CN-120822372-B - Quasi-regular double six-break triangular net construction method for searching potential sliding surface of side slope

CN120822372BCN 120822372 BCN120822372 BCN 120822372BCN-120822372-B

Abstract

The invention provides a construction method of a quasi-regular double six-intermittent triangular network for searching a potential sliding surface of a side slope, which comprises the steps of iteratively generating a quasi-regular initial triangular network adapting to a side slope model boundary; the method comprises the steps of dividing local part into six grids, encrypting to generate six-direction array arrangement topological grids, constructing six-node triangle units and a high-order break line data format, and solving and searching a slope potential sliding surface by a second-order cone planning model. The method is suitable for the geometric boundary of a discrete side slope model, can meet the special requirements of a quasi-regular double-six-intermittent triangular network, forms a six-direction through intermittent grid structure in any micro area, can further preset partial partitions, reduces the resource consumption of grid units in non-critical areas, is applied to limit analysis upper limit finite elements, realizes high-precision search of potential sliding surfaces of the side slope by quick solution of a second-order cone programming problem, and can realize the reduction of calculation load and guarantee of search precision.

Inventors

YANG FENG
Ding Zhanheng
Zheng Xiangcou
Qin Aohan
WANG SHUYING
ZHAO LIANHENG
LUO CHENGKAI
QIU XINYI

Assignees

中南大学

Dates

Publication Date: 20260505
Application Date: 20250707

Claims (8)

1. The construction method of the quasi-regular double six-break triangular net for searching the potential sliding surface of the side slope is characterized by comprising the following steps: S1, constructing a slope model initial point set according to a preset unit size, executing Delaunay triangulation to generate an initial grid, simulating a truss structure by using a triangular network, calculating node resultant force vectors of all truss elastic rod members by using Hooke' S law, adjusting node coordinates along the direction of the resultant force vectors, and circularly implementing node coordinate optimization and grid reconstruction until an approximate regular triangle grid which is suitable for the boundary of the slope model and is arranged in a quasi-regular array is generated; in S1, based on explicit time integral, node coordinate iterative update is executed to shift the nodes along the direction of resultant force vector, the nodes beyond the boundary after shift are projected along the negative gradient direction of the implicit distance function of the boundary, the nodes are constrained back to the boundary, S2, executing a local encryption strategy driven by encryption edges on a key area of the approximate regular triangle mesh to form a hexagonal triangle mesh with local array arrangement, wherein the key area of the slope model is divided into six encryptions, the passive encryption strategy is executed according to the number of the encryption edges in a transition area, and an original unit is reserved in a non-encryption area; S2 comprises the following substeps: s21, traversing all units, and screening triangle units positioned in a key area based on centroid coordinate discrimination criteria; S22, extracting and marking adjacent pre-encryption edge data according to encryption unit indexes, traversing all units to count the number of the included pre-encryption edges, and marking four types of encryption edge states, namely an encryption edge-free unit, an encryption edge unit, two encryption edge units and three-edge full encryption units; S23, for a unit without encryption edges, retaining an original grid topological structure and not executing encryption operation, when the unit only comprises one encryption edge, adopting a midpoint segmentation method, inserting a new node at the midpoint of the encryption edge, connecting the new node with the non-encryption edge vertex, splitting the original unit into two subunits, when the unit comprises two encryption edges, executing three-way segmentation encryption, namely identifying the longest encryption edge, taking the midpoint thereof as a pivot node, connecting the pivot node with the midpoint of the adjacent encryption edge and the corresponding vertex to generate three subunits, and when the three edges of the unit all need encryption, executing one division into six encryption, namely calculating the centroid node of the unit as a core node, connecting the centroid node with the midpoint of each edge and the original vertex in anticlockwise sequence, and deleting the original unit to generate six subunits; S3, extracting a coordinate matrix and a unit information matrix based on a hexagonal triangular network, generating a fifteen-degree-of-freedom six-node triangular unit through edge midpoint interpolation, constructing a public edge high-order break line, and adding non-negative auxiliary variables and constraint conditions to realize speed jump among units so as to form a double six-break triangular network data format required by a limit analysis upper limit finite element; s3 comprises the following substeps: S31, extracting a unit coordinate matrix [ P ] and a unit information matrix [ Q ] as output results of grid processing, wherein three vertex information of each unit is stored in the [ Q ]; S32, obtaining the edge numbers of all the units, and generating six-node triangle high-order units with fifteen degrees of freedom through edge midpoint interpolation; S33, constructing a high-order speed break line on the common edge of the unit according to boundary marks, wherein node speeds and plastic multipliers on two sides of the break line have transitions, searching, judging and establishing unit numbers on two sides of the speed break line and positions of the break line nodes on the unit nodes on two sides, and introducing auxiliary variables on the speed break line to remove absolute values in related flow rules; s4, establishing a slope stability second-order cone planning model based on limit analysis upper limit theory, searching a critical unstability state of plastic flow of the slope, outputting a high-order triangle unit and a dissipation energy density distribution point cloud of isomorphic speed break lines, and obtaining a slope limit state potential sliding surface.
2. The method for constructing a quasi-regular double six-break triangular network for searching a potential sliding surface of a side slope according to claim 1, wherein S1 comprises: generating an initial large-area regular array node set according to a preset grid initial size h 0 , screening nodes in a slope model, merging fixed point coordinates on the same boundary, and constructing an initial node set; Performing Delaunay triangulation on the input point set, updating the internal grid structure of the model, arranging vertex number indexes of the unit edges in ascending order, and removing repeated edges; let the unit side satisfy hooke's law, let equivalent spring rate be K, calculate the resultant force of unit node i department: Wherein, the For the component of the node i in the x-direction, For the component of the force of the node i in the y-direction, For the distance between node i and node j, The neighboring nodes are connected to each other by a node, 、 The coordinates of the nodes i, j respectively, For a desired length between node i and node j: Wherein, the The sum of the squares of the lengths of all cell edges in the grid, The sum of squares of the lengths of all cell edges in the desired grid; for nodes beyond the boundary after the nodes are shifted along the direction of the resultant force vector, implicit distance function along the boundary The negative gradient direction is projected, which is constrained back to the boundary: Wherein g is a distance function Sum of squares of x and y partial derivatives; The node coordinate offset and grid reconstruction are circularly realized, and the square sum of offset of all nodes in the model during each cycle is recorded Stopping when the sum of squares of the offsets of all nodes in the calculation domain is smaller than a threshold value or the preset iteration times are met, and generating an approximate regular triangle grid which is suitable for the quasi-regular array arrangement of the boundary inside the model.
3. The method for constructing a quasi-regular double six-break triangular network for searching a potential sliding surface of a side slope according to claim 2, wherein the node triangle higher order unit in S32 is characterized in that any point in the unit is at a speed The form function is used for representing as a quadratic function of the node coordinates: Wherein, the 、 The velocity components of node i in the x and y directions respectively, Is a unit-shaped function; Plastic multiplier at any point in unit Interpolation from three vertex values: Wherein, the Is the plastic multiplier at node i.
4. The method for constructing a quasi-regular double six-intermittent triangular network for searching potential sliding surfaces of a side slope according to claim 3, wherein the critical instability state of plastic flow of the side slope in S4 is obtained by limit analysis upper limit theory, and when the side slope reaches the limit state, a plurality of speed fields allowed by movement exist, so that the internal dissipation energy is not more than the external force to do work: Wherein, the For the purpose of internal dissipation of energy, And (3) with The plastic stress and strain vectors are respectively given, For the velocity vector on the break line, Doing work for external force, And Are all Is a function of (a) and (b), As a function of the yield point, A domain is calculated for the model.
5. The method for constructing a quasi-regular double six-break triangular network for searching a potential sliding surface of a side slope according to claim 4, wherein in S4, a minimum objective function is built by an upper limit theory to form a second order cone planning model: Wherein, the For plastic flow restriction on the cell and velocity break lines, For boundary velocity constraint, A is a coefficient matrix corresponding to a boundary constraint equation satisfied by nodes at the boundary, B is a coefficient matrix corresponding to a boundary constraint equation satisfied by nodes at the boundary, For a column vector consisting of all cell node speeds of the model, auxiliary variables and plastic multiplier unknowns, Additional constraints, parameters for second order cone planning , , Is the included angle between one point on the yield surface of Mohr-Coulomb yield criterion and Y axis, For the speed constraint associated with the dead weight, Is a load matrix.
6. The method for constructing a quasi-regular double six-break triangular network for searching a potential sliding surface of a side slope according to claim 4, wherein the internal dissipation energy comprises two parts of internal dissipation energy of a six-node triangular unit and dissipation energy on a high-order speed break line: Wherein, the For the plastic unit distribution domain, In order to provide a speed jump in the break line, Is a set of speed break lines.
7. The method for constructing a quasi-regular double six-break triangular network for searching a potential sliding surface of a side slope according to claim 4, wherein the dissipated density distribution point cloud is displayed by interpolating the model dissipated energy density to the unit node, and the dissipated energy density at the ith node of the unit k Expressed as: Wherein, the For the area of the cell k, j is the vertex node adjacent to the node i in the cell k, c, Respectively the cohesive force and the internal friction angle of the soil body, Is the plastic multiplier vector of the kth unit, A is a constant coefficient term, And the auxiliary variables corresponding to the nodes i and j.
8. The method for constructing a quasi-regular double six-break triangular network for searching a potential sliding surface of a side slope according to claim 7, wherein the potential sliding surface of the side slope is characterized by normalized dissipation energy density point cloud: Wherein, the The energy density maximum is dissipated for the model.

Description

Quasi-regular double six-break triangular net construction method for searching potential sliding surface of side slope Technical Field The invention relates to the technical field of geotechnical engineering numerical analysis, in particular to a quasi-regular double six-break triangular network construction method for searching a potential sliding surface of a side slope. Background The upper limit finite element analysis under the plastic limit analysis framework is a powerful tool for developing slope stability analysis and searching potential sliding surfaces and failure modes. The upper limit finite element analysis of the slope stability depends on a triangular net formed by discrete calculation models, and the structural characteristics of the triangular net obviously influence the calculation accuracy of the stability analysis. Unlike continuous medium elastoplastic finite elements, the limit analysis upper limit finite element triangulation network allows all cell common edges to set a speed break line to accommodate discontinuous deformation damage phenomena such as simulated shear bands. However, whether a speed break line in a triangle network is functioning effectively is limited by the location and direction in which it is located. For a specific slope stability analysis model, whether any point (or micro area) in the triangular network is subjected to shear failure or not and the dominant slip direction thereof cannot be known in advance, and the optimal break line orientation cannot be preset in advance. Therefore, even if a speed break line is globally set in a common triangular network, the actual calculation efficiency is still low, and the precision improvement effect on slope stability analysis is limited. Disclosure of Invention Aiming at the defects existing in the background technology, the invention provides a method for constructing a double-six intermittent triangular network with six-node triangular units and a six-direction topological structure, which applies a quasi-regular double-six intermittent triangular network to a limit analysis upper limit finite element and realizes high-precision search of a potential sliding surface of a side slope by fast solving a second-order cone planning problem. In order to achieve the above purpose, the invention provides a quasi-regular double six-break triangle network construction method for searching a potential sliding surface of a side slope, which comprises the following steps: S1, constructing a slope model initial point set according to a preset unit size, executing Delaunay triangulation to generate an initial grid, simulating a truss structure by using a triangular network, calculating node resultant force vectors of all truss elastic rod members by using Hooke' S law, adjusting node coordinates along the direction of the resultant force vectors, and circularly implementing node coordinate optimization and grid reconstruction until an approximate regular triangle grid which is suitable for the boundary of the slope model and is arranged in a quasi-regular array is generated; S2, executing a local encryption strategy driven by encryption edges on a key area of the approximate regular triangle mesh to form a hexagonal triangle mesh with local array arrangement, wherein the key area of the slope model is divided into six encryptions, the passive encryption strategy is executed according to the number of the encryption edges in a transition area, and an original unit is reserved in a non-encryption area; S3, extracting a coordinate matrix and a unit information matrix based on a hexagonal triangular network, generating a fifteen-degree-of-freedom six-node triangular unit through edge midpoint interpolation, constructing a public edge high-order break line, and adding non-negative auxiliary variables and constraint conditions to realize speed jump among units so as to form a double six-break triangular network data format required by a limit analysis upper limit finite element; s4, establishing a slope stability second-order cone planning model based on limit analysis upper limit theory, searching a critical unstability state of plastic flow of the slope, outputting a high-order triangle unit and a dissipation energy density distribution point cloud of isomorphic speed break lines, and obtaining a slope limit state potential sliding surface. Further, S1 includes: generating an initial large-area regular array node set according to a preset grid initial size h 0, screening nodes in a slope model, merging fixed point coordinates on the same boundary, and constructing an initial node set; Performing Delaunay triangulation on the input point set, updating the internal grid structure of the model, arranging vertex number indexes of the unit edges in ascending order, and removing repeated edges; let the unit side satisfy hooke's law, let equivalent spring rate be K, calculate the resultant force of unit node i department: Wherein, the For t