Method for analyzing failure of foundation above karst cave based on six-direction triple-triangle net

Abstract

Embodiments of the present application provide a karst cave above ground failure analysis method, device and equipment based on six-direction triple triangular net and a computer readable storage medium. The method comprises establishing a first triangular background grid based on the parameter data of anisotropic karst cave; performing multiple 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 optimization variables, an objective function and a constraint condition based on the third triangular background grid; and determining the upper limit solution and failure mode of the ultimate bearing capacity of the karst cave above ground based on the optimization variables, the objective function and the constraint condition. In this way, by constructing a multi-level triangular net, the six-direction discontinuous line layout of the key failure area can be preferentially met, and under the premise of ensuring the energy dissipation contribution of the discontinuous line, a high-order variable element is supplemented to realize accurate analysis of the ultimate state of the karst cave above ground under the premise of single calculation of the fixed grid.

Description

TECHNICAL FIELD

[0001] Embodiments of the present application relate to the field of data processing, and in particular to a karst cave above foundation failure analysis method, device and equipment based on six-direction triple triangular mesh and a computer readable storage medium. BACKGROUND

[0002] In the process of bridge foundation construction in karst area, the problem of foundation bearing capacity needs to be paid special attention to. The determination of the ultimate bearing capacity of the foundation above the karst cave usually adopts the upper bound finite element method. When the foundation reaches the ultimate state of bearing capacity, the soil under the foundation has a tendency to collapse into the karst area, and the soil on both sides of the main sliding surface has a strong tendency of relative sliding. For this, a nonlinear velocity discontinuity line can be introduced to form a high-order "mixed-discontinuous" upper bound analysis method with a six-node triangular element.

[0003] In the prior art, the arrangement direction of the velocity discontinuity line is significantly related to its contribution in the upper bound analysis process. The core lies in whether to form a discontinuity line path along the high strain rate gradient area. On the contrary, the disordered arrangement mode will lead to the fact that the effect of the discontinuity line cannot be fully played, and the existence of the discontinuity line brings unnecessary calculation burden. On the other hand, in the process of matching the boundary of the triangular mesh with the karst cave model, the boundary nodes are strictly limited by the geometric conditions. This limitation often interferes with the original layout structure of the discontinuity line, thereby affecting the exertion of its efficiency.

[0004] Therefore, how to reasonably arrange the mesh so that the six-node triangular element and the nonlinear velocity discontinuity line achieve the best synergy is a problem that needs to be solved at present. SUMMARY

[0005] According to the embodiments of the present application, a karst cave above foundation failure analysis scheme based on six-direction triple triangular mesh is provided. Starting from a first-order equilateral triangular mesh, through multiple whole four-fold division and final six-fold division around the center, etc. encryption measures, a second-order triangular mesh with six-direction through velocity discontinuity line path is formed. Further, measures such as cross-cutting cross-border elements and removing redundant elements are developed to realize the triangular mesh discretization of the upper bound finite element model of the ultimate bearing capacity of the foundation above the karst cave of any shape, i.e. a third-order triangular mesh. Further, a high-order six-node triangular element considering the second-order change of velocity and the linear change of strain rate is considered, and a high-order velocity discontinuity line therebetween is extracted to establish three analysis modules of optimization variables, objective functions and constraint conditions, and embedded into an upper bound finite element analysis program to realize high-precision solution of the ultimate bearing capacity and failure mode of the foundation above the karst cave of the special-shaped karst cave. Compared with the prior art, the calculation accuracy is greatly improved.

[0006] In a first aspect of the present application, a karst cave above foundation failure analysis method based on six-direction triple triangular mesh is provided. The method comprises:

[0007] Based on the parameter data of the irregular cave, a first triangular background grid covering a limit bearing capacity model of the foundation above the irregular cave is established;

[0008] The first triangular background grid is encrypted multiple times as a whole to generate a second triangular background grid;

[0009] The second triangular background grid is cross-cut to generate a third triangular background grid;

[0010] Based on the third triangular background grid, an optimization variable, an objective function and a constraint condition are established;

[0011] Based on the optimization variable, the objective function and the constraint condition, an upper limit solution of the limit bearing capacity of the foundation above the cave and a failure mode based on a six-direction and six-node triple triangular net are determined.

[0012] Further, the first triangular background grid is encrypted multiple times as a whole to generate a second triangular background grid, including:

[0013] All cells of the first triangular background grid are traversed, and based on a preset grid encryption number, the cell centroid and the corresponding edge midpoint and vertex are sequentially connected by edge midpoint quartering to generate a second triangular background grid.

[0014] Further, the second triangular background grid is a triangular background grid including a six-direction discontinuous line layout.

[0015] Further, the second triangular background grid is cross-cut to generate a third triangular background grid, including:

[0016] Traverse the second triangular background grid to obtain cells including boundary intersection points;

[0017] Connect the boundary intersection points and the cell vertices to obtain a target triangular background grid;

[0018] The number of boundary vertices and the number of cross-border cell intersection points of the target triangular background grid are calculated;

[0019] Based on the number of boundary vertices and the number of cross-border cell intersection points, the target triangular background grid is cut to generate a third triangular background grid.

[0020] Further, the target triangular background grid is cut based on the number of boundary vertices and the number of cross-border cell intersection points to generate a third triangular background grid, including:

[0021] If the number of intersection points and the number of cross-border cell intersection points of the current cell satisfy a first preset condition, the current cell is bisected;

[0022] If the number of intersection points of the current unit and the number of intersection points of the cross-border unit satisfy a second preset condition, the current unit is trisected.

[0023] Further, before the optimization variable, the objective function and the constraint condition are established based on the third triangular background grid, the method further includes:

[0024] The parameter data of the heterogeneous cave, and the redundant units in the third triangular background grid are removed.

[0025] Further, the upper limit solution and the failure mode of the ultimate bearing capacity of the foundation above the cave based on the six-direction and six-node triple triangular net are determined based on the optimization variable, the objective function and the constraint condition.

[0026] The large-scale linear programming model is established by sparse matrix based on the optimization variable, the objective function and the constraint condition.

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

[0028] In a second aspect of the present application, a device for analyzing the failure of the foundation above the cave based on the six-direction triple triangular net is provided. The device includes:

[0029] The construction module is configured to establish a first triangular background grid covering the ultimate bearing capacity model of the foundation above the heterogeneous cave based on the parameter data of the heterogeneous cave.

[0030] The first generation module is configured to generate a second triangular background grid by encrypting the first triangular background grid multiple times.

[0031] The second generation module is configured to generate a third triangular background grid by cross-cutting the second triangular background grid.

[0032] The establishment module is configured to establish an optimization variable, an objective function and a constraint condition based on the third triangular background grid.

[0033] The determination module is configured to determine the upper limit solution and the failure mode of the ultimate bearing capacity of the foundation above the cave based on the six-direction and six-node triple triangular net based on the optimization variable, the objective function and the constraint condition.

[0034] In a third aspect of the present application, an electronic device is provided. The electronic device includes a memory and a processor, the memory stores a computer program, and the processor executes the program to realize the method as described above.

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

[0036] The method for analyzing the damage of the foundation above the karst cave based on the six-direction triple triangle net provided by the embodiments of the present application establishes the first triangular background grid of the limit bearing capacity model of the foundation above the special-shaped karst cave based on the parameter data of the anisotropic karst cave; the first triangular background grid is encrypted multiple times as a whole to generate the second triangular background grid; the second triangular background grid is cross-cut to generate the third triangular background grid; the optimization variable, the objective function and the constraint condition are established based on the third triangular background grid; and the upper limit solution and the damage mode of the limit bearing capacity of the foundation above the karst cave based on the six-direction and six-node triple triangle net are determined based on the optimization variable, the objective function and the constraint condition, which greatly improves the calculation accuracy.

[0037] It should be understood that the content described in the summary section is not intended to limit the key or important features of the embodiments of the present application, nor to limit the scope of the present application. Other features of the present application will become apparent through the following description. BRIEF DESCRIPTION OF DRAWINGS

[0038] The above and other features, advantages and aspects of the embodiments of the present application will become more apparent by describing in detail the following embodiments with reference to the attached drawings. In the drawings, the same or similar reference numerals refer to the same or similar elements, in which:

[0039] Figure 1 A flowchart of the method for analyzing the damage of the foundation above the karst cave based on the six-direction triple triangle net according to the embodiments of the present application;

[0040] Figure 2 A calculation model diagram of the method for analyzing the limit bearing capacity and the damage mode of the foundation above the special-shaped karst cave according to the embodiments of the present application;

[0041] Figure 3 A background grid construction flowchart of the analysis model of the limit bearing capacity and the damage mode of the foundation above the special-shaped karst cave according to the embodiments of the present application;

[0042] Figure 4 A schematic diagram of the overall encryption of the grid of the analysis model of the limit bearing capacity and the damage mode of the foundation above the special-shaped karst cave according to the embodiments of the present application;

[0043] Figure 5 A schematic diagram of the construction of the six-direction discontinuous line of the grid of the analysis model of the limit bearing capacity and the damage mode of the foundation above the special-shaped karst cave according to the embodiments of the present application;

[0044] Figure 6 Flow chart of triangular mesh boundary crossing cutting algorithm for limit bearing capacity and failure mode analysis of foundation above special-shaped karst cave according to embodiments of the present application;

[0045] Figure 7 Schematic diagram of triangular mesh boundary crossing cutting algorithm for limit bearing capacity and failure mode analysis of foundation above special-shaped karst cave according to embodiments of the present application;

[0046] Figure 8 Schematic diagram of boundary cutting and redundant mesh removal of calculation model for limit bearing capacity and failure mode analysis of foundation above special-shaped karst cave according to embodiments of the present application;

[0047] Figure 9 Schematic diagram of boundary cutting and invalid mesh removal of special-shaped karst cave according to embodiments of the present application;

[0048] Figure 10 Flow chart of upper limit finite element triangular mesh data conversion of triangular mesh for limit bearing capacity and failure mode analysis of foundation above special-shaped karst cave according to embodiments of the present application;

[0049] Figure 11 Dissipation energy density nephogram under different encryption times for limit bearing capacity and failure mode analysis of foundation above special-shaped karst cave according to embodiments of the present application;

[0050] Figure 12 Dissipation energy density nephogram of superimposed mesh deformation in model for limit bearing capacity and failure mode analysis of foundation above special-shaped karst cave according to embodiments of the present application;

[0051] Figure 13 Result diagram of limit bearing capacity and failure mode of foundation above special-shaped karst cave obtained by using commercial software OPTUM G2 according to embodiments of the present application;

[0052] Figure 14 Block diagram of karst cave foundation failure analysis device based on six-direction triple triangular mesh according to embodiments of the present application;

[0053] Figure 15 Structural schematic diagram of terminal device or server suitable for implementing embodiments of the present application. DETAILED DESCRIPTION

[0054] In order to make the purposes, technical solutions and advantages of the embodiments of the present disclosure clearer, the technical solutions in the embodiments of the present disclosure will be described clearly and completely below with reference to the drawings in the embodiments of the present disclosure. Obviously, the described embodiments are only some of the embodiments of the present disclosure, rather than all the embodiments. Based on the embodiments in the present disclosure, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present disclosure.

[0055] In addition, the term "and / or" in this paper is only to describe the association relationship of the associated objects, which means that there can be three relationships, for example, A and / or B, which can represent the three cases of A alone, A and B together, and B alone. In addition, the character " / " in this paper generally represents that the front and rear associated objects are in an "or" relationship.

[0056] Figure 1 A flowchart of a karst cave above ground failure analysis method based on a six-direction triple triangular net according to an embodiment of the present disclosure is shown. The method comprises:

[0057] S110, based on the parameter data of the special-shaped karst cave, a first triangular background grid covering the limit bearing capacity model of the ground above the special-shaped karst cave is established.

[0058] The parameter data of the special-shaped karst cave includes data such as the width of the ground above the special-shaped karst cave, the cohesion and / or internal friction angle.

[0059] In some embodiments, based on the width of the ground above the special-shaped karst cave, the first triangular background grid covering the limit bearing capacity model of the ground above the special-shaped karst cave, i.e. the large-area background grid, is established. The background grid is an equilateral triangle, i.e. a regular triangle.

[0060] S120, the first triangular background grid is encrypted multiple times as a whole to generate a second triangular background grid.

[0061] In some embodiments, all cells of the first triangular background grid are traversed, and based on a preset grid encryption times, the second triangular background grid including a six-direction discontinuous line layout is generated by connecting the cell centroid and its corresponding edge midpoint and vertex in turn through edge midpoint quartering (encryption of the background grid in a one-to-four manner).

[0062] S130, the second triangular background grid is cross-cut to generate a third triangular background grid.

[0063] In some embodiments, the second triangular background grid is traversed to obtain a cell including a boundary intersection point;

[0064] The boundary intersection point and the cell vertex are connected to obtain a target triangular background grid.

[0065] counting the number of boundary vertices and the number of intersection points of the cross-border cells of the target triangular background grid;

[0066] cutting the target triangular background grid based on the number of boundary vertices and the number of intersection points of the cross-border cells, to generate a third triangular background grid.

[0067] Specifically, the boundary feature points are cut in advance to avoid the cells being identified as intersecting with multiple model boundaries:

[0068] traversing the second triangular background grid to search for cells containing boundary intersection points, connecting the boundary intersection points and the cell vertices, and dividing the cells into three parts according to the boundary intersection points.

[0069] judging the relative position relationship between the cells and the boundary, and respectively implementing "dividing into two parts through vertices" and "dividing into three parts without passing through vertices" operations:

[0070] extracting the cell vertex coordinates, combining them two by two to obtain the line segment expressions corresponding to the cell edges, and calculating the number of cell and boundary nodes k b , the process is as follows:

[0071] Setting the cell vertex coordinates as (x1, y1), (x2, y2), and the boundary feature point coordinates as (x3, y3), (x4, y4), the cell edge expressions and the boundary edge expressions can be obtained:

[0072]

[0073] Transformed into a standard form of straight line and represented by a matrix as follows:

[0074]

[0075] If the determinant of is not 0, i.e., Δ = a1b2-a2b1≠0, then the intersection point coordinates can be obtained by solving the Cramer's rule as:

[0076]

[0077] Further, to ensure the existence of the intersection point, the intersection coordinates should satisfy:

[0078]

[0079] If Δ = 0, the cell edge and the boundary are parallel, and there is no intersection point.

[0080] Superimposed calculation of the 3 cell edges associated with the cross-border cells, to obtain the number of intersection points k b ;

[0081] Further, 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-boundary cells meet the first preset condition, the current cell is divided into two equal parts to process the cells cut 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 background grid node is less likely to coincide with the non-critical boundary, the current cell is bisected, 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 units meet the second preset condition, the current unit is divided into three equal parts;

[0085] The precondition 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 the vertex" is performed.

[0086] Furthermore, it also includes:

[0087] Based on the parameter data of the heterogeneous karst cave, 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: Establish 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 the associated plastic flow equation constraints are applied to the elements and nodes 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 discontinuity 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 cells in the computational domain are traversed and the associated plastic flow constraints within the cells are applied in turn:

[0106]

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

[0108] S150, based on the optimization variables, objective function and constraints, determining an upper limit solution for the ultimate bearing capacity and a failure mode of the foundation above the cave based on a six-direction and six-node triple triangulated network.

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

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

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

[0112] The analysis model of the bearing capacity of the foundation above the special-shaped karst cave under the action of concentrated load is constructed. The cohesion c is set to 0.55 MPa, the internal friction angle φ is set to 5°, the foundation width B is set to 5 m, and the midpoint of the foundation is set as the coordinate origin O; the concentrated force P is equivalent to the uniform superimposed load P / B arranged along the foundation; the control points (randomly set) of the special-shaped karst cave are: (-1.58, 2), (6, 4), (7.9, 1.01), (4.06, -4.89), and (0.61, -4.39), and the corresponding line segment expressions are:

[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] As shown in Figure 3 , after the basic information of the calculation model is determined, the extension range coefficient m is set to 5, and the corresponding is calculated. i (i = 1, …, 4) are all in the area , after four times of integral one-fourth encryption, as shown in the gray background grid in Figure 4 , further centroid six-equal-division dissection triangular elements are taken, as shown in Figure 5 , to form six-direction velocity discontinuity line paths, and the background grid construction is completed.

[0119] It should be noted that the background grid is irrelevant to the bearing capacity analysis model of the foundation above the special-shaped karst cave at this time, and the cross-cutting algorithm needs to be executed to make the background grid fit the model boundary.

[0120] Referring to Figure 2 , Figure 6 and Figure 7, the triangular mesh intersection cutting algorithm is introduced. Firstly, the unit where the boundary intersection control point is located is cut, the unit where the boundary intersection point is located is searched by traversing the unit, the boundary intersection point and the unit vertex are connected to realize the division of the unit into three parts. Secondly, the number of intersection points of the boundary and the cross-border unit is calculated, and "divided into two through vertex" and "divided into three without passing through vertex" are respectively executed. After the boundary cutting is completed, the redundant triangular unit outside the model is identified and removed. As shown in Figure 8 ; as shown in Figure 9 , the triangular mesh completely fits the calculation model of the bearing capacity of the foundation above the karst cave, and the grid information conversion can be further continued, as shown in Figure 10 .

[0121] After the triangular mesh fitting the calculation model of the bearing capacity of the foundation above the karst cave is divided, the node coordinate matrix [P] and the unit connection relationship matrix [T] are extracted, and the internal discontinuous line matrix [D] is further extracted. In this embodiment, part of the data of [P], [T] and [D] can be referred to Table 1. After the data conversion is completed, the upper limit finite element analysis program of the plastic unit 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 karst cave is mainly controlled by the number of times of division into four n re . The bearing capacity coefficients P / (B·c) corresponding to three working conditions of n ee =4, 5 and 6 are discussed.

[0125] It should be noted that in the present disclosure, n re ≥m is required. For this embodiment, the minimum value of n re is 5. When n re <5, there is no corresponding node at the end point of the foundation on both sides, which will affect the calculation accuracy, but the influence degree is much smaller than the grid density. In this case, the influence of the number of times of encryption n re on the calculation accuracy can be ignored. As shown in Figure 11 , with the increase of n re , the number of grids increases exponentially, and P / (B·c) decreases from 14.94 to 12.18, and the calculation accuracy is greatly improved. Figure 12 The plastic flow state of the stratum when the foundation above the karst cave is unstable is shown, and it can be found from Figure 12 that the "cracking" of the rock-soil body directly below the foundation is the most significant.

[0126] Further, to verify the correctness of the method of the present disclosure, a commercial software OPTUM G2 is used to establish a model of the bearing capacity of the irregular solution cavity foundation under the same working condition, and the grid discrete mode is also "six-node triangular element + velocity discontinuity line". The results are shown in Figure 13 The triangular mesh division principle of OPTUM G2 is non-fully structured, and reference is made to the upper half of Figure 13 The mesh around the solution cavity is arranged in a different order from other areas to adapt to the boundary, but still maintains a certain order. The bearing capacity coefficient P / (B·c) calculated by the triangular mesh division mode of OPTUM G2 is 12.30, which is slightly larger than the calculation result of the present application. According to the upper bound theorem of limit analysis, it is illustrated that the calculation accuracy of the present application is higher under the condition of 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 first triangular mesh with six-directional through-type velocity discontinuity line passages in a way of equating the midpoint of an equilateral triangle to four and the centroid to six, etc. Compared with the conventional triangular mesh, the method provides more possible matching discontinuity line advantage directions for the potential sliding surface in the foundation failure process, which not only helps to improve the calculation accuracy, but also reveals the mesoscopic failure characteristics such as the interlaced sliding surface and plastic flow deformation in the form of dense mesh;

[0129] (2) The mesh intersection cutting algorithm of the present disclosure that matches the key boundary clarifies various possible relative position relationships between "edge-element" and corresponding processing measures, realizes the complete coupling of the second triangular mesh with six-directional through-type discontinuity line layout to the limit bearing capacity mechanical model of the irregular solution cavity foundation, and inherits the topological structure advantage of the background mesh and eliminates the geometric shape restrictions such as irregular solution cavity;

[0130] (3) The third-level six-directional through-type triangular mesh for the limit bearing capacity and failure mode analysis of the irregular solution cavity foundation is converted into grid data information of high-order six-node triangular deformation element + high-order velocity discontinuity line, and an upper limit finite element mathematical programming problem is further established and solved to obtain a bearing capacity coefficient upper limit solution that is significantly better than that of the OPTUM G2 software under the premise of the same number of grids, and the mesoscopic failure characteristics such as the interlaced sliding surface and plastic flow deformation are revealed;

[0131] (4) The six-directional and six-node triple triangular mesh obtained by the composite encryption, boundary cutting and other algorithms is used as a special mesh suitable for the bearing capacity analysis of the foundation above the solution cavity, which has the calculation advantages of high robustness and high accuracy, and can significantly improve the efficiency of the solution cavity bearing capacity batch operation in practical engineering applications, thereby greatly reducing the calculation cost.

[0132] It should be noted that, for the foregoing method embodiments, for the sake of simple description, they are all expressed as a combination of a series of actions, but those skilled in the art should know that the present application is not limited by the order of the actions described, because according to the present application, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should know 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 the introduction of the method embodiment, and the scheme described in the present application will be further described through the device embodiment.

[0134] Figure 14 A block diagram 1400 of a karst cave above ground failure analysis device based on a six-direction triple triangle net according to an embodiment of the present application is shown, as shown in Figure 14 includes:

[0135] The construction module 1401 is configured to establish a first triangular background grid covering the limit bearing capacity model of the ground above the special-shaped karst cave based on the parameter data of the special-shaped karst cave.

[0136] The first generation module 1402 is configured to perform multiple overall encryption on the first triangular background grid to generate a second triangular background grid.

[0137] The second generation module 1403 is configured to cross-cut the second triangular background grid to generate a third triangular background grid.

[0138] The establishment module 1404 is configured to establish optimization variables, objective functions and constraint conditions based on the third triangular background grid.

[0139] The determination module 1405 is configured to determine the upper limit solution and failure mode of the karst cave above ground limit bearing capacity based on the six-direction and six-node triple triangle net based on the optimization variables, objective functions and constraint conditions.

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

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

[0142] As Figure 15As shown, the terminal device or server includes a central processing unit (CPU) 1501, which can perform various appropriate actions and processes in accordance with a program stored in a read only memory (ROM) 1502 or a program loaded into a random access memory (RAM) 1503 from a storage section 1508. In the RAM 1503, various programs and data required for the operation of the terminal device or server are also stored. The CPU 1501, the ROM 1502, and the 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] Connected to the I / O interface 1505 are an input section 1506 including a keyboard, a mouse, etc.; an output section 1507 including a display such as 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 necessary. A removable recording medium 1511 such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc. is attached to the drive 1510 as necessary, so that a computer program read therefrom is installed in the storage section 1508 as necessary.

[0144] In particular, according to embodiments of the present application, the above method flow steps can be implemented as a computer software program. For example, embodiments of the present application include a computer program product comprising a computer program carried on a machine-readable medium, the computer program containing program code for executing the methods illustrated by the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via the communication section 1509, and / or installed from the removable recording medium 1511. When the computer program is executed by the central processing unit (CPU) 1501, the above-described functions defined in the system of the present application are performed.

[0145] It should be noted that the computer-readable medium shown in the application can be a computer-readable signal medium or a computer-readable storage medium or any combination of the two. The computer-readable storage medium may, for example, but is not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or component, or any combination of the above. More specific examples of computer-readable storage media can include, but are not limited to, an electrical connection having one or more wires, a portable computer diskette, 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 this application, the computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, device or component. In this application, the computer-readable signal medium can include a data signal carried in a baseband or as a carrier wave in a carrier wave, which carries computer-readable program code. Such a propagated data signal can take many forms, including but not limited to an electromagnetic signal, an optical signal, or any suitable combination of the above. The computer-readable signal medium can also be any computer-readable medium other than the computer-readable storage medium, which can send, propagate or transmit a program for use by or in conjunction with an instruction execution system, device or component. The program code contained on the computer-readable medium can be transmitted using any suitable medium, including but not limited to wireless, wire, optical cable, RF, etc., or any suitable combination of the above.

[0146] The flowcharts and block diagrams in the drawings illustrate the possible implementation architectures, functions and operations of the systems, methods and computer program products according to various embodiments of the application. In this regard, each block in the flowcharts or block diagrams can represent a module, a program segment, or a portion of code, which contains one or more executable instructions for implementing the specified logical functions. It should also be noted that in some alternative implementations, the functions noted in the blocks can occur in different orders than that shown in the drawings. For example, two blocks that are shown in succession can actually be executed substantially concurrently, or they can sometimes be executed in reverse order, depending on the involved functions. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented by a dedicated hardware-based system that performs the specified functions or operations, or can be implemented by a combination of special-purpose hardware and computer instructions.

[0147] The units or modules described in the embodiments of the present application can be implemented in the form of software or in the form of hardware. The units or modules described can also be arranged in a processor. In some cases, the names of the units or modules do not constitute a limitation on the units or modules themselves.

[0148] As another aspect, the present application also provides a computer readable storage medium, which can be included in the electronic device described in the above embodiments, or can exist separately without being assembled into the electronic device. The computer readable storage medium stores one or more programs, and the programs are used by one or more processors to execute the methods described in the present application.

[0149] The above description is merely preferred embodiments of the present application and a description of the principles of the technology used. Those skilled in the art should understand that the scope of the application described in the present application is not limited to the technical solutions formed by the specific combinations of the above technical features, and should also cover other technical solutions formed by the combinations of the above technical features or their equivalent features without departing from the above application concept. For example, the technical solutions formed by the mutual replacement of the above features and the technical features applied in the present application (but not limited to) having similar functions.

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 cave, the first triangle background grid of the ultimate bearing capacity model of the foundation above the heterogeneous cave is established; Performing multiple overall encryption on the first triangular background mesh to generate a second triangular background mesh includes: Traversing all cells of the first triangular background mesh, and based on a preset mesh encryption number, sequentially connecting the cell centroids and their corresponding side midpoints and vertices by quartering the side midpoints to generate a second triangular background mesh; Wherein, the second triangular background grid is a triangular background grid including a six-directional discontinuous line layout; Cross-cutting the second triangular background mesh to generate a third triangular background mesh includes: traversing the second triangular background mesh to obtain cells including boundary intersections; Connect boundary intersections 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, including: If the number of intersections of the current unit and the number of intersections of the cross-boundary units 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; 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 mode 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 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 grid are removed.

3. The method according to claim 2, characterized in that The method of determining the upper limit solution of the ultimate bearing capacity and the failure mode of the foundation above the cave based on the six-direction and six-node triple triangulated network based on the optimization variables, objective function and constraints 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 failure mode of the foundation above the cave based on a six-direction and six-node triple triangulated network are determined.

4. A device for analyzing foundation damage above a cave based on a six-directional triple triangulated network, characterized in that: include: A construction module is used to establish a first triangular background grid covering the ultimate bearing capacity model of the foundation above the irregular cave based on the parameter data of the irregular cave; The first generating module is configured to perform multiple overall encryption on the first triangular background mesh to generate a second triangular background mesh, including: Traversing all cells of the first triangular background mesh, and based on a preset mesh encryption number, sequentially connecting the cell centroids and their corresponding side midpoints and vertices by quartering the side midpoints to generate a second triangular background mesh; Wherein, the second triangular background grid is a triangular background grid including a six-directional discontinuous line layout; The second generating module is configured to cross-cut the second triangular background mesh to generate a third triangular background mesh, including: traversing the second triangular background mesh to obtain cells including boundary intersections; Connect boundary intersections 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, including: If the number of intersections of the current unit and the number of intersections of the cross-boundary units 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; An establishment module, configured to establish optimization variables, objective functions, and constraints based on the third triangular background mesh; A determination module is used to determine 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 based on the optimization variables, objective function and constraint conditions.

5. 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 3 is implemented.

6. 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 3 is implemented.

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