A finite element simulation method for deformation of a subway foundation pit in soft soil area

Abstract

The present application relates to the technical field of computer-aided design, in particular to a subway foundation pit deformation finite element simulation method in soft soil area, comprising: carrying out finite element simulation on the subway foundation pit model under different grid parameters, determining the deformation size and calculation time length of each position; according to the deformation size, determining a plurality of deformation regions and the regional influence degree of each deformation region; according to the deformation size and calculation time length of each position in each simulation, determining the optimization feasibility of each position in each deformation region; according to the regional influence degree and the optimization feasibility of each position, determining the grid optimization proportion of each deformation region; according to the grid parameters, hardware configuration and calculation time length of each simulation, determining the target reference grid parameter; according to the target reference grid parameter and the grid optimization proportion of each deformation region, determining the target grid parameter of each deformation region. The method can improve the accuracy of subway foundation pit deformation finite element simulation and reduce the consumption of computing resources.

Description

Technical Field

[0001] This invention relates to the field of computer-aided design technology, specifically to a finite element simulation method for the deformation of subway foundation pits in soft soil areas. Background Technology

[0002] With urban development, subways have gradually become the mainstream of public transportation. However, with the increasing number of subway constructions, it's inevitable that subway lines will become deeper. In such cases, due to the increased depth of the foundation pit and the soft soil of the surrounding area, deformation is more likely to occur during subway construction. To better protect against anomalies in the foundation pit during construction, finite element simulation (FEM) is often performed to assess its deformation before construction begins. The core idea of ​​FEM is to discretize the soft soil region of the subway foundation pit into a finite number of simple element bodies, such as tetrahedrons or hexahedrons. Then, through mathematical approximation, it simulates the mechanical and thermal conduction behaviors of the real physical system, thereby predicting the deformation of the subway foundation pit. In essence, it captures and simulates the stress and deformation at corresponding local locations within the foundation pit by analyzing the forces acting on numerous element bodies in each region. In FEM simulation, the finer the mesh of each region, the higher the accuracy of the simulation results, but the greater the computational resource consumption.

[0003] When two subway tunnels meet in a foundation pit, directional blasting with explosives is needed to create a narrow passage. This requires precise simulation of the blast area, but the accuracy of simulations for areas further away and unaffected by the blast's shockwave can be relatively lower. Currently, multi-scale adaptive meshing techniques are commonly used, employing local mesh refinement or adaptive thinning strategies to densify the mesh in critical areas such as the blast zone. However, this doesn't consider that the blast involves a relatively large area, and the airflow and particles generated by the blast can also affect other soft soil areas, causing deformation and resulting in lower simulation accuracy. Furthermore, uniformly adjusting mesh density or adjusting the area of ​​interest based on the model shape is computationally wasteful. During the blast, most areas of the foundation pit do not experience deformation and do not require significant computational resources. Summary of the Invention

[0004] To address the technical problems of inaccurate finite element simulation of subway foundation pit deformation and excessive computational resource consumption, the present invention aims to provide a finite element simulation method for subway foundation pit deformation in soft soil areas. The specific technical solution adopted is as follows:

[0005] This invention provides a finite element simulation method for the deformation of subway foundation pits in soft soil areas, the method comprising:

[0006] Finite element simulations were performed on a subway foundation pit model under different mesh parameters to determine the deformation dimensions and computation time at each location.

[0007] Based on the deformation dimensions at each location in each simulation, multiple deformation regions are determined, and the regional influence degree of each deformation region is determined.

[0008] Based on the deformation size and computation time at each location in each simulation, the optimization feasibility at each location in each deformation region is determined;

[0009] Based on the regional influence of each deformed region and the optimization feasibility of each location, the mesh optimization ratio of each deformed region is determined;

[0010] The target baseline mesh parameters are determined based on the mesh parameters, hardware configuration, and computation time of each simulation.

[0011] The target mesh parameters for each deformation region are determined based on the target reference mesh parameters and the mesh optimization ratio for each deformation region.

[0012] According to the finite element simulation method for subway foundation pit deformation in soft soil areas provided by the present invention, determining multiple deformation regions based on the deformation dimensions at each location in each simulation includes:

[0013] Based on the deformation dimensions at each location in each simulation, determine the degree of deformation at each location;

[0014] The positions where the degree of deformation is greater than or equal to a preset degree of deformation threshold are used as seed points;

[0015] Starting from each of the seed points, region growth is performed based on the degree of deformation of the surrounding locations to obtain multiple deformable regions.

[0016] According to the finite element simulation method for subway foundation pit deformation in soft soil areas provided by the present invention, starting from each of the seed points, region growth is performed based on the deformation degree of the surrounding locations to obtain multiple deformation regions, including:

[0017] Starting from each of the seed points, traverse the surrounding positions outwards step by step;

[0018] For each traversed position, the degree of merging of the traversed position is determined based on the difference between the degree of deformation of the traversed position and the average degree of deformation of each position in the neighborhood of the traversed position.

[0019] If the merging degree is greater than or equal to the preset merging degree threshold, then the positions traversed are merged into the deformation region corresponding to the seed point;

[0020] The traversal continues until the degree of merging at the traversed position is less than the preset degree of merging threshold, at which point the traversal stops and the deformed region corresponding to the seed point is obtained.

[0021] According to the finite element simulation method for subway foundation pit deformation in soft soil areas provided by the present invention, determining the regional influence degree of each deformation region includes:

[0022] For each of the deformation regions, determine the average distance from the seed point within the deformation region to each position on the edge of the deformation region;

[0023] The degree of deformation of the deformation region is determined based on the maximum value of the degree of deformation at each location within the deformation region and the average distance.

[0024] The regional influence degree of the deformed region is determined based on the size of the deformed region and the degree of deformation of the region.

[0025] According to the finite element simulation method for subway foundation pit deformation in soft soil areas provided by the present invention, determining the optimization feasibility of each location in each deformation region based on the deformation size and calculation time at each location in each simulation includes:

[0026] For each location in each of the deformation regions, determine the difference in deformation size between the deformation size of the location in each simulation and the deformation size of the location in the benchmark simulation;

[0027] Determine the difference in computation time between the location in each simulation and the location in the benchmark simulation;

[0028] The optimization feasibility of the position in the deformation region is determined based on the differences in deformation size and computation time corresponding to the position in each simulation.

[0029] According to the finite element simulation method for subway foundation pit deformation in soft soil areas provided by the present invention, determining the target reference mesh parameters based on the mesh parameters, hardware configuration, and computation time of each simulation includes:

[0030] Based on the mesh parameters, hardware configuration, and computation time of each simulation, determine the relationship between mesh parameters and computation time;

[0031] The grid parameters are sampled sequentially, and the computation time corresponding to the sampled grid parameters is determined based on the sampled grid parameters for each sampling and the relationship between the grid parameters and the computation time. The direction of sampling the grid parameters is the direction that increases the grid density, decreases the grid size, or increases the number of grids.

[0032] The target reference grid parameters are determined based on the increase in the calculation time obtained from each sampling.

[0033] According to the finite element simulation method for subway foundation pit deformation in soft soil areas provided by the present invention, determining the relationship between mesh parameters and computation time based on the mesh parameters, hardware configuration, and computation time of each simulation includes:

[0034] The mesh parameters and hardware configuration of each simulation are used as inputs, and the computation time of each simulation is used as outputs. The relationship between mesh parameters and computation time is obtained through random forest training.

[0035] According to the finite element simulation method for subway foundation pit deformation in soft soil areas provided by the present invention, the step of determining the target reference mesh parameters based on the growth of the calculation time obtained from each sampling includes:

[0036] For each sample, determine the increase in computation time obtained in the current sample relative to the computation time obtained in the previous sample;

[0037] Based on the duration increase of the previous preset number of samples, determine the duration increase threshold for the current sample.

[0038] If the duration increase of the current sample is less than the duration increase threshold of the current sample, then sampling continues;

[0039] If the duration increase of the current sampling is greater than or equal to the duration increase threshold of the current sampling, then the sampling grid parameters of the current sampling are determined as the target reference grid parameters, and sampling is stopped.

[0040] According to the finite element simulation method for subway foundation pit deformation in soft soil areas provided by the present invention, determining the target mesh parameters for each deformation region based on the target reference mesh parameters and the mesh optimization ratio for each deformation region includes:

[0041] For each of the deformed regions, the target mesh parameters are increased according to the mesh optimization ratio of the deformed region based on the target reference mesh parameters to obtain the target mesh parameters of the deformed region.

[0042] According to the finite element simulation method for subway foundation pit deformation in soft soil areas provided by the present invention, the method further includes:

[0043] The target reference mesh parameters are used as the target mesh parameters for the remaining regions, excluding each of the deformed regions.

[0044] This invention has the following beneficial effects: Finite element simulations of a subway foundation pit model are performed under different mesh parameters to determine the deformation dimensions and computation time at each location. Then, based on the deformation dimensions at each location in each simulation, multiple deformation regions are determined, and the regional influence of each deformation region is determined. Based on the deformation dimensions and computation time at each location in each simulation, the optimization feasibility of each location within each deformation region is determined. Based on the regional influence and optimization feasibility of each location, the mesh optimization ratio of each deformation region is determined. Then, the mesh optimization ratio of each deformation region is varied based on the target baseline mesh parameters, thereby enabling the accurate setting of different target mesh parameters for different regions. This improves the accuracy of finite element simulations of subway foundation pit deformation and avoids consuming large amounts of computational resources in areas with small deformations, reducing the consumption of computational data. Attached Figure Description

[0045] To more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1 This is a flowchart illustrating a finite element simulation method for the deformation of a subway foundation pit in soft soil areas, provided in one embodiment of the present invention.

[0047] Figure 2 This is a schematic diagram of the overall process for determining the deformation region according to an embodiment of the present invention;

[0048] Figure 3 This is a schematic diagram of a process for determining a deformable region based on seed points through region generation, provided in one embodiment of the present invention.

[0049] Figure 4 This is a schematic diagram of the overall process for determining target reference grid parameters according to an embodiment of the present invention;

[0050] Figure 5 This is a schematic diagram of a process for determining target reference grid parameters based on the time growth, as provided in an embodiment of the present invention. Detailed Implementation

[0051] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of a finite element simulation method for subway foundation pit deformation in soft soil areas proposed according to the present invention. In the following description, different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics in one or more embodiments can be combined in any suitable form.

[0052] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0053] The following description, in conjunction with the accompanying drawings, details the specific scheme of the finite element simulation method for subway foundation pit deformation in soft soil areas provided by this invention.

[0054] Please see Figure 1 The diagram illustrates a flowchart of a finite element simulation method for subway foundation pit deformation in soft soil areas, provided by an embodiment of the present invention, including the following steps:

[0055] Step 101: Perform finite element simulation on the subway foundation pit model under different mesh parameters to determine the deformation size and calculation time at each location.

[0056] It's understandable that when performing finite element simulations of the entire directional blasting process of a subway foundation pit, finer meshes in each region consume more computational resources during the simulation, but the obtained pit deformation data will be more accurate. Conversely, coarser meshes consume fewer resources and are faster to compute, but the accuracy of the obtained pit deformation data will decrease. Therefore, it's advisable to first perform multiple fuzzy simulations under different mesh parameters, and then compare the pit deformation data (deformation dimensions) obtained from these simulations to identify which regions have low computational efficiency—that is, those that consume more resources but do not significantly improve accuracy. Simultaneously, based on the deformation patterns across numerous regions of the foundation pit, identify the regions with the greatest deformation or those most susceptible to deformation and most affected by deformation. This allows for determining the relative importance of different pit regions, and then adaptively adjusting the mesh parameters for each region accordingly.

[0057] In one embodiment, mesh parameters may include the number of meshes, mesh density, and mesh type. For example, mesh type may include hexahedron and tetrahedron.

[0058] In one embodiment, a subway foundation pit model is constructed based on actual measurement data and construction drawings. Finite element simulations are then performed on the subway foundation pit model under different mesh parameters. The simulation results are compared with the original foundation pit model structure to obtain the deformation dimensions at each location. The simulation results may include data such as stress, strain, and displacement field distributions at different locations within the subway foundation pit at different time points.

[0059] In one embodiment, the calculation time at a location can be the time elapsed from the start of the simulation until the rate of change of data such as stress and deformation dimensions at that location becomes less than or equal to a preset rate of change threshold. For example, the preset rate of change threshold can be 5%.

[0060] In one embodiment, the construction process of the subway foundation pit model is as follows: First, a 3D laser scanner is placed in the foundation pit, and construction drawings of the subway foundation pit are retrieved to obtain the depth, length, width, and supporting structure data such as the diaphragm wall. Based on this, the basic geometric model of the subway foundation pit is completed. Then, geological data is obtained through geological exploration methods, including drilling and laboratory testing, and data from previous pre-construction geological explorations are retrieved. Furthermore, soil properties within the foundation pit, such as compression modulus, cohesion, and internal friction angle, are measured using triaxial experiments and numerous detection systems. Next, multiple environmental sensors are installed within the subway foundation pit to collect environmental data, including temperature and humidity sensors. Environmental data includes temperature, atmospheric pressure, groundwater level, and soil moisture. Finally, the detected environmental data is input into finite element software, and the subway foundation pit model is constructed based on this data and the corresponding model. The mechanical system of the subway foundation pit model includes a soil elastoplastic model, support structure beam elements, and a seepage field model. Parameters include example boundary conditions and force boundary conditions. Information on these parameters is then collected to form an information database.

[0061] In one embodiment, the process of performing finite element simulations on a subway foundation pit model under different mesh parameters and comparing the simulation results with the original foundation pit model to obtain the deformation dimensions at each location is as follows: After completing the parametric modeling of the subway foundation pit, nodes are gradually generated from the boundary to the interior using the wave pushing method, and a high-quality triangular mesh is generated using the Delaunay triangulation algorithm, i.e., the initialization mesh. Then, based on the initialization mesh, the subway foundation pit model, and the boundary conditions, a suitable solver is selected, such as the Newmark method (a method for simulating the dynamic response of a structure under transient loads) or the central difference method, etc. The time step is adjusted according to the dynamic process of directional blasting, and the simulation solution is performed. After obtaining the simulation results, data such as the stress, strain, and displacement field distribution at each location in the subway foundation pit at different times are extracted and compared with the original foundation pit model structure to obtain the deformation dimensions at each location. In the aforementioned wave-pushing method and Delaunay triangulation algorithm, by limiting the leading edge length, element growth rate, and density function, element meshes with a certain mesh size (limited by the leading edge length) and mesh density (limited by the element growth rate and density function) are generated. Finite element simulations are then performed to obtain the deformation dimensions at various locations under the corresponding mesh parameters. Similarly, by adjusting mesh parameters such as the leading edge length, element growth rate, and density function, meshes with different mesh sizes and densities can be further generated. Finite element simulations are then used to obtain the deformation dimensions at various locations under different mesh parameters.

[0062] Step 102: Based on the deformation dimensions at each location in each simulation, determine multiple deformation regions and the regional influence degree of each deformation region.

[0063] Among them, the regional impact degree is used to characterize the degree of impact of the explosion on the deformed area.

[0064] In one embodiment, the degree of deformation at each location is determined based on the deformation size at each location in each simulation, and then multiple deformation regions are determined based on the degree of deformation at each location.

[0065] In one embodiment, locations whose deformation degree meets a first preset condition can be used as seed points. Starting from various seed points, region growth is performed based on the deformation degree of surrounding locations to obtain multiple deformable regions. The first preset condition can be that the deformation degree is greater than or equal to a preset deformation degree threshold, or it can be that the deformation degree is ranked in descending order of a preset number or a preset proportion, or it can be other conditions, without limitation.

[0066] In one embodiment, for each deformed region, the regional influence of that deformed region is determined based on its size and the degree of deformation. In one embodiment, the size of the deformed region can be determined based on the total number of locations within the deformed region. In another embodiment, the degree of deformation of the deformed region can be determined based on the maximum value of the deformation degree at each location within the deformed region and the size of the deformed region.

[0067] Step 103: Determine the optimization feasibility of each position in each deformation region based on the deformation size and calculation time of each position in each simulation.

[0068] Among them, optimization feasibility is used to characterize the feasibility of investing more computational resources in the location of the deformed region to achieve greater accuracy.

[0069] In one embodiment, the optimization feasibility of each location in each deformation region is determined based on the changes in deformation size and computation time at each location as the mesh parameters change towards the target direction in each simulation. The target direction is the direction that increases mesh density, decreases mesh size, or increases the number of meshes.

[0070] Step 104: Determine the mesh optimization ratio for each deformation region based on the regional influence of each deformation region and the optimization feasibility of each location.

[0071] Among them, the mesh optimization ratio is used to characterize the degree to which the mesh density of the deformed region needs to be increased in order to complete the simulation more accurately and efficiently.

[0072] It's understandable that for finite element simulation of subway foundation pit deformation, not all areas worthy of computational resources need to be prioritized. More attention should be paid to the impact of explosions on soft soil areas. This necessitates adjusting mesh parameters primarily for areas with significant explosion impact and where increased computational resources can yield greater accuracy. In other words, areas with greater explosion impact and higher optimization feasibility should have finer meshes. Based on this, the mesh fineness for each deformation region is determined. Therefore, the following relationship can be found between the mesh optimization ratio of the deformation region, the regional impact of the deformation region, and the optimization feasibility at each location:

[0073] The mesh optimization ratio of the deformed region is positively correlated with the regional influence of the deformed region and with the optimization feasibility of each location in the deformed region.

[0074] In one embodiment, the reciprocal of the product between the regional influence of the deformed region and the optimization feasibility of a location within the deformed region can be taken. This reciprocal can then be inversely normalized, and the average of the inverse normalization results for each location can be calculated to obtain the mesh optimization ratio of the deformed region. The formula is as follows:

[0075] ;

[0076] in, Indicates the deformed area The mesh optimization ratio. Indicates the deformed area The degree of regional influence. Indicates the deformed area The first in The feasibility of optimization at each position. Indicates the deformed area The total number of positions in the text. This represents an exponential function with base e. This indicates taking the absolute value. Used to achieve inverse proportional normalization.

[0077] The larger the mesh optimization ratio, the greater the density of the deformed region should be when the mesh is refined in order to complete the finite element simulation more accurately and efficiently.

[0078] Step 105: Determine the target reference mesh parameters based on the mesh parameters, hardware configuration, and computation time of each simulation.

[0079] The target reference mesh parameters are the mesh parameters required to ensure accuracy while saving computational resources during finite element simulation of subway foundation pits. That is, under these target reference mesh parameters, further adjustments to the mesh parameters, such as increasing mesh density, decreasing mesh size, or increasing the number of meshes, will result in a significant increase in computation time and a substantial increase in computational resource investment.

[0080] Step 106: Determine the target mesh parameters for each deformation region based on the target reference mesh parameters and the mesh optimization ratio of each deformation region.

[0081] In one embodiment, the target reference mesh parameters can be used as the target mesh parameters for the remaining regions excluding each deformed region. The target mesh parameters for each deformed region are determined based on the target reference mesh parameters and the mesh optimization ratio for each deformed region.

[0082] In one embodiment, after obtaining the target mesh parameters at various locations in the subway foundation pit, the advancing wavefront method is used to generate the hexahedral dominant hybrid mesh corresponding to each region in the foundation pit. Then, based on the set boundary conditions and the corresponding solver, the deformation of the subway foundation pit is simulated.

[0083] The aforementioned finite element simulation method for subway foundation pit deformation in soft soil areas performs finite element simulations on the subway foundation pit model under different mesh parameters to determine the deformation size and computation time at each location. Then, based on the deformation size at each location in each simulation, multiple deformation regions are determined, and the regional influence of each deformation region is determined. Based on the deformation size and computation time at each location in each simulation, the optimization feasibility of each location in each deformation region is determined. Based on the regional influence and optimization feasibility of each location, the mesh optimization ratio of each deformation region is determined. Then, based on the mesh optimization ratio of each deformation region, the target reference mesh parameters are varied. This allows for the accurate setting of different target mesh parameters for different regions, improving the accuracy of the finite element simulation of subway foundation pit deformation and avoiding the consumption of large computational resources in areas with small deformation, thus reducing the consumption of computational data.

[0084] In one embodiment, see Figure 2 Based on the deformation dimensions at each location in each simulation, multiple deformation regions are determined, including the following steps:

[0085] Step 201: Determine the degree of deformation at each location based on the deformation dimensions at each location in each simulation.

[0086] It's understandable that subway foundation pit construction often involves a fixed process. To avoid affecting ventilation and other nearby lines, directional blasting is needed to open new air ducts. Therefore, directional blasting is performed when the foundation pit is relatively stable. Before the explosion, the subway foundation pit is essentially stable. However, when the explosion occurs, the blast wave and ejected particles cause varying degrees of deformation throughout the pit. Locations with greater deformation indicate a greater impact from the explosion, and simulations should be more accurate. Therefore, by analyzing the deformation dimensions at each location in each simulation, the degree of deformation at each location can be determined, and the deformation zone can be identified based on the degree of deformation at each location.

[0087] In one embodiment, for each location, the maximum value of the deformation dimensions in each direction obtained in each simulation is determined, and the degree of deformation at that location is determined based on the maximum value corresponding to each simulation at that location.

[0088] In one embodiment, the maximum value corresponding to each simulation at this location can be normally normalized proportionally, and the average of the normally normalized results can be calculated to obtain the degree of deformation at that location. The formula is as follows:

[0089] ;

[0090] in, Indicates position The degree of deformation. Indicates position First The result of the simulation in the ... Deformation dimensions in each direction. Indicates position First The maximum value of the deformation dimensions in each direction obtained from the simulation. This indicates the total number of simulations. This indicates direct proportional normalization.

[0091] Step 202: Select the positions where the degree of deformation is greater than or equal to the preset degree of deformation threshold as seed points.

[0092] For example, the preset deformation threshold can be set to 0.6.

[0093] It is understandable that locations with deformation levels greater than or equal to a preset deformation threshold are considered to have significant deformation, requiring close monitoring of this deformation to predict the blasting effect. Since the crater deformation caused by the explosion is often due to compression from vibrations and airflow, these deformations within the crater can become continuous. Therefore, multiple deformation zones are defined based on locations with deformation levels greater than or equal to the preset deformation threshold.

[0094] Step 203: Starting from various sub-points, perform region growth based on the degree of deformation at surrounding locations to obtain multiple deformed regions.

[0095] In one embodiment, starting from each seed point, the surrounding positions are traversed outward step by step. For each traversed position, the degree of merging of the traversed position is determined based on the degree of deformation of the traversed position and the degree of deformation of each position in the neighborhood of the traversed position. Based on the degree of merging, region growth is performed to obtain the deformed region corresponding to the seed point.

[0096] In one embodiment, if the merging degree is greater than or equal to a preset merging degree threshold, the traversed position is merged into the deformation region corresponding to the seed point until the merging degree of the traversed position does not meet the second preset condition, then the traversal stops and the deformation region corresponding to the seed point is obtained.

[0097] In the above embodiments, the degree of deformation at each position is determined based on the deformation size at each position in each simulation. Positions with a deformation degree greater than or equal to a preset deformation degree threshold are used as seed points, thereby accurately determining the positions of seed points with a large degree of deformation. Then, starting from various seed points, region growth is performed based on the deformation degree of surrounding positions, which can accurately obtain multiple deformation regions.

[0098] In one embodiment, see Figure 3 Step 203 starts from various sub-points and performs region growth based on the degree of deformation at surrounding locations to obtain multiple deformed regions, including the following steps:

[0099] Step 2031: Starting from each seed point, gradually traverse the surrounding positions outwards.

[0100] Step 2032: For each traversed position, determine the degree of merging of the traversed position based on the difference between the degree of deformation of the traversed position and the average degree of deformation of each position in the neighborhood of the traversed position.

[0101] For example, the neighborhood of the position to which the traversal is performed can be a range with a diameter of 1 cm centered at the position to which the traversal is performed.

[0102] In one embodiment, the degree of merging of the traversed locations is negatively correlated with the difference between the degree of deformation of the traversed location and the mean degree of deformation of the locations in the neighborhood of the traversed location.

[0103] In one embodiment, the difference between the deformation degree of the traversed location and the average deformation degree of all locations in the neighborhood of the traversed location can be calculated. Based on the ratio of this difference to the average deformation degree of all locations in the neighborhood of the traversed location, the difference between the deformation degree of the traversed location and the average deformation degree of all locations in the neighborhood of the traversed location is determined. The difference between the deformation degree of the traversed location and the average deformation degree of all locations in the neighborhood of the traversed location is then inversely normalized to obtain the merging degree of the traversed locations. The formula is as follows:

[0104] ;

[0105] in, Represents seed point The surrounding area has been traversed to the first Merging degree of each position. Represents seed point The surrounding area has been traversed to the first The degree of deformation at each location. Represents seed point The surrounding area has been traversed to the first The average degree of deformation at each location within the neighborhood of a given location. This represents an exponential function with base e. This indicates taking the absolute value. Used to achieve inverse proportional normalization.

[0106] Step 2033: If the merging degree is greater than or equal to the preset merging degree threshold, then merge the traversed positions into the deformation region corresponding to the seed point.

[0107] For example, the preset merging threshold can be set to 0.6.

[0108] Step 2034: Continue traversing until the merging degree of the traversed position is less than the preset merging degree threshold, then stop traversing and obtain the deformed region corresponding to the seed point.

[0109] In the above embodiments, starting from each seed point, the surrounding positions are traversed outward step by step. For each traversed position, the degree of merging of the traversed position is determined based on the difference between the degree of deformation of the traversed position and the average degree of deformation of each position in the neighborhood of the traversed position. Based on the comparison result of the degree of merging and the preset degree of merging threshold, region growth is performed, thereby realizing the accurate division of multiple deformed regions based on multiple positions with large degrees of deformation.

[0110] In one embodiment, determining the regional influence of each deformed region includes: for each deformed region, determining the average distance from the seed point within the deformed region to each position on the edge of the deformed region; determining the regional deformation degree of the deformed region based on the maximum value and the average distance among the deformation degrees at each position within the deformed region; and determining the regional influence of the deformed region based on the size of the deformed region and the regional deformation degree.

[0111] It is understandable that during an explosion, the vibration of the foundation pit, as well as the airflow and particles generated by the explosion, will impact various locations within the pit, causing varying degrees of deformation. Areas with larger deformation or wider deformation ranges indicate greater impact from the explosion, and the simulation needs to accurately capture the explosion's effects. Therefore, it is necessary to construct the magnitude of the explosion's impact on each deformed area, i.e., the regional influence degree, based on the deformation range (i.e., the size of the deformed area) and the degree of deformation within each area.

[0112] In one embodiment, the degree of deformation of the deformable region is determined based on the ratio between the maximum value of the deformation degree at each location within the deformable region and the average distance.

[0113] In one embodiment, the regional influence of the deformed region is positively correlated with the size of the deformed region and with the degree of regional deformation of the deformed region.

[0114] In one embodiment, the regional influence of the deformed region is determined by multiplying the size of the deformed region by the degree of regional deformation. The formula is as follows:

[0115] ;

[0116] in, Indicates the deformed area The degree of regional influence. Indicates the deformed area The size of the deformation region The number of pixels within. Indicates the deformed area Inner The degree of deformation at each location. Indicates the deformed area The maximum value among the deformation degrees at various locations within the interior. Indicates the deformed area Seed point within the deformation region The average distance at each position on the edge. Indicates the deformed area The degree of regional deformation. Used to achieve proportional normalization.

[0117] The greater the regional influence, the greater the deformation range and degree of the deformed area, indicating that the deformed area is more affected by the explosion and needs to be given more attention during simulation. The deformed area should be simulated in greater detail.

[0118] In the above embodiments, the regional influence of the deformed region can be accurately determined based on the size of the deformed region and the degree of regional deformation.

[0119] In one embodiment, the optimization feasibility of each location in each deformation region is determined based on the deformation size and computation time of each location in each simulation. This includes: determining the difference in deformation size between the location in each simulation and the location in the baseline simulation for each location in each deformation region; wherein the baseline simulation is the simulation in which the mesh parameters minimize the mesh density, maximize the mesh size, or minimize the number of meshes; determining the difference in computation time between the location in each simulation and the location in the baseline simulation; and determining the optimization feasibility of the location in the deformation region based on the difference in deformation size and computation time corresponding to the location in each simulation.

[0120] It is understandable that finer meshes lead to more accurate simulation results in finite element simulations, but this also significantly increases computational resource consumption. Furthermore, in some regions, increasing mesh density did not significantly improve the accuracy of deformation; that is, the change in deformation accuracy remained essentially unchanged with increasing computational difficulty, indicating that mesh parameters in these regions did not require further adjustment. Therefore, the feasibility of optimization at each location can be determined by assessing the consistency between computational difficulty (i.e., computation time) and changes in deformation accuracy (i.e., deformation size) with increasing mesh density in each simulation.

[0121] In one embodiment, the initial simulation can be used as a baseline simulation, with the lowest mesh density, largest mesh size, or fewest meshes. In subsequent simulations, the mesh parameters are gradually adjusted to increase the mesh density, decrease the mesh size, or increase the number of meshes.

[0122] In one embodiment, the optimization feasibility of a location in the deformable region is positively correlated with the difference in deformation size in each simulation at that location, and negatively correlated with the difference in computation time in each simulation at that location.

[0123] In one embodiment, for each location within each deformation region, the ratio between the difference in deformation size and the difference in computation time at that location in each simulation is calculated. This ratio is then normalized proportionally. Finally, the average of the normalized ratios for that location across all simulations is calculated to obtain the optimization feasibility for that location. The formula is as follows:

[0124] ;

[0125] in, Indicates the deformed area The first in The feasibility of optimization at each position. Indicates the first Deformation region in the simulation The first in The deformation dimensions at each location. Indicating the deformable region in the benchmark simulation The first in The deformation dimensions at each location. This indicates taking the absolute value. Indicates the first Deformation region in the simulation The first in The difference in deformation size at each location. Indicates the first Deformation region in the simulation The first in The calculation time for each location. Indicating the deformable region in the benchmark simulation The first in The calculation time for each location. Indicates the first Deformation region in the simulation The first in The difference in computation time corresponding to each position, generally speaking There is no possibility that the denominator is zero. If there is an extreme case, in order to avoid the possibility that the denominator of the fraction is zero, a non-zero constant, such as 0.001, is added to the position of the denominator. This represents the total number of simulations. Since the first simulation serves as the baseline simulation, the formula uses [a specific value] when calculating the average value. . Used to achieve proportional normalization.

[0126] The greater the optimization feasibility, the more accurate the result can be achieved by investing computational resources at that location.

[0127] In the above embodiments, based on the consistency between the computational difficulty (i.e., computation time) and the change in deformation accuracy (i.e., deformation size) as the mesh density increases in each simulation, the optimization feasibility at each location can be accurately determined.

[0128] In one embodiment, see Figure 4 Based on the mesh parameters, hardware configuration, and computation time of each simulation, the target baseline mesh parameters are determined, including the following steps:

[0129] Step 401: Determine the relationship between mesh parameters and computation time based on the mesh parameters, hardware configuration, and computation time of each simulation.

[0130] It is understandable that the computational difficulty gradually increases as the mesh density increases, the mesh size decreases, and the number of meshes increases during simulation. Therefore, the relationship between mesh parameters and computation time is first established based on the computation time of multiple simulations of subway foundation pits and the corresponding mesh parameters.

[0131] In one embodiment, the mesh parameters and hardware configuration of each simulation can be used as input, and the computation time of each simulation can be used as output. The relationship between the mesh parameters and the computation time can be determined by a machine learning algorithm.

[0132] Step 402: Sample the grid parameters sequentially. Based on the sampled grid parameters for each sampling and the relationship between the grid parameters and the computation time, determine the computation time corresponding to the sampled grid parameters. The direction of sampling the grid parameters is the direction that increases the grid density, decreases the grid size, or increases the number of grids.

[0133] For example, if the grid parameters include grid density, the grid density can be sampled by increasing it by a factor of 0.1 each time.

[0134] The sampling grid parameters can be substituted into the relationship between grid parameters and computation time to obtain the computation time corresponding to the sampling grid parameters.

[0135] Step 403: Determine the target reference grid parameters based on the increase in computation time obtained from each sampling.

[0136] In the above embodiments, the target reference mesh parameters can be accurately determined based on the growth of the calculation time obtained from each sampling of the mesh parameters. This ensures that the accuracy of the subway foundation pit is guaranteed while saving computational resources when performing finite element simulation under the target reference mesh parameters.

[0137] In one embodiment, the relationship between mesh parameters and computation time is determined based on the mesh parameters, hardware configuration, and computation time of each simulation. This includes: taking the mesh parameters and hardware configuration of each simulation as input and the computation time of each simulation as output, and obtaining the relationship between mesh parameters and computation time through random forest training.

[0138] In the above embodiments, the relationship between grid parameters and computation time can be accurately obtained through random forest training.

[0139] In one embodiment, see Figure 5 Step 403 determines the target reference grid parameters based on the increase in computation time obtained from each sampling, including the following steps:

[0140] Step 4031: For each sample, determine the increase in computation time obtained from the current sample relative to the computation time obtained from the previous sample.

[0141] The time increment is determined based on the difference between the calculation time obtained from the current sampling and the calculation time obtained from the previous sampling.

[0142] Step 4032: Determine the duration increase threshold for the current sampling based on the duration increase of the previous adjacent preset number of samplings.

[0143] For example, the preset number of times can be two.

[0144] In one embodiment, the duration increase threshold for the current sample can be determined based on the average duration increase of the previous preset number of samples.

[0145] In one embodiment, the threshold for the duration increase of the current sample can be the average of the duration increases of the previous preset number of samples multiplied by a preset multiple. For example, the preset multiple can be 1.5. That is, the threshold for the duration increase of the current sample can be expressed as... .in, This represents the average increase in duration over the previous preset number of samplings.

[0146] Step 4033: If the duration increase of the current sampling is less than the duration increase threshold of the current sampling, then continue sampling.

[0147] Step 4034: If the duration increase of the current sampling is greater than or equal to the duration increase threshold of the current sampling, then the sampling grid parameters of the current sampling are determined as the target reference grid parameters, and sampling is stopped.

[0148] For example: if the duration increase of the current sampling meets the following condition, then the sampling grid parameters of the current sampling will be determined as the target reference grid parameters:

[0149] ;

[0150] in, This indicates the amount of time increase for the current sampling. This represents the average increase in duration over the previous preset number of samplings. This represents the threshold for the duration increase of the current sampling.

[0151] In the above embodiments, the duration growth threshold of the current sampling is determined based on the duration growth of the previous preset number of samplings. If the duration growth of the current sampling is greater than or equal to the duration growth threshold of the current sampling, it indicates that the duration growth of the current sampling does not conform to the previous growth pattern. Therefore, the sampling grid parameters of the current sampling are determined as the target reference grid parameters, which enables the subway foundation pit to maintain accuracy and save computational resources when performing finite element simulation under the target reference grid parameters.

[0152] In one embodiment, determining the target mesh parameters for each deformation region based on the target reference mesh parameters and the mesh optimization ratio of each deformation region includes: for each deformation region, increasing the target mesh parameters according to the mesh optimization ratio of the deformation region based on the target reference mesh parameters to obtain the target mesh parameters of the deformation region.

[0153] ;

[0154] in, Indicates the deformed area The target mesh parameters. This represents the target reference grid parameters. Indicates the deformed area The mesh optimization ratio.

[0155] In the above embodiments, based on the target reference mesh parameters, the mesh is increased according to the mesh optimization ratio of the deformation region, which can accurately obtain the target mesh parameters of the deformation region. Different target mesh parameters can be accurately set for different regions, which improves the accuracy of finite element simulation of subway pit deformation and avoids consuming a lot of computing resources in areas with small deformation, thus reducing the consumption of computing data.

[0156] In one embodiment, the method further includes: using the target reference mesh parameters as the target mesh parameters for the remaining regions excluding each deformed region.

[0157] In the above embodiments, using the target reference mesh parameters as the target mesh parameters for the remaining regions other than the deformed regions enables the remaining regions to maintain accuracy while saving computational resources under the target reference mesh parameters.

[0158] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0159] The embodiments described above are merely examples of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these modifications and improvements all fall within the protection scope of this application.

[0160] It should be noted that the order of the above embodiments of the present invention is merely for descriptive purposes and does not represent the superiority or inferiority of the embodiments. The processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0161] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

Claims

1. A finite element simulation method for the deformation of subway foundation pits in soft soil areas, characterized in that, The method includes: Finite element simulations were performed on a subway foundation pit model under different mesh parameters to determine the deformation dimensions and computation time at each location. Based on the deformation dimensions at each location in each simulation, multiple deformation regions are determined, and the regional influence degree of each deformation region is determined. Based on the deformation size and computation time at each location in each simulation, the optimization feasibility at each location in each deformation region is determined; Based on the regional influence of each deformed region and the optimization feasibility of each location, the mesh optimization ratio of each deformed region is determined; The target baseline mesh parameters are determined based on the mesh parameters, hardware configuration, and computation time of each simulation. Based on the target reference mesh parameters and the mesh optimization ratio of each deformation region, the target mesh parameters of each deformation region are determined; The determination of multiple deformation regions based on the deformation dimensions at each location in each simulation includes: Based on the deformation dimensions at each location in each simulation, determine the degree of deformation at each location; The positions where the degree of deformation is greater than or equal to a preset degree of deformation threshold are used as seed points; Starting from each of the seed points, region growth is performed according to the degree of deformation of the surrounding locations to obtain multiple deformable regions; Determining the regional influence of each of the deformed regions includes: For each of the deformation regions, determine the average distance from the seed point within the deformation region to each position on the edge of the deformation region; The degree of deformation of the deformation region is determined based on the maximum value of the degree of deformation at each location within the deformation region and the average distance. The regional influence degree of the deformed region is determined based on the size of the deformed region and the degree of deformation of the region.

2. The finite element simulation method for subway foundation pit deformation in soft soil areas according to claim 1, characterized in that, Starting from each of the seed points, region growth is performed based on the degree of deformation at the surrounding locations to obtain multiple deformable regions, including: Starting from each of the seed points, traverse the surrounding positions outwards step by step; For each traversed position, the degree of merging of the traversed position is determined based on the difference between the degree of deformation of the traversed position and the average degree of deformation of each position in the neighborhood of the traversed position. If the merging degree is greater than or equal to the preset merging degree threshold, then the traversed positions are merged into the deformation region corresponding to the seed point; The traversal continues until the degree of merging at the traversed position is less than the preset degree of merging threshold, at which point the traversal stops and the deformed region corresponding to the seed point is obtained.

3. The finite element simulation method for subway foundation pit deformation in soft soil areas according to claim 1, characterized in that, The step of determining the optimization feasibility of each position in each deformation region based on the deformation size and computation time at each position in each simulation includes: For each location in each of the deformation regions, determine the difference in deformation size between the deformation size of the location in each simulation and the deformation size of the location in the benchmark simulation; wherein, the benchmark simulation is the simulation in which the mesh parameters result in the minimum mesh density, the maximum mesh size, or the minimum number of meshes; Determine the difference in computation time between the location in each simulation and the location in the benchmark simulation; The optimization feasibility of the position in the deformation region is determined based on the differences in deformation size and computation time corresponding to the position in each simulation.

4. The finite element simulation method for subway foundation pit deformation in soft soil areas according to claim 1, characterized in that, The determination of the target baseline mesh parameters based on the mesh parameters, hardware configuration, and computation time of each simulation includes: Based on the mesh parameters, hardware configuration, and computation time of each simulation, determine the relationship between mesh parameters and computation time; The grid parameters are sampled sequentially, and the computation time corresponding to the sampled grid parameters is determined based on the sampled grid parameters for each sampling and the relationship between the grid parameters and the computation time. The direction of sampling the grid parameters is the direction that increases the grid density, decreases the grid size, or increases the number of grids. The target reference grid parameters are determined based on the increase in the calculation time obtained from each sampling.

5. The finite element simulation method for subway foundation pit deformation in soft soil areas according to claim 4, characterized in that, The step of determining the relationship between mesh parameters and computation time based on the mesh parameters, hardware configuration, and computation time of each simulation includes: The mesh parameters and hardware configuration of each simulation are used as inputs, and the computation time of each simulation is used as outputs. The relationship between mesh parameters and computation time is obtained through random forest training.

6. The finite element simulation method for subway foundation pit deformation in soft soil areas according to claim 5, characterized in that, The step of determining the target reference grid parameters based on the growth of the computation time obtained from each sampling includes: For each sample, determine the increase in computation time obtained in the current sample relative to the computation time obtained in the previous sample; Based on the duration increase of the previous preset number of samples, determine the duration increase threshold for the current sample. If the duration increase of the current sample is less than the duration increase threshold of the current sample, then sampling continues; If the duration increase of the current sampling is greater than or equal to the duration increase threshold of the current sampling, then the sampling grid parameters of the current sampling are determined as the target reference grid parameters, and sampling is stopped.

7. The finite element simulation method for subway foundation pit deformation in soft soil areas according to any one of claims 1 to 6, characterized in that, The step of determining the target mesh parameters for each deformation region based on the target reference mesh parameters and the mesh optimization ratio for each deformation region includes: For each of the deformed regions, the target mesh parameters are increased according to the mesh optimization ratio of the deformed region based on the target reference mesh parameters to obtain the target mesh parameters of the deformed region.

8. The finite element simulation method for subway foundation pit deformation in soft soil areas according to any one of claims 1 to 6, characterized in that, The method further includes: The target reference mesh parameters are used as the target mesh parameters for the remaining regions, excluding each of the deformed regions.

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