Seismic landslide large deformation analysis method considering spatial variability

Abstract

The invention discloses a seismic landslide large deformation analysis method considering spatial variability, and belongs to the technical field of geotechnical engineering large deformation problem numerical simulation. The method comprises the following steps: firstly, constructing a material point analysis model with spatial variability based on a geometric model of a landslide area and random field statistical characteristics of mechanical parameters of a soil body; secondly, carrying out static analysis on the landslide mass under the action of a self-weight load to obtain a static balance stress field of each material point; and finally, taking the static balance stress field as an initial stress field, carrying out dynamic analysis under the action of self weight and earthquake load to obtain a landslide mass deformation result, and completing earthquake landslide large deformation analysis considering spatial variability. On the basis of a material point method, the spatial variability of soil body parameters is represented based on a random field theory, accurate simulation of the seismic load is realized by combining a two-stage solving strategy, the landslide evolution process of the soil body with the spatial variability under the action of an earthquake is reasonably described, and the seismic load simulation accuracy is improved. And an effective technical support is provided for research on the problem of large deformation of the soil body considering spatial variability.

Description

Technical Field

[0001] This invention belongs to the field of numerical simulation technology for large deformation problems in geotechnical engineering, and relates to a method for analyzing large deformation of earthquake landslides that considers spatial variability. Background Technology

[0002] In the field of geotechnical engineering, slopes are prone to large-deformation and damage disasters such as collapses and landslides under the action of their own weight and earthquake loads. These disasters not only directly threaten people's lives and property, but also cause serious damage to infrastructure such as transportation and buildings, posing huge hidden dangers to engineering construction and operation. Earthquake landslide disasters are characterized by their wide distribution, large scale of damage, and severe impact, making effective numerical simulation of earthquake landslides of significant engineering importance.

[0003] Mesh-based numerical simulation methods face significant technical bottlenecks when dealing with large soil deformation problems. Taking the finite element method (FEM) as an example, its simulation accuracy is highly dependent on mesh quality. During large soil deformation, mesh distortion and element degradation are prone to occur, leading to difficulties in computational convergence, reduced computational efficiency, and an inability to accurately reflect the true stress distribution and complete failure evolution process of the soil. The material point method, developed in recent years, utilizes material points to carry field variable information and solves governing equations on a background mesh. Through bidirectional information mapping between material points and the background mesh, it effectively avoids problems such as mesh distortion, giving it a natural advantage in large deformation analysis.

[0004] However, there are still some shortcomings in applying the material point method to landslide research. On the one hand, in parameter characterization, existing methods often ignore the inherent spatial variability of soil, that is, they use single and deterministic mechanical parameters for simulation. In fact, as a typical granular material, soil exhibits significant spatial variability in its physical and mechanical parameters, directly affecting the stress-deformation characteristics and failure evolution of the soil. On the other hand, in seismic load simulation, effectively applying seismic loads remains challenging. For example, Chinese invention patent CN202410796809.3 discloses a nonlocal simulation analysis method for earthquake-triggered landslides. This method uses nonlocal material point interactions to solve large deformation problems and embeds transmission and fixed boundaries into the model, improving computational stability and accuracy and facilitating the handling of complex terrain boundaries. However, it does not consider the spatial variability of soil parameters, resulting in deviations from actual conditions. For example, Chinese invention patent CN202510467564.4 discloses a landslide risk assessment method that considers the three-dimensional spatial variability of slag and soil. This method uses the limit equilibrium method to assess stability and estimate landslide volume, and can simulate the migration range under different landslide volume conditions. However, its analysis conditions are mainly limited to the effect of self-weight and do not consider the influence of seismic loads.

[0005] Therefore, it is necessary to propose a large deformation analysis method for earthquake landslides that considers spatial variability, which can effectively simulate the process of landslides under earthquake loading, taking into account the spatial variability of soil. Summary of the Invention

[0006] This invention addresses the challenge of existing numerical methods simultaneously representing the spatial variability of soil parameters and effectively simulating the large deformation process of earthquake-induced landslides within the same framework. It proposes an analytical method based on the material point method, specifically a method for analyzing the large deformation of earthquake-induced landslides that considers spatial variability. This invention employs random field theory to characterize the spatial variability of soil parameters and uses a two-stage solution strategy to achieve accurate simulation of seismic loads, thereby reasonably depicting the landslide evolution process of spatially variable soil under seismic loading. This invention provides effective technical support for simulating and subsequently numerically calculating large deformation problems of soils considering spatial variability.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for analyzing large deformations of earthquake-induced landslides that considers spatial variability, the method comprising the following steps: S1, based on the geometric model of the landslide area and the stochastic field statistical characteristics of soil mechanical parameters, constructs a spatially variable material point analysis model, specifically: S1.1, Based on the geometric model of the landslide, construct the material point model of the landslide; S1.2, Based on geological survey data, determine the statistical characteristics of soil mechanical parameters, including mean, coefficient of variation and fluctuation range; S1.3 Extract the three-dimensional spatial coordinates of all material points from the landslide material point model; S1.4 Based on the three-dimensional spatial coordinates of each material point, calculate the distance between any two material points, and use the correlation function to determine the correlation coefficient between any two material points in order to construct the covariance matrix between material points; The correlation function can be of single exponential, quadratic exponential, or cosine exponential type. S1.5 uses the covariance matrix decomposition method to generate a random field of mechanical parameters at the location of each material point, and assigns the generated mechanical parameter values ​​to the corresponding material points, thereby constructing a material point analysis model with spatial variability.

[0008] S2, based on the spatially variable material point analysis model constructed from S1, performs static analysis of the landslide body under self-weight load, obtaining the static equilibrium stress field of each material point, specifically: S2.1, Read the information required for static analysis, including material point information, background mesh information, load information and calculation parameters; The material point information includes the material point coordinates, mass, constitutive model, and mechanical parameter values ​​considering spatial variability; the background mesh information includes the background mesh range and background mesh size; the load information includes the self-weight load; and the calculation parameters include the calculation time step and the total number of calculation steps. S2.2, within each time step, the material point information is mapped to the background grid, the control equations on the background grid are established and solved, and the acceleration vector and the updated momentum vector of the background grid nodes are obtained; Determine the background grid where the material point is located, and map the mass and momentum of each material point to the corresponding background grid node, as shown in formula (1): (1) In the formula, , These represent the background mesh nodes. I The mass vector and momentum vector; , Representing material points respectively p mass vector and momentum vector p Indicates the first p One material point; n p Indicates the total number of material points within the background grid; subscript t Indicates the first t Time step; The mapping function from material points to background mesh nodes; Then, the nodal forces of the background mesh nodes are calculated according to formula (2): (2) In the formula: , These represent the background mesh nodes. I The internal force vector and the external force vector; This represents the partial derivative of the mapping function; p Indicates the first p One material point; , Represented as matter points p The stress tensor and density; , Representing material points respectively p Gravitational acceleration and seismic acceleration, where seismic acceleration exists only in dynamic analysis; subscript Indicates the first Time step; Finally, the governing equations on the background mesh are established and solved according to formula (3) to obtain the acceleration vector and the updated momentum vector of the background mesh nodes: (3) In the formula: , , These represent the background mesh nodes. I exist i The acceleration vector in the direction, the momentum vector before the update, and the momentum vector after the update; Indicates the time step; subscript Indicates the first Time step; S2.3, based on the solution results on the background mesh, update the position and momentum information of the material points, and update the stress of each material point in combination with the material constitutive model, and output the stress of each material point corresponding to this time step; According to formula (4), the solution results on the background mesh nodes are mapped back to the material points to update the position and momentum of the material points; (4) In the formula, , Representing material points respectively p The position vector and acceleration vector; , These represent the background mesh nodes. I The mass vector and the updated momentum vector, with subscripts I Indicates the first I One background grid node, Indicates the total number of background grid nodes; Indicates the time step, subscript t Indicates the first t Time step, subscript t+ 1 indicates the first t+ 1 time step; Based on the nodal momentum updated in S2.2, the strain increment and spinor increment of the material point are calculated according to formulas (5) and (6). The stress of the material point is updated according to the constitutive model of the material point, and the stress of each material point corresponding to the time step is output. (5) (6) In the formula, , Representing material points respectively p The strain increment and spinor increment; , Representing nodes respectively I exist i direction, j The momentum vector updated in the direction; Indicates the time step, subscript t Indicates the first t Time step; , They respectively represent the mapping function in i direction, j Partial derivatives in direction; subscript I Indicates the first I One background grid node, Indicates the total number of background grid nodes; S2.4, repeat S2.2 and S2.3 until all calculation steps of the static analysis are completed, and obtain the stress at the material point corresponding to the last time step, which is the static equilibrium stress field of each material point.

[0009] S3 uses the static equilibrium stress field obtained in S2 as the initial stress field. Dynamic analysis is carried out under the combined action of self-weight and seismic load to obtain the deformation results of the landslide body, and then completes the large deformation analysis of the seismic landslide considering spatial variability. S3.1 Reads the information required for dynamic analysis, including material point information, background mesh information, load information, and calculation parameters; The material point information includes the material point coordinates, initial stress, mass, constitutive model and mechanical parameter values ​​considering spatial variability; the background mesh information includes the background mesh range and background mesh size; the load information includes self-weight load and seismic load; and the calculation parameters include the calculation time step and the total number of calculation steps. S3.2, within each time step, the material point information is mapped to the background grid, the control equations on the background grid are established and solved, and the acceleration vector and the updated momentum vector of the background grid nodes are obtained. According to formula (1), determine the background grid where the material point is located, and map the mass and momentum of each material point to the background grid node where it is located; Calculate the nodal forces of the background mesh nodes according to formula (2); The control equations on the background grid are established and solved according to formula (3) to obtain the acceleration vector and the updated momentum vector of the background grid nodes. S3.3, based on the solution results on the background mesh, update the position and momentum information of the material points, output the position information of each material point at this time step, and update the stress of each material point in combination with the material constitutive model; According to formula (4), the solution results on the background grid nodes are mapped back to the material points to update the position and momentum of the material points, and the position information of each material point at this time step is output. Based on the nodal momentum vector updated by S3.2, the strain increment and spinor increment of the material point are calculated according to formulas (5) and (6), and the stress of the material point is updated according to the constitutive model of the material point. S3.4, repeat steps S3.2 and S3.3 until all calculation steps of the dynamic analysis are completed. Based on the material point location information output at each time step, the deformation results of the landslide body are obtained, thus completing the large deformation analysis of the seismic landslide considering spatial variability.

[0010] Compared with the prior art, the beneficial results of the present invention are as follows: (1) This invention characterizes the inherent spatial variability of soil based on random field theory, overcomes the limitations of the traditional homogeneous soil assumption, and makes the numerical simulation results more realistic and more accurate.

[0011] (2) This invention uses the static equilibrium stress field of material points obtained by static analysis as the initial stress for dynamic calculation. Through the two-stage solution strategy of static-dynamic analysis, it effectively simulates the induced effect of earthquake on landslide, providing technical support for landslide simulation considering ground motion.

[0012] (3) The present invention uses the material point method to perform large deformation numerical simulation, which effectively avoids the mesh distortion problem encountered in traditional finite element analysis and has stronger robustness.

[0013] In summary, this invention is based on the material point method, characterizes the spatial variability of soil parameters using random field theory, and combines a two-stage solution strategy to achieve accurate simulation of seismic loads. It reasonably depicts the landslide evolution process of spatially variable soil under seismic action, providing effective technical support for the study of large deformation problems of soil considering spatial variability. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of the main process of the method of the present invention; Figure 2 A schematic diagram of the geometric model of the landslide area; Figure 3 A schematic diagram of the material point model in the landslide area; Figure 4 A schematic diagram of the random field for the mechanical parameters of the soil in the landslide area; Figure 4 In the figure, (a) represents the cohesion random field of the landslide body; Figure 4 In the figure, (b) represents the internal friction angle of the landslide body and the random field friction angle. Figure 5 The graph shows the time history of triaxial acceleration for the 1995 Hanshin earthquake. Figure 5 (a) in the middle is x Seismic acceleration time history curves in the direction; Figure 5 (b) in the middle is y Seismic acceleration time history curves in the direction; Figure 5 (c) in the middle is z Seismic acceleration time history curves in the direction; Figure 6 This is a schematic diagram of the deformation of the landslide zone under seismic action at a typical moment; Figure 6 (a) shows the deformation of the landslide body at 15s; Figure 6 (b) shows the deformation of the landslide body at 18s; Figure 6 (c) shows the deformation of the landslide body at 21s; Figure 6 (d) in the figure represents the deformation of the landslide body at 24s; Figure 6 (e) in the figure represents the deformation of the landslide body at 27s; Figure 6 (f) in the figure represents the deformation of the landslide body at 30s; Figure 7 This is a diagram showing the deformation of the soil in the landslide area under seismic loading, without considering spatial variability. Figure 8 This is obtained from a random field sample set of soil material parameters and deterministic soil parameter values. x A comparison chart of directional sliding values. Detailed Implementation

[0015] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but the scope of protection of the present invention is not limited thereto.

[0016] See Figure 1 A method for analyzing large deformations of earthquake-induced landslides that considers spatial variability, taking a typical landslide as an example, includes the following steps: Example 1: Earthquake landslide simulation of a soil slope considering spatial variability (cohesion and internal friction angle); S1, based on the geometric model of the landslide area and the stochastic field statistical characteristics of soil mechanical parameters, constructs a spatially variable material point analysis model, specifically: S1.1, Geometric model of the landslide body (refer to...) Figure 2 It shows the geometric dimensions of the landslide, where L1=85m, L2=25m, L3=30m, L4=15m. =45°, based on the geometric model of the landslide, construct a material point model of the landslide, and the obtained material point model refers to Figure 3 ; S1.2, Based on geological survey data, the statistical characteristics of soil mechanical parameters are determined. In this embodiment, the mean value and coefficient of variation of cohesion are taken as 10 kPa and 0.2, respectively. x , y , z The fluctuation ranges in the direction were taken as 40m, 8m, and 40m, respectively; the mean and coefficient of variation of the internal friction angle were taken as 20°. 0 0.2, x , y ,z The fluctuation ranges in the directions are taken as 40m, 8m, and 40m respectively; Furthermore, in this embodiment x The direction is the primary sliding direction. y The direction is a horizontal direction perpendicular to the main sliding direction. z The direction is vertical; S1.3 Extract the three-dimensional spatial coordinates of all material points from the landslide material point model; S1.4 Based on the three-dimensional spatial coordinates of each material point, calculate the distance between any two material points, and use the correlation function to determine the correlation coefficient between any two material points in order to construct the covariance matrix between material points; The correlation function can be of single exponential, quadratic exponential, or cosine exponential type. This embodiment uses a single exponential correlation function. For the random fields of cohesion and internal friction angle, the correlation coefficient between any two material points should be determined using the correlation function to construct the covariance matrix between the material points, as shown in formula (7): (7) In the formula: The correlation coefficient value between two material points; , , These represent the two material points at... x, y, z The separation distance in the direction; , , They represent in x, y, z The directional separation distance is , , The two background mesh cells in x, y, z Correlation coefficient values ​​in the direction; , , Random fields are respectively x, y, z The range of fluctuations in direction; S1.5, the covariance matrix decomposition method is used to generate random fields of mechanical parameters at the locations of each material point, and the generated mechanical parameter values ​​are assigned to the corresponding material points, thereby constructing a material point analysis model with spatial variability; the landslide material point model with spatial variability is referenced. Figure 4 As shown, where Figure 4 In the figure, (a) represents the cohesion random field of the landslide body. Figure 4 (b) represents the random field of friction coefficient of the landslide body; S2, based on the spatially variable material point analysis model constructed from S1, performs static analysis of the landslide body under self-weight load, obtaining the static equilibrium stress field of each material point, specifically: S2.1, Read the information required for static analysis, including material point information, background mesh information, load information and calculation parameters; The material point information includes the material point coordinates, mass, constitutive model, and mechanical parameter values ​​considering spatial variability. In this embodiment, a DP constitutive model is used, and the constitutive model parameters are shown in Table 1. The background mesh information includes the background mesh range and background mesh size. In this embodiment, the background mesh size is 0.5m. The load information includes the self-weight load. The calculation parameters include the calculation time step and the total number of calculation steps. In this embodiment, they are 0.00005s and 1,200,000 steps, respectively, with a total calculation time of 1 minute. Table 1 Parameters of the DP elastic-plastic constitutive model for soil in the landslide area

[0017] S2.2, within each time step, the material point information is mapped to the background grid, the control equations on the background grid are established and solved, and the acceleration vector and the updated momentum vector of the background grid nodes are obtained; Determine the background grid where the material point is located, and map the mass and momentum of each material point to the corresponding background grid node, as shown in formula (1): (1) In the formula, , These represent the background mesh nodes. I The mass vector and momentum vector; , Representing material points respectively p mass vector and momentum vector p Indicates the first p One material point; n p Indicates the total number of material points within the background grid; subscript t Indicates the first t Time step; The mapping function from material points to background mesh nodes; Then, the nodal forces of the background mesh nodes are calculated according to formula (2): (2) In the formula: , These represent the background mesh nodes. I The internal force vector and the external force vector; This represents the partial derivative of the mapping function; p Indicates the firstp One material point; , Represented as matter points p The stress tensor and density; , Representing material points respectively p Gravitational acceleration and seismic acceleration, where seismic acceleration exists only in dynamic analysis; subscript Indicates the first Time step; Finally, the governing equations on the background mesh are established and solved according to formula (3) to obtain the acceleration vector and the updated momentum vector of the background mesh nodes: (3) In the formula: , , These represent the background mesh nodes. I exist i The acceleration vector in the direction, the momentum vector before the update, and the momentum vector after the update; Indicates the time step; subscript Indicates the first Time step; S2.3, based on the solution results on the background mesh, update the position and momentum information of the material points, and update the stress of each material point in combination with the material constitutive model, and output the stress of each material point corresponding to this time step; According to formula (4), the solution results on the background mesh nodes are mapped back to the material points to update the position and momentum of the material points; (4) In the formula, , Representing the material points respectively p The position vector and acceleration vector; , These represent the background mesh nodes. I The mass vector and the updated momentum vector, with subscripts I Indicates the first I One background grid node, Indicates the total number of background grid nodes; Indicates the time step, subscript t Indicates the first t Time step, subscript t+ 1 indicates the first t+ 1. Time step; Based on the nodal momentum updated in S2.2, calculate the strain increment and spinor increment of the material point according to formulas (5) and (6), update its stress according to the constitutive model of the material point, and output the stress of each material point corresponding to the time step; (5) (6) In the formula, , Representing material points respectively p The strain increment and spinor increment; , Representing nodes respectively I exist i direction, j The momentum vector updated in the direction; Indicates the time step, subscript t Indicates the first t Time step; , They respectively represent the mapping function in i direction, j Partial derivatives in direction; subscript I Indicates the first I One background grid node, Indicates the total number of background grid nodes; S2.4, repeat S2.2 and S2.3 until all calculation steps of the static analysis are completed, and obtain the stress of the material point corresponding to the last time step, which is the static equilibrium stress field of each material point. S3 uses the static equilibrium stress field obtained in S2 as the initial stress field. Dynamic analysis is carried out under the combined action of self-weight and seismic load to obtain the deformation results of the landslide body, and then completes the large deformation analysis of the seismic landslide considering spatial variability. S3.1 Reads the information required for dynamic analysis, including material point information, background mesh information, load information, and calculation parameters; The material point information includes the material point coordinates, initial stress, mass, constitutive model, and mechanical parameter values ​​considering spatial variability. This embodiment uses a DP constitutive model, and the constitutive model parameters are shown in Table 1. The background mesh information includes the background mesh range and size; in this embodiment, the background mesh size is 0.5m. The load information includes self-weight load and seismic load. In this embodiment, the seismic load is selected from the 1995 Great Hanshin Earthquake, using a 30s triaxial seismic wave. For details of the seismic load, see [link to seismic data]. Figure 5 ,in Figure 5 (a) in the middle is x Seismic acceleration in the direction of earthquake, Figure 5 (b) in the middle is y Seismic acceleration in the direction of earthquake, Figure 5 (c) in the middle is z The seismic acceleration in the direction; the calculation parameters include the calculation time step and the total number of calculation steps, which are 0.00005s and 6,000,000 steps respectively in this embodiment, with a total calculation time of 30s; S3.2, within each time step, the material point information is mapped to the background grid, the control equations on the background grid are established and solved, and the acceleration vector and the updated momentum vector of the background grid nodes are obtained. According to formula (1), determine the background grid where the material point is located, and map the mass and momentum of each material point to the background grid node where it is located; Calculate the nodal forces of the background mesh nodes according to formula (2); The control equations on the background grid are established and solved according to formula (3) to obtain the acceleration vector and the updated momentum vector of the background grid nodes. S3.3, based on the solution results on the background mesh, update the position and momentum information of the material points, output the position information of each material point at this time step, and update the stress of each material point in combination with the material constitutive model; According to formula (4), the solution results on the background grid nodes are mapped back to the material points to update the position and momentum of the material points, and the position information of each material point at this time step is output. Based on the nodal momentum vector updated by S3.2, the strain increment and spinor increment of the material point are calculated according to formulas (5) and (6), and the stress of the material point is updated according to the constitutive model of the material point. S3.4, repeat steps S3.2 and S3.3 until all calculation steps of the dynamic analysis are completed. Based on the material point location information output at each time step, the deformation results of the landslide body are obtained, thus completing the large deformation analysis of the seismic landslide considering spatial variability.

[0018] The simulation results of this invention on large soil deformation in landslide zones under seismic loading are summarized, such as... Figure 6 As shown, it illustrates the deformation at various typical moments between 15 and 30 seconds, specifically: Figure 6 (a) shows the deformation of the landslide body at 15s; Figure 6 (b) shows the deformation of the landslide body at 18s; Figure 6 (c) shows the deformation of the landslide body at 21s; Figure 6 (d) in the figure represents the deformation of the landslide body at 24s; Figure 6 (e) in the figure represents the deformation of the landslide body at 27s; Figure 6 (f) represents the deformation of the landslide at 30s; additionally, to assess the impact of spatial variability on landslide deformation, the landslide was simulated under the same seismic load without considering spatial variability, and the results are as follows. Figure 7 As shown, it presents the final deformation morphology of the landslide body without considering spatial variability; in contrast... Figure 6 and Figure 7It can be seen that, considering spatial variability, the deformation characteristics of the landslide are more consistent with the actual situation.

[0019] Furthermore, to further clarify the impact of spatial variability on the sliding distance, a random field sample set of soil in the landslide area was established, comprising 150 samples. Dynamic calculations were performed based on this sample set, and the results were then compared and summarized with those obtained when the soil mechanical parameters were set to fixed values. x Taking the maximum sliding distance in the direction as an example, the comparison results are shown below. Figure 8 Specifically, when the soil mechanical parameters are set to fixed values, the landslide body in x The maximum sliding distance in the direction is 15.37m, while considering the random field... x The upper and lower limits of the sliding distance in the direction are 18.31m and 14.04m, respectively.

[0020] according to Figures 6-8 The simulation results show that the present invention can effectively simulate the large deformation process of soil during landslides under earthquake action. Furthermore, by introducing a random field of soil parameters, the variation range of sliding distance under spatial variability conditions is obtained, which better reflects the influence of soil spatial variability on landslide distance and is more in line with actual conditions. It can provide scientific guidance for the analysis of large deformation of landslides in similar projects.

[0021] The above description describes a more feasible specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, improvements, or adaptive adjustments made within the technical concept and core principles disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for analyzing large deformations of earthquake-induced landslides considering spatial variability, characterized in that, The earthquake-induced landslide large deformation analysis method includes the following steps: S1, based on the geometric model of the landslide area and the random field statistical characteristics of soil mechanical parameters, constructs a material point analysis model with spatial variability; S2, based on the spatially variable material point analysis model constructed from S1, performs static analysis of the landslide body under self-weight load, obtaining the static equilibrium stress field of each material point, specifically: S2.1, Read the information required for static analysis, including material point information, background mesh information, load information and calculation parameters; S2.2, within each time step, the material point information is mapped to the background grid, the control equations on the background grid are established and solved, and the acceleration vector and the updated momentum vector of the background grid nodes are obtained; S2.3, based on the solution results on the background mesh, update the position and momentum information of the material points, and update the stress of each material point in combination with the material constitutive model, and output the stress of each material point corresponding to this time step; S2.4, repeat S2.2 and S2.3 until all calculation steps of the static analysis are completed, and obtain the stress of the material point corresponding to the last time step, which is the static equilibrium stress field of each material point. S3 uses the static equilibrium stress field obtained in S2 as the initial stress field. Dynamic analysis is carried out under the combined action of self-weight and seismic load to obtain the deformation results of the landslide body, and then completes the large deformation analysis of the seismic landslide considering spatial variability.

2. The earthquake landslide large deformation analysis method considering spatial variability according to claim 1, characterized in that, Specifically, S1 refers to: S1.1, Based on the geometric model of the landslide, construct the material point model of the landslide; S1.2, Based on geological survey data, determine the statistical characteristics of soil mechanical parameters, including mean, coefficient of variation and fluctuation range; S1.3 Extract the three-dimensional spatial coordinates of all material points from the landslide material point model; S1.4 Based on the three-dimensional spatial coordinates of each material point, calculate the distance between any two material points, and use the correlation function to determine the correlation coefficient between any two material points in order to construct the covariance matrix between material points; S1.5 uses the covariance matrix decomposition method to generate a random field of mechanical parameters at the location of each material point, and assigns the generated mechanical parameter values ​​to the corresponding material points to construct a material point analysis model with spatial variability.

3. The method for analyzing large deformations of earthquake-induced landslides considering spatial variability according to claim 2, characterized in that, In S1.4, the correlation function is selected from single exponential, quadratic exponential, or cosine exponential types.

4. The earthquake landslide large deformation analysis method considering spatial variability according to claim 3, characterized in that, In S2.1, the material point information includes the material point coordinates, mass, constitutive model, and mechanical parameter values ​​considering spatial variability; the background mesh information includes the background mesh range and background mesh size; and the load information includes the self-weight load. The calculation parameters include the calculation time step and the total number of calculation steps.

5. The earthquake landslide large deformation analysis method considering spatial variability according to claim 4, characterized in that, Specifically, S2.2 is as follows: Determine the background grid where the material point is located, and map the mass and momentum of each material point to the corresponding background grid node, as shown in formula (1): （1） In the formula, , These represent the background mesh nodes. I The mass vector and momentum vector; , Representing material points respectively p mass vector and momentum vector p Indicates the first p One material point; n p Indicates the total number of material points within the background grid; subscript t Indicates the first t Time step; The mapping function from material points to background mesh nodes; Then, the nodal forces of the background mesh nodes are calculated according to formula (2): （2） In the formula: , These represent the background mesh nodes. I The internal force vector and the external force vector; This represents the partial derivative of the mapping function; p Indicates the first p One material point; , Represented as matter points p The stress tensor and density; , Representing material points respectively p Gravitational acceleration and seismic acceleration, where seismic acceleration exists only in dynamic analysis; subscript Indicates the first Time step; Finally, the governing equations on the background mesh are established and solved according to formula (3) to obtain the acceleration vector and the updated momentum vector of the background mesh nodes: （3） In the formula: , , These represent the background mesh nodes. I exist i The acceleration vector in the direction, the momentum vector before the update, and the momentum vector after the update; Indicates the time step; subscript Indicates the first Time step.

6. The earthquake landslide large deformation analysis method considering spatial variability according to claim 5, characterized in that, Specifically, S2.3 is as follows: According to formula (4), the solution results on the background mesh nodes are mapped back to the material points to update the position and momentum of the material points; （4） In the formula, , Representing material points respectively p The position vector and acceleration vector; , These represent the background mesh nodes. I The mass vector and the updated momentum vector, with subscripts I Indicates the first I One background grid node, Indicates the total number of background grid nodes; Indicates the time step, subscript t Indicates the first t Time step, subscript t+ 1 indicates the first t+ 1 time step; Based on the nodal momentum updated in S2.2, the strain increment and spinor increment of the material point are calculated according to formulas (5) and (6). The stress of the material point is updated according to the constitutive model of the material point, and the stress of each material point corresponding to the time step is output. （5） （6） In the formula, , Representing material points respectively p The strain increment and spinor increment; , Representing nodes respectively I exist i direction, j The momentum vector updated in the direction; Indicates the time step, subscript t Indicates the first t Time step; , They respectively represent the mapping function in i direction, j Partial derivatives in direction; subscript I Indicates the first I One background grid node, This indicates the total number of background grid nodes.

7. The earthquake landslide large deformation analysis method considering spatial variability according to claim 6, characterized in that, Specifically, S3 is: S3.1 Reads the information required for dynamic analysis, including material point information, background mesh information, load information, and calculation parameters; S3.2, within each time step, the material point information is mapped to the background grid, the control equations on the background grid are established and solved, and the acceleration vector and the updated momentum vector of the background grid nodes are obtained. S3.3, based on the solution results on the background mesh, update the position and momentum information of the material points, output the position information of each material point at this time step, and update the stress of each material point in combination with the material constitutive model; S3.4, repeat steps S3.2 and S3.3 until all calculation steps of the dynamic analysis are completed. Based on the material point location information output at each time step, the deformation results of the landslide body are obtained, thus completing the large deformation analysis of the seismic landslide considering spatial variability.

8. The method for analyzing large deformations of earthquake-induced landslides considering spatial variability according to claim 7, characterized in that, In S3.1, the material point information includes the material point coordinates, initial stress, mass, constitutive model, and mechanical parameter values ​​considering spatial variability; the background mesh information includes the background mesh range and background mesh size; the load information includes self-weight load and seismic load; and the calculation parameters include the calculation time step and the total number of calculation steps.

9. The earthquake landslide large deformation analysis method considering spatial variability according to claim 8, characterized in that, Specifically, S3.2 is as follows: According to formula (1), determine the background grid where the material point is located, and map the mass and momentum of each material point to the background grid node where it is located; Calculate the nodal forces of the background mesh nodes according to formula (2); The control equations on the background grid are established and solved according to formula (3) to obtain the acceleration vector and the updated momentum vector of the background grid nodes.

10. The method for analyzing large deformations of earthquake-induced landslides considering spatial variability according to claim 9, characterized in that, Specifically, S3.3 is as follows: According to formula (4), the solution results on the background grid nodes are mapped back to the material points to update the position and momentum of the material points, and the position information of each material point at this time step is output. Based on the nodal momentum vector updated in S3.2, the strain increment and spinor increment of the material point are calculated according to formulas (5) and (6), and the stress of the material point is updated according to the constitutive model of the material point.

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