide a finite element-peridynamic tunnel large deformation calculation method considering creep, which can improve the efficiency and accuracy of tunnel deformation calculation.

[0004] To achieve the above objectives, this application provides the following solutions:

[0005] In a first aspect, the present application provides a finite element-peridynamic tunnel large deformation calculation method considering creep, comprising:

[0006] The research area of ​​the tunnel surrounding rock is meshed, and a finite element analysis area and a peridynamic analysis area are determined; the peridynamic area is a surrounding rock area with a tunnel contour as a starting line and a first preset distance away from the tunnel; the starting line of the finite element analysis area is located in the peridynamic analysis area; the finite element analysis area is a surrounding rock area with a corresponding starting line as a starting end and a second preset distance away from the tunnel; the finite element analysis area includes an overlapping area between the finite element analysis area and the peridynamic analysis area and a complete finite element analysis area; the peridynamic area includes the overlapping area and the complete finite element analysis area;

[0007] determining a peridynamic particle in the peridynamic region according to a grid in the peridynamic region;

[0008] Performing finite element analysis on the complete finite element analysis area to obtain deformation of the tunnel surrounding rock in the complete finite element analysis area;

[0009] Performing finite element analysis and peridynamic analysis on the overlapping area to obtain deformation of the tunnel surrounding rock in the overlapping area;

[0010] A peridynamic analysis taking into account the creep phenomenon of the surrounding rock material is performed on the complete peridynamic analysis area to obtain the deformation of the tunnel surrounding rock in the complete peridynamic analysis area.

[0011] According to the specific embodiments provided in this application, this application discloses the following technical effects:

[0012] The present application provides a finite element-peridynamic tunnel large deformation calculation method considering creep, meshing the study area of ​​the tunnel surrounding rock, and determining the finite element analysis area and the peridynamic analysis area, and there is an overlapping area between the finite element analysis area and the peridynamic analysis area. After the present invention meshes the study area of ​​the surrounding rock, part of it is used as the finite element analysis area, and part of it is used as the peridynamic analysis area. Compared with performing finite element analysis on the entire area, the deformation of the surrounding rock area close to the tunnel can be calculated more accurately, and the error problem existing in the single application of finite element analysis can be solved. In addition, when performing surrounding rock deformation analysis on the peridynamic analysis area, the present invention takes into account the creep properties of the surrounding rock material, introduces the creep constitutive model of the surrounding rock material in the peridynamic analysis process to analyze the creep phenomenon, and can more accurately predict the deformation of the surrounding rock area close to the tunnel. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0014] Figure 1 An application environment diagram of a finite element-peridynamic tunnel large deformation calculation method considering creep provided in one embodiment of the present application;

[0015] Figure 2 A schematic flow chart of a finite element-peridynamic tunnel large deformation calculation method considering creep provided in one embodiment of the present application;

[0016] Figure 3 A schematic diagram of a numerical calculation model for tunnel deformation analysis provided in an embodiment of the present application;

[0017] Figure 4 A schematic diagram of the relationship between a complete finite element analysis region, an overlapping region (coupling region) and a complete peridynamic analysis region provided in an embodiment of the present application;

[0018] Figure 5 A schematic diagram of the change of the tunnel vault and the convergence value over time provided in one embodiment of the present application;

[0019] Figure 6 A final deformation cloud map of a tunnel provided in an embodiment of the present application;

[0020] Figure 7 A schematic diagram of the structure of a computer device provided in one embodiment of the present application. DETAILED DESCRIPTION

[0021] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0022] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0023] The finite element-peridynamic tunnel large deformation calculation method considering creep provided in the embodiment of the present application can be applied to Figure 1 In the application environment shown. Among them, the terminal communicates with the server through the network. The data storage system can store the data that the server needs to process. The data storage system can be set up separately, integrated on the server, or placed on the cloud or other servers. The terminal can send the research area of ​​the tunnel surrounding rock to the server. After the server receives the research area of ​​the tunnel surrounding rock, the server grids the research area of ​​the tunnel surrounding rock and determines the finite element analysis area and the peridynamic analysis area; determines the peridynamic particles in the peridynamic area according to the grid in the peridynamic area; performs finite element analysis on the complete finite element analysis area to obtain the deformation of the tunnel surrounding rock in the complete finite element analysis area; performs finite element analysis and peridynamic analysis on the overlapping area between the finite element analysis area and the peridynamic analysis area to obtain the deformation of the tunnel surrounding rock in the overlapping area; performs peridynamic analysis considering the creep phenomenon of the surrounding rock material on the complete peridynamic analysis area to obtain the deformation of the tunnel surrounding rock in the complete peridynamic analysis area. The server can feedback the obtained tunnel surrounding rock deformation in the finite element analysis area, the peridynamic analysis area and the overlapping area to the terminal. In addition, in some embodiments, the finite element-peri-field dynamics tunnel large deformation calculation method considering creep can also be implemented independently by the server 104 or the terminal. For example, the terminal can directly perform tunnel surrounding rock deformation calculation on the study area of ​​the tunnel surrounding rock, or the server can obtain the study area of ​​the tunnel surrounding rock from the data storage system and perform tunnel surrounding rock deformation calculation.

[0024] The terminals may be, but are not limited to, various desktop computers, laptops, smart phones, tablet computers, IoT devices and portable wearable devices. IoT devices may be smart speakers, smart TVs, smart air conditioners, smart car-mounted devices, etc. Portable wearable devices may be smart watches, smart bracelets, head-mounted devices, etc. The server may be implemented as an independent server or a server cluster consisting of multiple servers, or a cloud server.

[0025] In an exemplary embodiment, Figure 2 As shown, a finite element-peridynamic tunnel large deformation calculation method considering creep is provided. The method is executed by a computer device, and can be executed by a computer device such as a terminal or a server alone, or by a terminal and a server together. In the embodiment of the present application, the method is applied to Figure 1 The server in the example is used to illustrate, including the following steps 101 to 105. Among them:

[0026] Step 101, meshing the research area of ​​the tunnel surrounding rock, and determining the finite element analysis area and the peridynamic analysis area; there is an overlapping area between the finite element analysis area and the peridynamic analysis area; the peridynamic area is the surrounding rock area within a first preset distance away from the tunnel with the tunnel contour as the starting line; the starting line of the finite element analysis area is located in the peridynamic analysis area; the finite element analysis area is the surrounding rock area within a second preset distance away from the tunnel with the corresponding starting line as the starting end; the finite element analysis area includes the overlapping area and the complete finite element analysis area; the peridynamic area includes the overlapping area and the complete finite element analysis area;

[0027] In this step, the size of the computational domain is determined, and the finite element analysis area and the peridynamic analysis area are determined respectively. In the deformation prediction calculation of large deformation of the tunnel, the surrounding rock part can be set up with the finite element analysis area and the peridynamic analysis area. Figure 3 and Figure 4 shown.

[0028] Step 102: determining peridynamic particles in the peridynamic region according to the grid in the peridynamic region.

[0029] In the process of modeling the actual peridynamic region, the material points in the peridynamic region are discretized. The discretization of PD particles requires the establishment of a finite element mesh first, and then a number of PD particles are discretized based on the finite element mesh. PD particles refer to peridynamic particles. Initially, the calculation time step must be established, and the model boundary conditions must be determined according to 5 times the diameter of the tunnel chamber.

[0030] Step 103: Perform finite element analysis on the complete finite element analysis area to obtain deformation of the tunnel surrounding rock in the complete finite element analysis area.

[0031] Step 104: perform finite element analysis and peridynamic analysis on the overlapping area to obtain deformation of the tunnel surrounding rock in the overlapping area.

[0032] Step 105 , performing peridynamic analysis on the complete peridynamic analysis area taking into account the creep phenomenon of the surrounding rock material, and obtaining the deformation of the tunnel surrounding rock in the complete peridynamic analysis area.

[0033] Implement the above steps 101 to 105, mesh the study area of ​​the tunnel surrounding rock, and determine the finite element analysis area and the peridynamic analysis area, and there is an overlapping area between the finite element analysis area and the peridynamic analysis area. After the present invention meshes the study area of ​​the surrounding rock, part of it is used as the finite element analysis area, and part of it is used as the peridynamic analysis area. Compared with performing finite element analysis on the entire area, the deformation of the surrounding rock area close to the tunnel can be calculated more accurately, and the error problem of single application of finite element analysis can be solved. In addition, when performing surrounding rock deformation analysis on the peridynamic analysis area, the present invention takes into account the creep properties of the surrounding rock material, introduces the creep constitutive model of the surrounding rock material in the peridynamic analysis process to analyze the creep phenomenon, and can more accurately predict the deformation of the surrounding rock area close to the tunnel.

[0034] In the present invention, the overall control equation of the overall area of ​​the tunnel surrounding rock is:

[0035]

[0036] Where: and are the first-order and second-order derivatives of displacement U with respect to time, which can be expressed as:

[0037]

[0038] matrix It can be written as:

[0039]

[0040] Vector It is expressed as:

[0041]

[0042] Among them, in the formula: represents the velocity field of the complete finite element analysis region at the nth time step; M is the diagonal mass matrix; c nis the damping coefficient. U is the displacement vector. Represents the velocity field of the overlapping area at the nth time step; represents the velocity field in the complete peridynamic region at time step n; express The first derivative of denote the body forces in the full peridynamic region, the full finite element analysis region, and the overlap region, respectively. The subscript f refers to the finite element analysis; the subscript p refers to the peridynamic analysis. The coefficients of the fictitious diagonal density matrix D can be determined by Greschgorin's theorem.

[0043] Damping coefficient c n It can be obtained by the following formula:

[0044]

[0045] in, F ii Indicates the overall control equation F n The component of the ith row and ith column of . According to Greschgorin's theorem, m ii represents the diagonal elements of the density matrix D, m ii ≧0.25Δt 2 ∑|K ab |, where the inequality sign ensures the stability of the central difference display integral.

[0046] The diagonal mass matrix M can be approximated as:

[0047]

[0048] Where: I is the unit matrix. The mass vector can be constructed as Where A is the assembly operator. Vector The components can be written as: Where: are the components of the element stiffness matrix of the finite element e. The meaning is that the elements of any column of the stiffness matrix are the nodal forces caused on each node b when the a-th node of the unit undergoes unit displacement along the coordinate direction.

[0049] Therefore, in another exemplary embodiment of the present application, in step 103, finite element analysis is performed on the complete finite element analysis area to obtain the deformation of the tunnel surrounding rock in the complete finite element analysis area, which specifically includes:

[0050] (a1) Determine the displacements and body forces of the finite element elements in the full finite element analysis region at the initial time step.

[0051] (a2) obtaining the displacement of the finite element unit in the complete finite element analysis region at the nth time step according to the displacement of the finite element unit in the complete finite element analysis region at the initial time step; n = 1, 2, 3, ..., N, where N is the maximum time step.

[0052] (a3) determining the body force exerted on the finite element unit in the complete finite element analysis region at the nth time step based on the displacement of the finite element unit in the complete finite element analysis region at the nth time step.

[0053] (a4) determining whether the displacement of the finite element unit in the complete finite element analysis area at the nth time step and the body force determine whether they satisfy the finite element FEM equation, and obtaining a first determination result.

[0054] (a5) If the first judgment result is yes, the displacement of the finite element unit in the complete finite element analysis area at the nth time step is regarded as the deformation of the tunnel surrounding rock in the complete finite element analysis area.

[0055] (a6) If the first judgment result is no, then determine whether the current number of iterations meets the preset number of iterations to obtain a second judgment result.

[0056] (a7) If the second judgment result is yes, the displacement of the finite element unit in the complete finite element analysis area at the nth time step is regarded as the deformation of the tunnel surrounding rock in the complete finite element analysis area.

[0057] (a8) If the second judgment result is no, the displacement of the finite element unit in the complete finite element analysis area at the n+1th time step is determined based on the displacement and body force of the finite element unit in the complete finite element analysis area at the nth time step.

[0058] (a9) determining the body force acting on the finite element unit in the complete finite element analysis region at the n+1th time step based on the displacement of the finite element unit in the complete finite element analysis region at the n+1th time step.

[0059] (a10) Replace the nth time step with the n+1th time step, and return to the step of "determining whether the displacement of the finite element unit in the complete finite element analysis area at the nth time step and the body force judgment satisfy the finite element FEM equation to obtain a first judgment result."

[0060] In another exemplary embodiment of the present application, for the update of the body force in the complete finite element analysis area, the force vector of the nth time step is It can be expressed as: Where: t is time; f ext is the external force vector. int The internal forces generated by unit deformation are assembled into a global internal force array. f(e) is the unit force vector, which can be expressed as: (e) =k (e) u (e) . k (e) is the element stiffness matrix of finite element e; u (e) is the node displacement vector of the e-th unit and is the element of the displacement vector U.

[0061] Therefore, step (a3), determining the body force exerted on the finite element unit in the complete finite element analysis region at the nth time step according to the displacement of the finite element unit in the complete finite element analysis region at the nth time step, specifically includes:

[0062] (1) Determine the global internal force of the finite element unit in the complete finite element analysis area at the nth time step based on the displacement of the finite element unit in the complete finite element analysis area at the nth time step and the corresponding finite element stiffness matrix.

[0063] (2) determining the body force exerted on the finite element unit in the complete finite element analysis area at the nth time step based on the global internal force and the external force exerted on the finite element unit in the complete finite element analysis area at the nth time step; the external force exerted on the finite element unit includes gravity.

[0064] In another exemplary embodiment of the present application, in step (a8), the calculation formula for the displacement of the finite element unit in the complete finite element analysis area at the n+1th time step is:

[0065]

[0066] in,

[0067] Since the initial integral t -1 / 2 The velocity field at time is unknown, so we assume that U 0 ≠0 and available

[0068] The displacement calculation formula here is for the entire surrounding rock study area and is an overall expression. If it is for the complete finite element analysis area, then in the formula, U n+1 represents the displacement of the finite element unit in the complete finite element analysis area at the n+1th time step; U n represents the displacement of the finite element in the complete finite element analysis area at the nth time step; Indicates Time step is the first derivative of the displacement of the finite element in the complete finite element analysis area; c n It represents the damping coefficient of the finite element unit in the complete finite element analysis area at the nth time step; Indicates Time step: the first derivative of the displacement of the finite element in the full finite element analysis region; F n Body forces of the finite element elements in the full finite element analysis region at the nth time step; M represents the diagonal mass matrix.

[0069] When the overlap region is used, the parameters in the previous paragraph are defined for the finite element elements in the overlap region. When the full peridynamic analysis region is used, the parameters in the previous paragraph are defined for the peridynamic particles in the full peridynamic analysis region.

[0070] In another exemplary embodiment of the present application, in step 104, a finite element analysis is performed on the overlapping area to obtain the displacement of the finite element unit, and then the displacement of the finite element unit is converted to the corresponding PD particle point to obtain the displacement of the PD particle point in the overlapping area. The displacement of a certain particle point p is: Where Ni is the shape function given by Zienkiewicz; vector is the displacement of the i-th node on the e-th finite element unit, which is given by the finite element global node displacement vector U f Extract from u p After determination, the displacement vector of the overlapping area can be calculated

[0071] Then, the force density is expressed as body force b(x p ,t) acts on the finite element area. Acting on the particle x p The physical strength can be calculated as follows.

[0072]

[0073] x (j) Represents other PD particles within the finite element unit e.

[0074] Mass x p The total force in the unit is:

[0075]

[0076] The calculated unit body force can be further transferred to the unit nodes.

[0077]

[0078] Where: ρ is the mass density of the e-th unit; I is the I-th node of the e-th unit. Therefore, Represents the external force acting on the Ith node. Superposition is performed to obtain the body force of the finite element unit in the overlapping area At this point, the displacement of the finite element unit in the overlapping area is combined with the calculation of the PD particle body force to obtain the body force of the finite element unit.

[0079] Therefore, step 104, performing finite element analysis and peridynamic analysis on the overlapping area to obtain the deformation of the tunnel surrounding rock in the overlapping area, specifically includes:

[0080] (b1) Determine the displacement and body force of the finite element unit in the overlapping region at the initial time step.

[0081] (b2) obtaining the displacement of the finite element unit in the overlapping area at the nth time step according to the displacement of the finite element unit in the overlapping area at the initial time step; n=1, 2, 3, ..., N.

[0082] (b3) determining the body force exerted on the finite element unit in the overlapping area at the nth time step based on the displacement of the finite element unit in the overlapping area at the nth time step.

[0083] (b4) determining whether the displacement of the finite element unit in the overlapping area at the nth time step and the body force satisfy the finite element FEM equation to obtain a third determination result.

[0084] (b5) If the third judgment result is yes, the displacement of the finite element unit in the overlapping area at the nth time step is regarded as the deformation of the tunnel surrounding rock in the overlapping area.

[0085] (b6) If the third judgment result is no, then determine whether the current number of iterations meets the preset number of iterations to obtain a fourth judgment result.

[0086] (b7) If the fourth judgment result is yes, the displacement of the finite element unit in the overlapping area at the nth time step is regarded as the deformation of the tunnel surrounding rock in the overlapping area.

[0087] (b8) If the fourth judgment result is no, determining the displacement in the overlapping area at the n+1th time step based on the displacement and body force of the finite element unit in the overlapping area at the nth time step.

[0088] (b9) determining the body force exerted on the finite element unit in the overlapping area at the n+1th time step based on the displacement of the finite element unit in the overlapping area at the n+1th time step.

[0089] (b10) Replace the nth time step with the n+1th time step, and return to the step of "determining whether the displacement of the finite element unit in the overlapping area of ​​the nth time step and the body force judgment satisfy the finite element FEM equation to obtain a third judgment result."

[0090] In another exemplary embodiment of the present application, step (b9), determining the body force exerted on the finite element unit in the overlapping area at the n+1th time step according to the displacement of the finite element unit in the overlapping area at the n+1th time step, specifically includes:

[0091] (1) Determining the displacement of the peridynamic particle in the finite element unit in the overlapping region at the n+1th time step based on the displacement of the finite element unit in the overlapping region at the n+1th time step.

[0092] (2) calculating the body force of each peridynamic particle in the finite element unit in the overlapping region at the n+1th time step according to the displacement of the peridynamic particle in the finite element unit in the overlapping region at the n+1th time step.

[0093] (3) Determine the total force of each peridynamic particle in the finite element unit in the overlapping region at the n+1th time step by using the body force of each peridynamic particle in the finite element unit in the overlapping region at the n+1th time step.

[0094] (4) The total force of each peridynamic particle in the finite element unit in the overlapping region at the n+1th time step is converted to the nodes of the corresponding finite element unit, and the body force of each node in the finite element unit in the overlapping region at the n+1th time step is obtained.

[0095] (5) The body forces of the nodes in the finite element unit in the overlapping area at the n+1th time step are superimposed to obtain the body forces on the finite element unit in the overlapping area at the n+1th time step.

[0096] In another exemplary embodiment of the present application, step 105, performing peridynamic analysis on the complete peridynamic analysis area taking into account the creep phenomenon of the surrounding rock material to obtain the deformation of the tunnel surrounding rock in the complete peridynamic analysis area, specifically includes:

[0097] (c1) determining the displacements and body forces of the peridynamic particles within the full peridynamic analysis region at the initial time step.

[0098] (c2) obtaining the displacement of the peridynamic particles in the complete peridynamic analysis region at the nth time step according to the displacement of the peridynamic particles in the complete peridynamic analysis region at the initial time step; n=1, 2, 3, ..., N.

[0099] (c3) calculating the strain of the peridynamic particles in the complete peridynamic analysis region at the nth time step based on the displacement of the peridynamic particles in the complete peridynamic analysis region at the nth time step.

[0100] (c4) calculating the stress of the peridynamic particles in the complete peridynamic analysis region at the nth time step based on the strain of the peridynamic particles in the complete peridynamic analysis region at the nth time step.

[0101] (c5) judging whether shear or tensile yielding occurs in the surrounding rock material according to the stress of the peridynamic particles in the complete peridynamic analysis region at the nth time step, and obtaining a fifth judgment result.

[0102] (c6) If the fifth judgment result is yes, the stress of the peridynamic particles in the complete peridynamic analysis region at the nth time step is updated to obtain an updated stress.

[0103] (c7) If the result of the fifth determination is negative, then the stress of the peridynamic particles in the complete peridynamic analysis region at the nth time step is not updated.

[0104] (c8) determining whether the current stress of the peridynamic particles in the complete peridynamic analysis region at the nth time step and the displacement of the peridynamic particles in the complete peridynamic analysis region at the nth time step satisfy the motion control equation of the creep constitutive model of the surrounding rock material, and obtaining a sixth determination result.

[0105] (c9) If the result of the sixth determination is negative, determining the body force on the peridynamic particle in the complete peridynamic analysis region at the nth time step based on the displacement of the peridynamic particle in the complete peridynamic analysis region at the nth time step.

[0106] (c10) determining whether the displacement and body force of the peridynamic particles in the complete peridynamic analysis region at the nth time step satisfy the peridynamic motion equation, and obtaining a seventh determination result.

[0107] (c11) If the seventh judgment result is yes, the displacement of the peridynamic particle in the complete peridynamic analysis area at the nth time step is regarded as the deformation of the tunnel surrounding rock in the complete peridynamic analysis area.

[0108] (c12) If the seventh judgment result is no, then determine whether the current number of iterations meets the preset number of iterations to obtain an eighth judgment result.

[0109] (c13) If the result of the eighth judgment is yes, the displacement of the peridynamic particle in the complete peridynamic analysis region at the nth time step is regarded as the deformation of the tunnel surrounding rock in the complete peridynamic analysis region.

[0110] (c14) If the result of the eighth determination is negative, determining the displacement of the peridynamic particles in the complete peridynamic analysis region at the (n+1)th time step based on the displacement and body force of the peridynamic particles in the complete peridynamic analysis region at the nth time step.

[0111] (c15) determining the body force on the peridynamic particle in the complete peridynamic analysis region at the n+1th time step based on the displacement of the peridynamic particle in the complete peridynamic analysis region at the n+1th time step.

[0112] (c16) replacing the nth time step with the n+1th time step, and returning to step "determining whether the displacement of the peridynamic particles in the complete peridynamic analysis area at the nth time step and the body force judgment satisfy the peridynamic motion equation, and obtaining the seventh judgment result".

[0113] In the deformation analysis process within the complete peridynamic analysis area, the creep constitutive model of the surrounding rock material is introduced. The addition of the creep constitutive model of the rock material is the process of calculating the stress based on the deformation. The difference between this patent and the traditional model is that it is necessary to determine whether the rock material breaks during the deformation process. The specific process is:

[0114] (1) The total strain is obtained based on the deformation calculation and decomposed into volumetric strain and deviatoric strain;

[0115] (2) Assuming that the plastic strain increment is 0, the average normal stress and the average deviator stress are calculated based on the strain;

[0116] (3) Determine whether yield occurs based on the average normal stress and tensile / yield strain criteria;

[0117] (4) If yielding does not occur, the trial average normal stress and the trial average deviator stress are assigned as the true new normal stress and the true new average deviator stress;

[0118] (5) If yielding occurs, the stress is corrected according to the plastic strain increment;

[0119] (6) After obtaining the true stress, update the Kelvin strain component;

[0120] (7) If damage occurs, calculate the elastic damage variable D:

[0121]

[0122] Where γ = σ cr / σ c0 is the residual compressive strength coefficient, σ cr is the residual compressive strength under uniaxial stress state, ε cr is the residual compressive strain corresponding to the residual compressive strength, εcu is the final compressive strain corresponding to the fully damaged state, and the final compressive strain coefficient is defined as η c =ε cu / ε c0。

[0123] (8) Update the Young's deformation modulus of rock material E = E0(1-D);

[0124] Then calculate the force density vector and update the acceleration, velocity and displacement of the material point. Repeat this process until the calculation stops.

[0125] It should be noted that in this implementation, the analysis process of the tunnel surrounding rock deformation in the full finite element analysis area, the overlapping area and the peridynamic analysis area is performed simultaneously. Figure 5 The tunnel crown and convergence value change over time based on the tunnel deformation in each area. Figure 6 This is the final deformation cloud map of the tunnel.

[0126] In this embodiment, a method of integrating peridynamics and finite element calculation is adopted. Since peridynamics has no grid and no grid distortion problem, it has the advantage of high accuracy for large deformation calculation, but its calculation efficiency is relatively low. The finite element method has high calculation efficiency and mature tunnel support units can be used, but it has grid restrictions for large deformation calculation of tunnel, which is a congenital deficiency. By taking advantage of the two methods and introducing the creep calculation model, the change of large deformation of the tunnel relative to time can be better calculated and the large deformation of the tunnel can be predicted.

[0127] The present application also provides an application scenario, which applies the above-mentioned finite element-peridynamic tunnel large deformation calculation method considering creep. Specifically: the finite element-peridynamic tunnel large deformation calculation method considering creep provided in this embodiment can be applied in the tunnel deformation scenario. The scenario includes a data acquisition link, a data processing link and a result display link. The data acquisition link is used to obtain the research area of ​​the tunnel surrounding rock; the data processing link is used to perform peridynamic analysis considering the creep phenomenon of the surrounding rock material on the complete finite element analysis area, the overlapping area and the complete peridynamic analysis area to obtain the deformation of the tunnel surrounding rock in each area; the result display link is used to display the deformation of the tunnel surrounding rock in each area. The finite element-peridynamic tunnel large deformation calculation method considering creep provided in this embodiment belongs to the data processing link.

[0128] In an exemplary embodiment, a computer device is provided. The computer device may be a server or a terminal. The internal structure diagram thereof may be as follows: Figure 7As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, referred to as I / O) and a communication interface. The processor, the memory and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store tunnel deformation data. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a finite element-peri-field dynamics tunnel large deformation calculation method considering creep is implemented.

[0129] Those skilled in the art will understand that Figure 7 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0130] In an exemplary embodiment, a computer device is further provided, including a memory and a processor, wherein a computer program is stored in the memory, and the processor implements the steps in the above-mentioned method embodiments when executing the computer program.

[0131] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program, and when the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0132] In an exemplary embodiment, a computer program product is provided, including a computer program, and when the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0133] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.

[0134] Those of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0135] The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. The non-relational database may include a distributed database based on blockchain, etc., but is not limited thereto. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but is not limited thereto.

[0136] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0137] This article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. At the same time, for those skilled in the art, according to the ideas of this application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A finite element-peridynamic tunnel large deformation calculation method considering creep, characterized in that: The finite element-peridynamic tunnel large deformation calculation method considering creep includes: The research area of ​​the tunnel surrounding rock is meshed, and a finite element analysis area and a peridynamic analysis area are determined; the peridynamic area is a surrounding rock area with a tunnel contour as a starting line and a first preset distance away from the tunnel; the starting line of the finite element analysis area is located in the peridynamic analysis area; the finite element analysis area is a surrounding rock area with a corresponding starting line as a starting end and a second preset distance away from the tunnel; the finite element analysis area includes an overlapping area between the finite element analysis area and the peridynamic analysis area and a complete finite element analysis area; the peridynamic area includes the overlapping area and the complete finite element analysis area; determining a peridynamic particle in the peridynamic region according to a grid in the peridynamic region; Performing finite element analysis on the complete finite element analysis area to obtain deformation of the tunnel surrounding rock in the complete finite element analysis area; Performing finite element analysis and peridynamic analysis on the overlapping area to obtain deformation of the tunnel surrounding rock in the overlapping area; A peridynamic analysis taking into account the creep phenomenon of the surrounding rock material is performed on the complete peridynamic analysis area to obtain the deformation of the tunnel surrounding rock in the complete peridynamic analysis area.

2. The finite element-peridynamic tunnel large deformation calculation method considering creep according to claim 1 is characterized in that: Performing finite element analysis on the complete finite element analysis area to obtain the deformation of the tunnel surrounding rock in the complete finite element analysis area specifically includes: Determining the displacements and body forces of the finite element elements within the full finite element analysis region at the initial time step; According to the displacement of the finite element unit in the complete finite element analysis area at the initial time step, the displacement of the finite element unit in the complete finite element analysis area at the nth time step is obtained; n=1, 2, 3, ..., N; Determine the body force exerted on the finite element unit in the complete finite element analysis area at the nth time step according to the displacement of the finite element unit in the complete finite element analysis area at the nth time step; Determine whether the displacement of the finite element unit in the complete finite element analysis area at the nth time step and the body force judgment satisfy the finite element FEM equation to obtain a first judgment result; If the first judgment result is yes, the displacement of the finite element unit in the complete finite element analysis area at the nth time step is regarded as the deformation of the tunnel surrounding rock in the complete finite element analysis area; If the first judgment result is no, then judging whether the current number of iterations meets the preset number of iterations, and obtaining a second judgment result; If the second judgment result is yes, the displacement of the finite element unit in the complete finite element analysis area at the nth time step is regarded as the deformation of the tunnel surrounding rock in the complete finite element analysis area; If the second judgment result is no, determining the displacement of the finite element unit in the complete finite element analysis area at the n+1th time step according to the displacement and body force of the finite element unit in the complete finite element analysis area at the nth time step; Determine the body force exerted on the finite element unit in the complete finite element analysis area at the n+1th time step according to the displacement of the finite element unit in the complete finite element analysis area at the n+1th time step; Replace the nth time step with the n+1th time step, and return to step "determine whether the displacement of the finite element unit in the complete finite element analysis area at the nth time step and the body force judgment satisfy the finite element FEM equation to obtain a first judgment result".

3. The finite element-peridynamic tunnel large deformation calculation method considering creep according to claim 2 is characterized in that: Determining the body force exerted on the finite element unit in the complete finite element analysis area at the nth time step according to the displacement of the finite element unit in the complete finite element analysis area at the nth time step specifically includes: Determine the global internal force of the finite element unit in the complete finite element analysis area at the nth time step according to the displacement of the finite element unit in the complete finite element analysis area at the nth time step and the corresponding finite element stiffness matrix; The body force exerted on the finite element unit in the complete finite element analysis area at the nth time step is determined according to the global internal force and the external force exerted on the finite element unit in the complete finite element analysis area at the nth time step; the external force exerted on the finite element unit includes gravity.

4. The finite element-peridynamic tunnel large deformation calculation method considering creep according to claim 2 is characterized in that: The calculation formula for the displacement of the finite element unit in the complete finite element analysis area at the n+1th time step is: in, In the formula, U n+1 represents the displacement of the finite element in the complete finite element analysis area at the n+1th time step; U n represents the displacement of the finite element in the complete finite element analysis area at the nth time step; Indicates Time step is the first derivative of the displacement of the finite element in the complete finite element analysis area; c n It represents the damping coefficient of the finite element unit in the complete finite element analysis area at the nth time step; Indicates Time step: the first derivative of the displacement of the finite element in the full finite element analysis region; F n Body forces of the finite element elements in the full finite element analysis region at the nth time step; M represents the diagonal mass matrix.

5. The finite element-peridynamic tunnel large deformation calculation method considering creep according to claim 1 is characterized in that: Finite element analysis and peridynamic analysis are performed on the overlapping area to obtain the deformation of the tunnel surrounding rock in the overlapping area, specifically including: Determining the displacement and body force of the finite element unit in the overlap region at the initial time step; The displacement of the finite element unit in the overlapping area at the nth time step is obtained according to the displacement of the finite element unit in the overlapping area at the initial time step; n=1, 2, 3, ..., N; Determine the body force exerted on the finite element unit in the overlapping area at the nth time step according to the displacement of the finite element unit in the overlapping area at the nth time step; Determine whether the displacement of the finite element unit in the overlapping area at the nth time step and the body force determine whether they satisfy the finite element FEM equation to obtain a third determination result; If the third judgment result is yes, the displacement of the finite element unit in the overlapping area at the nth time step is regarded as the deformation of the tunnel surrounding rock in the overlapping area; If the third judgment result is no, then judging whether the current number of iterations meets the preset number of iterations, and obtaining a fourth judgment result; If the fourth judgment result is yes, the displacement of the finite element unit in the overlapping area at the nth time step is regarded as the deformation of the tunnel surrounding rock in the overlapping area; If the fourth judgment result is no, determining the displacement in the overlapping area at the n+1th time step according to the displacement and body force of the finite element unit in the overlapping area at the nth time step; Determine the body force exerted on the finite element unit in the overlapping area at the n+1th time step according to the displacement of the finite element unit in the overlapping area at the n+1th time step; Replace the nth time step with the n+1th time step, and return to step "determine whether the displacement of the finite element unit in the overlapping area of ​​the nth time step and the body force judgment satisfy the finite element FEM equation to obtain a third judgment result".

6. The finite element-peridynamic tunnel large deformation calculation method considering creep according to claim 5 is characterized in that: Determining the body force exerted on the finite element unit in the overlapping area at the n+1th time step according to the displacement of the finite element unit in the overlapping area at the n+1th time step specifically includes: Determine the displacement of the peridynamic particle in the finite element unit in the overlapping region at the n+1th time step according to the displacement of the finite element unit in the overlapping region at the n+1th time step; Calculate the body force of each peridynamic particle in the finite element unit in the overlapping region at the n+1th time step according to the displacement of the peridynamic particle in the finite element unit in the overlapping region at the n+1th time step; Determine the total force of each peridynamic particle in the finite element unit in the overlapping region at the n+1th time step by using the body force of each peridynamic particle in the finite element unit in the overlapping region at the n+1th time step; Converting the total force of each peridynamic particle in the finite element unit in the overlapping region at the n+1th time step to the node of the corresponding finite element unit to obtain the body force of each node in the finite element unit in the overlapping region at the n+1th time step; The body forces of the nodes in the finite element unit in the overlapping area at the n+1th time step are superimposed to obtain the body forces on the finite element unit in the overlapping area at the n+1th time step.

7. The finite element-peridynamic tunnel large deformation calculation method considering creep according to claim 1 is characterized in that: The peridynamic analysis considering the creep phenomenon of the surrounding rock material is performed on the complete peridynamic analysis area to obtain the deformation of the tunnel surrounding rock in the complete peridynamic analysis area, specifically including: determining displacements and body forces of peridynamic particles within the full peridynamic analysis region at the initial time step; Obtaining the displacement of the peridynamic particle in the complete peridynamic analysis region at the nth time step according to the displacement of the peridynamic particle in the complete peridynamic analysis region at the initial time step; n=1, 2, 3, ..., N; calculating the strain of the peridynamic particle in the complete peridynamic analysis region at the nth time step according to the displacement of the peridynamic particle in the complete peridynamic analysis region at the nth time step; Calculating the stress of the peridynamic particles in the complete peridynamic analysis region at the nth time step according to the strain of the peridynamic particles in the complete peridynamic analysis region at the nth time step; determining whether shear or tensile yielding of the surrounding rock material occurs according to the stress of the peridynamic particles in the complete peridynamic analysis area at the nth time step, and obtaining a fifth determination result; If the fifth judgment result is yes, then updating the stress of the peridynamic particles in the complete peridynamic analysis region at the nth time step to obtain an updated stress; If the result of the fifth judgment is no, then the stress of the peridynamic particles in the complete peridynamic analysis region at the nth time step is not updated; Determine whether the current stress of the peridynamic particle in the complete peridynamic analysis region at the nth time step and the displacement of the peridynamic particle in the complete peridynamic analysis region at the nth time step satisfy the motion control equation of the creep constitutive model of the surrounding rock material, and obtain a sixth determination result; If the result of the sixth determination is no, determining the body force on the peridynamic particle in the complete peridynamic analysis region at the nth time step according to the displacement of the peridynamic particle in the complete peridynamic analysis region at the nth time step; Determine whether the displacement and body force of the peridynamic particle in the complete peridynamic analysis area at the nth time step satisfy the peridynamic motion equation, and obtain a seventh determination result; If the seventh judgment result is yes, the displacement of the peridynamic particle in the complete peridynamic analysis area at the nth time step is regarded as the deformation of the tunnel surrounding rock in the complete peridynamic analysis area; If the seventh judgment result is no, then judging whether the current number of iterations meets the preset number of iterations, and obtaining an eighth judgment result; If the eighth judgment result is yes, the displacement of the peridynamic particle in the complete peridynamic analysis area at the nth time step is regarded as the deformation of the tunnel surrounding rock in the complete peridynamic analysis area; If the result of the eighth determination is no, determining the displacement of the peridynamic particle in the complete peridynamic analysis region at the n+1th time step according to the displacement and body force of the peridynamic particle in the complete peridynamic analysis region at the nth time step; Determining the body force on the peridynamic particle in the complete peridynamic analysis region at the n+1th time step according to the displacement of the peridynamic particle in the complete peridynamic analysis region at the n+1th time step; The nth time step is replaced by the n+1th time step, and the process returns to step "determining whether the displacement of the peridynamic particle in the complete peridynamic analysis region at the nth time step and the body force judgment satisfy the peridynamic motion equation, and obtaining a seventh judgment result".

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