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

Abstract

The application discloses a finite element-near field dynamics tunnel large deformation calculation method considering creep, relates to the tunnel deformation calculation field, and comprises the following steps: meshing a research region of tunnel surrounding rock, and determining a finite element analysis region and a near field dynamics analysis region; the finite element analysis region and the near field dynamics analysis region have an overlapping region; determining near field dynamics particles according to the mesh in the near field dynamics region; performing finite element analysis on a complete finite element analysis region to obtain tunnel surrounding rock deformation in the complete finite element analysis region; performing finite element analysis and near field dynamics analysis on the overlapping region to obtain tunnel surrounding rock deformation in the overlapping region; performing near field dynamics analysis considering the creep phenomenon of surrounding rock material on a complete near field dynamics analysis region to obtain tunnel surrounding rock deformation in the complete near field dynamics analysis region. The application can improve the efficiency and accuracy of tunnel deformation calculation.

Description

Technical Field

[0001] This application relates to the field of tunnel deformation calculation, and in particular to a finite element-near-field dynamics method for calculating large deformations of tunnels that takes creep into account. Background Technology

[0002] In existing calculations of large tunnel deformation, the finite element method or finite difference method is typically used, based on the assumption of a continuous medium. However, in large tunnel deformation calculations, the mesh often exhibits excessive deformation, leading to significant errors and impacting computational efficiency when using the continuous medium assumption. Furthermore, creep is a common phenomenon in large tunnel deformation problems, meaning that tunnel deformation is correlated with time, but current calculations for large tunnel deformation do not consider creep. Summary of the Invention

[0003] The purpose of this application is to provide a finite element-near-field dynamics method for calculating large deformations in tunnels that considers creep, which can improve the efficiency and accuracy of tunnel deformation calculations.

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

[0005] Firstly, this application provides a finite element-near-field dynamics method for calculating large deformations of tunnels considering creep, including:

[0006] The study area of ​​the tunnel surrounding rock is gridded, and a finite element analysis region and a near-field dynamics analysis region are determined. The near-field dynamics region is the surrounding rock area within a first preset distance away from the tunnel, starting from the tunnel outline. The starting line of the finite element analysis region is located within the near-field dynamics analysis region. The finite element analysis region is the surrounding rock area within a second preset distance away from the tunnel, starting from the corresponding starting line. The finite element analysis region includes the overlapping region between the finite element analysis region and the near-field dynamics analysis region, and the fully finite element analysis region. The near-field dynamics region includes the overlapping region and the fully finite element analysis region.

[0007] The near-field dynamic particles within the near-field dynamic region are determined based on the grid within the near-field dynamic region.

[0008] Finite element analysis is performed on the fully finite element analysis region to obtain the deformation of the surrounding rock of the tunnel within the fully finite element analysis region;

[0009] Finite element analysis and near-field dynamic analysis were performed on the overlapping region to obtain the deformation of the tunnel surrounding rock within the overlapping region;

[0010] A near-field dynamic analysis considering the creep phenomenon of the surrounding rock material is performed on the fully near-field dynamic analysis area to obtain the deformation of the tunnel surrounding rock within the fully near-field dynamic analysis area.

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

[0012] This application provides a finite element-peripheral dynamics method for calculating large deformations in tunnels, considering creep. The method meshes the study area of ​​the tunnel surrounding rock and defines both the finite element analysis region and the periphery dynamics analysis region, with overlapping areas between them. By meshing the study area of ​​the surrounding rock and using a portion as the finite element analysis region and a portion as the periphery dynamics analysis region, compared to performing finite element analysis on the entire region, the deformation of the surrounding rock region near the tunnel can be calculated more accurately, solving the error problem inherent in applying finite element analysis alone. Furthermore, when performing deformation analysis on the surrounding rock in the periphery dynamics analysis region, this invention considers the creep properties of the surrounding rock material and introduces a creep constitutive model of the surrounding rock material to analyze creep phenomena, enabling more accurate prediction of the deformation of the surrounding rock region near the tunnel. Attached Figure Description

[0013] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0014] Figure 1 An application environment diagram of a finite element-near-field dynamics tunnel large deformation calculation method considering creep, provided for an embodiment of this application;

[0015] Figure 2 A flowchart illustrating a finite element-near-field dynamics method for calculating large deformation of a tunnel considering creep, provided as an embodiment of this application;

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

[0017] Figure 4 A schematic diagram showing the relationship between the fully finite element analysis region, the overlapping region (coupling region), and the fully near-field dynamics analysis region provided in an embodiment of this application;

[0018] Figure 5 A schematic diagram illustrating the changes in tunnel arch and convergence value over time, provided in an embodiment of this application;

[0019] Figure 6 A final deformation cloud map of a tunnel provided in one embodiment of this application;

[0020] Figure 7 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0021] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0022] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0023] The finite element-near-field dynamics tunnel large deformation calculation method considering creep provided in this application embodiment can be applied to, for example... Figure 1 The application environment shown is as follows. The terminal communicates with the server via a network. A data storage system stores the data the server needs to process. This data storage system can be set up independently, integrated into the server, or placed in the cloud or on another server. The terminal can send the study area of ​​the tunnel surrounding rock to the server. After receiving the study area, the server meshes the study area and determines the finite element analysis area and the near-field dynamics analysis area. Based on the mesh within the near-field dynamics area, it determines the near-field dynamic particles within that area. Finite element analysis is performed on the fully finite element analysis area to obtain the deformation of the tunnel surrounding rock within that area. Finite element analysis and near-field dynamics analysis are performed on the overlapping area between the finite element analysis area and the near-field dynamics analysis area to obtain the deformation of the tunnel surrounding rock within the overlapping area. Near-field dynamics analysis considering the creep phenomenon of the surrounding rock material is performed on the fully near-field dynamics analysis area to obtain the deformation of the tunnel surrounding rock within that area. The server can then feed back the obtained deformation data of the finite element analysis area, the near-field dynamics analysis area, and the overlapping area to the terminal. In addition, in some embodiments, the finite element-near field dynamics tunnel large deformation calculation method considering creep can also be implemented by the server 104 or the terminal alone. For example, the terminal can directly perform tunnel surrounding rock deformation calculation for 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 can be, but are not limited to, various desktop computers, laptops, smartphones, tablets, IoT devices, and portable wearable devices. IoT devices can include smart speakers, smart TVs, smart air conditioners, and smart in-vehicle systems. Portable wearable devices can include smartwatches, smart bracelets, and head-mounted devices. Servers can be implemented using independent servers, server clusters composed of multiple servers, or cloud servers.

[0025] In one exemplary embodiment, such as Figure 2 As shown, a finite element-near-field dynamics method for calculating large deformations in tunnels considering creep is provided. This method is executed by a computer device, specifically by a terminal or server alone, or by both a terminal and a server. In this embodiment, the method is applied to... Figure 1 Taking the server in the example, the explanation includes the following steps 101 to 105. Wherein:

[0026] Step 101: The study area of ​​the tunnel surrounding rock is meshed, and the finite element analysis area and the near-field dynamics analysis area are determined. There is an overlapping area between the finite element analysis area and the near-field dynamics analysis area. The near-field dynamics area is the surrounding rock region within a first preset distance away from the tunnel, starting from the tunnel outline. The starting line of the finite element analysis area is located within the near-field dynamics analysis area. The finite element analysis area is the surrounding rock region within a second preset distance away from the tunnel, starting from the corresponding starting line. The finite element analysis area includes the overlapping area and the fully finite element analysis area. The near-field dynamics area includes the overlapping area and the fully finite element analysis area.

[0027] In this step, the size of the computational domain is established, and the finite element analysis region and the peri-field dynamics analysis region are defined separately. In the deformation prediction calculation of large tunnel deformation, the surrounding rock portion can be divided into a finite element analysis region and a peri-field dynamics analysis region. The coupling of the finite element method and peri-field dynamics is as follows: Figure 3 and Figure 4 As shown.

[0028] Step 102: Determine the near-field dynamic particles within the near-field dynamic region based on the grid within the near-field dynamic region.

[0029] In the modeling of the actual near-field dynamic region, the near-field dynamic region is discretized into material points. Discretization of PD particles requires first establishing a finite element mesh, and then discretizing several PD particles based on the finite element mesh. PD particles refer to near-field dynamic particles. Initially, the calculation time step needs to be established, and the model boundary conditions are determined according to a ratio of 5 times the diameter of the tunnel chamber.

[0030] Step 103: Perform finite element analysis on the fully finite element analysis region to obtain the deformation of the surrounding rock of the tunnel within the fully finite element analysis region.

[0031] Step 104: Perform finite element analysis and near-field dynamic analysis on the overlapping area to obtain the deformation of the tunnel surrounding rock within the overlapping area.

[0032] Step 105: Perform near-field dynamic analysis on the fully near-field dynamic analysis area, taking into account the creep phenomenon of the surrounding rock material, to obtain the deformation of the tunnel surrounding rock within the fully near-field dynamic analysis area.

[0033] By performing steps 101 to 105 above, the study area of ​​the tunnel surrounding rock is meshed, and the finite element analysis area and the peri-field dynamics analysis area are determined, with overlapping areas between them. This invention meshes the study area of ​​the surrounding rock, using part as the finite element analysis area and part as the peri-field dynamics analysis area. Compared to performing finite element analysis on the entire area, this allows for more accurate calculation of the deformation of the surrounding rock area near the tunnel, solving the error problem inherent in applying finite element analysis alone. Furthermore, when performing deformation analysis on the peri-field dynamics analysis area, this invention considers the creep properties of the surrounding rock material and introduces a creep constitutive model of the surrounding rock material to analyze creep phenomena, enabling more accurate prediction of the deformation of the surrounding rock area near the tunnel.

[0034] In this invention, the overall governing equation for the entire surrounding rock region of the tunnel is:

[0035]

[0036] In the formula: and Let U be the first and second derivatives of displacement U with respect to time, respectively, which can be expressed as:

[0037]

[0038] matrix It can be written as:

[0039]

[0040] vector Represented as:

[0041]

[0042] Wherein: The velocity field of the fully finite element analysis region at time step n is represented; M is the diagonal mass matrix; c nis the damping coefficient. U is the displacement vector. This represents the velocity field of the overlapping region at time step n; This represents the velocity field of the fully near-field dynamic region at time step n. express The first derivative; These represent the body forces in the fully peridynamic region, the fully finite element analysis region, and the overlapping region, respectively. The subscript f refers to finite element analysis; the subscript p refers to peridynamic analysis. The coefficients of the virtual diagonal density matrix D can be determined using Greschgorin's theorem.

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

[0044]

[0045] in, F ii In the overall control equation, F represents n The component in the i-th row and i-th column. According to Greschgorin's theorem, m ii Denotes the diagonal elements of the density matrix D, m ii ≥0.25Δt 2 ∑|K ab The inequality sign here ensures the stability of the integral displayed by the central difference.

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

[0047]

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

[0049] Therefore, in another exemplary embodiment of this application, step 103, performing finite element analysis on the fully finite element analysis region to obtain the tunnel surrounding rock deformation within the fully finite element analysis region, specifically includes:

[0050] (a1) Determine the displacement and physical forces of the finite element elements within the fully finite element analysis region at the initial time step.

[0051] (a2) The displacement of the finite element in the complete finite element analysis region at the nth time step is obtained from the displacement of the finite element in the complete finite element analysis region at the initial time step; n = 1, 2, 3, ..., N. N is the maximum time step.

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

[0053] (a4) Determine whether the displacement of the finite element in the complete finite element analysis region at the nth time step and the body force satisfy the finite element FEM equation to obtain the first judgment result.

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

[0055] (a6) If the first judgment result is negative, then determine whether the current iteration number meets the preset iteration number to obtain the second judgment result.

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

[0057] (a8) If the second judgment result is negative, then the displacement of the finite element in the complete finite element analysis region at the n+1 time step is determined based on the displacement and body force of the finite element in the complete finite element analysis region at the nth time step.

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

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

[0060] In another exemplary embodiment of this application, for updating the body forces in the fully finite element analysis domain, the force vector at the nth time step... It can be represented as: Where: t is time; f ext f is the external force vector. int The internal forces generated by element deformation are assembled into a global internal force array. f(e) The element force vector can be expressed as: f (e) =k (e) u (e) k (e) Let u be the element stiffness matrix of the finite element e; (e) Let be the nodal displacement vector of the e-th element, and be the elements of the displacement vector U.

[0061] Therefore, step (a3), determining the body force on the finite element element within the complete finite element analysis region at time step n based on the displacement of the finite element element within the complete finite element analysis region at time step n, specifically includes:

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

[0063] (2) Determine the body forces acting on the finite element elements in the complete finite element analysis region at the nth time step based on the global internal forces and external forces acting on the finite element elements in the complete finite element analysis region at the nth time step; the external forces acting on the finite element elements include gravity.

[0064] In another exemplary embodiment of this application, in step (a8), the formula for calculating the displacement of the finite element within the fully finite element analysis region at the (n+1)th time step is:

[0065]

[0066] in,

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

[0068] The displacement calculation formula here applies to the entire surrounding rock study area and is a holistic expression. If the analysis is applied to the entire finite element analysis area, then in the formula, U... n+1 U represents the displacement of the finite element within the fully finite element analysis region at time step n+1; n This represents the displacement of the finite element within the fully finite element analysis region at time step n; Indicates the first The first derivative of the displacement of the finite element within the time-step fully finite element analysis region; c n This represents the damping coefficient of the finite element within the fully finite element analysis region at time step n; Indicates the first The first derivative of the displacement of the finite element within the time-step fully finite element analysis region; F n The body forces of finite element elements within the fully finite element analysis region at time step n; M represents the diagonal mass matrix.

[0069] When considering overlapping regions, the parameter definitions in the previous section apply to the finite element parameters within the overlapping region. When considering a fully peri-field dynamic analysis region, the parameters in the previous section apply to the peri-field dynamic particles within the fully peri-field dynamic analysis region.

[0070] In another exemplary embodiment of this application, in step 104, finite element analysis is performed on the overlapping region to obtain the displacement of the finite element elements. Then, the displacement of the finite element elements is transferred to the corresponding PD particles to obtain the displacement of the PD particles in the overlapping region. The displacement of a certain particle p is: In the formula; Ni is the shape function given by Zienkiewicz; vector Let U be the displacement of the i-th node in the e-th finite element, expressed by the global nodal displacement vector U of the finite element. f Extract from. u p Once determined, the displacement vector of the overlapping region can be calculated.

[0071] Then, the force density is expressed as body force b(x) p It acts on the finite element region in the manner of ,t). It acts on the particle x. p Physical strength can be calculated using the following formula.

[0072]

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

[0074] point mass x p The total force of the unit is:

[0075]

[0076] The physical forces of the element obtained from this calculation can be further transferred to the element nodes.

[0077]

[0078] In the formula: ρ is the mass density of the e-th element; I is the I-th node of the e-th element. Therefore, This represents the external force acting on the i-th node. It is determined by the body forces acting on the node. The body force of the finite element elements in the overlapping region is obtained by superposition. By utilizing the displacement of the finite element elements in the overlapping region and combining it with the calculation of the body force of the PD mass point, the body force of the finite element elements was obtained.

[0079] Therefore, step 104 involves performing finite element analysis and near-field dynamic analysis on the overlapping region to obtain the deformation of the tunnel surrounding rock within the overlapping region, specifically including:

[0080] (b1) Determine the displacement and physical forces of the finite element elements in the overlapping region at the initial time step.

[0081] (b2) The displacement of the finite element in the overlapping region at the nth time step is obtained from the displacement of the finite element in the overlapping region at the initial time step; n = 1, 2, 3, ..., N.

[0082] (b3) Determine the body force on the finite element in the overlapping region at the nth time step based on the displacement of the finite element in the overlapping region at the nth time step.

[0083] (b4) Determine whether the displacement of the finite element in the overlapping region at the nth time step and the physical force satisfy the finite element FEM equation to obtain the third judgment result.

[0084] (b5) If the third judgment result is yes, then the displacement of the finite element 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 negative, then determine whether the current iteration number meets the preset iteration number to obtain the fourth judgment result.

[0086] (b7) If the fourth judgment result is yes, then the displacement of the finite element 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 negative, then the displacement in the overlapping region at the (n+1)th time step is determined based on the displacement and body force of the finite element in the overlapping region at the nth time step.

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

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

[0090] In another exemplary embodiment of this application, step (b9), determining the body force on the finite element element in the overlapping region at the (n+1)th time step based on the displacement of the finite element element in the overlapping region at the (n+1)th time step, specifically includes:

[0091] (1) Determine the displacement of the near-field dynamic particles in the finite element element within the overlapping region at the (n+1)th time step based on the displacement of the finite element element within the overlapping region at the (n+1)th time step.

[0092] (2) Calculate the body force of each near-field dynamic particle in the finite element element in the overlapping region at time step n+1 based on the displacement of the near-field dynamic particle in the finite element element in the overlapping region at time step n+1.

[0093] (3) Determine the total force of each near-field dynamic particle in the finite element unit within the overlapping region at time step n+1.

[0094] (4) The total force of each near-field dynamic particle in the finite element unit in the overlapping region at time step n+1 is converted to the node of the corresponding finite element unit, so as to obtain the body force of each node in the finite element unit in the overlapping region at time step n+1.

[0095] (5) The physical forces of each node in the finite element unit in the overlapping area of ​​the (n+1)th time step are superimposed to obtain the physical forces of the finite element unit in the overlapping area of ​​the (n+1)th time step.

[0096] In another exemplary embodiment of this application, step 105, performing a near-field dynamic analysis considering the creep phenomenon of the surrounding rock material on the fully near-field dynamic analysis region to obtain the deformation of the tunnel surrounding rock within the fully near-field dynamic analysis region, specifically includes:

[0097] (c1) Determine the displacement and physical forces acting on the near-field dynamic particles within the fully near-field dynamic analysis region at the initial time step.

[0098] (c2) The displacement of the near-field dynamic particles in the complete near-field dynamic analysis region at the nth time step is obtained based on the displacement of the near-field dynamic particles in the complete near-field dynamic analysis region at the initial time step; n = 1, 2, 3, ..., N.

[0099] (c3) Calculate the strain of the near-field dynamic particles in the complete near-field dynamic analysis region at the nth time step based on the displacement of the near-field dynamic particles in the complete near-field dynamic analysis region at the nth time step.

[0100] (c4) Calculate the stress of the near-field dynamic particles in the fully near-field dynamic analysis region at the nth time step based on the strain of the near-field dynamic particles in the fully near-field dynamic analysis region at the nth time step.

[0101] (c5) Based on the stress of the near-field dynamic particles in the fully near-field dynamic analysis area described in the nth time step, determine whether the surrounding rock material has undergone shear or tensile yielding, and obtain the fifth judgment result.

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

[0103] (c7) If the fifth judgment result is negative, then the stress of the near-field dynamic particles in the fully near-field dynamic analysis region described in the nth time step will not be updated.

[0104] (c8) Determine whether the current stress of the near-field dynamic particles in the fully near-field dynamic analysis region at time step n and the displacement of the near-field dynamic particles in the fully near-field dynamic analysis region at time step n satisfy the motion control equation of the creep constitutive model of the surrounding rock material, and obtain the sixth judgment result.

[0105] (c9) If the result of the sixth judgment is negative, then the body force on the near-field dynamic particle in the complete near-field dynamic analysis region at the nth time step is determined based on the displacement of the near-field dynamic particle in the complete near-field dynamic analysis region at the nth time step.

[0106] (c10) Determine whether the displacement and body force of the near-field dynamic particles in the complete near-field dynamic analysis region at the nth time step satisfy the near-field dynamic motion equation, and obtain the seventh judgment result.

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

[0108] (c12) If the seventh judgment result is negative, then determine whether the current iteration number meets the preset iteration number to obtain the eighth judgment result.

[0109] (c13) If the eighth judgment result is yes, then the displacement of the near-field dynamic particle in the complete near-field dynamic analysis area at the nth time step shall be regarded as the deformation of the tunnel surrounding rock in the complete near-field dynamic analysis area.

[0110] (c14) If the eighth judgment result is negative, then the displacement of the near-field dynamic particles in the complete near-field dynamic analysis region at the nth time step is determined based on the displacement and body force of the near-field dynamic particles in the complete near-field dynamic analysis region at the nth time step.

[0111] (c15) Determine the body forces acting on the near-field dynamic particles within the complete near-field dynamic analysis region at the (n+1)th time step based on the displacement of the near-field dynamic particles within the complete near-field dynamic analysis region.

[0112] (c16) Replace the nth time step with the (n+1)th time step and return to the step "determine whether the displacement of the near-field dynamic particle in the complete near-field dynamic analysis region at the nth time step and the body force judgment satisfy the near-field dynamic motion equation, and obtain the seventh judgment result".

[0113] In the deformation analysis within the fully near-field dynamic analysis region, a creep constitutive model of the surrounding rock material is introduced. The addition of the rock material creep constitutive model is based on the stress calculation process during deformation. The difference between this patent and traditional models lies in the need to determine whether the rock material fractures during the deformation process. The specific process is as follows:

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

[0115] (2) Assuming that the plastic strain increment is 0, calculate the average normal stress and the average deviatoric stress based on the strain.

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

[0117] (4) If yielding does not occur, then the trial mean normal stress and the trial mean deviatoric stress are assigned the true new normal stress and the true new mean deviatoric 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 components;

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

[0121]

[0122] Where γ=σ cr / σ c0 σ is the residual compressive strength coefficient. cr ε represents the residual compressive strength under uniaxial stress. cr ε is the residual compressive strain corresponding to the residual compressive strength.cu The final compressive strain corresponds 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 the rock material E=E0(1-D);

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

[0125] It should be noted that in this implementation, the analysis of the tunnel surrounding rock deformation in the fully finite element analysis region, the overlapping region, and the near-field dynamic analysis region is carried out simultaneously. Figure 5 The tunnel arch and convergence values, obtained based on tunnel deformation in each region, change over time. Figure 6 This is a cloud map showing the final deformation of the tunnel.

[0126] In this embodiment, a method combining near-field dynamics and finite element analysis is adopted. Near-field dynamics, lacking a mesh, avoids mesh distortion and thus offers high accuracy for large deformation calculations, but its computational efficiency is relatively low. The finite element method is highly efficient and has mature tunnel support elements available, but it suffers from inherent limitations in large tunnel deformation calculations due to mesh constraints. By combining the strengths of both methods and introducing a creep calculation model, the relative changes in tunnel deformation over time can be better calculated, thus predicting large tunnel deformations.

[0127] This application also provides an application scenario in which the above-mentioned finite element-peripheral dynamics method for calculating large deformation of tunnels considering creep is applied. Specifically, the finite element-peripheral dynamics method for calculating large deformation of tunnels considering creep provided in this embodiment can be applied in tunnel deformation scenarios. This scenario includes a data acquisition stage, a data processing stage, and a result display stage. The data acquisition stage is used to acquire the study area of ​​the tunnel surrounding rock; the data processing stage is used to perform periphery dynamics analysis considering the creep phenomenon of the surrounding rock material on the fully finite element analysis area, the overlapping area, and the fully periphery dynamics analysis area to obtain the deformation of the tunnel surrounding rock in each area; the result display stage is used to display the deformation of the tunnel surrounding rock in each area. The finite element-peripheral dynamics method for calculating large deformation of tunnels considering creep provided in this embodiment belongs to the data processing stage.

[0128] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 7As shown, the computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The database stores tunnel deformation data. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements a finite element-near-field dynamics method for calculating large deformations of tunnels, considering creep.

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

[0130] In one exemplary embodiment, a computer device is also provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0131] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0132] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[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, data stored, data displayed, 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 the relevant data must comply with relevant regulations.

[0134] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this 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 can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0135] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0136] The technical features of the above embodiments can be combined in any way. For the sake of brevity, 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 document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A finite element-near-field dynamics method for calculating large deformations of tunnels considering creep, characterized in that, The finite element-near-field dynamics method for calculating large deformations of tunnels considering creep includes: The study area of ​​the tunnel surrounding rock is gridded, and a finite element analysis region and a near-field dynamics analysis region are determined. The near-field dynamics region is the surrounding rock area within a first preset distance away from the tunnel, starting from the tunnel outline. The starting line of the finite element analysis region is located within the near-field dynamics analysis region. The finite element analysis region is the surrounding rock area within a second preset distance away from the tunnel, starting from the corresponding starting line. The finite element analysis region includes the overlapping region between the finite element analysis region and the near-field dynamics analysis region, and the fully finite element analysis region. The near-field dynamics region includes the overlapping region and the fully finite element analysis region. The near-field dynamic particles within the near-field dynamic region are determined based on the grid within the near-field dynamic region. Finite element analysis is performed on the fully finite element analysis region to obtain the deformation of the surrounding rock of the tunnel within the fully finite element analysis region; Finite element analysis and near-field dynamic analysis were performed on the overlapping region to obtain the deformation of the tunnel surrounding rock within the overlapping region; A near-field dynamic analysis considering the creep phenomenon of the surrounding rock material is performed on the fully near-field dynamic analysis area to obtain the deformation of the tunnel surrounding rock within the fully near-field dynamic analysis area; Specifically, finite element analysis is performed on the fully finite element analysis region to obtain the deformation of the tunnel surrounding rock within the fully finite element analysis region, including: Determine the displacement and body forces acting on the finite element elements within the fully finite element analysis region at the initial time step; The displacement of the finite element in the complete finite element analysis region at the initial time step is obtained from the displacement of the finite element in the complete finite element analysis region at the nth time step; n = 1, 2, 3, ..., N; The body forces acting on the finite element elements within the complete finite element analysis region at time step n are determined based on the displacements of the finite element elements within the complete finite element analysis region at time step n. Determine whether the displacement of the finite element in the complete finite element analysis region at time step n and the body force satisfy the finite element FEM equation to obtain the first determination result; If the first judgment result is yes, then the displacement of the finite element in the fully finite element analysis area at the nth time step is regarded as the deformation of the tunnel surrounding rock in the fully finite element analysis area. If the first judgment result is negative, then determine whether the current iteration number meets the preset iteration number to obtain the second judgment result; If the second judgment result is yes, then the displacement of the finite element in the fully finite element analysis area at the nth time step is regarded as the deformation of the surrounding rock of the tunnel in the fully finite element analysis area. If the second judgment result is negative, then the displacement of the finite element in the complete finite element analysis region at the (n+1)th time step is determined based on the displacement and body force of the finite element in the complete finite element analysis region at the nth time step. The body forces acting on the finite element elements in the complete finite element analysis region at time step n+1 are determined based on the displacements of the finite element elements in the complete finite element analysis region at time step n+1. Replace the nth time step with the (n+1)th time step, and return to the step "determine whether the displacement of the finite element in the complete finite element analysis region at the nth time step and the body force satisfy the finite element FEM equation, and obtain the first judgment result"; Specifically, determining the body forces acting on the finite element elements within the complete finite element analysis region at time step n, based on the displacements of the finite element elements within that region, includes: The element force vector at time step n is determined based on the displacement of the finite element elements and the corresponding stiffness matrix of the finite element elements within the complete finite element analysis region at time step n. The global internal forces of the finite element elements within the fully finite element analysis region are determined based on the element force vector at the nth time step. The body forces acting on the finite element elements within the complete finite element analysis region at time step n are determined based on the global internal forces and external forces acting on the finite element elements within the complete finite element analysis region at time step n; the external forces acting on the finite element elements include gravity. Specifically, finite element analysis and near-field dynamic analysis are performed on the overlapping region to obtain the deformation of the tunnel surrounding rock within the overlapping region, including: Determine the displacement and body force of the finite element elements in the overlapping region at the initial time step; The displacement of the finite element in the overlapping region at the initial time step is obtained from the displacement of the finite element in the overlapping region at the nth time step; n = 1, 2, 3, ..., N; The body force on the finite element in the overlapping region at time step n is determined based on the displacement of the finite element in the overlapping region at time step n. Determine whether the displacement of the finite element element and the body force in the overlapping region at the nth time step satisfy the finite element FEM equation to obtain the third determination result; If the third judgment result is yes, then the displacement of the finite element 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 negative, then it is determined whether the current iteration number meets the preset iteration number, and a fourth judgment result is obtained; If the fourth judgment result is yes, then the displacement of the finite element 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 negative, then the displacement in the overlapping region at the (n+1)th time step is determined based on the displacement and body force of the finite element in the overlapping region at the nth time step. The body force on the finite element in the overlapping region at time step n+1 is determined based on the displacement of the finite element in the overlapping region at time step n+1. Replace the nth time step with the (n+1)th time step, and return to the step "determine whether the displacement of the finite element element and the body force in the overlapping area of ​​the nth time step satisfy the finite element FEM equation, and obtain the third judgment result"; Specifically, a near-field dynamic analysis considering the creep phenomenon of the surrounding rock material is performed on the fully near-field dynamic analysis region to obtain the deformation of the tunnel surrounding rock within the fully near-field dynamic analysis region, including: Determine the displacement and body forces acting on the near-field dynamic particles within the fully near-field dynamic analysis region at the initial time step; The displacement of the near-field dynamic particles in the fully near-field dynamic analysis region at the initial time step is obtained from the displacement of the near-field dynamic particles in the fully near-field dynamic analysis region at the nth time step; n = 1, 2, 3, ..., N; Calculate the strain of the near-field dynamic particles within the fully near-field dynamic analysis region at time step n based on the displacement of the near-field dynamic particles within the fully near-field dynamic analysis region at time step n; The stress of the near-field dynamic particles in the fully near-field dynamic analysis region at the nth time step is calculated based on the strain of the near-field dynamic particles in the fully near-field dynamic analysis region at the nth time step. Based on the stress of the near-field dynamic particles in the fully near-field dynamic analysis region described at the nth time step, it is determined whether the surrounding rock material undergoes shear or tensile yielding, and the fifth judgment result is obtained. If the fifth judgment result is yes, then the stress of the near-field dynamic particles in the complete near-field dynamic analysis region at the nth time step is updated to obtain the updated stress; If the fifth judgment result is negative, then the stress of the near-field dynamic particles in the fully near-field dynamic analysis region described in the nth time step will not be updated; Determine whether the current stress and displacement of the near-field dynamic particles within the fully near-field dynamic analysis region at time step n satisfy the motion control equation of the creep constitutive model of the surrounding rock material, and obtain the sixth judgment result; If the sixth judgment result is negative, then the body force on the near-field dynamic particle in the complete near-field dynamic analysis region at the nth time step is determined based on the displacement of the near-field dynamic particle in the complete near-field dynamic analysis region at the nth time step. Determine whether the displacement and body force of the near-field dynamic particles within the complete near-field dynamic analysis region at time step n satisfy the near-field dynamic equation of motion, and obtain the seventh determination result; If the seventh judgment result is yes, then the displacement of the near-field dynamic particles in the fully near-field dynamic analysis area at the nth time step is regarded as the deformation of the tunnel surrounding rock in the fully near-field dynamic analysis area; If the seventh judgment result is negative, then it is determined whether the current iteration number meets the preset iteration number, and the eighth judgment result is obtained; If the eighth judgment result is yes, then the displacement of the near-field dynamic particles in the fully near-field dynamic analysis area at the nth time step is regarded as the deformation of the tunnel surrounding rock in the fully near-field dynamic analysis area; If the eighth judgment result is negative, then the displacement of the near-field dynamic particles in the complete near-field dynamic analysis region at the n+1 time step is determined based on the displacement and body force of the near-field dynamic particles in the complete near-field dynamic analysis region at the nth time step. The body forces acting on the near-field dynamic particles within the fully near-field dynamic analysis region at time step n+1 are determined based on the displacement of the near-field dynamic particles within the fully near-field dynamic analysis region at time step n+1. Replace the nth time step with the (n+1)th time step, and return to the step "Determine whether the displacement of the near-field dynamic particle in the complete near-field dynamic analysis region at the nth time step and the body force judgment satisfy the near-field dynamic equation of motion, and obtain the seventh judgment result".

2. The finite element-near-field dynamics tunnel large deformation calculation method considering creep according to claim 1, characterized in that, The formula for calculating the displacement of the finite element in the complete finite element analysis region at time step n+1 is: in, In the formula, U n+1 This represents the displacement of the finite element within the fully finite element analysis region at time step (n+1). U n This represents the displacement of the finite element within the fully finite element analysis region at time step n; Indicates the first The first derivative of the displacement of the finite element within the time-step fully finite element analysis region; c n This represents the damping coefficient of the finite element within the fully finite element analysis region at time step n; Indicates the first The first derivative of the displacement of the finite element within the time-step fully finite element analysis region; F n The body forces of finite element elements within the fully finite element analysis region at time step n; M represents the diagonal mass matrix.

3. The finite element-near-field dynamics tunnel large deformation calculation method considering creep according to claim 1, characterized in that, The body forces acting on the finite element elements in the overlapping region at time step (n+1) are determined based on the displacements of the finite element elements in the overlapping region at time step (n+1), specifically including: The displacement of the near-field dynamic particles within the finite element elements in the overlapping region at time step n+1 is determined based on the displacement of the finite element elements in the overlapping region at time step n+1. Calculate the body forces of each near-field dynamic particle in the finite element element within the overlapping region at time step n+1 based on the displacement of the near-field dynamic particles in the finite element element within the overlapping region at time step n+1. The body force of each near-field dynamic particle in the finite element element within the overlapping region at time step n+1 determines the total force of each near-field dynamic particle in the finite element element within the overlapping region at time step n+1. The total force of each near-field dynamic particle in the finite element element within the overlapping region at time step n+1 is converted to the node of the corresponding finite element element, thus obtaining the body force of each node in the finite element element within the overlapping region at time step n+1. The body forces of each node in the finite element element within the overlapping region at time step n+1 are superimposed to obtain the body forces acting on the finite element element within the overlapping region at time step n+1.

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