MPM-based three-dimensional slope deformation analysis method and system

Abstract

The invention provides an MPM-based three-dimensional slope deformation analysis method and system, and the method comprises the steps: firstly obtaining the spatial geometric structure data of a slope region, constructing a three-dimensional material point model based on the spatial geometric structure data, discretizing a slope material into a material point set containing position coordinates and physical attribute information, and carrying out the discretization of the material point set; establishing a background grid system covering the material point set, then performing interaction calculation on the material point set and the background grid system, solving a kinetic equation on background grid nodes to obtain motion state parameters, mapping the motion state parameters back to material point updating information, generating a material point state set containing deformation characteristics, and finally performing deformation calculation on the material point state set. And finally, based on the position coordinate variable quantity and the physical attribute change parameters in the material point state set, analyzing the deformation trend and the potential instability area of the three-dimensional slope, and generating a slope deformation analysis report containing deformation gradient distribution and a stress concentration area, so that the geometric and stratum information of the slope can be comprehensively considered, and the deformation process can be accurately simulated.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent slope engineering, and in particular to a three-dimensional slope deformation analysis method and system based on MPM. Background Art

[0002] In the field of slope engineering, accurate analysis of slope deformation is crucial for ensuring slope stability and preventing geological disasters. Traditional slope deformation analysis methods are mainly based on the finite element method (FEM) or the discrete element method (DEM). The FEM is difficult to mesh when dealing with complex geometries and material nonlinearities. Furthermore, mesh distortion is prone to occur when simulating complex mechanical behaviors such as large deformations and fractures, resulting in reduced computational accuracy or even inability to perform calculations. While the DEM can effectively simulate the discrete properties of granular materials, it is computationally inefficient for continuous media or slope materials with mixed continuous-discrete properties, and it is difficult to accurately describe the stress-strain relationship within the material. Furthermore, most of these traditional methods only consider deformation information on the slope surface, insufficiently considering the influence of the internal stratum distribution and material properties of the slope. Consequently, they are unable to fully and accurately reflect the deformation characteristics and potential instability risks of three-dimensional slopes, making it difficult to meet the requirements of modern slope engineering for high-precision and high-reliability deformation analysis. Summary of the Invention

[0003] In view of the above-mentioned problems, in combination with the first aspect of the present invention, an embodiment of the present invention provides a three-dimensional slope deformation analysis method based on MPM, the method comprising: Acquiring spatial geometric structure data of the slope area, wherein the spatial geometric structure data includes a point cloud coordinate set of the slope surface and interface geometric parameters of stratum distribution; Constructing a three-dimensional material point model based on the spatial geometric structure data, discretizing the slope material into a material point set containing position coordinates and physical property information, and establishing a background grid system covering the material point set, wherein the background grid system includes regularly distributed grid nodes and node connection relationships; performing interaction calculations on the material point set and the background grid system, transferring the mass, momentum, and force of the material points to the background grid nodes, solving the dynamic equations including the displacement field and the stress field on the background grid nodes, and obtaining the motion state parameters of the background grid nodes; Mapping the motion state parameters of the background grid nodes back to the material points, updating the position coordinates and physical property information of the material points, and generating a material point state set containing deformation characteristics; Based on the position coordinate changes and physical property change parameters in the material point state set, the deformation trend and potential unstable areas of the three-dimensional slope are analyzed, and a slope deformation analysis report including deformation gradient distribution and stress concentration areas is generated.

[0004] On the other hand, an embodiment of the present invention also provides a three-dimensional slope deformation analysis system based on MPM, including a processor and a machine-readable storage medium, wherein the machine-readable storage medium is connected to the processor, the machine-readable storage medium is used to store programs, instructions or codes, and the processor is used to execute the programs, instructions or codes in the machine-readable storage medium to implement the above method.

[0005] Based on the above aspects, by obtaining the spatial geometric structure data including the slope surface point cloud coordinate set and the stratum distribution interface geometric parameters, the geometric morphological characteristics of the slope and the stratum distribution are fully covered. A three-dimensional material point model is constructed based on the obtained spatial geometric structure data, and the slope material is discretized into a material point set containing position coordinates and physical property information. A background grid system covering the material point set is established, which realizes the reasonable discretization of the slope material and the regular arrangement of the grid, effectively avoiding the problems of grid distortion in traditional methods, and providing a stable and reliable computing environment for subsequent mechanical calculations. The interaction calculation is performed by the material point set and the background grid system, and the mass, momentum and force of the material point are transferred to the background grid nodes. The dynamic equations containing displacement field and stress field are solved on the background grid nodes to obtain the motion state parameters of the background grid nodes. The motion state parameters of the background grid nodes are then mapped back to the material points, the position coordinates and physical property information of the material points are updated, and a material point state set containing deformation characteristics is generated. This can accurately simulate the deformation process of the slope under various mechanical effects, fully considering the continuous-discrete mixed characteristics of the slope material. Finally, based on the position coordinate change and physical property change parameters in the material point state set, the deformation trend and potential unstable area of ​​the three-dimensional slope are analyzed, and a slope deformation analysis report containing deformation gradient distribution and stress concentration areas is generated, which significantly improves the level of slope deformation analysis and helps to more effectively ensure the safety of slope projects. BRIEF DESCRIPTION OF THE DRAWINGS

[0006] Figure 1 It is a schematic diagram of the execution flow of the MPM-based three-dimensional slope deformation analysis method provided by an embodiment of the present invention.

[0007] Figure 2 Schematic diagram of exemplary hardware and software components of the MPM-based three-dimensional slope deformation analysis system provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0008] The present invention will be described in detail below with reference to the accompanying drawings. Figure 1 FIG3 is a flow chart of a three-dimensional slope deformation analysis method based on MPM provided by an embodiment of the present invention. The three-dimensional slope deformation analysis method based on MPM is introduced in detail below.

[0009] Step S110: obtaining spatial geometric structure data of the slope area, wherein the spatial geometric structure data includes a point cloud coordinate set of the slope surface and interface geometric parameters of stratum distribution.

[0010] When performing deformation analysis on a slope, the first step is to obtain the spatial geometric structure data of the slope area. To obtain the point cloud coordinate set of the slope surface, a three-dimensional laser scanning method is used. A laser scanning device emits a laser beam toward the slope surface. The laser beam reflects back upon encountering the slope surface. The laser scanning device receives the reflected signal and calculates the three-dimensional coordinates of numerous points on the slope surface based on information such as the laser's propagation time and angle. During the scanning process, the laser scanning device can scan the slope from different positions and angles to ensure that complete slope surface information is obtained. By splicing and processing the data obtained from multiple scans, a point cloud coordinate set of the slope surface is ultimately formed. Each coordinate point in this point cloud coordinate set represents a specific location on the slope surface. The combination of these numerous coordinate points can accurately depict the shape and contours of the slope surface.

[0011] The interface geometric parameters of stratum distribution are obtained through the comprehensive application of various geological exploration methods. Drilling is an important method. By drilling holes at different locations in the slope area with a drilling rig and extracting samples of underground rock and soil layers, these samples are then analyzed to obtain information on the type and properties of rock and soil layers at different depths. At the same time, combined with geophysical exploration methods such as geological radar, geological radar uses the propagation characteristics of electromagnetic waves in underground media to detect the distribution of underground strata. By analyzing the characteristics of the geological radar's reflected waves, information such as the interface position, shape, and direction of the strata can be determined. The rock and soil layer information obtained through drilling and the geological radar detection results are integrated and analyzed to obtain the interface geometric parameters of the stratum distribution.

[0012] Step S120: construct a three-dimensional material point model based on the spatial geometric structure data, discretize the slope material into a set of material points containing position coordinates and physical property information, and establish a background grid system covering the set of material points, wherein the background grid system includes regularly distributed grid nodes and node connection relationships.

[0013] After obtaining the spatial geometric structure data of the slope area, the next step is to construct a three-dimensional material point model based on this spatial geometric structure data. This process mainly includes two key steps: discretizing the slope material into a set of material points and establishing a background grid system.

[0014] Step S121: spatially divide the slope material according to a preset discrete rule, generate uniformly distributed material points within the constraint range of the point cloud coordinate set, and form a spatial mapping relationship between the position coordinates of the material points and the coordinate points in the point cloud coordinate set.

[0015] When spatially dividing the slope material, the preset discrete rules are determined based on the geometric complexity of the slope and the analysis objectives. For slopes with simpler geometric shapes, the discrete spacing can be relatively large; while for slopes with complex geometric shapes, the discrete spacing needs to be smaller to ensure that the characteristics of the slope material can be accurately described. Taking the coordinate points in the point cloud coordinate set as the reference, the material point grid is arranged in three-dimensional space according to the generation rules of the discrete precision parameters. Specifically, in the directions of the three coordinate axes X, Y, and Z, material points are generated in sequence according to the set spacing. For example, in the X-axis direction, starting from one end of the slope, material points are generated one by one according to the preset spacing until the entire slope range in the X-axis direction is covered. The same operation is then performed in the Y-axis and Z-axis directions to eventually form a three-dimensional material point grid.

[0016] After generating material points, it's necessary to adjust the positions of those outside the slope surface's point cloud coordinates. By calculating the distance and direction from these material points to the slope surface, their positions are adjusted to fit the slope's surface geometry. Using the coordinate information in the point cloud coordinate set, a geometric model of the slope surface is constructed. The shortest distance and direction from the outer material points to this geometric model are then calculated, and the material points are moved to appropriate positions along this direction, ensuring that the material point set fully covers the spatial extent of the slope material.

[0017] At the same time, an index relationship is established between the material point's location coordinates and the corresponding coordinate points in the point cloud coordinate set, forming a spatial mapping table. This spatial mapping table records the point cloud coordinates corresponding to each material point and the stratigraphic region to which it belongs. For example, for each material point, the closest point cloud coordinate is found and the point cloud coordinate number and stratigraphic region information to which the material point belongs are recorded. This allows for convenient querying of the corresponding point cloud coordinates and stratigraphic region information based on the material point's location coordinates during subsequent data processing and analysis.

[0018] Finally, the generated set of material points is checked for density uniformity. The uniformity of the material point distribution is assessed by calculating the standard deviation of the number of material points per unit volume. If the standard deviation is within a preset range, the material point distribution meets the preset discrete accuracy requirements. If it is outside the preset range, the material point positions must be further adjusted or regenerated to ensure a uniform distribution of material points within the slope material space.

[0019] Step S1211: Determine discrete precision parameters of the slope material. The discrete precision parameters are determined according to the geometric complexity of the slope and the analysis objectives, and are used to control the distribution density of material points.

[0020] The determination of the discrete precision parameters is based on the geometric complexity of the slope and the analysis objective. For geometrically simple slopes, such as those that are approximately planar, the discrete precision parameters can be set larger, meaning that the material points can be spaced relatively wide apart and the number of material points per unit volume is relatively small. However, for geometrically complex slopes, such as those with multiple undulations and wrinkles, the discrete precision parameters need to be set smaller. This reduces the material point spacing, increases the number of material points per unit volume, and enables a more accurate description of the slope material's characteristics. The analysis objective is also an important factor in determining the discrete precision parameters. If the analysis objective is to perform a rough deformation analysis of the slope, the discrete precision parameters can be appropriately relaxed. However, if a high-precision deformation analysis is required, such as the precise prediction of potential unstable areas on the slope, more stringent discrete precision parameters are required to ensure that the material points accurately reflect even small changes in the slope material.

[0021] Step S1212: Based on the coordinate points in the point cloud coordinate set, a material point grid is arranged in three-dimensional space according to the generation rule of the discrete precision parameter, and the nodes of the material point grid serve as the initial position coordinates of the material points.

[0022] Arrange the material point grid in three-dimensional space based on the coordinate points in the point cloud coordinate set. During the arrangement process, strictly follow the generation rules of the discrete precision parameters. In the three coordinate axis directions of X, Y, and Z, material points are generated in sequence at the set intervals. For example, in the X-axis direction, starting from the starting point of the slope, material points are generated one by one according to the intervals determined by the discrete precision parameters until the entire slope in the X-axis direction is covered. During the generation process, refer to the coordinate points in the point cloud coordinate set to ensure that the distribution of material points matches the actual shape and structure of the slope. For the Y-axis and Z-axis directions, the material points are generated in the same way as above. The nodes of the material point grid finally formed are the initial position coordinates of the material points.

[0023] Step S1213: adjusting the positions of the material points outside the point cloud coordinates of the slope surface so that their position coordinates fit the geometric shape of the slope surface, so that the material point set completely covers the spatial range of the slope material.

[0024] After generating a set of material points, some may be located outside the point cloud coordinates of the slope surface. To ensure that the material point set fully covers the spatial extent of the slope material, these outer material points need to be repositioned. First, a geometric model of the slope surface is constructed. Using the coordinate point information in the point cloud coordinate set, a geometric model that accurately describes the slope surface shape is constructed through interpolation or fitting. Next, the shortest distance and direction from the outer material points to this geometric model are calculated. Distance calculation algorithms, such as the Euclidean distance algorithm, can be used to calculate the distance from the material points to each point on the geometric model and find the shortest distance and corresponding direction. Finally, the material points are moved to the appropriate position along this direction so that their positions fit the geometric shape of the slope surface.

[0025] Step S1214: establishing an index relationship between the material point position coordinates and the corresponding coordinate points in the point cloud coordinate set to form a spatial mapping table, which is used to record the point cloud coordinates corresponding to each material point and the stratum region to which it belongs.

[0026] An index relationship is established between the coordinates of the material point locations and the corresponding coordinate points in the point cloud coordinate set, forming a spatial mapping table. For each material point, the closest point cloud coordinate is found in space and the number of the point cloud coordinate is recorded. Spatial search algorithms, such as the KD tree algorithm, can be used to quickly find the closest point cloud coordinates. Simultaneously, the stratigraphic region to which the material point belongs is recorded. This can be determined by the geometric parameters of the stratigraphic interface. The spatial position of each material point determines the stratigraphic region to which it belongs. The position and shape of the stratigraphic interface determine the stratigraphic region within which the material point is located. The resulting spatial mapping table records the point cloud coordinates and stratigraphic region information corresponding to each material point.

[0027] Step S1215: performing a density uniformity check on the generated material point set, by calculating the standard deviation of the number of material points within a unit volume, so that the material point distribution meets the preset discrete accuracy requirements.

[0028] Checking the density uniformity of the generated material point set is an important step in ensuring that the material point distribution meets the preset discrete accuracy requirements. The spatial extent of the slope material is divided into several small volume units, and the number of material points within each volume unit is calculated. The standard deviation of these material point counts is then calculated. The standard deviation reflects the degree of fluctuation in the number of material points between different volume units. If the standard deviation is within the preset range, the material point distribution meets the preset discrete accuracy requirements. If it is outside the range, the material point positions must be further adjusted or the material points must be regenerated. The uniformity of the material point distribution can be improved by adjusting the discrete accuracy parameters or redistributing the material points in a local area.

[0029] Step S122: assigning physical property information to each material point, wherein the physical property information includes a material density parameter, an elastic modulus parameter, and a Poisson's ratio parameter. The material density parameter is determined according to the rock and soil type of the area corresponding to the interface geometric parameters of the stratum distribution.

[0030] After discretizing the slope material into a set of material points, each material point needs to be assigned physical property information. This physical property information includes material density parameters, elastic modulus parameters, and Poisson's ratio parameters. The material density parameters are determined based on the geotechnical type of the region corresponding to the interface geometry parameters of the stratum distribution. Different geotechnical types have different densities. The interface geometry parameters of the stratum distribution can be used to determine the stratum region and geotechnical type to which each material point belongs. Then, referring to relevant geological data and experimental data, the corresponding material density parameters are assigned to the material points of different geotechnical types.

[0031] Elastic modulus and Poisson's ratio are important parameters that reflect the mechanical properties of materials. These parameters can be obtained through laboratory experiments or field tests. Experiments and tests are conducted on geotechnical materials from different strata to determine their elastic modulus and Poisson's ratio values. Each material point is then assigned a corresponding elastic modulus and Poisson's ratio based on the stratum region and geotechnical type to which it belongs. This physical property information can be used to describe the mechanical behavior and deformation characteristics of the material point.

[0032] Step S123: Generate a background grid system containing hexahedral units with the spatial distribution range of the material point set as the boundary, wherein the grid node coordinates of the background grid system cover the position coordinates of all material points, and the spacing between adjacent grid nodes meets the stability condition of numerical calculation.

[0033] A background grid system consisting of hexahedral elements is generated, using the spatial distribution range of the material point set as the boundary. First, the boundary range of the background grid system is determined, namely the spatial range enclosed by the maximum and minimum coordinate values ​​of the material point set in the X, Y, and Z coordinate axes. Then, within this boundary range, hexahedral elements are divided according to the predefined rules. The vertices of these hexahedral elements become the grid nodes of the background grid system.

[0034] When dividing hexahedral elements, it is necessary to ensure that the grid node coordinates cover the position coordinates of all material points. By properly setting the spacing and distribution of the grid nodes, each material point can be located inside a hexahedral element or on its boundary. At the same time, the spacing between adjacent grid nodes must meet the stability conditions of the numerical calculation. The stability conditions of the numerical calculation are related to the numerical calculation method used and the physical properties of the material. Generally speaking, smaller grid node spacing can improve the accuracy of the calculation, but increase the amount of calculation; larger grid node spacing can reduce the amount of calculation, but may affect the stability of the calculation. Therefore, it is necessary to select an appropriate grid node spacing based on the specific calculation requirements and material properties to ensure the accuracy and stability of the numerical calculation.

[0035] Step S124: establishing a spatial association relationship between the material points and the background grid nodes, determining the background grid unit where each material point is located and the weight coefficient with the grid node, wherein the weight coefficient is used to characterize the effect strength of the material point on the background grid node.

[0036] Establishing the spatial relationship between material points and background grid nodes is a crucial foundation for subsequent calculations and analysis. First, determine the background grid cell where each material point resides. This is determined by determining whether the material point's coordinates lie within or on the boundary of a hexahedral cell. Spatial geometry algorithms, such as those for determining if a point is inside a polyhedron, can be used to quickly determine the background grid cell where the material point resides.

[0037] Then, trilinear interpolation is used to calculate the weight coefficients between the material point and the four vertex nodes of the background grid cell. Trilinear interpolation is a commonly used spatial interpolation method. Based on the position of the material point within the background grid cell, the relative position relationship between the material point and the four vertex nodes is calculated to obtain the weight coefficients. The sum of these weight coefficients is equal to 1, and each weight coefficient is greater than or equal to 0. The weight coefficient is used to represent the strength of the material point's influence on the background grid node. The larger the weight coefficient, the stronger the influence of the material point on the background grid node.

[0038] A weight coefficient matrix is ​​established for the material points and background grid nodes. The rows of this matrix correspond to the material points, the columns correspond to the background grid nodes, and the matrix elements are the corresponding weight coefficients. This weight coefficient matrix can be used to conveniently represent the weight relationship between the material points and the background grid nodes. A symmetry check is performed on the weight coefficient matrix to ensure that the weight coefficients of adjacent material points for the same background grid node conform to the principle of spatial symmetry. If the weight coefficient matrix does not conform to the principle of symmetry, inaccurate calculation results may result. Finally, the weight coefficient matrix is ​​stored in a sparse matrix format for rapid recall and updating in subsequent interaction calculations. The sparse matrix format can reduce storage space usage and improve computational efficiency.

[0039] Step S1241: Determine the coordinate position of each material point in the background grid system, and determine the background grid unit to which the material point belongs based on the coordinate range of the grid node.

[0040] Determine the coordinate position of each material point in the background grid system. By comparing the material point's position coordinates with the grid node coordinates of the background grid system, determine the background grid cell to which the material point belongs. This determination can be made using the material point's coordinate range and the boundary conditions of the background grid cell. For each material point, check whether its coordinates in the X, Y, and Z coordinate axes are within the boundary range of a hexahedral cell. If the material point's coordinates are within the boundary range of a hexahedral cell, then the material point belongs to that background grid cell. This method allows for the rapid and accurate determination of the background grid cell to which each material point belongs.

[0041] Step S1242: using a trilinear interpolation method to calculate weight coefficients of the material point and the four vertex nodes of the background grid unit, the sum of the weight coefficients is equal to 1 and each weight coefficient is greater than or equal to 0.

[0042] The trilinear interpolation method is used to calculate the weight coefficients of the material point and the four vertex nodes of the background grid unit. The trilinear interpolation method calculates the weight coefficients based on the position of the material point in the background grid unit. First, the position coordinates of the material point are converted into relative coordinates in the background grid unit. Then, the relative position relationship between the material point and the four vertex nodes is calculated based on the relative coordinates. By interpolating these relative position relationships, the weight coefficients of the material point and the four vertex nodes are obtained. The sum of these weight coefficients is equal to 1, and each weight coefficient is greater than or equal to 0. This ensures that the sum of the effect of the material point on the four vertex nodes of the background grid unit is 1, and the effect intensity of each vertex node is non-negative.

[0043] Step S1243: establishing a weight coefficient matrix of material points and background grid nodes, wherein rows of the weight coefficient matrix correspond to material points, columns correspond to background grid nodes, and matrix elements are corresponding weight coefficients.

[0044] Create a weight coefficient matrix for material points and background grid nodes. The rows of this matrix correspond to material points, the columns correspond to background grid nodes, and the matrix elements are the corresponding weight coefficients. For each material point, fill in the corresponding weight coefficients in the weight coefficient matrix based on its weight coefficient with the background grid node. For example, for the i-th material point and the j-th background grid node, fill in the weight coefficient between them in the i-th row and j-th column of the matrix. In this way, a complete weight coefficient matrix is ​​constructed to represent the weight relationship between the material point and the background grid node.

[0045] Step S1244: performing a symmetry check on the weight coefficient matrix so that the weight coefficients of adjacent material points to the same background grid node comply with the principle of spatial symmetry.

[0046] Checking the symmetry of the weight coefficient matrix is ​​an important step in ensuring the accuracy of calculation results. The principle of spatial symmetry requires that the weight coefficients of adjacent material points for the same background grid node should be symmetrical. By checking whether the weight coefficients of adjacent material points in the weight coefficient matrix for the same background grid node meet the symmetry condition, it can be determined whether the weight coefficient matrix complies with the spatial symmetry principle. If the symmetry principle is not met, the weight coefficients can be adjusted to meet the symmetry condition. This can be achieved by recalculating the weight coefficients or correcting the weight coefficients.

[0047] Step S1245: The weight coefficient matrix is ​​stored in a sparse matrix format so as to be quickly called and updated in subsequent interaction calculations.

[0048] The weight coefficient matrix is ​​stored in a sparse matrix format. Because most elements in the weight coefficient matrix may be zero, using a sparse matrix format can reduce storage space and improve computational efficiency. Sparse matrix storage and manipulation algorithms, such as the Compressed Sparse Row (CSR) format, can be used to store the weight coefficient matrix in a sparse matrix format. In subsequent interaction calculations, elements in the sparse matrix can be quickly called and updated, improving computational speed and efficiency.

[0049] Step S125: performing consistency check on the initial position coordinates and physical property information of the material point set, so that the position coordinates of each material point are within the geometric range of the corresponding formation area, and the physical property parameters conform to the mechanical properties of the material in the formation area.

[0050] Verifying the consistency of the initial position coordinates and physical property information of a set of material points is a crucial step in ensuring data accuracy and reliability. First, the coordinates of each material point are checked to ensure they are within the geometric range of the corresponding stratigraphic region. A geometric model of each stratigraphic region is constructed using the interface geometry parameters of the stratigraphic distribution. The coordinates of the material point are then determined to be within or on the boundary of this geometric model. If the coordinates of the material point are found to be outside the geometric range of the corresponding stratigraphic region, the coordinates must be adjusted or the stratigraphic region reassigned.

[0051] At the same time, the physical property parameters are checked to ensure they conform to the mechanical properties of the materials in the stratum region. Based on the stratum region and geotechnical type to which the material point belongs, and referring to relevant geological data and experimental data, the appropriateness of the physical property parameters (such as material density, elastic modulus, and Poisson's ratio) is determined. If the physical property parameters are found to be inconsistent with the mechanical properties of the materials in the stratum region, they must be corrected or reassigned. This consistency check ensures the accuracy and reliability of the initial position coordinates and physical property information of the material point set.

[0052] Step S130: performing interaction calculations on the material point set and the background grid system, transferring the mass, momentum, and force of the material points to the background grid nodes, solving the dynamic equations including the displacement field and stress field on the background grid nodes, and obtaining the motion state parameters of the background grid nodes.

[0053] After constructing the three-dimensional material point model and the background grid system, it is necessary to perform interaction calculations on the material point set and the background grid system. The purpose is to transfer the relevant physical quantities of the material points to the background grid nodes and solve the dynamic equations on the background grid nodes to obtain their motion state parameters.

[0054] Step S131: For each material point, calculate the inertial force and contact force based on its position coordinates and physical property information. The inertial force is related to the mass and acceleration of the material point, and the contact force is determined based on the relative position change between adjacent material points.

[0055] For each material point, the inertial force is calculated based on its mass and acceleration. The mass of the material point is determined when its physical properties are assigned, while the acceleration can be determined by analyzing the change in its velocity. Specifically, at a given moment, the acceleration of the material point can be approximated by the ratio of the change in velocity over a short period of time before and after that moment to the time interval. The direction of the inertial force is opposite to that of the acceleration, and its magnitude is proportional to the mass and acceleration of the material point.

[0056] Contact force is determined by the change in relative position between adjacent material points. This change in relative position reflects the interaction between them. When the distance between adjacent material points changes, a mutual force, known as contact force, is generated. The magnitude and direction of the contact force can be determined by analyzing information such as the relative displacement and relative velocity between adjacent material points. For example, if the distance between adjacent material points decreases, a compressive contact force may be generated; if the distance increases, a tensile contact force may be generated.

[0057] Step S132: using the weight coefficients to distribute the mass, momentum and force of each material point to the corresponding background grid node, and generating a mass matrix and a force vector set of the background grid node.

[0058] After calculating the inertial and contact forces at each material point, the mass, momentum, and force of the material point are distributed to the corresponding background mesh node using the previously established weight coefficients between the material point and the background mesh node. The weight coefficients represent the strength of the material point's effect on the background mesh node, distributing the relevant physical quantities of the material point to the background mesh node in a weighted manner.

[0059] To allocate mass, the mass of each material point is multiplied by its weight coefficient with the background grid node, and then these weighted masses are accumulated on the corresponding background grid nodes to generate the mass matrix of the background grid nodes. This mass matrix records the total mass allocated to each background grid node.

[0060] To distribute momentum and force, we similarly multiply the momentum and force of each material point by its weight coefficient relative to the background mesh node. These weighted momentum and force are then added to the corresponding background mesh node to generate a force vector set for the background mesh node. This force vector set contains information about the total force acting on each background mesh node, including its magnitude and direction.

[0061] Step S133: establishing a dynamic equilibrium equation in the background grid system, wherein the dynamic equilibrium equation includes displacement variables, velocity variables, and acceleration variables of the background grid nodes, as well as material constitutive relations and boundary conditions.

[0062] Establishing the dynamic equilibrium equation in the background grid system is a key step in analyzing the motion state of the background grid nodes. The dynamic equilibrium equation describes the motion law of the background grid nodes under the action of forces.

[0063] Step S1331: define the displacement variable of the background grid node as a vector field, where the components of the displacement variable in the spatial dimension correspond to the displacement of the grid node in the directions of the three coordinate axes.

[0064] First, define the displacement variables of the background mesh nodes as a vector field. In three-dimensional space, the displacement of each background mesh node can be decomposed into displacement components along the X, Y, and Z coordinate axes. Therefore, the displacement variable is a three-dimensional vector, with its components along each coordinate axis representing the node's displacement in that direction. By defining the displacement variable as a vector field, we can fully describe the displacement of the background mesh nodes in three-dimensional space.

[0065] Step S1332: establishing a stress-strain relationship equation based on a material constitutive relationship, wherein the material constitutive relationship is set for geotechnical materials in different stratum regions, and includes an elastic constitutive model or an elastoplastic constitutive model.

[0066] The stress-strain relationship equation is established based on the material constitutive relationship. Because the geotechnical materials in different strata of the slope have different mechanical properties, it is necessary to set up a material constitutive relationship for each stratum. The material constitutive relationship can adopt an elastic constitutive model or an elastoplastic constitutive model.

[0067] The elastic constitutive model applies to deformation within the elastic range of a material and describes the linear relationship between stress and strain. In this model, the ratio of stress to strain is the elastic modulus. The corresponding stress can be calculated from the elastic modulus and strain.

[0068] Elastoplastic constitutive models consider the mechanical behavior of materials during the plastic deformation phase and can more accurately describe the stress-strain relationship of geomaterials under large deformations. Elastoplastic constitutive models typically include yield criteria and hardening laws to describe the transition from elastic to plastic deformation.

[0069] Step S1333: applying boundary conditions, which include fixed displacement constraints at the bottom of the slope, free boundary conditions on the slope surface, and body force loads such as groundwater pressure.

[0070] Applying boundary conditions is an important step in establishing the dynamic equilibrium equation. Boundary conditions reflect the actual forces and constraints on the slope. Specific boundary conditions include: Fixed displacement constraint at the bottom of the slope: The bottom of the slope is usually connected to bedrock or other stable strata, so the displacement of the background mesh nodes at the bottom of the slope can be assumed to be zero. This means that in the dynamic equilibrium equations, the components of the displacement variables of the background mesh nodes at the bottom of the slope are fixed to zero in all coordinate axes.

[0071] Free boundary condition of the slope surface: The slope surface is in contact with air or other unconstrained media, so the background mesh nodes on the slope surface are not subject to external constraints. Under the free boundary condition, the external force on the background mesh nodes on the slope surface is zero.

[0072] Body force loads such as groundwater pressure: Groundwater exerts pressure on slope materials, which can be considered a body force. The effects of body forces such as groundwater pressure need to be considered when establishing dynamic equilibrium equations. This can be achieved by calculating the groundwater pressure distribution and applying it as a body force to the background mesh nodes.

[0073] Step S1334: Substitute the displacement variable, velocity variable, acceleration variable, material constitutive relation and boundary conditions into the dynamic equilibrium equation to form a group of partial differential equations including the time variable. The group of partial differential equations is converted into a group of algebraic equations applicable to the background grid nodes through spatial discretization.

[0074] Substituting displacement, velocity, acceleration, material constitutive relations, and boundary conditions into the dynamic equilibrium equations yields a system of partial differential equations that includes a time variable. This system describes the temporal relationship between the displacement, velocity, and acceleration of the background mesh nodes, as well as their interactions with stress and strain.

[0075] Since the partial differential equations are difficult to solve directly, they need to be converted into a system of algebraic equations applicable to the background grid nodes through spatial discretization. There are many methods for spatial discretization, such as the finite difference method and the finite element method. In this embodiment, the finite difference method can be used to convert the partial differential equations into a system of algebraic equations. The basic idea of ​​the finite difference method is to approximate the derivatives with difference quotients, and express the derivatives in the partial differential equations as the differences between the function values ​​at the nodes, thereby converting the partial differential equations into a system of algebraic equations.

[0076] Step S1335: performing sparse matrix optimization processing on the algebraic equation group, and optimizing the computational efficiency of the dynamic equilibrium equation through compressed storage and fast solution algorithm.

[0077] Sparse matrix optimization is performed on the transformed algebraic equations to improve computational efficiency. Since the coefficient matrix in an algebraic equation is typically sparse, meaning that most elements are zero, sparse matrix compression can be used to reduce storage space. Common sparse matrix storage formats include the Compressed Sparse Row (CSR) format and the Coordinate On-Line (COO) format.

[0078] At the same time, fast algorithms are used to solve sparse matrix algebraic equations. For example, the conjugate gradient method and the GMRES algorithm are commonly used to quickly solve sparse matrix equations. These algorithms can obtain approximate solutions to the equations in a relatively small number of iterations, thereby improving computational efficiency.

[0079] Step S134: A numerical integration method is used to solve the dynamic equilibrium equation to obtain the displacement increment, velocity vector and stress tensor of each background grid node in the current calculation time step as the motion state parameters of the background grid node. The time step of the numerical integration method meets the stability condition.

[0080] After the dynamic equilibrium equation is established and optimized, the numerical integration method is used to solve the equation to obtain the motion state parameters of each background grid node in the current calculation time step.

[0081] There are various numerical integration methods, such as explicit and implicit. Explicit integration methods offer the advantages of computational simplicity and ease of implementation, but they impose strict time step restrictions and require stability conditions to be met. Implicit integration methods have relatively loose time step restrictions but are computationally more complex. In this embodiment, the appropriate numerical integration method can be selected based on the specific situation.

[0082] During the solution process, it is necessary to ensure that the time step of the numerical integration method meets the stability requirements. The choice of time step affects the accuracy and stability of the calculation. If the time step is too large, it may lead to unstable results and numerical oscillation. If the time step is too small, the calculation workload will increase and the efficiency will decrease. Therefore, it is necessary to choose a reasonable time step based on the characteristics of the dynamic equilibrium equation and the physical parameters of the material to ensure the accuracy and stability of the calculation.

[0083] By numerically integrating the dynamic equilibrium equations, we can obtain the displacement increment, velocity vector, and stress tensor for each background mesh node at the current computational time step. These parameters constitute the kinematic state parameters of the background mesh node, reflecting its motion and stress state at the current moment.

[0084] Step S135: performing a spatiotemporal continuity check on the motion state parameters of the background grid nodes, so that the displacement increments and velocity vector changes between adjacent calculation time steps conform to the physical laws of material deformation.

[0085] After obtaining the motion state parameters of the background grid nodes, a spatiotemporal continuity check is required. The purpose of the spatiotemporal continuity check is to ensure that the displacement increments and velocity vector changes between adjacent calculation time steps conform to the physical laws of material deformation.

[0086] During material deformation, changes in displacement and velocity should be continuous, without sudden changes. Therefore, it's necessary to check whether the displacement increments and velocity vectors of the background mesh nodes between adjacent calculation time steps are within a reasonable range. If the change in displacement increments or velocity vectors is found to be excessive, exceeding the range permitted by the physical laws of material deformation, errors or instability may have occurred during the calculation. In this case, the calculation process needs to be reviewed and adjusted, such as by reducing the time step and checking the boundary condition settings, to ensure the accuracy and stability of the results.

[0087] Step S140: mapping the motion state parameters of the background grid nodes back to the material points, updating the position coordinates and physical property information of the material points, and generating a material point state set containing deformation features.

[0088] After obtaining the motion state parameters of the background grid nodes, these parameters need to be mapped back to the material points to update the position coordinates and physical property information of the material points, thereby generating a material point state set containing deformation characteristics.

[0089] Step S141: Calculate the deformation gradient tensor of the background grid unit according to the displacement increment and velocity vector of the background grid node, where the deformation gradient tensor represents the degree of deformation of the background grid unit in the spatial dimension.

[0090] Based on the displacement increment and velocity vector of the background grid node, the deformation gradient tensor of the background grid cell is calculated. The deformation gradient tensor is a second-order tensor that describes the degree of deformation of the background grid cell in the spatial dimension.

[0091] The deformation gradient tensor is calculated based on the displacement increments and velocity vectors of the background mesh nodes. By interpolating and calculating the displacement increments and velocity vectors of the background mesh nodes, the displacement and velocity changes of each point within the background mesh cell can be obtained. The components of the deformation gradient tensor are then calculated based on these displacement and velocity changes. Each component of the deformation gradient tensor reflects the tensile, compressive, and shear deformation of the background mesh cell in different directions.

[0092] Step S142: Mapping the displacement increment and deformation gradient tensor of the background grid node to each material point using the weight coefficient to obtain the displacement vector and strain tensor of the material point, wherein the strain tensor is determined according to the decomposition result of the deformation gradient tensor.

[0093] Using the previously established weight coefficients between the material points and the background grid nodes, the displacement increments and deformation gradient tensors of the background grid nodes are mapped to each material point. Using a weighted average method, the displacement increments and deformation gradient tensors of the background grid nodes are transferred to the material points, thereby obtaining the displacement vector and strain tensor of the material point.

[0094] The strain tensor is determined by decomposing the deformation gradient tensor. The deformation gradient tensor can be decomposed into the product of the rotation tensor and the strain tensor. By decomposing the deformation gradient tensor, the components of the strain tensor can be obtained. The strain tensor describes the deformation of a material point, including linear strain and shear strain.

[0095] Step S143: Calculate the stress state parameters of the material point according to the strain tensor of the material point and the elastic modulus parameter and Poisson's ratio parameter in the physical property information. The stress state parameters include a normal stress component and a shear stress component.

[0096] The stress state parameters of the material point are calculated based on the strain tensor of the material point and the elastic modulus parameters and Poisson's ratio parameters in the physical property information.

[0097] Step S1431: For each material point, calculate the normal strain component and the shear strain component according to its strain tensor, wherein the normal strain component corresponds to the linear deformation in the three coordinate axis directions, and the shear strain component corresponds to the angular deformation in the coordinate axis plane.

[0098] First, the strain tensor of each material point is analyzed to calculate its normal and shear strain components. The normal strain component reflects the linear deformation of the material point in the three coordinate axes, that is, the degree of elongation or shortening. The shear strain component reflects the angular deformation of the material point within the coordinate axis plane, that is, the degree of shear deformation.

[0099] By calculating and analyzing the components of the strain tensor, we can obtain the values ​​of the normal and shear strain components. For example, the diagonal elements of the strain tensor usually correspond to the normal strain components, while the off-diagonal elements correspond to the shear strain components.

[0100] Step S1432: using the generalized Hooke's law to establish a relationship equation between strain and stress, wherein the relationship equation incorporates the effects of the elastic modulus parameter and the Poisson's ratio parameter on the normal stress and the shear stress.

[0101] The strain-stress relationship equation is established using the generalized Hooke's law. The generalized Hooke's law describes the relationship between stress and strain in linear elastic materials and takes into account the effects of the elastic modulus and Poisson's ratio on normal and shear stresses.

[0102] Regarding the relationship between normal stress and normal strain, generalized Hooke's law states that normal stress is proportional to normal strain, with the proportionality factor being the elastic modulus. Furthermore, the Poisson's ratio parameter reflects the contraction or expansion of a material in other directions when it deforms in one direction, which can affect the calculation of normal stress.

[0103] Regarding the relationship between shear stress and shear strain, generalized Hooke's law also states that shear stress is proportional to shear strain, with the proportionality coefficient being the shear modulus, which is related to the elastic modulus and Poisson's ratio.

[0104] Step S1433: The normal stress components in the three coordinate axis directions and the shear stress components in the three planes are calculated by the relational equation to form six-component stress state parameters.

[0105] Using the strain-stress relationship equation established by generalized Hooke's law, the normal stress components in the three coordinate axes and the shear stress components in the three planes are calculated. These six components constitute the stress state parameters of the material point.

[0106] Specifically, the normal stress components in the three coordinate axes are calculated based on the normal strain component, elastic modulus, and Poisson's ratio. The shear stress components in the three planes are calculated based on the shear strain component and shear modulus.

[0107] Step S1434: performing coordinate transformation on the stress state parameters to convert them into stress components consistent with the background grid system coordinate system.

[0108] Since the calculation of stress state parameters may be performed in different coordinate systems, it is necessary to perform coordinate transformation on them and convert them into stress components consistent with the coordinate system of the background grid system.

[0109] Coordinate transformation can be achieved using methods such as rotation matrices. A rotation matrix is ​​constructed based on the angle and orientation between the background grid system coordinate system and the coordinate system used to calculate the stress state parameters. The stress state parameters are then multiplied by the rotation matrix to obtain the stress components in the background grid system coordinate system.

[0110] Step S1435: Perform physical rationality check on the calculated stress state parameters to eliminate abnormal stress values ​​caused by numerical calculation errors.

[0111] Perform physical rationality checks on the calculated stress state parameters. During the calculation process, abnormal stress values ​​may appear due to numerical calculation errors and other reasons. These abnormal stress values ​​may not conform to the physical properties of the material and will affect subsequent analysis results.

[0112] By setting a reasonable stress range and physical constraints, the calculated stress state parameters are checked. If a stress value is found to be outside the reasonable range, it is considered abnormal and needs to be eliminated or corrected. Abnormal stress values ​​can be handled by recalculation or filtering.

[0113] Step S144: updating the position coordinates of the material point according to the displacement vector of the material point, and generating a material point state set including the position coordinates, stress parameters and strain parameters in combination with the stress state parameters and the strain tensor, wherein each data item in the material point state set is associated with a unique identifier of the material point.

[0114] Update the position coordinates of the material point according to the displacement vector of the material point. Add the displacement vector to the current position coordinates of the material point to obtain the updated position coordinates.

[0115] Combining the stress state parameters and strain tensor, a material point state set containing position coordinates, stress parameters, and strain parameters is generated. This material point state set records the latest position, stress state, and strain of each material point.

[0116] To facilitate subsequent data management and querying, each data item in the material point state set is associated with a unique identifier for that material point. For example, each material point can be assigned a unique number, and the material point number corresponding to each data item is recorded in the material point state set. This way, when querying the state information of a material point, the corresponding position coordinates, stress parameters, and strain parameters can be quickly found using its unique identifier.

[0117] Step S145: performing boundary constraint check on the updated material point position coordinates to ensure that the material points do not penetrate the geometric boundary of the slope surface or the stratum interface.

[0118] Perform boundary constraint check on the updated material point position coordinates. After the material point is displaced, it is necessary to ensure that its position coordinates do not exceed the geometric boundary of the slope surface or the stratum interface.

[0119] By constructing geometric models of the slope surface and the ground interface, the updated coordinates of the material points are checked to ensure they are within these boundaries. If the coordinates of the material point are outside the boundaries, the position needs to be adjusted. This can be done by bringing the point back within the boundaries or by correcting its displacement based on the boundary conditions to ensure that the point does not penetrate the geometric boundaries of the slope surface or the ground interface.

[0120] Step S150: Based on the position coordinate changes and physical property change parameters in the material point state set, the deformation trend and potential unstable areas of the three-dimensional slope are analyzed, and a slope deformation analysis report including deformation gradient distribution and stress concentration areas is generated.

[0121] After generating a set of material point states containing deformation characteristics, the deformation trend and potential unstable areas of the three-dimensional slope are analyzed based on the position coordinate changes and physical property change parameters, and a slope deformation analysis report is generated.

[0122] Step S151: Calculate the vector difference of the position coordinate changes between adjacent material points to generate a relative displacement vector set between the material points. The relative displacement vector set is used to characterize the deformation distribution inside the slope material.

[0123] Calculate the vector differences of the position coordinate changes between adjacent material points. By comparing the position coordinates of adjacent material points at different times, the position changes between them are calculated and expressed as vector differences. These vector differences constitute the set of relative displacement vectors between the material points.

[0124] The relative displacement vector set can intuitively reflect the deformation distribution within the slope material. Large relative displacement vectors between adjacent material points indicate significant deformation in that area; small relative displacement vectors indicate minimal deformation. By analyzing the relative displacement vector set, the deformation distribution within the slope material can be determined.

[0125] Step S152: performing spatial interpolation processing on the strain tensor and stress state parameters in the material point state set to generate continuous strain fields and stress fields on the background grid nodes, wherein the strain field includes a normal strain component field and a shear strain component field, and the stress field includes a normal stress component field and a shear stress component field.

[0126] The strain tensor and stress state parameters in the material point state set are spatially interpolated to generate continuous strain and stress fields at the background grid nodes. Since material points are discretely distributed, their strain tensor and stress state parameters are only defined at their locations. Spatial interpolation is required to obtain the strain and stress distribution across the entire slope area.

[0127] There are many spatial interpolation methods, such as nearest neighbor interpolation, linear interpolation, and spline interpolation. In this embodiment, linear interpolation can be used. The basic idea of ​​linear interpolation is to calculate the strain and stress values ​​at the background grid nodes through a linear combination method based on the location of the material point and its corresponding strain tensor and stress state parameters.

[0128] For the strain field, the normal strain component and the shear strain component are interpolated to generate the normal strain component field and the shear strain component field. The normal strain component field reflects the linear deformation distribution of the slope in the three coordinate axis directions, while the shear strain component field reflects the shear deformation distribution of the slope in the coordinate axis plane.

[0129] For the stress field, the normal stress component and shear stress component are interpolated separately to generate the normal stress component field and the shear stress component field. The normal stress component field reflects the normal stress distribution of the slope in the three coordinate axis directions, while the shear stress component field reflects the shear stress distribution of the slope in the coordinate axis plane.

[0130] Step S153: Identify areas in the stress field where the shear stress component exceeds a material shear strength threshold as potential unstable areas, where the material shear strength threshold is determined according to the material type in the physical property information of the material point.

[0131] For example, step S1531: establishing a correspondence table between material types and shear strength thresholds, the correspondence table including cohesion parameters and internal friction angle parameters of different rock and soil types, and the shear strength thresholds are calculated using the Mohr-Coulomb strength criterion.

[0132] Establishing a mapping table between material types and shear strength thresholds is fundamental to identifying potential areas of instability. Different geotechnical types have varying mechanical properties and shear strengths. Through extensive laboratory and field testing, we determined the cohesion and internal friction parameters for different geotechnical types.

[0133] The Mohr-Coulomb strength criterion is a commonly used strength criterion in geotechnical engineering. It describes the relationship between a material's shear strength and normal stress, cohesion, and internal friction angle. Based on the Mohr-Coulomb strength criterion, the shear strength threshold can be calculated from cohesion parameters, internal friction angle parameters, and normal stress. For each geotechnical type, the cohesion parameters, internal friction angle parameters, and corresponding shear strength threshold are recorded in a corresponding relationship table.

[0134] Step S1532: For each material point, the cohesion parameter and the internal friction angle parameter are obtained from the corresponding relationship table according to the material type of the formation area to which the material point belongs, and the shear strength threshold of the material point is calculated.

[0135] For each material point, the corresponding cohesion and internal friction parameters are searched from the corresponding relationship table based on the material type of the formation region to which it belongs. Then, combined with the normal stress at the material point, the shear strength threshold of the material point is calculated according to the Mohr-Coulomb strength criterion.

[0136] During the calculation process, it is necessary to ensure that the normal stress used is the normal stress in the coordinate system that is compatible with the Mohr-Coulomb strength criterion. If the coordinate system of the normal stress is inconsistent with the coordinate system required by the Mohr-Coulomb strength criterion, a coordinate transformation is required.

[0137] Step S1533: Compare the shear stress component in the stress state parameter of the material point with the shear strength threshold. When the shear stress component is greater than or equal to the shear strength threshold, mark the area where the material point is located as a potential instability candidate area.

[0138] The shear stress component of the stress state parameters at each material point is compared with the calculated shear strength threshold. If the shear stress component is greater than or equal to the shear strength threshold, it indicates that the shear stress in the area where the material point is located has exceeded the shear capacity of the material, and the area is likely to be unstable, so it is marked as a potential candidate for instability.

[0139] During the comparison process, attention should be paid to the dimensional consistency of the shear stress component and the shear strength threshold to ensure that the comparison results are of practical significance.

[0140] Step S1534: performing connectivity analysis on adjacent potential unstable candidate regions, and merging continuously connected candidate regions into potential unstable regions, wherein the connectivity analysis is performed based on the spatial adjacency relationship between material points.

[0141] Connectivity analysis is performed on the marked potential unstable candidate regions. Since a potential unstable region may be composed of multiple adjacent candidate regions, connectivity analysis can be used to merge continuously connected candidate regions into one potential unstable region.

[0142] Connectivity analysis is based on the spatial adjacency between material points. If the material points in two potential instability candidate regions are spatially adjacent, meaning the distance between them is less than a preset threshold, the two candidate regions are considered connected. By traversing all potential instability candidate regions, interconnected regions are identified and merged into a single potential instability region.

[0143] Step S1535: The potential instability area is divided into different levels, and different levels of instability risk are determined according to the degree to which the shear stress component exceeds the material shear strength threshold and the size of the area, and corresponding warning signs are assigned.

[0144] The identified potential instability areas are classified into different levels. Different levels of instability risk are determined based on the degree to which the shear stress component exceeds the material shear strength threshold and the size of the area.

[0145] If the shear stress component exceeds the shear strength threshold to a large extent and the area is large, it means that the instability risk of the potential unstable area is high and it can be divided into a high-level instability risk area; if the shear stress component exceeds the shear strength threshold to a small extent and the area is small, it can be divided into a low-level instability risk area.

[0146] Different levels of instability risk areas are assigned corresponding warning signs, such as red for high-level instability risk, yellow for medium-level instability risk, and green for low-level instability risk. This allows for intuitive understanding of the instability risk situation in different areas during subsequent analysis and decision-making.

[0147] Step S154: Calculate the deformation gradient distribution, which is characterized by the spatial gradient value of each component in the strain field, reflecting the severity and change trend of the slope deformation.

[0148] The purpose of calculating the deformation gradient distribution is to gain a deeper understanding of the slope deformation. The deformation gradient distribution is represented by the spatial gradient values ​​of each component in the strain field.

[0149] For the normal and shear strain components of the strain field, their spatial gradients are calculated. This spatial gradient reflects the rate of change of strain over space, that is, the severity of the strain change. A large strain gradient in a region indicates rapid strain change and more severe slope deformation. A small strain gradient indicates slower strain change and more gradual slope deformation.

[0150] By calculating the spatial gradient values ​​of each component in the strain field, the deformation gradient distribution can be obtained. The deformation gradient distribution can reflect the severity and changing trend of slope deformation.

[0151] Step S155: Integrate the spatial position, deformation gradient distribution data, and stress field distribution characteristics of the potential instability area into a slope deformation analysis report. The slope deformation analysis report includes a three-dimensional visual deformation cloud map and stress distribution map, and each visual map is accompanied by a corresponding coordinate system and physical quantity unit description.

[0152] The spatial location of the identified potential instability area, the calculated deformation gradient distribution data, and the stress field distribution characteristics are integrated into a slope deformation analysis report. This report is a comprehensive analysis and summary of the slope deformation situation, providing a basis for decision-making by relevant personnel.

[0153] The slope deformation analysis report includes a 3D visualization of the deformation contour and stress distribution diagram. The deformation contour uses different colors to represent the degree of deformation in different slope regions, with darker colors indicating greater deformation. The stress distribution diagram uses colors to represent the stress levels in different slope regions, with darker colors indicating greater stress.

[0154] To ensure that visualizations accurately convey information, each visualization is accompanied by a corresponding coordinate system and physical unit description. The coordinate system is used to determine the actual spatial location of each location in the visualization, and the physical unit description is used to clarify the units of the physical quantity represented by the color in the visualization. For example, the unit of stress may be Pascal (Pa), and the unit of deformation may be meter (m).

[0155] Through the three-dimensional visualization of deformation cloud maps and stress distribution maps, relevant personnel can intuitively understand the deformation and stress distribution of the slope. Combined with the information on potential unstable areas, they can take corresponding measures in a timely manner to prevent and deal with slope instability problems.

[0156] Figure 2 The following diagram illustrates exemplary hardware and software components of an MPM-based 3D slope deformation analysis system 100 that can implement the concepts of the present application, as provided in some embodiments of the present application. For example, a processor 120 can be used in the MPM-based 3D slope deformation analysis system 100 to perform the functions described in the present application.

[0157] The MPM-based 3D slope deformation analysis system 100 can be a general-purpose server or a special-purpose server, both of which can be used to implement the MPM-based 3D slope deformation analysis method of this application. Although only one server is shown in this application, for convenience, the functions described in this application can be implemented in a distributed manner on multiple similar platforms to balance the processing load.

[0158] For example, the MPM-based three-dimensional slope deformation analysis system 100 may include a network port 110 connected to a network, one or more processors 120 for executing program instructions, a communication bus 130, and various forms of storage media 140, such as a disk, ROM, or RAM, or any combination thereof. For example, the MPM-based three-dimensional slope deformation analysis system 100 may also include program instructions stored in ROM, RAM, or other types of non-transitory storage media, or any combination thereof. The method of the present application may be implemented based on these program instructions. The MPM-based three-dimensional slope deformation analysis system 100 also includes an I / O interface 150 between the computer and other input and output devices.

[0159] For ease of explanation, only one processor is described in the MPM-based three-dimensional slope deformation analysis system 100. However, it should be noted that the MPM-based three-dimensional slope deformation analysis system 100 in this application can also include multiple processors, so the steps performed by one processor described in this application can also be performed jointly or individually by multiple processors. For example, if the processor of the MPM-based three-dimensional slope deformation analysis system 100 performs steps A and B, it should be understood that steps A and B can also be performed jointly by two different processors or individually in one processor. For example, the first processor performs step A and the second processor performs step B, or the first processor and the second processor perform steps A and B together.

[0160] In addition, an embodiment of the present invention further provides a readable storage medium, in which computer-executable instructions are preset. When a processor executes the computer-executable instructions, the above-mentioned three-dimensional slope deformation analysis method based on MPM is implemented.

[0161] It should be noted that in order to simplify the description of the present invention and thus help understand one or more embodiments of the invention, in the foregoing description of the embodiments of the present invention, multiple features are sometimes combined into one embodiment, figure or description thereof.

Claims

1. A three-dimensional slope deformation analysis method based on MPM, characterized in that: The method comprises: Acquiring spatial geometric structure data of the slope area, wherein the spatial geometric structure data includes a point cloud coordinate set of the slope surface and interface geometric parameters of stratum distribution; Constructing a three-dimensional material point model based on the spatial geometric structure data, discretizing the slope material into a set of material points containing position coordinates and physical property information, and establishing a background grid system covering the set of material points, wherein the background grid system includes regularly distributed grid nodes and node connection relationships; performing interaction calculations on the material point set and the background grid system, transferring the mass, momentum, and force of the material points to the background grid nodes, solving the dynamic equations including the displacement field and the stress field on the background grid nodes, and obtaining the motion state parameters of the background grid nodes; Mapping the motion state parameters of the background grid nodes back to the material points, updating the position coordinates and physical property information of the material points, and generating a material point state set containing deformation characteristics; Based on the position coordinate changes and physical property change parameters in the material point state set, the deformation trend and potential unstable areas of the three-dimensional slope are analyzed, and a slope deformation analysis report including deformation gradient distribution and stress concentration areas is generated.

2. The three-dimensional slope deformation analysis method based on MPM according to claim 1 is characterized in that: The method of constructing a three-dimensional material point model based on the spatial geometric structure data, discretizing the slope material into a material point set containing position coordinates and physical property information, and establishing a background grid system covering the material point set includes: The slope material is spatially divided according to a preset discrete rule, and uniformly distributed material points are generated within the constraint range of the point cloud coordinate set. The position coordinates of the material points form a spatial mapping relationship with the coordinate points in the point cloud coordinate set; Assigning physical property information to each material point, wherein the physical property information includes a material density parameter, an elastic modulus parameter, and a Poisson's ratio parameter, wherein the material density parameter is determined according to the rock and soil type of the area corresponding to the interface geometric parameters of the stratum distribution; Generate a background grid system containing hexahedral units with the spatial distribution range of the material point set as the boundary, wherein the grid node coordinates of the background grid system cover the position coordinates of all material points, and the spacing between adjacent grid nodes satisfies the stability condition of the numerical calculation; Establishing a spatial correlation between material points and background grid nodes, determining the background grid unit where each material point is located and its weight coefficient with the grid node, wherein the weight coefficient is used to characterize the effect of the material point on the background grid node; The initial position coordinates and physical property information of the material point set are checked for consistency, so that the position coordinates of each material point are within the geometric range of the corresponding formation area, and the physical property parameters conform to the mechanical properties of the material in the formation area.

3. The three-dimensional slope deformation analysis method based on MPM according to claim 2 is characterized in that: The spatial division of the slope material according to the preset discrete rule and the generation of uniformly distributed material points within the constraint range of the point cloud coordinate set include: Determine discrete precision parameters of slope materials, wherein the discrete precision parameters are determined according to the geometric complexity of the slope and the analysis objectives and are used to control the distribution density of material points; A material point grid is arranged in three-dimensional space according to the generation rule of the discrete precision parameter based on the coordinate points in the point cloud coordinate set, and the nodes of the material point grid serve as the initial position coordinates of the material points; Adjust the positions of the material points outside the point cloud coordinates of the slope surface so that their position coordinates fit the geometric shape of the slope surface, so that the material point set completely covers the spatial range of the slope material; Establishing an index relationship between the position coordinates of the material point and the corresponding coordinate points in the point cloud coordinate set to form a spatial mapping table, wherein the spatial mapping table is used to record the point cloud coordinates corresponding to each material point and the stratigraphic region to which it belongs; The density uniformity of the generated material point set is checked by calculating the standard deviation of the number of material points within a unit volume to ensure that the distribution of material points meets the preset discrete accuracy requirements.

4. The three-dimensional slope deformation analysis method based on MPM according to claim 2 is characterized in that: The step of establishing a spatial association relationship between material points and background grid nodes and determining the background grid unit where each material point is located and the weight coefficient between the material point and the grid node includes: Determine the coordinate position of each material point in the background grid system, and determine the background grid unit to which the material point belongs based on the coordinate range of the grid node; The weight coefficients of the material point and the four vertex nodes of the background grid unit are calculated using a trilinear interpolation method, where the sum of the weight coefficients is equal to 1 and each weight coefficient is greater than or equal to 0; Establishing a weight coefficient matrix of material points and background grid nodes, wherein rows of the weight coefficient matrix correspond to material points, columns correspond to background grid nodes, and matrix elements are corresponding weight coefficients; Performing a symmetry check on the weight coefficient matrix so that the weight coefficients of adjacent material points to the same background grid node conform to the principle of spatial symmetry; The weight coefficient matrix is ​​stored in a sparse matrix format so as to be quickly called and updated in subsequent interaction calculations.

5. The three-dimensional slope deformation analysis method based on MPM according to claim 2 is characterized in that: The interaction calculation is performed on the material point set and the background grid system, the mass, momentum and force of the material points are transferred to the background grid nodes, the dynamic equations including the displacement field and the stress field are solved on the background grid nodes, and the motion state parameters of the background grid nodes are obtained, including: For each material point, the inertial force and contact force are calculated based on its position coordinates and physical property information. The inertial force is related to the mass and acceleration of the material point, and the contact force is determined based on the relative position change between adjacent material points. The mass, momentum and force of each material point are distributed to the corresponding background grid node using the weight coefficient to generate a mass matrix and a force vector set of the background grid node; Establishing a dynamic equilibrium equation in the background grid system, wherein the dynamic equilibrium equation includes displacement variables, velocity variables, and acceleration variables of the background grid nodes, as well as material constitutive relations and boundary conditions; The dynamic equilibrium equation is solved by a numerical integration method to obtain the displacement increment, velocity vector and stress tensor of each background grid node in the current calculation time step as the motion state parameters of the background grid node, and the time step of the numerical integration method satisfies the stability condition; The motion state parameters of the background grid nodes are checked for spatiotemporal continuity, so that the displacement increments and velocity vector changes between adjacent calculation time steps conform to the physical laws of material deformation.

6. The three-dimensional slope deformation analysis method based on MPM according to claim 5 is characterized in that: The step of establishing a dynamic equilibrium equation in the background grid system includes: The displacement variables of the background grid nodes are defined as vector fields, wherein the components of the displacement variables in the spatial dimensions correspond to the displacements of the grid nodes in the directions of the three coordinate axes; Establishing a stress-strain relationship equation based on a material constitutive relationship, wherein the material constitutive relationship is set for geotechnical materials in different strata, including an elastic constitutive model or an elastic-plastic constitutive model; applying boundary conditions, including fixed displacement constraints at the bottom of the slope and free boundary conditions on the slope surface, as well as body force loads such as groundwater pressure; Substituting the displacement variable, velocity variable, acceleration variable, material constitutive relation and boundary conditions into the dynamic equilibrium equation to form a system of partial differential equations including a time variable, and converting the system of partial differential equations into a system of algebraic equations applicable to background grid nodes through spatial discretization; The algebraic equations are subjected to sparse matrix optimization processing, and the computational efficiency of the dynamic equilibrium equations is optimized through compressed storage and fast solution algorithms.

7. The three-dimensional slope deformation analysis method based on MPM according to claim 2 is characterized in that: Mapping the motion state parameters of the background grid nodes back to the material points, updating the position coordinates and physical property information of the material points, and generating a material point state set containing deformation characteristics, includes: Calculating a deformation gradient tensor of a background grid unit based on a displacement increment and a velocity vector of a background grid node, wherein the deformation gradient tensor represents a degree of deformation of the background grid unit in a spatial dimension; Mapping the displacement increment and deformation gradient tensor of the background grid node to each material point using the weight coefficient to obtain the displacement vector and strain tensor of the material point, wherein the strain tensor is determined according to the decomposition result of the deformation gradient tensor; Calculating stress state parameters of the material point based on the strain tensor of the material point and the elastic modulus parameter and Poisson's ratio parameter in the physical property information, wherein the stress state parameters include a normal stress component and a shear stress component; updating the position coordinates of the material point according to the displacement vector of the material point, and generating a material point state set including the position coordinates, stress parameters, and strain parameters in combination with the stress state parameter and the strain tensor, wherein each data item in the material point state set is associated with a unique identifier of the material point; The updated material point position coordinates are checked for boundary constraints so that the material points do not penetrate the geometric boundaries of the slope surface or the ground interface.

8. The three-dimensional slope deformation analysis method based on MPM according to claim 7 is characterized in that: Calculating the stress state parameters of the material point according to the strain tensor of the material point and the elastic modulus parameter and Poisson's ratio parameter in the physical property information includes: For each material point, the normal strain component and the shear strain component are calculated according to its strain tensor. The normal strain component corresponds to the linear deformation in the three coordinate axis directions, and the shear strain component corresponds to the angular deformation in the coordinate axis plane. The generalized Hooke's law is used to establish a relationship equation between strain and stress, wherein the relationship equation incorporates the effects of elastic modulus parameters and Poisson's ratio parameters on normal stress and shear stress; The normal stress components in the three coordinate axis directions and the shear stress components in the three planes are calculated by the relational equation to form a six-component stress state parameter; Performing coordinate transformation on the stress state parameters to convert them into stress components consistent with the background grid system coordinate system; The calculated stress state parameters are checked for physical rationality to eliminate abnormal stress values ​​caused by numerical calculation errors.

9. The three-dimensional slope deformation analysis method based on MPM according to claim 7 is characterized in that: The method of analyzing the deformation trend and potential instability area of ​​the three-dimensional slope based on the position coordinate change and physical property change parameters in the material point state set, and generating a slope deformation analysis report including deformation gradient distribution and stress concentration areas, includes: Calculating the vector difference of the position coordinate changes between adjacent material points to generate a set of relative displacement vectors between the material points, wherein the relative displacement vector set is used to characterize the deformation distribution inside the slope material; Performing spatial interpolation processing on the strain tensor and stress state parameters in the material point state set to generate continuous strain fields and stress fields on background grid nodes, wherein the strain field includes a normal strain component field and a shear strain component field, and the stress field includes a normal stress component field and a shear stress component field; Identifying areas in the stress field where shear stress components exceed a material shear strength threshold as potential instability areas, where the material shear strength threshold is determined based on a material type in the physical property information of the material point; Calculate the deformation gradient distribution, which is characterized by the spatial gradient values ​​of each component in the strain field, reflecting the severity and change trend of the slope deformation; The spatial position of the potential unstable area, deformation gradient distribution data and stress field distribution characteristics are integrated into a slope deformation analysis report, which includes a three-dimensional visual deformation cloud map and stress distribution map, and each visual map is accompanied by a corresponding coordinate system and physical quantity unit description.

10. A three-dimensional slope deformation analysis system based on MPM, characterized in that: It includes a processor and a memory, the memory is connected to the processor, the memory is used to store programs, instructions or codes, and the processor is used to execute the programs, instructions or codes in the memory to implement the three-dimensional slope deformation analysis method based on MPM as described in any one of claims 1 to 9.

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