Railway tunnel fracture zone rock mass random field simulation method, medium and equipment

Abstract

The present application relates to the technical field of geotechnical engineering, in particular to a railway tunnel fracture zone rock mass random field simulation method, medium and equipment. The method comprises: dividing the railway tunnel fracture zone rock mass space into grids; interpolating through the nodes in the grid; artificially reducing the dimension of the three-dimensional random field covariance structure of the rock mass; introducing the Galerkin method to solve the characteristic vector and characteristic value of K-L expansion; solving the truncation term number of K-L expansion; generating a random field sample according to the characteristic vector, characteristic value and truncation term number of K-L expansion. The present application method establishes a railway tunnel fracture zone rock mass grid that meets the finite element mechanics simulation, combines the finite element weak form integral equation solving method of the Galerkin method, realizes efficient and accurate simulation of the parameter random field of the railway tunnel fracture zone rock mass under the condition of spatial variation of the parameters, and the method can be used to process complex rock mass geometric conditions, and has strong practical significance in engineering.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering technology, specifically to a method, medium, and equipment for simulating random fields of rock mass in fault zones of railway tunnels. Background Technology

[0002] When constructing high-speed railways with speeds exceeding 200 km / h in some regions, the railway and its foundation structure not only need to overcome the harsh conditions of high-altitude and frigid climates but also require strong resilience to complex geological conditions. Furthermore, due to the complex geological conditions, predominantly mountainous terrain, and location in earthquake zones, railway foundation structures are often presented in the form of tunnels. However, many active fault zones exist in the surrounding rock mass of these tunnels, thus affecting the safety of railway tunnels during construction and operation. To simulate the mechanical and deformation states of tunnel structures under complex fault zone conditions, it is necessary to develop geological uncertainty quantification analysis techniques applicable to railway tunnel fault zone areas.

[0003] In numerical simulations of random fields in geotechnical engineering, the traditional Monte Carlo method suffers from low simulation efficiency due to its high computational resource requirements, making it unsuitable for simulating random fields in rock masses within tunnel fault zones. Furthermore, the Monte Carlo method struggles to handle complex geological conditions, particularly the intricate geometry of fault zones, where determining node distribution and local refinement is a tedious process. Similarly, Fourier transform-based random field generation methods require prior knowledge of the power spectral density function of the random field, and the mesh generation typically necessitates uniform meshing, failing to address irregular boundaries. Currently, the Karl von Leffs (KL) expansion method is widely used in simulating random fields in rock masses and has significant application value. However, solving the second-kind Ferdholm integral equation is a key challenge in applying KL expansion to random field simulations of rock masses in railway tunnel fault zones. Due to complex geometric boundaries, eigenvalue problems cannot utilize uniform meshing, thus preventing direct construction of the covariance matrix for eigenvalue calculations. Moreover, the finite difference method for solving the second-kind Ferdholm integral equation suffers from accuracy limitations imposed by mesh generation and low processing efficiency, requiring iterative computation.

[0004] Therefore, the current solutions for random field simulation of rock masses in fault zones have the following difficulties: 1) The geometric boundaries between fault zones and non-fault zones make it difficult to uniformly divide the mesh; 2) For three-dimensional random field problems, the efficiency of random fields is limited; 3) Solving the second-kind Ferdholm integral equation using KL expansion is quite difficult.

[0005] In summary, there is an urgent need for a random field simulation method for rock mass in fault zones of railway tunnels to address the problems existing in current technologies. Summary of the Invention

[0006] The purpose of this invention is to provide a method, medium, and equipment for simulating random fields of rock mass in fault zones of railway tunnels. The specific technical solution is as follows: A random field simulation method for rock mass in a fault zone of a railway tunnel includes the following steps: S1: Grid division of the rock mass space in the fault zone of the railway tunnel; S2: Interpolate the nodes within the grid of the rock mass space in the fault zone of the railway tunnel using an interpolation function; S3: Artificial dimensionality reduction is performed on the three-dimensional random field covariance structure of the rock mass to obtain the covariance matrix after artificial dimensionality reduction; S4: Introduce Galerkin's method to perform KL expansion and solve for the eigenvectors and eigenvalues ​​of the covariance matrix after artificial dimensionality reduction; S5: Calculate the number of truncated terms in the KL expansion with a predetermined accuracy, used to truncate the KL expansion terms; S6: Generate random field samples with predetermined precision based on the eigenvectors and eigenvalues ​​of the covariance matrix and the number of truncated terms in the KL expansion.

[0007] Preferably, S1 specifically includes: To construct the spatial boundary of the rock mass required for mechanical simulation of the fault zone in a railway tunnel, specifically, to establish the outer boundary region of the rock mass within an area 8-10 times the tunnel diameter. ; Establish internal boundaries based on tunnel diameter. ; Delineate the outer boundary area and internal boundaries The grid between; and The grid within uses a close proximity Small and close Divide into major strategies.

[0008] Preferably, S2 specifically includes: The covariance function of the spatial elements in the rock mass of the railway tunnel fault zone is interpolated using an 8-node isoparametric element interpolation function. The expression of this interpolation function is as follows: ; In the formula, For the interpolation function vector, , and They are respectively , and Local coordinates of direction, Number the isoparametric element nodes. =1, 2, 3…8, For nodes The shape function, parameters , and The value of is calculated using the following formula: .

[0009] Preferably, S3 specifically includes: The three-dimensional random field covariance structure of the rock mass can be written in the following form: ; In the formula, It is a generalized continuous covariance function. For the spatial dimension variable of the random field, , To extend the spatial dimension of a random field, ,but For a three-dimensional random field, the covariance function is a continuous function with an extended dimension. Using the grid of the rock mass space in the railway tunnel fault zone established in S1, the three-dimensional random field covariance function is discretized, and the expression is as follows: ; In the formula, For three-dimensional continuous random fields discrete form, and All coordinates are discretized node coordinates, and the mesh size is uniform: , and ; Discretized three-dimensional random field covariance matrix using degree-of-freedom rearrangement The covariance matrix is ​​rearranged to obtain the artificially reduced dimensionality covariance matrix. The expression is as follows: ; In the formula, and These are the dimension-reduced coupled coordinate system and the extended coupled coordinate system, respectively. For the covariance matrix in The number of elements in the direction; For the covariance matrix in The number of elements in the direction; Covariance matrix Direction One element; For the covariance matrix in Direction One element; For the covariance matrix in Direction One element; For the covariance matrix in Direction Each element.

[0010] Preferably, S4 specifically includes: The covariance matrix after manual dimensionality reduction We integrate the second kind of Ferdholm integral equation, which is expressed as follows: ; In the formula, For the domain of the unit, = For characteristic function, For eigenvalues; The interpolation function described in S2 is used to discretize the second kind of Ferdholm integral equation, as shown in the following expression: ; In the formula, For unit nodes The function value is used to establish a weak form of the second kind of Ferdholm integral equation using the Galerkin method, as shown below: ; In the formula, For global characteristic functions, The nodal characteristic function value of the current integrand. The nodal shape function of the current integrand; The node number of the current integrand; For model unit indexing, This represents the total number of units in the model. Based on the above equation, we can obtain two sub-equations of the eigenvalue equation. and ,as follows: , ; In the formula, Indexed by row number; Based on the combination of degrees of freedom, the weak form of the second kind of Ferdholm integral equation is assembled into an algebraic equation, as follows: ; The algebraic equation was solved using the eigs function in MATLAB to obtain the eigenvalues. and eigenvectors .

[0011] Preferably, S5 specifically includes: The precision of the number of terms in the KL expansion is determined by the following formula: ; In the formula, It is positive infinity; The index for the number of truncated items. Number of truncated terms Corresponding precision; For accuracy The number of truncated terms in the KL expansion when it reaches 95% or higher.

[0012] Preferably, the following formula is used to generate a product with... High-precision random field samples: ; In the formula, These are simulated samples of a random field; Let be the mean of the random field. Refers to random variables. To be related to random field variables Related independent random variables, satisfying , , for The index of the number of truncated items, For the Kronecker product, when hour, =1, otherwise when , , For the first 1 eigenvector Let be the mathematical expectation.

[0013] The present invention also provides a readable storage medium storing computer program instructions, which, when executed by a processor, implement the random field simulation method for rock mass in fault zones of railway tunnels as described above.

[0014] The present invention also provides an electronic device, comprising: at least one processor, at least one memory, and computer program instructions stored in the memory, wherein the computer program instructions are executed by the processor to perform the random field simulation method for rock mass in fault zone of railway tunnel as described above.

[0015] The application of the technical solution of the present invention has the following beneficial effects: A random field simulation method for rock mass in a railway tunnel fault zone includes the following steps: S1: dividing the space of the rock mass in the railway tunnel fault zone into a grid; S2: interpolating the nodes within the grid of the rock mass space in the railway tunnel fault zone using an interpolation function; S3: artificially reducing the dimensionality of the three-dimensional random field covariance structure of the rock mass to obtain the artificially reduced covariance matrix; S4: introducing the Galerkin method to perform KL expansion and solving for the eigenvectors and eigenvalues ​​of the artificially reduced covariance matrix; S5: solving for the number of truncated terms in the KL expansion at a predetermined accuracy, used to truncate the KL expansion terms; S6: generating random field samples with a predetermined accuracy based on the eigenvectors and eigenvalues ​​of the covariance matrix and the number of truncated terms in the KL expansion. The method of this invention establishes a rock mass mesh in the fault zone of a railway tunnel that satisfies the requirements of finite element mechanical simulation. Combined with the solution method of the weak form integral equation of the finite element method based on Galerkin's method, it realizes efficient and accurate simulation of the parametric random field under the spatial variation of rock mass parameters in the fault zone of a railway tunnel. It has strong reliability and can be used to deal with complex rock mass geometry conditions, which has strong practical engineering significance.

[0016] In addition to the objectives, features, and advantages described above, the present invention has other objectives, features, and advantages. The invention will now be described in further detail with reference to the figures. Attached Figure Description

[0017] The accompanying drawings, which form part of this application, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a flowchart illustrating a random field simulation method for rock mass in a fault zone of a railway tunnel according to an embodiment of the present invention. Figure 2 The grid shown in this example is the mesh after dividing the rock mass space in the fault zone of the railway tunnel into grids. Figure 3(a) shows the first-order eigenvector of the covariance matrix in the embodiment; Figure 3(b) shows the second-order eigenvector of the covariance matrix in the embodiment; Figure 3(c) shows the third-order eigenvector of the covariance matrix in the embodiment; and Figure 3(d) shows the eigenvalues ​​of the covariance matrix after KL expansion in the embodiment. Figure 4 For the example along with A diagram illustrating the changes; Figure 5 This is a schematic diagram illustrating the correlation of the KL expansion coefficients in the embodiment; Figure 6(a) is a schematic diagram of the yz plane view of the first sample of the final rock mass elastic modulus random field in the embodiment, and Figure 6(b) is a schematic diagram of the xz plane view of the final rock mass elastic modulus random field in the embodiment. Figure 7(a) is a schematic diagram of the yz plane view of the 100th sample of the final rock mass elastic modulus random field in the embodiment, and Figure 7(b) is a schematic diagram of the xz plane view of the 100th sample of the final rock mass elastic modulus random field in the embodiment. Figure 8(a) is a schematic diagram comparing the simulated value and the theoretical value of the mean of the random field in the embodiment, and Figure 8(b) is a schematic diagram comparing the simulated value and the theoretical value of the standard deviation of the random field in the embodiment. Detailed Implementation

[0018] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings. However, the present invention can be implemented in many different ways as defined and covered by the claims.

[0019] In one embodiment, see Figure 1 A random field simulation method for rock mass in fault zones of railway tunnels includes the following steps: S1: The rock mass space in the fault zone of the railway tunnel is divided into grids, specifically including: To construct the spatial boundary of the rock mass required for mechanical simulation of the fault zone in a railway tunnel, specifically, to establish the outer boundary region of the rock mass within a range of 8-10 times the tunnel diameter. ;like Figure 2 As shown, in this embodiment, the tunnel diameter is 10m (outer diameter) and 9m (inner diameter). Therefore, the required length, width, and height of the rock mass spatial boundary are set to 200m (x-direction), 100m (y-direction), and 80m (z-direction), which meets the requirement of 8-10 times. The rock mass shape is as follows. Figure 2 As shown.

[0020] Establish internal boundaries based on tunnel diameter. ; Delineate the outer boundary area and internal boundaries The mesh between them; specifically, commercial software ABAQUS can be used to automatically generate the mesh; and The grid within uses a close proximity Small and close The main strategy is to divide the data into smaller, more manageable sections. The resulting grid is as follows: Figure 2As shown, the internal fault zone (green area) has a denser mesh, while the external rock mass increases in size with distance. The node coordinates of this model can be extracted using the following method: A script for the commercial finite element software ABAQUS is written in Python. In different working conditions calculated by ABAQUS, the nodes of the tunnel outer wall are set as a set. The Python script extracts the node numbers, node coordinates, and node displacements from the node set and generates a txt file. The extracted txt file is then rearranged using MATLAB to create a node information file arranged along the longitudinal direction of the tunnel, which is used for random field simulation.

[0021] S2: Interpolating the nodes within the grid of the rock mass space in the fault zone of the railway tunnel using an interpolation function, specifically including: The covariance function of the spatial elements in the rock mass of the railway tunnel fault zone is interpolated using an 8-node isoparametric element interpolation function. Alternatively, Lagrange interpolation, Hermite interpolation, linear interpolation, etc., can be used as needed. The expression for this interpolation function is as follows: ; In the formula, For the interpolation function vector, , and They are respectively , and Local coordinates of direction, Number the isoparametric element nodes. =1, 2, 3…8, For nodes The shape function, parameters , and The value of is calculated using the following formula: .

[0022] S3: Artificial dimensionality reduction is performed on the three-dimensional random field covariance structure of the rock mass to obtain the artificially reduced covariance matrix, which specifically includes: The three-dimensional random field covariance structure of the rock mass can be written in the following form: ; Taking the basic exponential covariance structure as an example, based on the fundamental definition of stochastic processes, the three-dimensional stochastic field covariance structure of the rock mass can be written in the following form: ; In the formula, It is a generalized continuous covariance function. For the spatial dimension variable of the random field, , To extend the spatial dimension of a random field, ,but Let be the extended-dimensional continuous covariance function of a three-dimensional random field; since the covariance function involves a tensor product of functions, it is a 6-dimensional function, with the dimensional variables being respectively... and ;parameter , and They are , and The relevant distances in the direction are taken as 40m, 20m, and 20m in this embodiment; and To represent the covariance of the random field, in this embodiment, the random variable is a log-Gaussian random variable, which can be used in the simulation. To simulate a random field after logarithmic processing The standard deviation is given by , where cov = 0.1 is the coefficient of variation. The mean of the random field is 1000 MPa for the rock mass elastic modulus and 200 MPa for the fault zone elastic modulus; therefore, the equations are 100 MPa and 20 MPa respectively.

[0023] Using the grid of the rock mass space in the railway tunnel fault zone established in S1, the three-dimensional random field covariance function is discretized, and the expression is as follows: ; In the formula, For three-dimensional continuous random fields discrete form, and All coordinates are discretized node coordinates, and the mesh size is uniform: , and ; Discretized three-dimensional random field covariance matrix using degree-of-freedom rearrangement The covariance matrix is ​​rearranged to obtain the artificially reduced dimensionality covariance matrix. The expression is as follows: ; In the formula, and These are the dimension-reduced coupled coordinate system and the extended coupled coordinate system, respectively. For the covariance matrix in The number of elements in the direction; For the covariance matrix in The number of elements in the direction; Covariance matrix Direction One element; For the covariance matrix in Direction One element; For the covariance matrix in Direction One element; For the covariance matrix in Direction Each element.

[0024] S4: Introduce the Galerkin method for KL expansion to solve for the eigenvectors and eigenvalues ​​of the covariance matrix after artificial dimensionality reduction. Specifically, this includes: The covariance matrix after manual dimensionality reduction We integrate the second kind of Ferdholm integral equation, which is expressed as follows: ; In the formula, For the domain of the unit, = For characteristic function, For eigenvalues; The interpolation function described in S2 is used to discretize the second kind of Ferdholm integral equation, as shown in the following expression: ; In the formula, For unit nodes The function value is used to establish a weak form of the second kind of Ferdholm integral equation using the Galerkin method, as shown below: ; In the formula, For global characteristic functions, The nodal characteristic function value of the current integrand. The nodal shape function of the current integrand; The node number of the current integrand; For model unit indexing, This represents the total number of units in the model. Based on the above equation, we can obtain two sub-equations of the eigenvalue equation. and ,as follows: , ; In the formula, Indexed by row number; The integral of the function can be calculated using a 6th-order Gaussian integral, with Gaussian points at [-0.7745966692 0 0.7745966692] and weights at [0.5555555556 0.8888888889 0.5555555556].

[0025] Based on the combination of degrees of freedom, the weak form of the second kind of Ferdholm integral equation is assembled into an algebraic equation, as follows: ; The algebraic equation was solved using the eigs function in MATLAB to obtain the eigenvalues. and eigenvectors Specifically, the code in MATLAB [ , ]=eigs( , By using the formula (500, 'largestreal', 'Tolerance', 1e-9), we can obtain the first 500 eigenvectors and eigenvalues. The obtained eigenvectors and eigenvalues ​​are shown in Figures 3(a) to 3(d), where Figure 3(a) shows the first-order eigenvectors, Figure 3(b) shows the second-order eigenvectors, Figure 3(c) shows the third-order eigenvectors, and Figure 3(d) shows the eigenvalues ​​after KL expansion.

[0026] S5: Calculates the number of truncation terms in the KL expansion at a predetermined precision, used to truncate the KL expansion terms, specifically including: The precision of the number of terms in the KL expansion is determined by the following formula: ; In the formula, It is positive infinity; The index for the number of truncated items. Number of truncated terms Corresponding precision; For accuracy The number of truncation terms in the KL expansion when it reaches 95% or higher. It can be seen that the first 400 terms are taken ( =400) The accuracy of the eigenvalues ​​is sufficient for the numerical simulation in this embodiment.

[0027] S6: Based on the eigenvectors and eigenvalues ​​of the covariance matrix, and the number of truncated terms in the KL expansion, generate the following formula: High-precision random field samples: ; In the formula, These are simulated samples of a random field; Let be the mean of the random field. Refers to random variables. To be related to random field variables Related independent random variables, satisfying , , for The index of the number of truncated items, For the Kronecker product, when hour, =1, otherwise when , , For the first 1 eigenvector Let be the mathematical expectation.

[0028] The first 400 KL expansion coefficients were generated using the Latin hypercube sampling method. 1000 unrelated samples, satisfying , Its correlation is as follows Figure 5 As shown.

[0029] The above formula can be used to generate samples that satisfy the target covariance structure. For a log-normal distribution, the final random field sample of rock mass elastic modulus can be directly calculated using the exp function in MATLAB. As shown in Figures 6(a) to 7(b), where Figure 6(a) is the yz plane view of the first sample of the random field, Figure 6(b) is the xz plane view of the first sample of the random field, Figure 7(a) is the yz plane view of the 100th sample of the random field, and Figure 7(b) is the xz plane view of the 100th sample of the random field.

[0030] For the simulated random field The sample mean and standard deviation were calculated and compared with the theoretical values, as shown in Figures 8(a) and 8(b). In Figure 8(a), the vertical axis E represents the mean of the random field, and in Figure 8(b), the vertical axis std represents the standard deviation of the random field. The comparison results show that the random field simulation method for rock mass in the fault zone of a railway tunnel proposed in this embodiment has high accuracy. In particular, by closely integrating S1, S2, and S3, the numerical solution of the random field covariance structure integral eigenvalue problem in step S4 is achieved. Furthermore, the dimensionality of the random variables in the random field simulation of the rock mass structure surrounding the fault zone of the tunnel is further reduced by truncating the series terms in step S5, ultimately achieving accurate and efficient simulation of random field samples of rock mass parameters in the fault zone of a railway tunnel. This numerical method for simulating random fields of rock masses in fault zones of railway tunnels establishes a weak finite element form for solving the covariance structure of the random field using the Galerkin method. While meeting accuracy requirements, it can simulate complex rock mass types, such as the dip angle and width of fault zones, and exhibits high robustness. This method meets the needs of structural mechanical analysis, simulation, and reliability assessment for railway tunnels constructed in fault zones in western my country and has high application prospects.

[0031] This embodiment also includes a readable storage medium storing computer program instructions, which, when executed by a processor, implement the random field simulation method for rock mass in the fault zone of a railway tunnel as described above.

[0032] For example, the computer program may be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the present invention. The one or more modules / units may be a series of computer program instruction segments capable of performing a specific function, which describe the execution process of the computer program in the electronic device.

[0033] This embodiment also includes an electronic device, comprising: at least one processor, at least one memory, and computer program instructions stored in the memory, wherein the computer program instructions are executed by the processor to perform the random field simulation method for rock mass in the fault zone of a railway tunnel as described above.

[0034] The electronic device can be a mobile phone, desktop computer, laptop, handheld computer, cloud server, or other computing device. The electronic device may include, but is not limited to, processors and memory. For example, the electronic device may also include input / output devices, network access devices, buses, etc.

[0035] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A random field simulation method for rock mass in fault zones of railway tunnels, characterized in that, Includes the following steps: S1: Grid division of the rock mass space in the fault zone of the railway tunnel; S1 specifically includes: To construct the spatial boundary of the rock mass required for mechanical simulation of the fault zone in a railway tunnel, specifically, to establish the outer boundary region of the rock mass within an area 8-10 times the tunnel diameter. ; Establish internal boundaries based on tunnel diameter. ; Delineate the outer boundary area and internal boundaries The grid between; and The grid within uses a close proximity Small and close Divide into major strategies; S2: Interpolate the nodes within the grid of the rock mass space in the fault zone of the railway tunnel using an interpolation function; S2 specifically includes: The covariance function of the spatial elements in the rock mass of the railway tunnel fault zone is interpolated using an 8-node isoparametric element interpolation function. The expression of this interpolation function is as follows: ； In the formula, For the interpolation function vector, , and They are respectively , and Local coordinates of direction, Number the isoparametric element nodes. =1, 2, 3…8, For nodes The shape function, parameters , and The value of is calculated using the following formula: ； S3: Artificial dimensionality reduction is performed on the three-dimensional random field covariance structure of the rock mass to obtain the covariance matrix after artificial dimensionality reduction; S4: Introduce Galerkin's method to perform KL expansion and solve for the eigenvectors and eigenvalues ​​of the covariance matrix after artificial dimensionality reduction; S5: Calculate the number of truncated terms in the KL expansion with a predetermined accuracy, used to truncate the KL expansion terms; S4 specifically includes: The covariance matrix after manual dimensionality reduction We integrate the second kind of Ferdholm integral equation, which is expressed as follows: ； In the formula, For the domain of the unit, = For characteristic function, For eigenvalues; The interpolation function described in S2 is used to discretize the second kind of Ferdholm integral equation, as shown in the following expression: ； In the formula, For unit nodes The function value is used to establish a weak form of the second kind of Ferdholm integral equation using the Galerkin method, as shown below: ； In the formula, For global characteristic functions, The nodal characteristic function value of the current integrand. The nodal shape function of the current integrand; The node number of the current integrand; For model unit indexing, M This represents the total number of units in the model. Based on the above equation, we can obtain two sub-equations of the eigenvalue equation. and ,as follows: ， ； Based on the combination of degrees of freedom, the weak form of the second kind of Ferdholm integral equation is assembled into an algebraic equation, as follows: ； The algebraic equation was solved using the eigs function in MATLAB to obtain the eigenvalues. and eigenvectors ; S6: Generate random field samples with predetermined precision based on the eigenvectors and eigenvalues ​​of the covariance matrix and the number of truncated terms in the KL expansion.

2. The random field simulation method for rock mass in a fault zone of a railway tunnel according to claim 1, characterized in that, S3 specifically includes: The three-dimensional random field covariance structure of the rock mass can be written in the following form: ； In the formula, It is a generalized continuous covariance function. For the spatial dimension variable of the random field, , To extend the spatial dimension of a random field, ,but For a three-dimensional random field, the covariance function is a continuous function with an extended dimension. Using the grid of the rock mass space in the railway tunnel fault zone established in S1, the three-dimensional random field covariance function is discretized, and the expression is as follows: ； In the formula, For three-dimensional continuous random fields discrete form, and All coordinates are discretized node coordinates, and the mesh size is uniform: , and ; Discretized three-dimensional random field covariance matrix using degree-of-freedom rearrangement The covariance matrix is ​​rearranged to obtain the artificially reduced dimensionality covariance matrix. The expression is as follows: ； In the formula, and These are the dimension-reduced coupled coordinate system and the extended coupled coordinate system, respectively. For the covariance matrix in The number of elements in the direction; For the covariance matrix in The number of elements in the direction; Covariance matrix Direction One element; For the covariance matrix in Direction One element; For the covariance matrix in Direction One element; For the covariance matrix in Direction Each element.

3. The random field simulation method for rock mass in a fault zone of a railway tunnel according to claim 1, characterized in that, S5 specifically includes: The precision of the number of terms in the KL expansion is determined by the following formula: ； In the formula, It is positive infinity; The index for the number of truncated items. Number of truncated terms Corresponding precision; For accuracy The number of truncated terms in the KL expansion when it reaches 95% or higher.

4. The random field simulation method for rock mass in a fault zone of a railway tunnel according to claim 3, characterized in that, Generate by the following formula High-precision random field samples: ； In the formula, These are simulated samples of a random field; Let be the mean of the random field. Refers to random variables. To be related to random field variables Related independent random variables, satisfying , , and All are indexes of the number of truncated items. For the Kronecker product, when hour, =1, otherwise when , , For the first 1 eigenvector Let be the mathematical expectation.

5. A readable storage medium, characterized in that, It stores computer program instructions, which, when executed by a processor, implement the random field simulation method for rock mass in the fault zone of a railway tunnel as described in any one of claims 1 to 4.

6. An electronic device, characterized in that, include: At least one processor, at least one memory, and computer program instructions stored in the memory, wherein the computer program instructions are executed by the processor according to any one of claims 1 to 4, a random field simulation method for rock mass in fault zones of railway tunnels.

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