Method for analyzing damage of foundation above karst cave based on six-direction triple triangulation network

Abstract

The embodiment of the invention provides a damage analysis method, device and equipment for a foundation above a karst cave based on a six-direction triple triangulation network and a computer readable storage medium. The method comprises the following steps: establishing a first triangular background grid based on parameter data of an anisotropic karst cave; performing multiple times of overall encryption on the first triangular background grid to generate a second triangular background grid; performing cross cutting on the second triangular background grid to generate a third triangular background grid; establishing an optimization variable, a target function and a constraint condition based on the third triangular background grid; and based on the optimization variable, the objective function and the constraint condition, determining the upper limit solution of the ultimate bearing capacity of the foundation above the karst cave and the failure form. In this way, by constructing a multi-layer triangulation network, six-direction broken line layout of a key damage area can be preferably met, and on the premise of guaranteeing broken line dissipated energy contribution, a high-order deformation unit is supplemented, and accurate analysis of the limit state of the foundation above the karst cave on the premise of single calculation of a fixed grid is achieved.

Description

Technical Field

[0001] Embodiments of the present application relate to the field of data processing, and in particular to a method, device, equipment and computer-readable storage medium for analyzing foundation damage above a cave based on a six-directional triple triangulation network. Background Art

[0002] During the construction of bridge foundations in karst areas, special attention should be paid to the bearing capacity of the foundation. The determination of the ultimate bearing capacity of the foundation above the cave usually adopts the upper limit finite element method. When the foundation reaches the ultimate bearing capacity, the soil below the foundation has a tendency to collapse toward the karst area, and the soil on both sides of the main sliding surface has a strong relative sliding tendency. For this, nonlinear velocity discontinuities can be introduced, and a high-order "mixed-discontinuous" upper limit analysis method can be formed with six-node triangular elements.

[0003] In the prior art, the arrangement orientation of velocity discontinuities is significantly related to their contribution in the upper limit analysis process, and the core lies in whether a discontinuity path is formed along the high strain rate gradient area; on the contrary, an unordered arrangement will result in the discontinuity not being able to fully play its role, and the existence of the discontinuity brings unnecessary computational burden. On the other hand, in the process of triangulating the boundary of the cave model, the boundary nodes are strictly restricted by geometric conditions, which often interferes with the original discontinuity layout structure, thereby affecting its performance.

[0004] Therefore, how to reasonably layout the grid so that the six-node triangular unit and the nonlinear velocity discontinuity line can achieve the best coordination is a problem that needs to be solved urgently. Summary of the invention

[0005] According to the embodiment of the present application, a solution for analyzing the damage of foundation above karst cave based on six-direction triple triangulation is provided. Starting from the first-level regular triangular mesh, after multiple overall quadrisections and final centroid sextupling, a second-level triangular mesh with six-direction through-type velocity discontinuity path is formed; further research and development of cross-cutting cross-boundary units, elimination of redundant units and other measures are carried out to realize the triangulation discretization of the upper limit finite element model of the ultimate bearing capacity of karst foundation of arbitrary shape, i.e., the third-level triangular mesh; further consideration of the second-order change of velocity and the linear change of strain rate of high-order six-node triangular units, and extraction of high-order velocity discontinuity lines therebetween, establishment of three major analysis modules such as optimization variables, objective functions and constraints, and embedding the upper limit finite element analysis program to realize the high-precision solution of the ultimate bearing capacity and damage form of foundation above irregular karst cave, which greatly improves the calculation accuracy compared with the prior art. .

[0006] In a first aspect of the present application, a method for analyzing foundation damage above a cave based on a six-directional triple triangulation network is provided. The method comprises:

[0007] Based on the parameter data of the heterogeneous karst cave, the first triangle background grid of the ultimate bearing capacity model of the foundation above the heterogeneous karst cave is established;

[0008] Performing multiple overall encryption on the first triangular background mesh to generate a second triangular background mesh;

[0009] Cross-cutting the second triangular background mesh to generate a third triangular background mesh;

[0010] Based on the third triangular background mesh, establishing optimization variables, objective functions and constraints;

[0011] Based on the optimization variables, objective function and constraints, the upper limit solution of the ultimate bearing capacity and the failure form of the foundation above the cave based on the six-direction and six-node triple triangulated network are determined.

[0012] Furthermore, the step of performing multiple overall encryption on the first triangular background mesh to generate a second triangular background mesh comprises:

[0013] All cells of the first triangular background mesh are traversed, and based on the preset number of mesh encryption times, the centroids of the cells and their corresponding side midpoints and vertices are sequentially connected by dividing the side midpoints into four equal parts to generate a second triangular background mesh.

[0014] Furthermore, the second triangular background mesh is a triangular background mesh including a six-directional discontinuous line layout.

[0015] Furthermore, cross-cutting the second triangular background mesh to generate a third triangular background mesh includes:

[0016] traversing the second triangular background mesh to obtain cells including boundary intersection points;

[0017] Connect boundary intersection points and unit vertices to obtain the target triangle background mesh;

[0018] Calculating the number of boundary vertices and the number of cross-boundary unit intersections of the target triangular background mesh;

[0019] Based on the number of boundary vertices and the number of cross-boundary unit intersections, the target triangular background mesh is cut to generate a third triangular background mesh.

[0020] Furthermore, the step of cutting the target triangular background mesh based on the number of boundary vertices and the number of cross-boundary unit intersections to generate a third triangular background mesh includes:

[0021] If the number of intersections of the current unit and the number of intersections of the cross-boundary unit meet the first preset condition, the current unit is divided into two equal parts;

[0022] If the number of intersections of the current unit and the number of intersections of the cross-boundary units meet the second preset condition, the current unit is divided into three equal parts.

[0023] Furthermore, before establishing the optimization variables, objective function and constraint conditions based on the third triangular background mesh, the method further includes:

[0024] Parameter data of the heterogeneous cave, removing redundant units in the third triangular background grid.

[0025] Furthermore, based on the optimization variables, objective function and constraint conditions, determining the upper limit solution of the ultimate bearing capacity and the failure form of the foundation above the cave based on the six-direction and six-node triple triangulated network includes:

[0026] Based on the optimization variables, objective function and constraints, a large-scale linear programming model is established through a sparse matrix;

[0027] Based on a large-scale linear programming model, the upper limit solution of the ultimate bearing capacity and the failure mode of the foundation above the cave based on a six-direction and six-node triple triangulated network are determined.

[0028] In a second aspect of the present application, a device for analyzing foundation damage above a cave based on a six-directional triple triangulation network is provided. The device comprises:

[0029] A construction module is used to establish a first triangular background grid of the ultimate bearing capacity model of the foundation above the irregular karst cave based on the parameter data of the irregular karst cave;

[0030] A first generating module, used for performing multiple overall encryption on the first triangular background mesh to generate a second triangular background mesh;

[0031] A second generating module, used for cross-cutting the second triangular background mesh to generate a third triangular background mesh;

[0032] An establishment module, used for establishing optimization variables, objective functions and constraints based on the third triangular background mesh;

[0033] The determination module is used to determine the upper limit solution and failure form of the ultimate bearing capacity of the foundation above the cave based on the six-direction and six-node triple triangulation network based on the optimization variables, objective function and constraint conditions.

[0034] In a third aspect of the present application, an electronic device is provided, which includes a memory and a processor, wherein a computer program is stored in the memory, and when the processor executes the program, the method described above is implemented.

[0035] In a fourth aspect of the present application, a computer-readable storage medium is provided, on which a computer program is stored, and when the program is executed by a processor, the method according to the first aspect of the present application is implemented.

[0036] The embodiment of the present application provides a method for analyzing foundation damage above a cave based on a six-directional triple triangulated network. Based on parameter data of the heterogeneous cave, a first triangular background mesh covering the ultimate bearing capacity model of the foundation above the heterogeneous cave is established; the first triangular background mesh is encrypted as a whole multiple times to generate a second triangular background mesh; the second triangular background mesh is cross-cut to generate a third triangular background mesh; based on the third triangular background mesh, optimization variables, objective functions and constraints are established; based on the optimization variables, objective functions and constraints, the upper limit solution and damage form of the ultimate bearing capacity of the foundation above the cave based on the six-directional and six-node triple triangulated network are determined, thereby greatly improving the calculation accuracy.

[0037] It should be understood that the contents described in the summary of the invention are not intended to limit the key or important features of the embodiments of the present application, nor are they intended to limit the scope of the present application. Other features of the present application will become easily understood through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The above and other features, advantages and aspects of the embodiments of the present application will become more apparent with reference to the following detailed description in conjunction with the accompanying drawings. In the accompanying drawings, the same or similar reference numerals represent the same or similar elements, wherein:

[0039] Figure 1 It is a flow chart of a method for analyzing foundation damage above a cave based on a six-directional triple triangulated network according to an embodiment of the present application;

[0040] Figure 2 A calculation model diagram of the ultimate bearing capacity and failure form analysis method of the foundation above the irregular karst cave provided in an embodiment of the present application;

[0041] Figure 3 A flow chart of constructing a background grid for an analysis model of the ultimate bearing capacity and failure form of foundation above an irregular karst cave provided in accordance with an embodiment of the present application;

[0042] Figure 4 A schematic diagram of the overall encryption of the grid of the ultimate bearing capacity and failure form analysis model of the foundation above the irregular karst cave provided in accordance with an embodiment of the present application;

[0043] Figure 5 A schematic diagram of the construction of six-directional discontinuous lines according to the centroid of the grid of the model for analyzing the ultimate bearing capacity and failure form of the foundation above the irregular karst cave provided in the embodiment of the present application;

[0044] Figure 6 A flow chart of a triangular cross-boundary unit cutting algorithm for analyzing the ultimate bearing capacity and failure morphology of foundation above an irregular karst cave provided in an embodiment of the present application;

[0045] Figure 7 A schematic diagram of a triangulated network boundary cross-cutting algorithm for analyzing the ultimate bearing capacity and failure form of the foundation above an irregular karst cave provided in an embodiment of the present application;

[0046] Figure 8 A schematic diagram of boundary cutting and redundant mesh elimination of a calculation model for analyzing the ultimate bearing capacity and failure form of foundation above an irregular karst cave provided in accordance with an embodiment of the present application;

[0047] Fig. 9 A schematic diagram of the boundary cutting of irregular caves and the removal of invalid grids according to an embodiment of the present application;

[0048] Fig.10 A flow chart of the conversion of triangulated upper limit finite element triangulated network data for the analysis of the ultimate bearing capacity and failure form of the foundation above the irregular karst cave provided in accordance with the embodiment of the present application;

[0049] Fig.11 The cloud diagram of dissipated energy density under different densification times for analyzing the ultimate bearing capacity and failure form of the foundation above the irregular karst cave provided in the embodiment of the present application;

[0050] Fig.12 A cloud diagram of dissipated energy density of superimposed grid deformation in the ultimate bearing capacity and failure form model of the foundation above the irregular karst cave provided in an embodiment of the present application;

[0051] Fig.13 The ultimate bearing capacity and failure form result diagram of the foundation above the irregular karst cave obtained by using the commercial software OPTUM G2 according to the embodiment of the present application;

[0052] Fig.14 is a block diagram of a foundation damage analysis device above a cave based on a six-directional triple triangulated network according to an embodiment of the present application;

[0053] Fig.15 It is a schematic diagram of the structure of a terminal device or a server suitable for implementing the embodiments of the present application. DETAILED DESCRIPTION

[0054] In order to make the purpose, technical solution and advantages of the embodiments of the present disclosure clearer, the technical solution in the embodiments of the present disclosure will be clearly and completely described below in conjunction with the drawings in the embodiments of the present disclosure. Obviously, the described embodiments are part of the embodiments of the present disclosure, not all of the embodiments. Based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present disclosure.

[0055] In addition, the term "and / or" in this article is only a description of the association relationship between the associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character " / " in this article generally indicates that the associated objects before and after are in an "or" relationship.

[0056] Figure 1 A flow chart of a method for analyzing foundation damage above a cave based on a six-directional triple triangulated network according to an embodiment of the present disclosure is shown. The method comprises:

[0057] S110, based on the parameter data of the heterogeneous karst cave, a first triangular background grid of the ultimate bearing capacity model of the foundation covering the heterogeneous karst cave is established.

[0058] Among them, the parameter data of the heterogeneous caves include data such as the width of the foundation above the heterogeneous caves, cohesion and / or internal friction angle.

[0059] In some embodiments, based on the width of the foundation above the irregular shaped cave, a first triangular background grid covering the ultimate bearing capacity model of the foundation above the irregular shaped cave is established, that is, a large-area background grid; the background grid is an equilateral triangle, that is, a regular triangle.

[0060] S120, performing overall encryption on the first triangular background mesh multiple times to generate a second triangular background mesh.

[0061] In some embodiments, all cells of the first triangular background mesh are traversed, and based on a preset number of mesh encryption times, the background mesh is encrypted by dividing the edge midpoints into four equal parts (dividing one into four), and the cell centroids and their corresponding edge midpoints and vertices are connected in sequence to generate a second triangular background mesh including a six-directional discontinuous line layout.

[0062] S130: cross-cut the second triangular background mesh to generate a third triangular background mesh.

[0063] In some embodiments, traversing the second triangular background mesh to obtain cells including boundary intersections;

[0064] Connect boundary intersection points and unit vertices to obtain the target triangle background mesh;

[0065] Calculating the number of boundary vertices and the number of cross-boundary unit intersections of the target triangular background mesh;

[0066] Based on the number of boundary vertices and the number of cross-boundary unit intersections, the target triangular background mesh is cut to generate a third triangular background mesh.

[0067] Specifically, pre-cut boundary feature points to prevent cells from being identified as crossing multiple model boundaries:

[0068] The second triangular background grid is traversed to search for cells containing boundary intersections, the boundary intersections are connected with cell vertices, and the cells are divided into three according to the boundary intersections.

[0069] Determine the relative position relationship between the unit and the boundary, and implement the "divide into two if passing through the vertex" and "divide into three if not passing through the vertex" operations respectively:

[0070] Extract the coordinates of the unit vertices, combine them two by two to get the line segment expression corresponding to the unit edge, and calculate the number of unit and boundary nodes k by combining the boundary function b , the process is as follows:

[0071] By setting the coordinates of the cell vertices to (x1, y1) and (x2, y2) and the coordinates of the boundary feature points to (x3, y3) and (x4, y4), we can get the cell edge expression and boundary edge expression:

[0072]

[0073] Convert to straight line standard form and express it in matrix as follows:

[0074]

[0075] like The determinant is not 0, that is, Δ = a1b2-a2b1≠0, then the intersection coordinates can be solved by Cramer's rule:

[0076]

[0077] Furthermore, to ensure the existence of the intersection, the handover coordinates should satisfy:

[0078]

[0079] If Δ = 0, the cell edge is parallel to the boundary and there is no intersection;

[0080] Superimpose and calculate the three unit edges associated with the cross-border unit to obtain the number of intersections k b ;

[0081] Furthermore, the number of intersection points k band the number of vertices on the boundary k q , determine the relative position relationship between the unit and the boundary:

[0082] If the number of intersections of the current cell and the number of intersections of the cross-border cell meet the first preset condition, the current cell is divided into two equal parts to process the cut cells near the boundary intersections;

[0083] For example, the precondition is k b =1 and k q =1, that is, there is a vertex on the boundary of the cross-boundary cell. Since the possibility of the background grid node coinciding with the non-critical boundary is small, the current cell is divided into two equal parts, that is, the "split into two through the vertex" operation is performed;

[0084] If the number of intersections of the current unit and the number of intersections of the cross-boundary unit meet the second preset condition, the current unit is divided into three equal parts;

[0085] The default condition is k b = 0 and k q =2, that is, no vertex of the cross-boundary cell is located on the boundary (a common form of cross-boundary cell cutting). At this time, the original cell is divided into three parts, that is, the operation of "dividing into three without changing vertices" is performed.

[0086] Furthermore, it also includes:

[0087] Based on the parameter data of the heterogeneous karst cave, the redundant cells in the third triangular background grid are removed. The redundant cells outside the ultimate bearing capacity model of the heterogeneous karst cave foundation and the empty cells within the karst cave boundary are selected and removed from the cell connection relationship matrix.

[0088] S140, establishing optimization variables, objective functions and constraints based on the third triangular background mesh.

[0089] In some embodiments, based on the third triangular background mesh, the midpoint information of the unit edge is added to the node coordinate index, the speed discontinuity line with nonlinear speed jump between units is extracted, the unit connection relationship matrix and the node coordinate index on both sides of the discontinuity line are located, and the associated unit speed information and geometric orientation information are generated.

[0090] Traverse all high-order velocity discontinuities and impose associated flow equality constraints on the velocities corresponding to the two nodes.

[0091] Based on the plastic flow constraint of the Mohr-Coulomb yield criterion on the velocity discontinuity line, the general formula can be expressed as:

[0092] Δv=|Δu|tanφ, and apply the associated plastic flow equation constraints to the unit and node information on the discontinuity line:

[0093] a 21 x1-a 23 x3=0

[0094] in,

[0095]

[0096] Furthermore, for the nonlinear velocity jump u on the high-order velocity discontinuity line ± =[u + ,u - ] T , it should be ensured that it is non-negative everywhere on the discontinuous line, that is:

[0097]

[0098] Among them, u ± for:

[0099]

[0100] in,

[0101]

[0102] Furthermore, to form a second-order cone programming model, we can set ρ3 = ξ + k2, and we can get:

[0103]

[0104] Among them, ρ3 is the auxiliary variable of the second-order cone programming.

[0105] Furthermore, all the cells in the computational domain are traversed and the associated plastic flow constraints inside the cells are applied in turn:

[0106]

[0107] in, is the plastic strain rate, Plasticity multiplier ω=[cosα+si nφ,si nφ–cosα,2s i nα] T .

[0108] S150, based on the optimization variables, objective function and constraint conditions, determine the upper limit solution of the ultimate bearing capacity and the failure form of the foundation above the cave based on the six-direction and six-node triple triangulation network.

[0109] In some embodiments, based on the optimization variables, objective function and constraints, a large-scale linear programming model is established through a sparse matrix;

[0110] Based on a large-scale linear programming model, the upper limit solution of the ultimate bearing capacity and the failure mode of the foundation above the cave based on a six-direction and six-node triple triangulated network are determined.

[0111] A specific embodiment based on the present disclosure is given below:

[0112] Construct a bearing capacity analysis model for the foundation above the irregular karst cave under concentrated load. Set the cohesion c = 0.55MPa, the internal friction angle φ = 5°, the foundation width B = 5m, and the midpoint of the foundation as the coordinate origin O; the concentrated force P is equivalent to the uniformly distributed overload P / B set along the foundation; for the irregular karst cave control points (randomly set): (-1.58, 2), (6, 4), (7.9, 1.01), (4.06, -4.89), (0.61, -4.39), the corresponding line segment expression is:

[0113] f1:y=0.2857x+2.45,x∈[-1.58,6]

[0114] f2:y=-2.973x+21.838,x∈[6,7.9]

[0115] f3:y=1.98x-14.75,x∈[4.06,7.9]

[0116] f4:y=0.11x-5.34,x∈[0.61,4.06]

[0117] f5:y=-4.62x-1.17,x∈[-1.58,0.61]

[0118] like Figure 3 As shown, after the basic information of the calculation model is determined, the expansion range coefficient m is set to 5, corresponding to Calculate Z i (i=1,…,4) are all in the region After being divided into four parts and encrypted four times, Figure 4 As shown in the gray background grid in the figure, the centroid is further divided into six equal parts into triangular elements, as shown in Figure 5 As shown, a six-directional speed discontinuous line path is formed and the background grid is constructed.

[0119] It should be noted that at this time, the background grid has nothing to do with the foundation bearing capacity analysis model above the irregular karst cave, and a cross-cutting algorithm needs to be executed to make the background grid fit the model boundary.

[0120] refer to Figure 2 , Figure 6 and Figure 7, introduce the triangulated network cross-cutting algorithm, first cut the unit where the boundary intersection control point is located, traverse the unit to search for the unit where the boundary intersection point is located, connect the boundary intersection point with the unit vertex, and realize the unit is divided into three, then calculate the number of intersection points between the boundary and the cross-boundary unit, and execute "divide into two if the vertex is crossed" and "divide into three if the vertex is not crossed" respectively. After the boundary cutting is completed, the redundant triangular units outside the model are identified and eliminated. Among them, the mesh schematic diagram after the external boundary of the model is cut and eliminated is shown as follows Figure 8 As shown; the schematic diagram of the grid after the cave boundary is cut and removed is as follows Fig. 9 As shown in the figure, the triangulated network is now completely consistent with the calculation model of the bearing capacity of the foundation above the cave, and the grid information conversion can be further carried out. Fig.10 .

[0121] After the triangulation matching the calculation model of the foundation bearing capacity above the cave is completed, the node coordinate matrix [P] and the unit connection relationship matrix [T] are extracted, and the internal discontinuity matrix [D] is further extracted. In this embodiment, the data of [P], [T], and [D] can be found in Table 1. After the data conversion is completed, the plastic unit upper limit finite element analysis program is imported and the calculation is carried out.

[0122] Table 1

[0123]

[0124] The calculation accuracy of the ultimate bearing capacity of the foundation above the cave is mainly divided into four times n re Control, with n ee The bearing capacity coefficient P / (B·c) corresponding to the three working conditions of =4, 5, and 6 is discussed.

[0125] It should be noted that in this disclosure, n re ≥m, for this embodiment, n re The minimum value is 5. re <5, the absence of corresponding nodes at the two ends of the foundation will affect the calculation accuracy, but its impact is much smaller than the grid density. re The impact on the calculation accuracy can be ignored. Fig.11 As shown, with n re As the value of B·c increases, the number of grids increases exponentially. Meanwhile, P / (B·c) decreases from 14.94 to 12.18, and the calculation accuracy is greatly improved. Fig.12 The plastic flow state of the stratum when the foundation above the cave is unstable is shown. Fig.12 It can be found that the "cracks" of the rock and soil directly below the foundation are most significant.

[0126] Furthermore, in order to verify the correctness of the disclosed method, the commercial software OPTUM G2 was used to establish the bearing capacity model of the irregular cave foundation under the same working conditions. The grid discretization mode also adopted “six-node triangle unit + velocity discontinuity line”. The results are as follows: Fig.13 As shown. The triangulation principle of OPTUM G2 is non-completely structured. Fig.13 In the upper part, the grids around the cave are arranged differently from other areas to adapt to the boundary, but still maintain a certain order. The OPTUM G2 triangulation method calculates the bearing capacity coefficient P / (B·c) = 12.30, which is slightly larger than the calculation result of the present invention. According to the upper limit theorem of limit analysis, the present invention has higher calculation accuracy under the same number of grids.

[0127] According to the embodiments of the present disclosure, the following technical effects are achieved:

[0128] The method provided by the present disclosure generates a primary triangular mesh with features such as six-directional through-type velocity discontinuity line paths by dividing the midpoint of an equilateral triangle into four equal parts and the centroid into six equal parts. Compared with conventional triangulated meshes, this method provides more possible discontinuity line advantage directions for potential sliding surfaces in the process of foundation damage, which not only helps to improve the calculation accuracy, but also can reveal the microscopic damage features such as staggered sliding surfaces and plastic flow deformation in the form of dense meshes.

[0129] (2) The mesh cross-cutting algorithm disclosed in the present invention that fits the key boundary clarifies the various possible relative position relationships between "edges and units" and the corresponding processing measures, and realizes the complete coupling of the secondary triangular mesh with six-directional through-type discontinuous line layout to the ultimate bearing capacity mechanical model of the irregular karst cave foundation, which not only inherits the topological structure advantages of the background mesh, but also removes the geometric morphological restrictions such as irregular karst caves;

[0130] (3) The three-level six-directional through-type triangulated network used for the analysis of the ultimate bearing capacity and failure morphology of the irregular cave foundation was converted into the mesh data information of high-order six-node triangular deformation unit + high-order velocity discontinuity line, and the upper limit finite element mathematical programming problem was further established and solved. Under the premise of the same number of grids, the calculation accuracy was significantly better than the upper limit solution of the bearing capacity coefficient of the OPTUM G2 software, and the micro-destruction characteristics such as staggered sliding surface and plastic flow deformation were revealed;

[0131] (4) The six-directional and six-node triple triangulated network obtained through composite encryption, boundary cutting and other algorithms is a proprietary grid suitable for the bearing capacity analysis of foundations above caves. It has the computational advantages of high robustness and high precision. In actual engineering applications, it can significantly improve the efficiency of batch processing operations of cave bearing capacity, thereby greatly reducing the computational cost.

[0132] It should be noted that, for the aforementioned method embodiments, for the sake of simplicity, they are all expressed as a series of action combinations, but those skilled in the art should be aware that the present application is not limited by the described order of actions, because according to the present application, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in the specification are all optional embodiments, and the actions and modules involved are not necessarily required by the present application.

[0133] The above is an introduction to the method embodiment. The following is a further explanation of the scheme described in this application through an apparatus embodiment.

[0134] Fig.14 FIG. 14 shows a block diagram 1400 of a foundation damage analysis device above a cave based on a six-directional triple triangulated network according to an embodiment of the present application, as shown in FIG. Fig.14 Shown include:

[0135] A construction module 1401 is used to establish a first triangular background grid covering the ultimate bearing capacity model of the foundation above the irregular karst cave based on the parameter data of the irregular karst cave;

[0136] A first generating module 1402 is used to perform multiple encryption on the first triangular background mesh to generate a second triangular background mesh;

[0137] A second generating module 1403 is used to perform cross cutting on the second triangular background mesh to generate a third triangular background mesh;

[0138] Establishing module 1404, used for establishing optimization variables, objective functions and constraints based on the third triangular background mesh;

[0139] The determination module 1405 is used to determine the upper limit solution of the ultimate bearing capacity and the failure form of the foundation above the cave based on the six-direction and six-node triple triangulation network based on the optimization variables, objective function and constraints.

[0140] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working process of the described module can refer to the corresponding process in the aforementioned method embodiment, and will not be repeated here.

[0141] Fig.15 A schematic diagram of the structure of a terminal device or server suitable for implementing an embodiment of the present application is shown.

[0142] like Fig.15As shown, the terminal device or server includes a central processing unit (CPU) 1501, which can perform various appropriate actions and processes according to the program stored in the read-only memory (ROM) 1502 or the program loaded from the storage part 1508 to the random access memory (RAM) 1503. In the RAM 1503, various programs and data required for the operation of the terminal device or server are also stored. CPU1501, ROM 1502 and RAM 1503 are connected to each other through a bus 1504. An input / output (I / O) interface 1505 is also connected to the bus 1504.

[0143] The following components are connected to the I / O interface 1505: an input section 1506 including a keyboard, a mouse, etc.; an output section 1507 including a cathode ray tube (CRT), a liquid crystal display (LCD), etc., and a speaker, etc.; a storage section 1508 including a hard disk, etc.; and a communication section 1509 including a network interface card such as a LAN card, a modem, etc. The communication section 1509 performs communication processing via a network such as the Internet. A drive 1510 is also connected to the I / O interface 1505 as needed. A removable medium 1511, such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc., is installed on the drive 1510 as needed, so that a computer program read therefrom is installed into the storage section 1508 as needed.

[0144] In particular, according to an embodiment of the present application, the above method flow steps can be implemented as a computer software program. For example, an embodiment of the present application includes a computer program product, which includes a computer program carried on a machine-readable medium, and the computer program includes a program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from the network through the communication part 1509, and / or installed from the removable medium 1511. When the computer program is executed by the central processing unit (CPU) 1501, the above-mentioned functions defined in the system of the present application are executed.

[0145] It should be noted that the computer-readable medium shown in the present application may be a computer-readable signal medium or a computer-readable storage medium or any combination of the above two. The computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or device, or any combination of the above. More specific examples of computer-readable storage media may include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present application, a computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in combination with an instruction execution system, device or device. In the present application, a computer-readable signal medium may include a data signal propagated in a baseband or as part of a carrier wave, which carries a computer-readable program code. This propagated data signal may take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. Computer-readable signal media may also be any computer-readable medium other than computer-readable storage media, which may send, propagate or transmit a program for use by or in conjunction with an instruction execution system, apparatus or device. The program code contained on the computer-readable medium may be transmitted using any appropriate medium, including but not limited to: wireless, wire, optical cable, RF, etc., or any suitable combination of the above.

[0146] The flow chart and block diagram in the accompanying drawings illustrate the possible architecture, function and operation of the system, method and computer program product according to various embodiments of the present application. In this regard, each box in the flow chart or block diagram can represent a module, a program segment or a part of the code, and the aforementioned module, program segment or a part of the code contains one or more executable instructions for realizing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in a different order from the order marked in the accompanying drawings. For example, two boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flow chart, and the combination of the boxes in the block diagram and / or flow chart can be implemented with a dedicated hardware-based system that performs the specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.

[0147] The units or modules involved in the embodiments described in the present application may be implemented by software or hardware. The units or modules described may also be arranged in a processor. The names of these units or modules do not, in some cases, constitute limitations on the units or modules themselves.

[0148] As another aspect, the present application further provides a computer-readable storage medium, which may be included in the electronic device described in the above embodiment; or may exist independently without being assembled into the electronic device. The above computer-readable storage medium stores one or more programs, and when the above programs are used by one or more processors to execute the method described in the present application.

[0149] The above description is only a preferred embodiment of the present application and an explanation of the technical principles used. Those skilled in the art should understand that the scope of application involved in the present application is not limited to the technical solution formed by a specific combination of the above technical features, but should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the aforementioned application concept. For example, the above features are replaced with (but not limited to) technical features with similar functions applied in the present application.

Claims

1. A method for analyzing foundation damage above a cave based on a six-directional triple triangulated network, characterized in that: include: Based on the parameter data of the heterogeneous karst cave, the first triangle background grid of the ultimate bearing capacity model of the foundation above the heterogeneous karst cave is established; Performing multiple overall encryption on the first triangular background mesh to generate a second triangular background mesh; Cross-cutting the second triangular background mesh to generate a third triangular background mesh; Based on the third triangular background mesh, establishing optimization variables, objective functions and constraints; Based on the optimization variables, objective function and constraints, the upper limit solution of the ultimate bearing capacity and the failure form of the foundation above the cave based on the six-direction and six-node triple triangulated network are determined.

2. The method according to claim 1, characterized in that The step of performing multiple overall encryption on the first triangular background mesh to generate a second triangular background mesh comprises: All cells of the first triangular background mesh are traversed, and based on the preset number of mesh encryptions, the centroids of the cells and their corresponding side midpoints and vertices are sequentially connected by dividing the side midpoints into four equal parts to generate a second triangular background mesh.

3. The method according to claim 2, characterized in that The second triangular background mesh is a triangular background mesh including a six-directional discontinuous line layout.

4. The method according to claim 3, characterized in that The cross-cutting of the second triangular background mesh to generate a third triangular background mesh comprises: traversing the second triangular background mesh to obtain cells including boundary intersection points; Connect boundary intersection points and unit vertices to obtain the target triangle background mesh; Calculating the number of boundary vertices and the number of cross-boundary unit intersections of the target triangular background mesh; Based on the number of boundary vertices and the number of cross-boundary unit intersections, the target triangular background mesh is cut to generate a third triangular background mesh.

5. The method according to claim 4, characterized in that The step of cutting the target triangular background mesh based on the number of boundary vertices and the number of cross-boundary unit intersections to generate a third triangular background mesh comprises: If the number of intersections of the current unit and the number of intersections of the cross-boundary unit meet the first preset condition, the current unit is divided into two equal parts; If the number of intersections of the current unit and the number of intersections of the cross-boundary units meet the second preset condition, the current unit is divided into three equal parts.

6. The method according to claim 5, characterized in that Before establishing the optimization variables, objective function and constraint conditions based on the third triangular background mesh, the method further includes: Based on the parameter data of the heterogeneous cave, redundant cells in the third triangular background mesh are removed.

7. The method according to claim 6, characterized in that The determination of the upper limit solution of the ultimate bearing capacity of the foundation above the cave and the failure form based on the six-direction and six-node triple triangulated network based on the optimization variables, objective function and constraint conditions includes: Based on the optimization variables, objective function and constraints, a large-scale linear programming model is established through a sparse matrix; Based on a large-scale linear programming model, the upper limit solution of the ultimate bearing capacity and the failure mode of the foundation above the cave based on a six-direction and six-node triple triangulated network are determined.

8. A foundation damage analysis device above a cave based on a six-directional triple triangulation network, characterized in that: include: A construction module is used to establish a first triangular background grid of the ultimate bearing capacity model of the foundation above the irregular karst cave based on the parameter data of the irregular karst cave; A first generating module, used for performing multiple overall encryption on the first triangular background mesh to generate a second triangular background mesh; A second generating module, used for cross-cutting the second triangular background mesh to generate a third triangular background mesh; An establishment module, used for establishing optimization variables, objective functions and constraints based on the third triangular background mesh; The determination module is used to determine the upper limit solution and failure form of the ultimate bearing capacity of the foundation above the cave based on the six-direction and six-node triple triangulation network based on the optimization variables, objective function and constraint conditions.

9. An electronic device comprising a memory and a processor, wherein a computer program is stored in the memory, wherein: When the processor executes the computer program, the method according to any one of claims 1 to 7 is implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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