A method for analyzing the vulnerability of masonry structures under extreme conditions

Abstract

The application relates to the technical field of vulnerability analysis of masonry structures, in particular to a vulnerability analysis method of a masonry structure under a limit state, which comprises the following steps: determining a comprehensive geometric characteristic value based on the similarity degree dispersion and the average similarity of the outer normal vectors between each grid element and all connected grid elements thereof; determining a stress characteristic value based on the distance between each grid element and each local grid element thereof, and in combination with stress data of the grid element; and determining a refined characteristic value based on the stress characteristic value and the comprehensive geometric characteristic value, so as to perform vulnerability analysis on the masonry structure. The application improves the accuracy of vulnerability analysis of the masonry structure by analyzing the influence of different damage degrees and different stress distributions of different parts of the masonry structure under the action of an earthquake on grid division.

Description

Technical Field

[0001] This application relates to the field of vulnerability analysis technology for masonry structures, and specifically to a vulnerability analysis method for masonry structures under extreme conditions. Background Technology

[0002] Masonry structures, which use walls and columns as the main load-bearing components, are widely used in civil and industrial buildings due to their simple construction and low cost. However, brick masonry is a brittle material, and the insufficient bonding strength of the mortar makes masonry structures more susceptible to earthquake damage compared to other structural forms. Therefore, vulnerability analysis of masonry structures under different extreme states can provide basic data for earthquake damage prediction and post-earthquake disaster assessment.

[0003] The main purpose of vulnerability analysis is to establish the mathematical relationship between seismic motion parameters and structural damage indices. This is typically measured using vulnerability curves of the structure under different limit states, which are usually obtained using finite element analysis (FEM) techniques. Mesh generation is crucial before FEM, as its results determine the quality of subsequent FEM calculations. However, because different parts of masonry structures experience varying degrees of damage and stress distributions under seismic loading, the mesh generation of a three-dimensional finite element model of a masonry structure often fails to accurately simulate the stress distribution in different parts during vulnerability analysis, thus reducing the accuracy of subsequent vulnerability analysis of masonry structures. Summary of the Invention

[0004] To address the aforementioned technical problems, this application provides a method for analyzing the vulnerability of masonry structures under extreme conditions, thereby resolving the existing issues.

[0005] The vulnerability analysis method for masonry structures under extreme conditions proposed in this application adopts the following technical solution:

[0006] One embodiment of this application provides a method for vulnerability analysis of masonry structures under extreme conditions, the method comprising the following steps:

[0007] A three-dimensional finite element model of a masonry structure is obtained, the finite element model is meshed to obtain mesh elements, the three-dimensional coordinates of all nodes on each mesh element are obtained, and the stress data of each mesh element is obtained in real time.

[0008] Based on the centroid of the finite element model and its projection points on the plane of each mesh element, the outward normal vector of each mesh element is constructed; the degree of commonality between each mesh element and all other mesh elements is analyzed, and the connected mesh elements of each mesh element are selected from all other elements; based on the similarity dispersion and the mean similarity of the outward normal vectors between each mesh element and all connected mesh elements, the comprehensive geometric characteristic value of each mesh element is determined.

[0009] Based on the distance between the geometric centers of each grid cell and all other grid cells, local grid cells of each grid cell are selected from all other grid cells. Based on the distance between the geometric centers of each grid cell and each of its local grid cells, and combined with the stress data of each grid cell and each of its local grid cells at any given time, the stress concentration of each grid cell at any given time is determined to determine the stress characteristic value of each grid cell. Based on the stress characteristic value and the comprehensive geometric characteristic value, the refinement characteristic value of each grid cell is determined.

[0010] Based on the refined feature values, target mesh elements are selected from all mesh elements, and the target mesh elements are refined to obtain a refined finite element model, which is then used to perform vulnerability analysis on the masonry structure.

[0011] Preferably, the outward normal vector of each mesh element is a vector that starts from the centroid of the finite element model and ends at the projection point of the centroid of the finite element model onto the plane where each mesh element is located.

[0012] Preferably, the connecting mesh element of each mesh element is: a mesh element that has at least one common node with each mesh element in all mesh elements of the finite element model.

[0013] Preferably, the comprehensive geometric feature value of each grid cell is the result of the normalized value of the standard deviation of the similarity between each grid cell and all its connected grid cells divided by the normalized value of the mean similarity.

[0014] Preferably, the local grid cells of each grid cell include: each grid cell, and the grid cells corresponding to the first preset number of distances in the ascending order of the distances between each grid cell and the geometric centers of all other grid cells.

[0015] Preferably, the method for determining the stress concentration of each grid element at any given time is as follows:

[0016] The distance between the geometric center of each grid cell and each of its local grid cells is denoted as the grid distance between each grid cell and each of its local grid cells;

[0017] Calculate the sum of the grid distance and the preset value, calculate the ratio of the stress data of each grid cell and each local grid cell at any given time to the corresponding sum, and take the average of the ratios of each grid cell and all local grid cells at any given time as the stress concentration of each grid cell at any given time.

[0018] Preferably, the stress characteristic value of each grid element is the result of averaging the stress concentration of each grid element at all times during the seismic simulation analysis of the finite element model.

[0019] Preferably, the refined characteristic value of each mesh element is the average of the normalized comprehensive geometric characteristic value and the normalized stress characteristic value of each mesh element.

[0020] Preferably, the step of selecting target mesh cells from all mesh cells based on the refined feature values ​​includes:

[0021] The refinement eigenvalues ​​of all mesh elements in the finite element model are used as input to the threshold segmentation algorithm, which outputs a segmentation threshold. Mesh elements with refinement eigenvalues ​​greater than the segmentation threshold are used as target mesh elements.

[0022] Preferably, the vulnerability analysis of the masonry structure based on the refined finite element model includes:

[0023] Different peak ground accelerations were set, and different ground motion records under each peak ground acceleration were obtained using the ground motion database. Seismic simulation was performed on the refined finite element model to obtain the maximum inter-story drift angle under each ground motion record.

[0024] The damage state of masonry structures during an earthquake is divided into minor damage, moderate damage, severe damage, and collapse. The four damage states are quantified by the maximum inter-story drift angle as 1 / 1600, 1 / 700, 1 / 350, and 1 / 200, respectively.

[0025] The probability of the maximum inter-story drift angle corresponding to all ground motion records under each peak ground acceleration occurring in four failure states is statistically calculated and denoted as the probability of occurrence of each failure state under each peak ground acceleration. All peak ground accelerations and the probability of occurrence of each failure state under them are used as inputs to the vulnerability function, and the seismic vulnerability curve under each failure state is output. Vulnerability analysis is performed on the masonry structure corresponding to the refined finite element model.

[0026] This application has at least the following beneficial effects:

[0027] This application constructs a comprehensive geometric eigenvalue by calculating the outward normal vector of the grid element and its similarity with adjacent elements. This quantifies and evaluates the degree of geometric abrupt change in each element, effectively identifying weak geometric abrupt changes in masonry structures. This provides a basis for refining the mesh in these critical areas, thereby improving the accuracy of seismic vulnerability analysis. Furthermore, this application constructs a refinement eigenvalue by combining the geometric abrupt change characteristics and stress concentration characteristics of the grid element. This value effectively identifies critical areas in the masonry structure that may fail due to geometric abrupt changes or stress concentration, guiding the mesh refinement of these high-risk areas, thus significantly improving the accuracy of seismic vulnerability analysis. Furthermore, based on the refinement eigenvalue, this application identifies key areas in the masonry structure and refines their mesh, more accurately simulating the stress distribution of the masonry structure under earthquakes, especially the complex behavior at geometric abrupt changes and cross-sectional changes, improving the accuracy of masonry structure vulnerability analysis. Attached Figure Description

[0028] To more clearly illustrate the technical solutions and advantages in the embodiments of this application 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 this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0029] Figure 1 A flowchart illustrating the steps of a method for analyzing the vulnerability of masonry structures under extreme conditions, provided in one embodiment of this application;

[0030] Figure 2 This is a schematic diagram of a refined feature value extraction process provided in one embodiment of this application. Detailed Implementation

[0031] To further illustrate the technical means and effects adopted by this application to achieve the intended purpose of the invention, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of a method for analyzing the vulnerability of masonry structures under extreme conditions proposed in this application. 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.

[0032] 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 application pertains.

[0033] The following description, in conjunction with the accompanying drawings, details the specific scheme of the vulnerability analysis method for masonry structures under extreme conditions provided in this application.

[0034] This application provides an embodiment of a vulnerability analysis method for masonry structures under extreme conditions. Specifically, it provides the following vulnerability analysis method for masonry structures under extreme conditions. Please refer to [link to relevant documentation]. Figure 1 The method includes the following steps:

[0035] Step S1: Obtain a three-dimensional finite element model of the masonry structure building, mesh the finite element model to obtain mesh elements, obtain the three-dimensional coordinates of all nodes on each mesh element, and obtain the stress data of each mesh element in real time.

[0036] A three-dimensional building solid model of the target masonry structure house is created using CAD software. During the modeling process, it is necessary to simplify appropriately and not consider non-masonry structures such as doors, windows, and stairs. The constructed three-dimensional building solid model is then imported into finite element analysis software to create a finite element model of the masonry structure house.

[0037] It should be noted that there are many commonly used finite element analysis software programs. This embodiment uses ABAQUS finite element analysis technology. In practical applications, as other implementation methods, implementers may also choose other finite element analysis software such as ANSYS or MSC depending on the specific circumstances.

[0038] The methods for constructing the 3D building solid model and the finite element model are well-known technologies, and the specific construction process of the 3D building solid model and the finite element model will not be described in detail.

[0039] In the finite element analysis software ABAQUS, the constructed finite element model is meshed using a finite element mesh generation method. The finite element mesh generation method can be either the MedialAxis algorithm or the Advancing Front algorithm. In this embodiment, the Advancing Front algorithm is selected as the finite element mesh generation method. In practical applications, as other implementation methods, the implementer may also choose other finite element mesh generation methods such as the MedialAxis algorithm according to the specific situation. This embodiment does not impose any special restrictions on the selection of the finite element mesh generation method. The mesh elements obtained are all triangular in shape, and the mesh elements are two-dimensional planes.

[0040] In the finite element analysis software ABAQUS, the three-dimensional coordinates of all nodes on each mesh element in the finite element model are obtained. Furthermore, a certain seismic load is applied to the finite element model using ABAQUS to perform seismic simulation analysis. Stress data for each mesh element in the finite element model is extracted in real time during the seismic simulation analysis. All obtained stress data are normalized. There are many methods for normalization; in this embodiment, the maximum-minimum normalization method is used to normalize the element stress data. In practical applications, as other implementation methods, the implementer can also use the z-score normalization method to normalize the data, depending on the specific circumstances. This embodiment does not impose any special restrictions on the selection of normalization methods.

[0041] Among them, the seismic simulation analysis, stress data extraction, and maximum and minimum value normalization in the ABAQUS finite element analysis software are all well-known techniques, and their specific principles and processes will not be elaborated here.

[0042] It should be noted that in this embodiment, all content involving normalization processing adopts the maximum-minimum value normalization method.

[0043] Step S2: Based on the centroid of the finite element model and its projection points on the plane of each mesh element, construct the outward normal vector of each mesh element; analyze the degree of commonality between each mesh element and all other mesh elements, and select the connected mesh elements of each mesh element from all other elements; based on the similarity dispersion and mean similarity of the outward normal vectors between each mesh element and all connected mesh elements, determine the comprehensive geometric characteristic value of each mesh element.

[0044] In masonry structures, geometrically abrupt locations such as corners between adjacent walls, connections between walls and columns, and corners between door and window openings and walls are typically weak points in the masonry structure. Compared to other parts of the masonry structure, these geometrically abrupt locations are more prone to damage under seismic loads. Therefore, to better simulate the stress distribution at these geometrically abrupt locations in the vulnerability analysis of masonry structures, it is necessary to perform more detailed meshing on these locations, thereby enabling a more accurate vulnerability analysis of masonry structures.

[0045] Therefore, based on the above analysis, this embodiment constructs the outward normal vector of each mesh element based on the centroid of the finite element model and its projection points on the plane where each mesh element is located; analyzes the degree of commonality between each mesh element and all other mesh elements, and selects the connecting mesh elements of each mesh element from all other elements; based on the similarity dispersion and mean similarity of the outward normal vectors between each mesh element and all its connecting mesh elements, determines the comprehensive geometric characteristic value of each mesh element to evaluate whether the location of each mesh element in the finite element model is at a geometric abrupt change in the masonry structure. The specific process is as follows:

[0046] In this embodiment, firstly, the centroid coordinates of the three-dimensional finite element model are calculated based on the three-dimensional coordinates of all nodes in the three-dimensional finite element model. The process of calculating the centroid of the finite element model based on the three-dimensional coordinates of all nodes in all mesh elements in the three-dimensional finite element model is a well-known technique, and the specific calculation principle and steps will not be described in detail.

[0047] Furthermore, in this embodiment, based on the centroid of the finite element model and its projection points on the plane of each mesh element, an outward normal vector for each mesh element is constructed. This vector is used to characterize a normal vector in the plane of the mesh element pointing towards the outside of the masonry structure house where the finite element model is located. Specifically:

[0048] In this embodiment, the plane equation of each grid cell is calculated based on the three-dimensional coordinates of all nodes on each grid cell; the coordinates of the centroid coordinates are calculated as the projection points of the plane corresponding to the plane equation of each grid cell; and the vector formed by taking the centroid of the finite element model as the starting point and the projection points of the centroid on the plane of each grid cell as the ending point is used as the outward normal vector of each grid cell.

[0049] The calculation of the plane equation and the coordinates of the projection point are well-known techniques, and the specific process will not be described in detail.

[0050] Furthermore, this embodiment analyzes the degree of commonality between each mesh element and all other mesh elements, and filters out the connected mesh elements of each mesh element from all other elements, so as to filter out all mesh elements in the finite element model that are connected to each mesh element and contain the same mesh element nodes. Specifically:

[0051] In the finite element model, the mesh element that shares at least one common node with each other is designated as the connecting mesh element.

[0052] Furthermore, since the geometric abrupt changes in masonry structures are usually located at the intersection of two different surfaces, the mesh elements on the surface of the geometric abrupt change in the three-dimensional finite element model of the masonry structure usually do not have coplanar geometric features with their adjacent mesh elements. Although the curved structures such as columns, openings, and arches in the finite element model of the masonry structure are not mesh elements on the surface of the geometric abrupt change in the masonry structure, all the mesh elements adjacent to them usually do not have coplanar geometric features.

[0053] The difference lies in the following: For columns, openings, and arches in masonry structures, the curvature changes of the corresponding mesh elements and all their adjacent mesh elements on the surface of the curved structure are usually relatively gentle. That is, these mesh elements still maintain a certain degree of geometric continuity in a local range, making the degree of curvature change between the mesh elements on the surface of the curved structure and their adjacent mesh elements relatively similar. However, since the geometrically abrupt parts are located at the junction of two surfaces in a masonry structure, the degree of curvature change between the mesh elements on the surface of the geometrically abrupt parts and their adjacent mesh elements in the three-dimensional finite element model usually has a significant difference.

[0054] Therefore, based on the above analysis, this embodiment determines the comprehensive geometric feature value of each mesh cell based on the similarity dispersion and mean similarity of the outward normal vectors between each mesh cell and all its connected mesh cells. Specifically:

[0055] In this embodiment, the standard deviation and mean of the similarity between each mesh element and all its connected mesh elements are calculated respectively. The standard deviation and mean of the similarity of all mesh elements in the finite element model are normalized respectively. The ratio of the normalized value of the standard deviation of the similarity between each mesh element and all its connected mesh elements to the normalized value of the mean of the similarity is used as the comprehensive geometric feature value of each mesh element.

[0056] It should be noted that there are many methods to measure the similarity between vectors. In this embodiment, the cosine similarity between the outward normal vectors of each grid cell and all connected grid cells is used as the outward similarity between each grid cell and all connected grid cells. In practical applications, as other implementation methods, implementers may also adopt other methods to measure the similarity between vectors according to specific circumstances. This embodiment does not impose any special restrictions on the selection of methods to measure the similarity between vectors.

[0057] The method for calculating cosine similarity is a well-known technique, and its specific calculation process will not be elaborated here.

[0058] Based on the comprehensive geometric feature values ​​of each grid cell, it can be understood that the standard deviation of the similarity between each grid cell and all its connected grid cells reflects the difference in the degree of surface change between each grid cell and its neighboring grid cells, while the mean of the similarity between each grid cell and all its connected grid cells reflects the degree of coplanarity between each grid cell and its neighboring grid cells. The larger the comprehensive feature value, the more likely the grid cell is located at a sudden change in the masonry structure. If the mean of the similarity between the current grid cell and all its connected grid cells is smaller, it indicates that the current grid cell is less likely to be coplanar with all its neighboring grid cells. At the same time, if the standard deviation of the similarity between the current grid cell and all its connected grid cells is larger, it indicates that the difference in the degree of surface change between the grid cell and its neighboring grid cells is more significant, indicating that the masonry structure corresponding to the area where the current grid cell is located is more likely to undergo a geometrical abrupt change, and the corresponding comprehensive geometric feature value is also larger.

[0059] Conversely, if the mean similarity between the current mesh cell and all its connected mesh cells is larger, it indicates that the current mesh cell is more likely to be coplanar with all its adjacent mesh cells, meaning they are more likely to be located on a relatively flat or smoothly transitioning surface. At the same time, if the standard deviation of the similarity between the current mesh cell and all its connected mesh cells is smaller, it indicates that the difference in the degree of surface change between the mesh cell and its adjacent mesh cells is less significant, meaning that the geometric changes between them are relatively gentle and uniform. This indicates that the masonry structure corresponding to the area where the current mesh cell is located is less likely to undergo geometric abrupt changes, and the corresponding comprehensive geometric feature value is also smaller, indicating that the mesh cell is more likely to be located in a non-abrupt part of the masonry structure.

[0060] Thus, this embodiment constructs a comprehensive geometric feature value by calculating the outward normal vector of the grid cell and its similarity with adjacent cells, quantitatively assesses the degree of geometric abrupt change in each cell, and can effectively identify weak geometric abrupt changes in masonry structures, providing a basis for fine-grained meshing of these key areas, thereby helping to improve the accuracy of seismic vulnerability analysis.

[0061] Step S3: Based on the distance between the geometric centers of each mesh cell and all other mesh cells, select the local mesh cells of each mesh cell from all other mesh cells; based on the distance between the geometric centers of each mesh cell and each of its local mesh cells, and combined with the stress data of each mesh cell and each of its local mesh cells at any given time, determine the stress concentration of each mesh cell at any given time, so as to determine the stress characteristic value of each mesh cell; based on the stress characteristic value and the comprehensive geometric characteristic value, determine the refinement characteristic value of each mesh cell.

[0062] In masonry structures, sudden changes in wall thickness or abrupt shifts in beam and column dimensions, along with other abrupt changes in cross-sectional area, alter the force transmission path. This causes stress to concentrate on the reduced cross-section, resulting in localized high stress—a phenomenon known as stress concentration. Therefore, to better simulate the rapidly changing stress distribution at these cross-sectional areas due to stress concentration, more detailed meshing is needed to more accurately analyze the vulnerability of masonry structures.

[0063] Therefore, based on the above analysis, this embodiment uses the distance between the geometric centers of each mesh element and all other mesh elements to filter out the local mesh elements of each mesh element from all other mesh elements; based on the distance between the geometric centers of each mesh element and each of its local mesh elements, and combined with the stress data of each mesh element and each of its local mesh elements at any given time, the stress concentration of each mesh element at any given time is determined to determine the stress characteristic value of each mesh element; based on the stress characteristic value and the comprehensive geometric characteristic value, the refinement characteristic value of each mesh element is determined to evaluate whether the mesh elements need to be refined, so as to better simulate the stress distribution at the geometrically abrupt parts and the abruptly changing sections of the target masonry structure in the three-dimensional finite element model, thereby improving the accuracy of subsequent vulnerability analysis of the masonry structure. The specific process is as follows:

[0064] First, this embodiment uses the distance between the geometric centers of each grid cell and all other grid cells to filter out local grid cells from all other grid cells. These local grid cells are used to characterize the local region where each grid cell is located. Specifically:

[0065] In this embodiment, the grid cells corresponding to the first preset number of distances in the ascending order of the distances between each grid cell and the geometric centers of all other grid cells are all regarded as local grid cells of each grid cell.

[0066] It should be noted that the preset quantity is set manually. In this embodiment, the preset quantity is 7. In actual application, as other implementation methods, implementers can also set it according to specific circumstances. This embodiment does not impose any special restrictions.

[0067] Furthermore, this embodiment determines the stress concentration of each grid cell at any given time based on the distance between the geometric centers of each grid cell and each of its local grid cells, and in conjunction with the stress data of each grid cell and each of its local grid cells at any given time. This determines the stress characteristic value of each grid cell, which is used to assess whether a local high stress concentration phenomenon has occurred in the local area where the grid cell is located. Specifically:

[0068] In this embodiment, firstly, the geometric center of each grid cell is calculated based on the coordinates of all nodes on each grid cell. The method for calculating the geometric center is a well-known technique, and its specific calculation process will not be described in detail.

[0069] Furthermore, the distance between the geometric center of each grid cell and each of its local grid cells is denoted as the grid distance between each grid cell and each of its local grid cells;

[0070] The sum of the grid distance and the preset value is calculated. The ratio of the stress data of each grid cell and each local grid cell at any given time to the corresponding sum is calculated. The average of the ratios of each grid cell and all local grid cells at any given time is taken as the stress concentration of each grid cell at any given time. The preset value is set manually to prevent the denominator from being 0 when the sum is used as the denominator. In this embodiment, the preset value is 0.01. In actual application, the implementer can set it according to the specific situation, provided that the denominator is not 0 and does not excessively affect the calculation result. This embodiment does not impose any special restrictions.

[0071] Furthermore, the average stress concentration of each grid element at all times during the seismic simulation analysis of the finite element model will be used as the stress characteristic value of each grid element.

[0072] Based on the stress characteristic values ​​of each grid cell, it can be understood that the stress characteristic values ​​reflect whether stress concentration occurs in the local area of ​​each grid cell during the earthquake simulation analysis, and quantify the relative difference in stress distribution between each grid cell and its neighboring cells. If the stress characteristic value of the current grid cell is larger, it means that the stress distribution difference in the local area of ​​the current grid cell is more significant under the earthquake action, and the more likely there is a phenomenon of local high stress. This usually corresponds to the part of the masonry structure where the stress transmission path changes, such as: the place where the cavity thickness changes suddenly, the place where the beam and column cross-sectional dimensions change abruptly, or other possible stress concentration points. Therefore, the larger the stress characteristic value, the greater the stress challenge that the grid cell and its surrounding area bear during the earthquake, which is a potential weak link in the masonry structure and a high-risk area that needs final attention.

[0073] Conversely, if the stress characteristic value of the current grid cell is smaller, it indicates that the stress distribution in the local area of ​​the grid cell is relatively uniform under seismic action, and there is no obvious stress concentration phenomenon. This usually corresponds to a relatively gentle and uniform stress transmission area in the masonry structure. The smaller the stress characteristic value, the smaller the stress challenge that the current grid cell and its surrounding area are subjected to during the earthquake, and the lower the possibility of serious damage.

[0074] Furthermore, based on the stress characteristic values ​​and comprehensive geometric characteristic values ​​obtained above, this embodiment determines the refinement characteristic values ​​of each mesh element. This is used to assess whether the mesh elements need to be refined to better simulate the stress distribution at geometrically abrupt locations and abruptly changing cross-sections of the target masonry structure in the three-dimensional finite element model. This improves the accuracy of subsequent vulnerability analysis of the masonry structure. Specifically:

[0075] In this embodiment, the comprehensive geometric feature value and stress feature value of all grid cells are normalized respectively, and the average of the normalized comprehensive geometric feature value and stress feature value of each grid cell is used as the refinement feature value of each grid cell.

[0076] Preferably, the schematic diagram of the refined feature value extraction process provided in this embodiment is as follows: Figure 2 As shown.

[0077] Based on the refinement eigenvalues ​​of each mesh element, it can be understood that the refinement eigenvalues ​​directly indicate the importance of the mesh element in simulating the seismic response of masonry structures and the necessity of refinement. A larger comprehensive geometric eigenvalue means that the current mesh element is more likely to be located at a geometrically abrupt change, which itself requires a finer mesh to accurately capture stress concentration and deformation modes. Therefore, an increase in the comprehensive geometric eigenvalue leads to an increase in the refinement eigenvalue, indicating that the current mesh element needs more refinement due to its geometric characteristics. Simultaneously, a larger stress eigenvalue means that the current mesh element and its adjacent area exhibit significant stress concentration under seismic loading. High stress concentration areas are potential weak points in masonry structures, with large stress distribution gradients, requiring a finer mesh to capture stress changes and deformations. Therefore, an increase in the stress eigenvalue directly leads to an increase in the refinement eigenvalue, indicating that the mesh element needs more refinement due to its stress characteristics to more accurately simulate the mechanical response and potential failure modes at that location.

[0078] Conversely, if the comprehensive geometric eigenvalue of the current mesh element is smaller, it means that the element is less likely to be located at a geometrically abrupt point, and is usually in a relatively flat or gently transitioning region. These regions have relatively low requirements for mesh accuracy. Therefore, the reduction of the comprehensive geometric eigenvalue will lead to a reduction in the refinement eigenvalue, indicating that the mesh element has low necessity for refinement due to its geometric characteristics. At the same time, if the stress eigenvalue of the current mesh element is smaller, it means that the stress distribution of the element and its adjacent area is relatively uniform under seismic loading, and there is no significant stress concentration. These areas are not the main weak points of the structure, and the stress gradient is also small. The requirements for mesh accuracy are also not high. Therefore, the reduction of the stress eigenvalue will also lead to a reduction in the refinement eigenvalue, indicating that the mesh element also has low necessity for refinement due to its stress characteristics, and a relatively coarse mesh can be used for simulation.

[0079] Thus, this embodiment constructs a refinement feature value by combining the geometric abrupt change characteristics and stress concentration characteristics of the mesh element. This value can effectively identify key areas in the masonry structure that may be damaged due to geometric abrupt changes or stress concentration, and guide the mesh refinement of these high-risk parts, thereby helping to significantly improve the accuracy of seismic vulnerability analysis.

[0080] Step S4: Based on the refined feature values, select the target mesh element from all mesh elements, refine the target mesh element to obtain a refined finite element model, and perform vulnerability analysis on the masonry structure based on the refined finite element model.

[0081] Based on the refined feature values ​​obtained in step S3, this embodiment further selects target mesh elements from all mesh elements based on the refined feature values, refines the target mesh elements to obtain a refined finite element model, and performs vulnerability analysis on the masonry structure based on the refined finite element model, specifically as follows:

[0082] In this embodiment, firstly, the refinement feature values ​​of all mesh elements in the finite element model are used as the input of the threshold segmentation algorithm, and the segmentation threshold is output. Mesh elements with refinement feature values ​​greater than the segmentation threshold are used as target mesh elements.

[0083] It should be noted that there are many commonly used threshold segmentation algorithms. In this embodiment, the Otsu's inter-class variance algorithm is used to divide the grid cells. In practical applications, implementers may also choose other threshold segmentation methods according to specific circumstances. This embodiment does not impose any special restrictions on the selection of threshold segmentation methods.

[0084] Among them, the Otsu's inter-class variance algorithm is a well-known technique, and the specific process of using it to divide the grid cells will not be described in detail.

[0085] Furthermore, in this embodiment, the adaptive mesh refinement (ARM) algorithm is used to refine all target mesh elements in the finite element model, and the resulting finite element model after mesh refinement is denoted as the refined finite element model.

[0086] In this embodiment, the failure state of the masonry structure is divided into five levels: intact, slightly damaged, moderately damaged, severely damaged, and collapsed. The maximum inter-story drift angle is used as the classification standard to divide the masonry structure into four extreme states: slightly damaged, moderately damaged, severely damaged, and collapsed. The inter-story drift angles of the four extreme states are 1 / 1600, 1 / 700, 1 / 350, and 1 / 200, respectively.

[0087] Furthermore, in this embodiment, different peak ground accelerations are set, and different ground motion records under each peak ground acceleration are obtained using a ground motion database. Seismic simulation is performed on the refined finite element model to obtain the maximum inter-story drift angle under each ground motion record. In one implementation method, the different peak ground accelerations are set to 0.1g, 0.2g, 0.3g, 0.4g, 0.5g, 0.6g, 0.7g, 0.8g, and 0.9g, where g is the gravitational acceleration. 100 different earthquake records are obtained under each peak ground acceleration. The above numerical settings are for illustrative purposes only. In actual applications, implementers can set them according to specific circumstances. This embodiment does not impose any special limitations.

[0088] Furthermore, in this embodiment, the damage state of masonry structures during an earthquake is divided into minor damage, moderate damage, severe damage, and collapse. The four damage states are quantified by the maximum inter-story drift angle as 1 / 1600, 1 / 700, 1 / 350, and 1 / 200, respectively.

[0089] The probability of the maximum inter-story drift angle corresponding to all ground motion records under each peak ground acceleration occurring in four failure states is statistically calculated and denoted as the probability of occurrence of each failure state under each peak ground acceleration. All peak ground accelerations and the probability of occurrence of each failure state under them are used as inputs to the vulnerability function, and the seismic vulnerability curve under each failure state is output. Vulnerability analysis is performed on the masonry structure corresponding to the refined finite element model.

[0090] Peak ground acceleration, ground motion database, maximum inter-story drift angle, and vulnerability function are all well-known technologies, and their specific principles and usage will not be elaborated here.

[0091] Thus, this embodiment analyzes the geometric abrupt changes and stress concentration characteristics of mesh elements, calculates refined characteristic values ​​to identify key areas in masonry structures, and refines the mesh accordingly. This more accurately simulates the stress distribution of masonry structures under earthquakes, especially the complex behavior at geometric abrupt changes and cross-sectional changes, significantly improving the accuracy of vulnerability analysis of masonry structures.

[0092] It should be noted that the order of the embodiments described above is merely for descriptive purposes and does not represent the superiority or inferiority of the embodiments. Furthermore, specific embodiments of this specification have been described above. Additionally, the processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired results. In some implementations, multitasking and parallel processing are possible or may be advantageous.

[0093] 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.

[0094] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them; modifications to the technical solutions described in the foregoing embodiments, or equivalent substitutions of some of the technical features, do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for analyzing the vulnerability of masonry structures under extreme conditions, characterized in that, The method includes the following steps: A three-dimensional finite element model of a masonry structure is obtained, the finite element model is meshed to obtain mesh elements, the three-dimensional coordinates of all nodes on each mesh element are obtained, and the stress data of each mesh element is obtained in real time. Based on the centroid of the finite element model and its projection points on the plane of each mesh element, the outward normal vector of each mesh element is constructed; the degree of commonality between each mesh element and all other mesh elements is analyzed, and the connected mesh elements of each mesh element are selected from all other elements; based on the similarity dispersion and the mean similarity of the outward normal vectors between each mesh element and all connected mesh elements, the comprehensive geometric characteristic value of each mesh element is determined. Based on the distance between the geometric centers of each grid cell and all other grid cells, local grid cells of each grid cell are selected from all other grid cells. Based on the distance between the geometric centers of each grid cell and each of its local grid cells, and combined with the stress data of each grid cell and each of its local grid cells at any given time, the stress concentration of each grid cell at any given time is determined to determine the stress characteristic value of each grid cell. Based on the stress characteristic value and the comprehensive geometric characteristic value, the refinement characteristic value of each grid cell is determined. Based on the refined feature values, target mesh elements are selected from all mesh elements, and the target mesh elements are refined to obtain a refined finite element model, so as to perform vulnerability analysis on masonry structures based on the refined finite element model. The method for determining the stress concentration of each grid element at any given time is as follows: The distance between the geometric center of each grid cell and each of its local grid cells is denoted as the grid distance between each grid cell and each of its local grid cells; Calculate the sum of the grid distance and the preset value, calculate the ratio of the stress data of each grid cell and each local grid cell at any time to the corresponding sum, and take the average of the ratios of each grid cell and all local grid cells at any time as the stress concentration of each grid cell at any time. The stress characteristic value of each grid element is the result of taking the average stress concentration of each grid element at all times during the seismic simulation analysis of the finite element model.

2. The method for analyzing the vulnerability of masonry structures under extreme conditions as described in claim 1, characterized in that, The outward normal vector of each mesh element is a vector that starts from the centroid of the finite element model and ends at the projection point of the centroid of the finite element model onto the plane where each mesh element is located.

3. The method for analyzing the vulnerability of masonry structures under extreme conditions as described in claim 1, characterized in that, The connecting mesh element of each mesh element is: a mesh element that has at least one common node with each mesh element in all mesh elements of the finite element model.

4. The method for analyzing the vulnerability of masonry structures under extreme conditions as described in claim 1, characterized in that, The comprehensive geometric feature value of each grid cell is the result of the normalized value of the standard deviation of the similarity between each grid cell and all its connected grid cells, divided by the normalized value of the mean similarity.

5. The method for analyzing the vulnerability of masonry structures under extreme conditions as described in claim 1, characterized in that, The local grid cells of each grid cell include: each grid cell, and the grid cells corresponding to the first preset number of distances in the ascending order of the distances between each grid cell and the geometric centers of all other grid cells.

6. The method for analyzing the vulnerability of masonry structures under extreme conditions as described in claim 1, characterized in that, The refined characteristic value of each grid cell is the average of the normalized comprehensive geometric characteristic value and the normalized stress characteristic value of each grid cell.

7. The method for analyzing the vulnerability of masonry structures under extreme conditions as described in claim 1, characterized in that, The step of selecting target mesh cells from all mesh cells based on the refined feature values ​​includes: The refinement eigenvalues ​​of all mesh elements in the finite element model are used as input to the threshold segmentation algorithm, which outputs a segmentation threshold. Mesh elements with refinement eigenvalues ​​greater than the segmentation threshold are used as target mesh elements.

8. The method for analyzing the vulnerability of masonry structures under extreme conditions as described in claim 1, characterized in that, The vulnerability analysis of masonry structures based on the refined finite element model includes: Different peak ground accelerations were set, and different ground motion records under each peak ground acceleration were obtained using the ground motion database. Seismic simulation was performed on the refined finite element model to obtain the maximum inter-story drift angle under each ground motion record. The damage state of masonry structures during an earthquake is divided into minor damage, moderate damage, severe damage, and collapse. The four damage states are quantified by the maximum inter-story drift angle as 1 / 1600, 1 / 700, 1 / 350, and 1 / 200, respectively. The probability of the maximum inter-story drift angle corresponding to all ground motion records under each peak ground acceleration occurring in four failure states is statistically calculated and denoted as the probability of occurrence of each failure state under each peak ground acceleration. All peak ground accelerations and the probability of occurrence of each failure state under them are used as inputs to the vulnerability function, and the seismic vulnerability curve under each failure state is output. Vulnerability analysis is performed on the masonry structure corresponding to the refined finite element model.

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