Grid encryption method, device and equipment for finite element model of dam slope and medium

Abstract

The invention relates to the technical field of hydraulic engineering, and discloses a mesh encryption method, device, equipment and medium for a dam slope finite element model.The mesh encryption method for the dam slope finite element model comprises the steps that a first finite element mesh model of a target dam slope is constructed according to a first preset mesh size; selecting a target sliding arc in the first finite element mesh model, and determining a mesh encryption range according to the target sliding arc; the target sliding arc is an arc sliding surface with the minimum slope stability coefficient; encrypting grids in a grid encryption range in the first finite element grid model according to a second preset grid size to obtain a second finite element grid model; the second preset mesh size is the preset mesh size minimum value, the first finite element mesh model is initially constructed, and then the mesh within the encryption range is encrypted, so that the consumption of computing resources is reduced, and the mesh encryption efficiency of the dam slope finite element model is improved.

Description

Technical Field

[0001] This invention relates to the field of water conservancy engineering technology, specifically to a method, device, equipment, and medium for mesh refinement of finite element models of dam slopes. Background Technology

[0002] Slope instability refers to an engineering geological hazard in which natural slopes and artificial slopes (such as dam slopes, roadbed slopes, foundation pit slopes, embankment slopes, mine pit slopes, etc.) are subjected to factors such as their own weight, groundwater, earthquakes, and engineering disturbances, and the shear strength of the soil and rock mass is insufficient to balance the sliding force, resulting in overall sliding, collapse, toppling, and landslide.

[0003] To prevent slope instability events, dynamic time history analysis is often used to analyze slope stability. Dynamic time history analysis directly inputs the actual seismic acceleration time history into a refined slope numerical model, progressively integrating to solve the complete response process of the slope under dynamic loads. Finally, stability is assessed by accumulating permanent displacements or observing the development of failure modes.

[0004] However, dynamic time history analysis has high computational costs and extremely high hardware resource requirements. In particular, the determination of the fine-grained edge during the overall finite element mesh refinement process consumes a lot of computing power, resulting in a long overall finite element mesh refinement process and easy occurrence of mesh refinement instability. Summary of the Invention

[0005] This invention provides a method, apparatus, equipment, and medium for mesh refinement of finite element models of dam slopes, in order to solve the problems of high computational cost, long overall finite element mesh refinement time, and unstable mesh refinement caused by dynamic time history analysis in related technologies.

[0006] In a first aspect, the present invention provides a mesh refinement method for a finite element model of a dam slope, comprising: constructing a first finite element mesh model of a target dam slope according to a first preset mesh size; the first preset mesh size is a pre-set basic size parameter used to construct the finite element mesh model; selecting a target slip arc in the first finite element mesh model, and determining the mesh refinement range according to the target slip arc; the target slip arc is a circular arc slip surface with the minimum slope stability coefficient; refining the mesh within the mesh refinement range of the first finite element mesh model according to a second preset mesh size to obtain a second finite element mesh model; the second preset mesh size is a pre-set minimum mesh size value.

[0007] The mesh refinement method for finite element models of dam slopes of the present invention constructs a first finite element mesh model of the target dam slope based on a pre-set first mesh size for building the finite element mesh model. This method ensures the basic geometric accuracy of the first finite element mesh model while avoiding excessive refinement of the initial mesh, thus reducing unnecessary computation. The present invention selects the target slip arc with the smallest slope stability coefficient in the first finite element mesh model. Based on the target slip arc, the mesh refinement range is determined, accurately locking the critical risk areas of the dam slope. Based on a second pre-set mesh size, the mesh within the refinement range of the first finite element mesh model is refined, only refining the area corresponding to the target slip arc. This avoids the high computational cost caused by uniform refinement of the entire model, achieving on-demand refinement, ensuring the computational accuracy of risk areas while controlling computational resource consumption. Compared with related technologies, the present invention ensures the basic geometric integrity of the dam slope model while specifically improving the mesh accuracy of instability risk areas, significantly improving the computational efficiency of large-scale dam models while maintaining the accuracy of slope stability analysis.

[0008] In one optional implementation, a first finite element mesh model of the target dam slope is constructed according to a first preset mesh size, including: drawing the geometric boundary of the target dam slope according to the design scheme of the target dam slope; determining the first preset mesh size according to the dam height of the target dam slope; and dividing the geometric boundary of the target dam slope into meshes according to the first preset mesh size to obtain the first finite element mesh model.

[0009] In one optional implementation, a target slip arc is selected in the first finite element mesh model, and the mesh refinement range is determined based on the target slip arc, including: obtaining multiple slip arcs in the first finite element mesh model, selecting a target slip arc based on the slope stability coefficient of each slip arc; obtaining the radius of the target slip arc, and expanding the range corresponding to the radius according to a preset fluctuation range to obtain the mesh refinement range.

[0010] In one optional implementation, the mesh within the mesh encryption range of the first finite element mesh model is encrypted according to the second preset mesh size to obtain the second finite element mesh model. This includes: obtaining the second preset mesh size; determining the encryption number based on the first preset mesh size and the second preset mesh size; performing quadtree decomposition on the mesh within the mesh encryption range of the first finite element mesh model; resetting the mesh encryption range; and using the reset mesh encryption range to return to the step of performing quadtree decomposition on the mesh within the mesh encryption range of the first finite element mesh model until the number of decompositions reaches the number of encryptions, thereby obtaining the second finite element mesh model.

[0011] In an optional implementation, the mesh refinement method for the finite element model of the dam slope further includes: obtaining multiple target meshes in the second finite element mesh model; substituting the first coordinate of each node in each target mesh into the standard equation corresponding to the target slip arc to obtain the second coordinate; the first coordinate is a river-direction coordinate, and the second coordinate is a coordinate perpendicular to the first coordinate; determining the position of each target mesh relative to the target slip arc based on the relationship between the first coordinate and the second coordinate of multiple nodes in each target mesh and the domain of the target slip arc; and determining the intersection coordinates of multiple multi-node meshes intersecting with the target slip arc based on the position of each target mesh relative to the target slip arc.

[0012] The mesh refinement method for the finite element model of dam slope of the present invention further includes obtaining multiple target meshes in the second finite element mesh model, substituting the first coordinates of each node in each target mesh into the standard equation corresponding to the target slip arc to obtain the second coordinates. For multi-node meshes, which are usually fine mesh elements in key areas, targeted processing can improve efficiency. By calculating the second coordinates using the river-direction coordinates combined with the standard equation of the slip arc, the geometric relationship between the nodes of the multi-node mesh and the slip arc can be accurately described. Based on the relationship between the first and second coordinates of multiple nodes in each target mesh and the domain of the target slip arc, the present invention determines the position of each target mesh relative to the target slip arc, achieving accurate quantitative determination of the positional relationship between the multi-node mesh and the target slip arc, ensuring the accuracy of subsequent intersecting mesh positioning. Based on the position of each target mesh relative to the target slip arc, the present invention determines the intersection coordinates of multiple multi-node meshes intersecting with the target slip arc, clarifying the contact boundary between the target slip arc and the multi-node mesh, providing an accurate geometric basis for subsequent stress and displacement analysis of the slip arc region, and improving the reliability of slope stability analysis.

[0013] In one optional implementation, determining the intersection coordinates of multiple multi-node grids intersecting with the target slip arc based on the position of each target grid relative to the target slip arc includes: determining the intersection position in each multi-node grid intersecting with the target slip arc based on the position of each target grid relative to the target slip arc; and determining the intersection coordinates of multiple multi-node grids intersecting with the target slip arc based on the intersection position and the standard equation corresponding to the target slip arc.

[0014] Secondly, the present invention provides a mesh refinement device for a finite element model of a dam slope, comprising: a preliminary mesh generation module, used to construct a first finite element mesh model of a target dam slope according to a first preset mesh size; the first preset mesh size is a pre-set basic size parameter for constructing the finite element mesh model; a refinement range determination module, used to select a target slip arc in the first finite element mesh model and determine the mesh refinement range according to the target slip arc; the target slip arc is a circular arc slip surface with the smallest slope stability coefficient; and a refinement module, used to refine the mesh within the mesh refinement range of the first finite element mesh model according to a second preset mesh size to obtain a second finite element mesh model; the second preset mesh size is a pre-set minimum mesh size value.

[0015] Thirdly, the present invention provides an electronic device, comprising: a memory and a processor, wherein the memory and the processor are communicatively connected to each other, the memory stores computer instructions, and the processor executes the computer instructions to perform the mesh refinement method for the finite element model of the dam slope described in the first aspect or any corresponding embodiment.

[0016] Fourthly, the present invention provides a computer-readable storage medium storing computer instructions for causing a computer to execute the mesh refinement method for a dam slope finite element model as described in the first aspect or any corresponding embodiment thereof.

[0017] Fifthly, the present invention provides a computer program product, including computer instructions for causing a computer to execute the mesh refinement method for a dam slope finite element model of the first aspect or any corresponding embodiment described above. Attached Figure Description

[0018] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0019] Figure 1 This is a schematic diagram of an application scenario according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the first process of a mesh refinement method for a finite element model of a dam slope according to an embodiment of the present invention. Figure 3 This is a schematic diagram of the second process for mesh refinement of a finite element model of a dam slope according to an embodiment of the present invention. Figure 4This is a coarse-scale grid diagram illustrating the confirmed target slip arc range according to an embodiment of the present invention; Figure 5 This is a schematic diagram of an automatically encrypted cross-scale mesh according to an embodiment of the present invention; Figure 6 This is a schematic diagram of the third process of mesh refinement method for finite element model of dam slope according to an embodiment of the present invention; Figure 7 This is a schematic diagram showing the position where the target slip arc is tangent to the multi-node mesh according to an embodiment of the present invention; Figure 8 This is a schematic diagram of a cross-scale five-node element tangent to a sliding arc according to an embodiment of the present invention; Figure 9 This is a schematic diagram of a fine mesh related to an embodiment of the present invention; Figure 10 This is a schematic diagram of the fourth process of the mesh refinement method for the finite element model of a dam slope according to an embodiment of the present invention; Figure 11 This is a structural block diagram of a mesh refinement device for a finite element model of a dam slope according to an embodiment of the present invention; Figure 12 This is a schematic diagram of the hardware structure of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] It is understood that before using the technical solutions disclosed in the various embodiments of the present invention, users should be informed of the types, scope of use, and usage scenarios of the personal information involved in the present invention and their authorization should be obtained in accordance with relevant laws and regulations through appropriate means.

[0022] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0023] As an optional application scenario of this invention, such as Figure 1As shown, the mesh refinement system for the finite element model of the dam slope may include at least one terminal device and at least one server. Figure 1 The system is illustrated in the example, which includes a computer 101, a mobile terminal 102, and a server 103, and the terminal devices such as the computer 101 and the mobile terminal 102 are connected to the server 103 through a network 110.

[0024] Specifically, the terminal device can be a smartphone, tablet, laptop, PDA, desktop computer, game console, smart TV, smart wearable device, in-vehicle terminal, VR (Virtual Reality) device, AR (Augmented Reality) device, etc. Server 103 can be a standalone physical server, a server cluster, a distributed system, or a cloud server providing cloud services. Network 110 can be a wired or wireless network, examples of which include, but are not limited to, the Internet, corporate intranet, local area network, wide area network, mobile communication network, and combinations thereof.

[0025] Slope instability is one of the most serious natural disasters causing loss of life and property worldwide. To prevent slope instability events, dynamic time-history analysis is often used to calculate slope stability. Dynamic time-history analysis directly inputs the actual seismic acceleration time history into a refined slope numerical model, progressively integrating to solve the complete response process of the slope under dynamic loads. Stability is ultimately assessed by accumulating permanent displacement or observing the development of failure modes, providing the most realistic simulation of the time-varying characteristics of seismic motions and their propagation, reflection, and amplification effects within the slope. However, it is computationally expensive and requires extremely high hardware resources, especially the fineness of its overall finite element mesh, which results in significant computational consumption.

[0026] In the calculation process of dynamic time history analysis, a very fine mesh is required to achieve high computational accuracy, which is the main reason for the consumption of computing power. However, the edges of the overburden layer and the lower part of the landslide, which are far from the overburden layer, are often not the causes of slope instability. Fine meshing in these parts usually leads to a waste of computing power. In order to improve the calculation speed, the mesh fineness is usually appropriately reduced. This series of issues creates a contradiction between solution accuracy and computational efficiency.

[0027] This invention provides a mesh refinement method for a finite element model of a dam slope. By first constructing a preliminary first finite element mesh model and then refining the mesh within the refinement range, the method aims to reduce the consumption of computational resources and improve the efficiency of mesh refinement for the finite element model of the dam slope.

[0028] According to an embodiment of the present invention, a mesh refinement method for a finite element model of a dam slope is provided. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.

[0029] This embodiment provides a mesh refinement method for a finite element model of a dam slope, which can be used with computer equipment. Figure 2 This is a flowchart of the first method for mesh refinement of a finite element model of a dam slope according to an embodiment of the present invention, as follows: Figure 2 As shown, the process includes the following steps: Step S201: Construct a first finite element mesh model of the target dam slope according to the first preset mesh size; the first preset mesh size is a pre-set basic size parameter used to construct the finite element mesh model.

[0030] The first preset grid size is a pre-set basic grid size parameter, which is the reference for constructing the initial grid. The first preset grid size can be set according to the actual situation. For example, the first preset grid size can be 10% of the target dam height.

[0031] In some alternative implementations, the target dam slope is the dam side slope structure whose stability needs to be analyzed; the first finite element mesh model is an initial mesh model built with a first preset mesh size.

[0032] In some optional implementations, a first finite element mesh model of the target dam slope is constructed using finite element software based on a first preset mesh size. Specifically, the first preset mesh size is set to 10% of the dam height. The geometric model of the target dam slope is imported into the finite element software, the software's mesh generation function is called, structured mesh is selected, and the mesh size is set to the first preset mesh size to automatically generate the first finite element mesh model.

[0033] Step S202: Select the target slip arc in the first finite element mesh model, and determine the mesh refinement range based on the target slip arc; the target slip arc is the circular arc slip surface with the smallest slope stability coefficient.

[0034] Among them, the target slip arc is the most dangerous circular surface on the slope of the target dam that is most likely to slide. The slope stability coefficient of different slip arcs is calculated by the slope stability analysis module of the finite element software, and the target slip arc corresponding to the minimum value is selected. The slope stability coefficient is used to measure the ratio of the slope's anti-sliding force to the sliding force. The smaller the slope stability coefficient, the more dangerous the slope.

[0035] In some alternative implementations, the mesh densification range is an area extending outward from the target slip arc as the center. For example, the mesh densification range is determined by using 15% of the dam height as the upper and lower limits of the radius range of the target slip arc.

[0036] Step S203: According to the second preset mesh size, the mesh within the mesh refinement range of the first finite element mesh model is refined to obtain the second finite element mesh model; the second preset mesh size is the preset minimum mesh size.

[0037] The second preset grid size is the minimum grid size set in advance. Based on the accuracy requirements of the actual calculation, the finest second preset grid size is set. The first preset grid size and the second preset grid size satisfy the following relationship: the second preset grid size is [amount missing] times the first preset grid size. ,in, The number of times the grid is encrypted.

[0038] The mesh refinement method for finite element models of dam slopes provided in this embodiment constructs a first finite element mesh model of the target dam slope based on a pre-set first mesh size for building the finite element mesh model. This method ensures the basic geometric accuracy of the first finite element mesh model while avoiding excessive refinement of the initial mesh, thus reducing unnecessary computation. In this embodiment, the target slip arc with the smallest slope stability coefficient is selected in the first finite element mesh model. Based on the target slip arc, the mesh refinement range is determined, accurately locking the critical risk areas of the dam slope. According to a second pre-set mesh size, the mesh within the refinement range of the first finite element mesh model is refined, only refining the area corresponding to the target slip arc. This avoids the high computational cost caused by uniform refinement of the entire model, achieving on-demand refinement, ensuring the computational accuracy of risk areas while controlling computational resource consumption. Compared with related technologies, this embodiment ensures the basic geometric integrity of the dam slope model while specifically improving the mesh accuracy of instability risk areas, significantly improving the computational efficiency of large-scale dam models while maintaining the accuracy of slope stability analysis.

[0039] This embodiment provides a mesh refinement method for a finite element model of a dam slope, which can be used with computer equipment. Figure 3 This is a second flowchart of a mesh refinement method for a finite element model of a dam slope according to an embodiment of the present invention, as shown below. Figure 3 As shown, the process includes the following steps: Step S301: Construct the first finite element mesh model of the target dam slope according to the first preset mesh size; the first preset mesh size is a pre-set basic size parameter used to construct the finite element mesh model.

[0040] Specifically, step S301 includes: Step S3011: Based on the design scheme of the target dam slope, draw the geometric boundary of the target dam slope, and determine the first preset grid size based on the dam height of the target dam slope.

[0041] The design scheme of the target dam slope is input into the finite element software to draw the geometric boundary of the target dam slope. The first preset mesh size is determined based on 10% of the dam height of the target dam slope.

[0042] Step S3012: Based on the first preset mesh size, the geometric boundary of the target dam slope is meshed to obtain the first finite element mesh model.

[0043] Specifically, a first finite element mesh model of the target dam slope is constructed using finite element software based on a first preset mesh size.

[0044] Step S302: Select the target slip arc in the first finite element mesh model, and determine the mesh refinement range based on the target slip arc; the target slip arc is the circular arc slip surface with the smallest slope stability coefficient.

[0045] Specifically, step S302 includes: Step S3021: Obtain multiple slip arcs in the first finite element mesh model, and select the target slip arc based on the slope stability coefficient of each slip arc.

[0046] Among them, multiple slip arc ranges are based on the geometry (slope height, slope) of the slope or dam body, and a series of possible slip arcs are preset (usually a circular arc with the center in the area above the top of the slope and the arc surface passing through the toe of the slope or the foundation of the dam).

[0047] In some optional implementations, the sliding body (the rock and soil mass above the sliding arc) corresponding to each sliding arc is divided into several vertical strips. The sliding force (gravity, water pressure, etc.) and the anti-sliding force (shear strength of the rock and soil mass) of each strip are calculated. For each sliding arc, the anti-sliding force and sliding force of all strips are summarized to obtain the stability coefficient of the sliding arc. The center position and radius of the sliding arc are adjusted, and the stability coefficient of different sliding arcs is calculated repeatedly. The sliding arc with the smallest stability coefficient is the target sliding arc.

[0048] Step S3022: Obtain the radius of the target arc, expand the range corresponding to the radius according to the preset fluctuation range, and obtain the mesh refinement range.

[0049] The preset fluctuation range can be set according to the actual situation. For example, the preset fluctuation range can be a range with 15% of the dam height as the upper and lower fluctuation limits. Based on the radius, the preset fluctuation range is expanded to obtain the grid densification range.

[0050] In some alternative implementations, the mesh refinement range is the area where further mesh refinement is required; for example, Figure 4 This is a coarse-scale grid diagram illustrating the confirmed target slip arc range according to an embodiment of the present invention, such as... Figure 4 As shown, Figure 4 The diagram illustrates the target slip arc, the center and radius of the target slip arc, the location of the mesh refinement area, and the first preset mesh size being 10% of the dam height of the target dam slope. Figure 4 The horizontal axis represents the coordinate along the river, and the vertical axis represents the coordinate along the river.

[0051] Step S303: According to the second preset mesh size, the mesh within the mesh refinement range of the first finite element mesh model is refined to obtain the second finite element mesh model; the second preset mesh size is the preset minimum mesh size.

[0052] Specifically, step S303 includes: Step S3031: Obtain the second preset grid size, and determine the number of encryption times based on the first preset grid size and the second preset grid size.

[0053] Given the first and second preset dimensions, the number of encryption attempts is determined using the following formula:

[0054] in, For the second preset size, The first preset size, This represents the number of encryption attempts.

[0055] Step S3032: Perform quadtree decomposition on the mesh within the mesh refinement range in the first finite element mesh model, reset the mesh refinement range, and use the reset mesh refinement range to return to the step of performing quadtree decomposition on the mesh within the mesh refinement range in the first finite element mesh model until the number of decompositions reaches the number of refinements, and obtain the second finite element mesh model.

[0056] The quadtree decomposition involves dividing the mesh into four equal-sized sub-regions. For each mesh within the mesh refinement range, a quadtree decomposition with a certain number of refinements is performed to obtain the second finite element mesh model.

[0057] In some alternative implementations, an adaptive quadtree decomposition technique is employed to decompose the mesh within the encryption range, with the mesh size adjusted accordingly. Decreasing by a factor of two, the number of encryption attempts is [number]. Next, the mesh gradually becomes finer from the boundary of the encrypted range towards the target sliding arc position. For example, a quadtree decomposition is performed on all meshes within the encrypted range, equally dividing them into four sub-regions. The decomposed meshes are all four-node square meshes with a side length of 5% of the dam height. A new encrypted range is set closer to the target sliding arc position, and the quadtree decomposition is performed again. The finest units after decomposition are mostly four-node square meshes with a side length of 2.5% of the dam height. Multi-node square meshes appear near the boundary of the new encrypted range. The process of setting a new encrypted range closer to the target sliding arc position and performing quadtree decomposition again is repeated until the required number of encryption steps is reached.

[0058] For example, Figure 5 This is a schematic diagram of an automatically encrypted cross-scale mesh according to an embodiment of the present invention. Figure 5 This diagram illustrates the cross-scale grid obtained after refining the cross-scale grid within the encrypted range.

[0059] The mesh refinement method for the finite element model of dam slope provided in this embodiment achieves an optimized balance between high-precision calculation and overall computational efficiency in dynamic stability analysis, effectively balancing the contradiction between solution accuracy and computational efficiency. This embodiment of the invention utilizes cross-scale automatic mesh generation technology to amplify the computational accuracy near the most dangerous slip arc while reducing the computational accuracy at locations far from the most dangerous slip arc, thereby improving computational efficiency and fully utilizing computing power.

[0060] This embodiment provides a mesh refinement method for a finite element model of a dam slope, which can be used with computer equipment. Figure 6 This is a third flowchart of a mesh refinement method for a dam slope finite element model according to an embodiment of the present invention, as shown below. Figure 6 As shown, the process includes the following steps: Step S601: Construct a first finite element mesh model of the target dam slope based on the first preset mesh size; the first preset mesh size is a pre-defined basic size parameter used to construct the finite element mesh model. For details, please refer to... Figure 3 Step S301 of the illustrated embodiment will not be described again here.

[0061] Step S602: Select the target slip arc in the first finite element mesh model, and determine the mesh refinement range based on the target slip arc; the target slip arc is the circular arc slip surface with the minimum slope stability coefficient. For details, please refer to [link to relevant documentation]. Figure 3 Step S302 of the illustrated embodiment will not be described again here.

[0062] Step S603: Based on the second preset mesh size, refine the mesh within the mesh refinement range of the first finite element mesh model to obtain the second finite element mesh model; the second preset mesh size is a pre-set minimum mesh size. For details, please refer to... Figure 3 Step S303 of the illustrated embodiment will not be described again here.

[0063] Step S604: Obtain multiple target meshes in the second finite element mesh model, substitute the first coordinate of each node in each target mesh into the standard equation corresponding to the target slip arc to obtain the second coordinate; the first coordinate is the coordinate along the river, and the second coordinate is the coordinate perpendicular to the first coordinate.

[0064] In some alternative implementations, the standard equation corresponding to the target slip arc is the standard equation of a circle, which can be expressed as:

[0065] in, Let the coordinates of the center of the target arc be . Let the radius of the target arc be . Let be any point on the target arc.

[0066] In some optional implementations, the riverine coordinates of the four nodes in each target grid are substituted into the standard equation corresponding to the target slip arc to obtain the vertical coordinates (second coordinates) of each node in each target grid.

[0067] Step S605: Determine the position of each target grid relative to the target arc based on the relationship between the first and second coordinates of multiple nodes in each target grid and the domain of the target arc.

[0068] For example, if the longitudinal coordinates of all nodes of the target mesh are not within the domain of the longitudinal coordinates of the target slip arc, the target mesh is directly determined to be outside the slip arc, and no marking is required. If all actual vertical coordinates of the target mesh are less than the vertical coordinates obtained by substituting them into the equation, the target mesh is determined to be outside the target slip arc, and no marking is required. If all actual vertical coordinates of the target mesh are greater than the vertical coordinates obtained by substituting them into the equation, the target mesh is determined to be inside the target slip arc, and marking is required. The target mesh is recorded in the internal element information of the target slip arc, with a number of internal elements of m. If the actual vertical coordinates of some nodes of the target mesh are less than the vertical coordinates obtained by substituting them into the equation, while the actual vertical coordinates of some nodes are greater than the vertical coordinates obtained by substituting them into the equation, the target mesh is determined to be cut by the target slip arc, and marking is required. After iterating through all target meshes, the target meshes inside the target slip arc and those intersecting with the target slip arc are identified and recorded, with a number of intersecting meshes of n.

[0069] Step S606: Based on the position of each target grid relative to the target arc, determine the coordinates of the intersection points of multiple multi-node grids that intersect with the target arc.

[0070] Among them, multi-node grids are grids with more than 4 nodes. Normally, each square grid has 4 nodes. Due to the setting of a new encryption range closer to the target arc position and the quadtree decomposition again, the target arc may intersect with the target grid, resulting in multi-node grids with more than 4 nodes.

[0071] In some optional implementations, determining the intersection coordinates of multiple multi-node grids intersecting the target slip arc based on the position of each target grid relative to the target slip arc includes: determining the intersection position in each multi-node grid intersecting the target slip arc based on the position of each target grid relative to the target slip arc; and determining the intersection coordinates of multiple multi-node grids intersecting the target slip arc based on the intersection position and the standard equation corresponding to the target slip arc.

[0072] Specifically, for each multi-node mesh, starting from the bottom left node, the four nodes are named counter-clockwise. The specific names can be set according to the actual situation. For example, the four nodes are named a, b, c, and d counter-clockwise. Nodes resulting from cross-scale refinement are named starting from e. The edges formed by the nodes are named counter-clockwise starting from point a. For example, in a five-node mesh, nodes a and b form the first edge, nodes b and e form the second edge, nodes e and c form the third edge, nodes c and d form the fourth edge, and nodes d and a form the fifth edge. Point d is the top left node of the five-node mesh, meaning point d is the node with the smallest x-coordinate and the largest y-coordinate in this five-node mesh. , Let d be its coordinate point, and the distance from point d to the center O of the circle is... Then point d has a relationship with the center of the circle:

[0073] in, Let the coordinates of the center of the target arc be . Let d be the distance from point d to the center O of the circle. Let be any point on the target arc.

[0074] In some optional implementations, node b is the bottom right corner node of the multi-node mesh, that is, node b is the node with the largest x-coordinate and the smallest y-coordinate in this five-node mesh. , Let this be the coordinate point, and let the distance from this point to the center O of the circle be... Then point b has a relationship with the center of the circle:

[0075] in, Let the coordinates of the center of the target arc be . Let b be the distance from point b to the center O of the circle. Let be any point on the target arc.

[0076] In some alternative implementations, node e is a node that appears in a multi-node mesh due to cross-scale subdivision, located between nodes b and c. , Let this be the coordinate point, and let the distance from this point to the center O of the circle be... Then point e has a relationship with the center of the circle:

[0077] in, Let the coordinates of the center of the target arc be . Let e ​​be the distance from point e to the center O of the circle. Let be any point on the target arc.

[0078] In some alternative implementations, by determining With the target arc radius R To determine the location of the intersection point, based on the relationship between the two points, if... If node d is outside the target arc, meaning the target arc intersects the multi-node mesh at edge cd, and the intersection point is named point 4', then the coordinates of intersection point 4' are:

[0079]

[0080] in, Let be the coordinates of the intersection point 4'. Let the coordinates of the center of the target arc be . Let d be the vertical coordinate value of node d. R The target arc radius.

[0081] In some alternative implementations, if If node d is inside the target slip arc, meaning the target slip arc intersects the multi-node mesh at edge da, and the intersection point is named point 5', then the coordinates of intersection point 5' are:

[0082]

[0083] in, Let 5' be the coordinates of the intersection point. Let the coordinates of the center of the target arc be . Let d be the coordinate value along the river. R The target arc radius.

[0084] In some alternative implementations, if If node d lies on the target slip arc, meaning the target slip arc intersects the multi-node mesh at node d, and this intersection point is named d', then the coordinates of intersection point d' are:

[0085]

[0086] in, Let d' be the coordinates of the intersection point. Let d be the coordinates of node d.

[0087] In some alternative implementations, by determining With the target arc radius R To determine the location of the intersection point, based on the relationship between the two points, if... If node b is inside the target slip arc, meaning the target slip arc intersects the multi-node mesh at edge ab, and the intersection point is named point 1', then the coordinates of intersection point 1' are:

[0088]

[0089] in, Let be the coordinates of intersection point 1'. Let the coordinates of the center of the target arc be . Here are the river-direction coordinates of node b. R The target arc radius.

[0090] In some alternative implementations, if If node b is on the target slip arc, meaning the target slip arc intersects the multi-node mesh at node b, and this intersection point is named point b', then the coordinates of intersection point b' are:

[0091]

[0092] in, Let b' be the coordinates of the intersection point. Here are the coordinates of node b.

[0093] In some alternative implementations, if Then node b is outside the target sliding arc. Since node e is a node that appears in the schematic five-node element and is located between nodes b and c, that is, the bc edge is composed of the be edge and the ec edge. By judging... With the target arc radius R Based on the relationship, determine the location of the intersection point.

[0094] In some alternative implementations, if If node e is outside the target slip arc, meaning the target slip arc intersects the multi-node mesh at edge ec, and this intersection point is named point 3', then the coordinates of intersection point 3' are:

[0095]

[0096] in, Let 3' be the coordinates of the intersection point. Let the coordinates of the center of the target arc be . Here are the river-direction coordinates of node e. R The target arc radius.

[0097] In some alternative implementations, if If node e is inside the target slip arc, meaning the target slip arc intersects the multi-node mesh at edge be, and the intersection point is named point 2', then the coordinates of intersection point 2' are:

[0098]

[0099] in, Let 2' be the coordinates of the intersection point. Let the coordinates of the center of the target arc be . Here are the river-direction coordinates of node e. R The target arc radius.

[0100] In some alternative implementations, if If node e lies on the target slip arc, meaning the target slip arc intersects the multi-node mesh at node e, and this intersection point is named point e', then the coordinates of intersection point e' are:

[0101]

[0102] in, Let e' be the coordinates of the intersection point. Here are the coordinates of node e.

[0103] For example, Figure 7 This is a schematic diagram showing the position where the target slip arc is tangent to the multi-node mesh according to an embodiment of the present invention. Figure 7 The coordinate axes in the diagram include longitudinal and vertical coordinates, and the diagonal lines represent the boundary lines of the target sliding arc. Figure 7In the diagram, the area to the lower left of the diagonal line represents the region outside the target sliding arc (e.g., grid C, part of grid A, and part of grid D), while the area to the upper right of the diagonal line represents the region inside the target sliding arc (grid B and part of grid A). The dashed line is a reference line originating from a point on the boundary (e.g., C1), which is the reference line for the mesh refinement range. For grid D, there are 5 edges: 1, 2, 3, 4, and 5. The intersection points of the multi-node grid with the target sliding arc are 4' (C1), 2' (C2), C3, C4, and C5, respectively.

[0104] Figure 8 This is a schematic diagram of a multi-scale five-node element tangent to a sliding arc according to an embodiment of the present invention. Figure 8 In the example of the multi-node quadrilateral element, for the largest multi-node quadrilateral element, starting from the bottom left node, the nodes are named counterclockwise as follows: a, b, c, d, e. The edges formed by these nodes are named counterclockwise starting from point a. Nodes a and b form the first edge, nodes b and c form the second edge, nodes d and c form the third edge, nodes e and d form the fourth edge, and nodes e and a form the fifth edge. The diagonal line represents the boundary line of the target sliding arc, which intersects with the largest multi-node quadrilateral element at two points. The intersection points of the target sliding arc boundary line and the largest multi-node quadrilateral element are cut to obtain the effective region. Within the effective region, the intersection points of the target sliding arc boundary line and the largest multi-node quadrilateral element are 4' and 2'. Key information about the effective region is obtained, including the length of a certain edge within the effective region. Angle of the side Distance from the effective area to the center of the target arc The distance from the boundary of the target arc to the center of the target arc. Area of ​​the effective region Effective area density and effective area quality .

[0105] Figure 9 This is a schematic diagram of a fine mesh related to an embodiment of the present invention. Figure 9 The grid size for all areas is 2.5% of the landslide height, and the grid within the densification zone is not further refined, compared to... Figure 5 The mesh refinement method of the finite element model of the dam slope in this embodiment of the invention refines the mesh in dangerous parts and makes the mesh size larger in other parts.

[0106] In some optional implementations, the intersection coordinates are recorded in each multi-node grid. All multi-node grids are iterated to determine the intersection coordinates of multiple multi-node grids that intersect with the target arc. The start and end positions and coverage area of ​​the target arc can be accurately delineated by the intersection coordinates, avoiding ambiguity in the range of the target arc. The intersection coordinates are the boundary anchor points of the grid densification range, and efficient grid partitioning is selected based on the intersection coordinates.

[0107] The mesh refinement method for the finite element model of dam slope provided in this embodiment uses multi-scale element calculations, reducing the computational waste of traditional dynamic time history methods while achieving high accuracy. Compared with related technologies, this embodiment of the invention achieves an optimized balance between high-precision calculation and overall computational efficiency in dynamic stability analysis, effectively balancing the contradiction between solution accuracy and computational efficiency. It employs a strategy of initial coarse-scale model positioning and dynamic multi-scale refinement: in the initial stage, coarse-scale elements are used to quickly confirm the slip arc range, and then quadtree mesh dynamic subdivision technology is used to automatically generate multi-scale fine elements within the slip arc range. This method improves computational efficiency while achieving high-precision calculations in key areas.

[0108] This embodiment provides a mesh refinement method for a finite element model of a dam slope, which can be used with computer equipment. Figure 10 This is a fourth flowchart of the mesh refinement method for the finite element model of a dam slope according to an embodiment of the present invention, as shown below. Figure 10 As shown, the process includes the following steps: Construct a coarse-scale finite element mesh model; identify the most dangerous slip arc location and set the cross-scale densification range; set the finest mesh size to automatically densify the mesh across scales; determine whether the cross-scale multi-node element intersects with the slip arc. If they intersect, calculate the intersection point of the multi-node element and the slip arc, record the element information, and proceed to the next element. If they do not intersect, proceed directly to the next element.

[0109] This embodiment also provides a mesh refinement device for a finite element model of a dam slope. This device is used to implement the above embodiments and preferred embodiments, and details already described will not be repeated. As used below, the term "module" can refer to a combination of software and / or hardware that performs a predetermined function. Although the device described in the following embodiments is preferably implemented in software, hardware implementation, or a combination of software and hardware, is also possible and contemplated.

[0110] This embodiment provides a mesh refinement device for a finite element model of a dam slope, such as... Figure 11 As shown, it includes: The preliminary mesh generation module 1101 is used to construct the first finite element mesh model of the target dam slope according to the first preset mesh size; the first preset mesh size is a pre-set basic size parameter used to construct the finite element mesh model.

[0111] The encryption range determination module 1102 is used to select the target slip arc in the first finite element mesh model and determine the mesh encryption range based on the target slip arc; the target slip arc is the circular arc slip surface with the smallest slope stability coefficient.

[0112] The encryption and refinement module 1103 is used to encrypt the mesh within the mesh encryption range of the first finite element mesh model according to the second preset mesh size to obtain the second finite element mesh model; the second preset mesh size is the minimum value of the preset mesh size.

[0113] In some alternative implementations, the preliminary mesh generation module 1101 includes: The size determination unit is used to draw the geometric boundary of the target dam slope according to the design scheme of the target dam slope, and to determine the first preset grid size according to the dam height of the target dam slope.

[0114] The initial meshing unit is used to mesh the geometric boundary of the target dam slope according to the first preset mesh size, so as to obtain the first finite element mesh model.

[0115] In some optional implementations, the encryption range determination module 1102 includes: The slip arc selection element is used to obtain multiple slip arcs in the first finite element mesh model, and select the target slip arc based on the slope stability coefficient of each slip arc.

[0116] The encryption range determination unit is used to obtain the radius of the target sliding arc, and expand the range corresponding to the radius according to the preset fluctuation range to obtain the grid encryption range.

[0117] In some alternative implementations, the encryption refinement module 1103 includes: The encryption count determination unit is used to obtain a second preset grid size and determine the encryption count based on the first preset grid size and the second preset grid size.

[0118] The mesh decomposition unit is used to perform quadtree decomposition on the mesh within the mesh refinement range of the first finite element mesh model, reset the mesh refinement range, and use the reset mesh refinement range to return to the step of performing quadtree decomposition on the mesh within the mesh refinement range of the first finite element mesh model until the number of decompositions reaches the number of refinement times, thus obtaining the second finite element mesh model.

[0119] In some alternative implementations, the mesh refinement device for the finite element model of the dam slope also includes: The coordinate determination module is used to obtain multiple target meshes in the second finite element mesh model. It substitutes the first coordinate of each node in each target mesh into the standard equation corresponding to the target slip arc to obtain the second coordinate. The first coordinate is the river-direction coordinate, and the second coordinate is the coordinate perpendicular to the first coordinate.

[0120] The grid position determination module is used to determine the position of each target grid relative to the target slip arc based on the relationship between the first and second coordinates of multiple nodes in each target grid and the domain of the target slip arc.

[0121] The intersection point coordinate determination module is used to determine the intersection point coordinates of multiple multi-node grids that intersect with the target sliding arc based on the position of each target grid relative to the target sliding arc.

[0122] In some optional implementations, the intersection point coordinate determination module includes: The intersection point determination unit is used to determine the intersection point position in each target multi-node grid that intersects with the target slip arc based on the position of each multi-node grid relative to the target slip arc.

[0123] The intersection point coordinate determination unit is used to determine the intersection point coordinates of multiple target multi-node grids that intersect with the target arc based on the intersection point position and the standard equation corresponding to the target arc.

[0124] The mesh refinement device for the finite element model of dam slope provided in this embodiment of the invention can execute the mesh refinement method for the finite element model of dam slope provided in any embodiment of the invention, and has the corresponding functional modules and beneficial effects of the method. Further functional descriptions of the above modules and units are the same as in the corresponding embodiments described above, and will not be repeated here.

[0125] Figure 12 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention.

[0126] The following is a detailed reference. Figure 12 The diagram illustrates a structural schematic suitable for implementing an electronic device according to embodiments of the present invention. The electronic device may include a processor (e.g., a central processing unit, graphics processor, etc.) 1201, which can perform various appropriate actions and processes according to a program stored in read-only memory (ROM) 1202 or a program loaded from memory 1208 into random access memory (RAM) 1203. The RAM 1203 also stores various programs and data required for the operation of the electronic device. The processor 1201, ROM 1202, and RAM 1203 are interconnected via a bus 1204. An input / output (I / O) interface 1205 is also connected to the bus 1204.

[0127] Typically, the following devices can be connected to I / O interface 1205: input devices 1206 including, for example, touchscreens, touchpads, keyboards, mice, cameras, microphones, accelerometers, gyroscopes, etc.; output devices 1207 including, for example, liquid crystal displays (LCDs), speakers, vibrators, etc.; memory devices 1208 including, for example, magnetic tapes, hard disks, etc.; and communication devices 1209. Communication device 1209 allows electronic devices to communicate wirelessly or wiredly with other devices to exchange data. Although Figure 12 Electronic devices with various devices are shown, but it should be understood that it is not required to implement or have all of the devices shown, and more or fewer devices may be implemented or have instead.

[0128] In particular, according to embodiments of the present invention, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of the present invention include a computer program product comprising a computer program carried on a non-transitory computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication device 1209, or installed from a memory 1208, or installed from a ROM 1202. When the computer program is executed by the processor 1201, it performs the functions defined in the mesh refinement method for the dam slope finite element model according to embodiments of the present invention.

[0129] Figure 12 The electronic device shown is merely an example and should not be construed as limiting the functionality and scope of use of the embodiments of the present invention.

[0130] This invention also provides a computer-readable storage medium. The methods described above according to embodiments of the invention can be implemented in hardware or firmware, or implemented as computer code that can be recorded on a storage medium, or implemented as computer code downloaded via a network and originally stored on a remote storage medium or a non-transitory machine-readable storage medium and then stored on a local storage medium. Thus, the methods described herein can be processed by software stored on a storage medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware. The storage medium can be a magnetic disk, optical disk, read-only memory, random access memory, flash memory, hard disk, or solid-state drive, etc.; further, the storage medium can also include combinations of the above types of memory. It is understood that computers, processors, microprocessor controllers, or programmable hardware include storage components capable of storing or receiving software or computer code. When the software or computer code is accessed and executed by the computer, processor, or hardware, the mesh refinement method for the finite element model of the dam slope shown in the above embodiments is implemented.

[0131] A portion of this invention can be applied as a computer program product, such as computer program instructions, which, when executed by a computer, can invoke or provide the methods and / or technical solutions according to the invention through the operation of the computer. Those skilled in the art will understand that the forms in which computer program instructions exist in a computer-readable medium include, but are not limited to, source files, executable files, installation package files, etc. Correspondingly, the ways in which computer program instructions are executed by a computer include, but are not limited to: the computer directly executing the instructions, or the computer compiling the instructions and then executing the corresponding compiled program, or the computer reading and executing the instructions, or the computer reading and installing the instructions and then executing the corresponding installed program. Here, the computer-readable medium can be any available computer-readable storage medium or communication medium accessible to a computer.

[0132] Although embodiments of the invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the invention, and all such modifications and variations fall within the scope defined by the appended claims.

Claims

1. A mesh refinement method for a finite element model of a dam slope, characterized in that, The method includes: Based on the first preset mesh size, a first finite element mesh model of the target dam slope is constructed; the first preset mesh size is a pre-set basic size parameter used to construct the finite element mesh model. In the first finite element mesh model, a target slip arc is selected, and the mesh refinement range is determined based on the target slip arc; the target slip arc is the circular arc slip surface with the minimum slope stability coefficient; According to the second preset mesh size, the mesh within the mesh encryption range in the first finite element mesh model is encrypted to obtain the second finite element mesh model; the second preset mesh size is the minimum value of the preset mesh size.

2. The method according to claim 1, characterized in that, The step of constructing a first finite element mesh model of the target dam slope according to a first preset mesh size includes: Based on the design scheme of the target dam slope, draw the geometric boundary of the target dam slope, and determine the size of the first preset grid based on the dam height of the target dam slope; Based on the first preset mesh size, the geometric boundary of the target dam slope is meshed to obtain the first finite element mesh model.

3. The method according to claim 1 or 2, characterized in that, The step of selecting a target slip arc in the first finite element mesh model and determining the mesh refinement range based on the target slip arc includes: Obtain multiple slip arcs from the first finite element mesh model, and select the target slip arc based on the slope stability coefficient of each slip arc; Obtain the radius of the target arc, and expand the range corresponding to the radius according to a preset fluctuation range to obtain the mesh densification range.

4. The method according to claim 1 or 2, characterized in that, The step of refining the mesh within the mesh refinement range of the first finite element mesh model according to the second preset mesh size to obtain the second finite element mesh model includes: Obtain the second preset grid size, and determine the number of encryption attempts based on the first preset grid size and the second preset grid size; Perform quadtree decomposition on the mesh within the mesh encryption range in the first finite element mesh model, reset the mesh encryption range, and use the reset mesh encryption range to return to the step of performing quadtree decomposition on the mesh within the mesh encryption range in the first finite element mesh model until the number of decompositions reaches the number of encryptions, and obtain the second finite element mesh model.

5. The method according to claim 1 or 2, characterized in that, The method further includes: Multiple target meshes are obtained from the second finite element mesh model. The first coordinate of each node in each target mesh is substituted into the standard equation corresponding to the target slip arc to obtain the second coordinate. The first coordinate is the river-direction coordinate, and the second coordinate is the coordinate perpendicular to the first coordinate. Based on the relationship between the first and second coordinates of multiple nodes in each target grid and the domain of the target slip arc, the position of each target grid relative to the target slip arc is determined; Based on the position of each target grid relative to the target slip arc, determine the coordinates of the intersection points of multiple multi-node grids that intersect with the target slip arc.

6. The method according to claim 5, characterized in that, The step of determining the intersection coordinates of multiple multi-node grids intersecting the target slip arc based on the position of each target grid relative to the target slip arc includes: Based on the position of each of the multi-node grids relative to the target slip arc, determine the intersection point position in each of the target multi-node grids that intersects with the target slip arc; Based on the intersection point location and the standard equation corresponding to the target slip arc, determine the intersection point coordinates of the multiple target multi-node grids that intersect with the target slip arc.

7. A mesh refinement device for a finite element model of a dam slope, characterized in that, The device includes: The preliminary mesh generation module is used to construct the first finite element mesh model of the target dam slope based on the first preset mesh size; the first preset mesh size is a pre-set basic size parameter used to construct the finite element mesh model; The encryption range determination module is used to select a target slip arc in the first finite element mesh model and determine the mesh encryption range based on the target slip arc; the target slip arc is the circular arc slip surface with the smallest slope stability coefficient; The encryption and refinement module is used to encrypt the mesh within the encryption range of the first finite element mesh model according to the second preset mesh size to obtain the second finite element mesh model; the second preset mesh size is a preset minimum mesh size.

8. An electronic device, characterized in that, include: A memory and a processor are interconnected, the memory stores computer instructions, and the processor executes the computer instructions to perform the mesh refinement method for the finite element model of the dam slope as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions for causing the computer to execute the mesh refinement method for the finite element model of the dam slope as described in any one of claims 1 to 6.

10. A computer program product, characterized in that, Includes computer instructions for causing a computer to execute the mesh refinement method for the finite element model of the dam slope as described in any one of claims 1 to 6.

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