A method for extracting potential slip surfaces of slopes based on the energy dissipation rate

Abstract

The present invention discloses a method for extracting potential slip surfaces of slopes based on the energy dissipation rate, belonging to the technical field of extracting potential slip surfaces of slopes, and can solve the problem that the existing methods ignore the energy dissipation mechanism in the slope instability process, resulting in a low recognition accuracy of potential slip surfaces. The method includes: S1, determining the centroid coordinates of each grid cell on the two-dimensional numerical model of the longitudinal section of the slope and predicting the energy dissipation rate of each grid cell; S2, determining multiple maximum value feature points of the energy dissipation rate on the longitudinal section of the slope according to the centroid coordinates and energy dissipation rate of each grid cell; S3, determining the potential slip surface of the slope according to the multiple maximum value feature points. The present invention is used for extracting the potential slip surface of the slope.

Description

Technical Field

[0001] The present invention relates to a method for extracting potential slip surfaces of slopes based on the energy dissipation rate, belonging to the technical field of extracting potential slip surfaces of slopes. Background Art

[0002] In engineering fields such as water conservancy, transportation, and mining, slope stability analysis can provide a scientific decision-making basis for slope design, slope state discrimination, slope reinforcement and treatment, etc., and is of great significance for ensuring project safety and personnel safety. The extraction of potential slip surfaces of slopes is a key link in slope stability analysis.

[0003] Currently, the extraction of potential slip surfaces of slopes usually identifies potential slip surfaces based on methods such as the limit equilibrium method, numerical simulation method, and unsupervised learning algorithm. These methods mostly rely on indicators such as displacement, plastic strain, and shear strain of slope material zoning, while ignoring the energy conversion and dissipation mechanism during slope instability. Therefore, it is difficult to accurately describe the generation of potential slip surfaces from the perspective of energy conversion, resulting in a low recognition accuracy of potential slip surfaces. At the same time, existing methods are usually only applicable to the identification of a single potential slip surface, and it is difficult to handle the identification scenario where multiple potential slip surfaces coexist. Therefore, there are relatively large limitations. Summary of the Invention

[0004] The present invention provides a method for extracting potential slip surfaces of slopes based on the energy dissipation rate, which can solve the problem that the existing methods ignore the energy dissipation mechanism during slope instability, resulting in a low recognition accuracy of potential slip surfaces.

[0005] The present invention provides a method for extracting potential slip surfaces of slopes based on the energy dissipation rate, and the method includes:

[0006] S1. Determine the centroid coordinates of each grid cell on the two-dimensional numerical model of the longitudinal section of the slope, and predict the energy dissipation rate of each grid cell;

[0007] S2. Determine multiple maximum value feature points of the energy dissipation rate on the longitudinal section of the slope according to the centroid coordinates and energy dissipation rate of each grid cell;

[0008] S3. Determine the potential slip surface of the slope according to multiple maximum value feature points.

[0009] Optionally, predicting the energy dissipation rate of each grid cell in S1 specifically includes:

[0010] Obtain the elastoplastic parameters and creep parameters of different material zones of the slope;

[0011] Based on the visco-elastoplastic creep damage model, predict the energy dissipation rate of each grid cell according to the elastoplastic parameters and the creep parameters.

[0012] Optionally, S2 specifically includes:

[0013] S21. Construct a regular grid model according to the two-dimensional numerical model, and determine the energy dissipation rate of each regular grid on the regular grid model according to the centroid coordinates and energy dissipation rate of each grid cell on the two-dimensional numerical model;

[0014] S22. Determine multiple maximum value feature points of the energy dissipation rate on the longitudinal section of the slope according to the energy dissipation rate of each regular grid.

[0015] Optionally, determining the energy dissipation rate of each regular grid on the regular grid model in S21 specifically includes:

[0016] Use the interpolation algorithm to determine the energy dissipation rate of each regular grid on the regular grid model.

[0017] Optionally, S22 specifically includes:

[0018] S221. Determine multiple maximum value points of the energy dissipation rate on the regular grid model along the horizontal path and / or vertical path according to the energy dissipation rate of each regular grid;

[0019] S222. Determine multiple maximum value feature points of the energy dissipation rate on the longitudinal section of the slope according to the multiple maximum value points.

[0020] Optionally, S222 specifically includes:

[0021] According to the multiple maximum value points and the boundary information of the longitudinal section of the slope, use the convex hull detection algorithm to determine multiple maximum value feature points of the energy dissipation rate on the longitudinal section of the slope.

[0022] Optionally, S3 specifically includes:

[0023] S31. Determine the clustering clusters according to the multiple maximum value feature points by using the clustering algorithm;

[0024] S32. Determine the potential sliding surface of the slope according to the clustering clusters by using the random sample consensus algorithm.

[0025] Optionally, S31 specifically includes:

[0026] S311. Remove the maximum value feature points with an energy dissipation rate less than the preset threshold from the multiple maximum value feature points to obtain a set of feature points;

[0027] S312. Determine the clustering clusters according to the set of feature points by using the density-based clustering algorithm.

[0028] Optionally, S312 specifically includes:

[0029] Based on the contour score index, and using a hyperparameter optimization algorithm to optimize multiple hyperparameters of the density-based clustering algorithm, the best hyperparameter combination is obtained;

[0030] According to the best hyperparameter combination and the set of feature points, and using the density-based clustering algorithm to determine the clustering clusters.

[0031] Optionally, the S32 specifically includes:

[0032] S321. Using the random sample consensus algorithm to extract the current inlier set and the current outlier set from the clustering clusters, and fitting the current inlier set to obtain the current potential sliding surface;

[0033] S322. Using the random sample consensus algorithm to extract the next inlier set and the next outlier set from the current outlier set, and fitting the next inlier set to obtain the next potential sliding surface;

[0034] S323. Taking the next outlier set as the new current outlier set, and repeating S322 until the number of outliers in the current outlier set is less than the preset number.

[0035] The beneficial effects that the present invention can produce include:

[0036] By determining the energy dissipation rate of each grid unit in the two-dimensional numerical model of the longitudinal section of the slope, the present invention can comprehensively reflect the irreversible energy conversion process inside the slope, thereby accurately locating the local failure area inside the slope, and extracting the potential sliding surface from the local failure area, effectively improving the recognition accuracy of the potential sliding surface of the slope.

[0037] The present invention uses a clustering algorithm to initially identify and separate the local failure areas inside the slope, and then uses the random sample consensus algorithm to identify and extract multiple potential sliding surfaces one by one from the local failure areas, so as to be able to handle the recognition scenarios where multiple potential sliding surfaces coexist, and has a wider scope of application. At the same time, the combination of the clustering algorithm and the random sample consensus algorithm significantly improves the recognition accuracy and recognition efficiency of the potential sliding surface of the slope. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a flowchart of the method for extracting the potential sliding surface of the slope based on the energy dissipation rate provided by the embodiment of the present invention;

[0039] Figure 2 It is a schematic diagram of the two-dimensional numerical model of the soft interlayer slope provided by the embodiment of the present invention;

[0040] Figure 3 It is a schematic diagram of the energy dissipation rate distribution of the two-dimensional numerical model provided by the embodiment of the present invention;

[0041] Figure 4 Schematic diagram of the energy dissipation rate distribution of the regular grid model provided by an embodiment of the present invention;

[0042] Figure 5 Schematic diagram of the set C of maximum points provided by an embodiment of the present invention;

[0043] Figure 6 Schematic diagram of the distribution of multiple maximum feature points after filtering out external noise by using the convex hull detection algorithm provided by an embodiment of the present invention;

[0044] Figure 7 Schematic diagram of the result after ideal clustering of the feature point set by using the DBSCAN algorithm provided by an embodiment of the present invention;

[0045] Figure 8 Schematic diagram of the fitting curve of the potential sliding surface provided by an embodiment of the present invention;

[0046] Figure 9 Schematic diagram of cluster 3 provided by an embodiment of the present invention;

[0047] Figure 10 Schematic diagram of the process of extracting the main sliding surface from cluster 3 provided by an embodiment of the present invention;

[0048] Figure 11 Schematic diagram of the process of extracting the secondary sliding surface from cluster 3 provided by an embodiment of the present invention. Detailed implementation manners

[0049] The present invention will be described in detail below in conjunction with embodiments, but the present invention is not limited to these embodiments.

[0050] An embodiment of the present invention provides a method for extracting a potential sliding surface of a slope based on the energy dissipation rate. As Figure 1 shown, the method includes:

[0051] S1. Determine the centroid coordinates of each grid unit on the two-dimensional numerical model of the longitudinal section of the slope, and predict the energy dissipation rate of each grid unit.

[0052] Specifically, the two-dimensional numerical model of the longitudinal section of the slope can be constructed according to the geological information and geometric information of the slope, and the two-dimensional numerical model has multiple grid units.

[0053] Exemplarily, taking a soft interlayer slope as an example, the material partition of the slope includes soil and soft interlayer. According to the geological information and geometric information of the slope, a two-dimensional numerical model of the longitudinal section of the slope can be constructed on the X-Z plane in the XYZ space rectangular coordinate system. As Figure 2As shown. Then, normal constraints are applied to the left and right boundaries of the two-dimensional numerical model, and the bottom boundary is completely fixed. The grid density of the two-dimensional numerical model can be controlled at 1 m. Based on this XYZ rectangular coordinate system, in this embodiment, the centroid coordinates of each grid cell on the two-dimensional numerical model can be determined.

[0054] In S1, predicting the energy dissipation rate of each grid cell specifically may include:

[0055] Obtaining the elastoplastic parameters and creep parameters of different material partitions of the slope;

[0056] Based on the visco-elastoplastic creep damage model, predicting the energy dissipation rate of each grid cell according to the elastoplastic parameters and creep parameters.

[0057] Specifically, the visco-elastoplastic creep damage model is an existing model, which can simulate the internal failure behavior and instability process of the slope according to the elastoplastic parameters and creep parameters of the slope, and predict the energy dissipation rate of each grid cell on the two-dimensional numerical model of the slope at a future preset time through iterative calculation.

[0058] Exemplarily, the elastoplastic parameters of the above soft interlayer slope are shown in Table 1.

[0059] Table 1 Elastoplastic parameters of the soft interlayer slope

[0060]

[0061] Exemplarily, the creep parameters of the above soft interlayer slope are shown in Table 2.

[0062] Table 2 Creep parameters of the soft interlayer slope

[0063]

[0064] Specifically, setting the calculation step of the visco-elastoplastic creep damage model to 1 hour and the number of iterations to 8000 times, the energy dissipation rate of each grid cell on the two-dimensional numerical model of the above soft interlayer slope after 8000 hours can be predicted. The schematic diagram of the energy dissipation rate distribution of the two-dimensional numerical model of the soft interlayer slope is as Figure 3 shown.

[0065] S2. According to the centroid coordinates and energy dissipation rate of each grid cell, determining multiple maximum value feature points of the energy dissipation rate on the longitudinal section of the slope.

[0066] S2 may specifically include:

[0067] S21. Constructing a regular grid model according to the two-dimensional numerical model, and determining the energy dissipation rate of each regular grid on the regular grid model according to the centroid coordinates and energy dissipation rate of each grid cell on the two-dimensional numerical model.

[0068] Determine the energy dissipation rate of each regular grid on the regular grid model in S21. Specifically, it can be:

[0069] Use the interpolation algorithm to determine the energy dissipation rate of each regular grid on the regular grid model.

[0070] Specifically, in this embodiment, a regular grid model is constructed according to the boundary of the two-dimensional numerical model. By way of example, the regular grid model of the above soft interlayer slope is a rectangle as shown in Figure 4 The boundary of the regular grid model coincides with the maximum boundaries of the two-dimensional numerical model in the X direction and the Z direction. The regular grid model consists of multiple regular grids, and each regular grid is a square with a side length of 0.1 m. Then, in this embodiment, according to the centroid coordinates and energy dissipation rate of each grid cell on the two-dimensional numerical model, the energy dissipation rate of the corresponding regular grid in the regular grid model is determined, and the interpolation algorithm is used to determine the energy dissipation rates of all the remaining regular grids in the regular grid model. The schematic diagram of the energy dissipation rate distribution of the regular grid model of the soft interlayer slope is as shown in Figure 4 shown.

[0071] By constructing a regular grid model and interpolating the energy dissipation rate from the two-dimensional numerical model to the regular grid model, the interference caused by the grid non-uniformity of the two-dimensional numerical model to the subsequent extraction of potential slip surfaces can be reduced.

[0072] S22. Determine multiple maximum value feature points of the energy dissipation rate on the longitudinal section of the slope according to the energy dissipation rate of each regular grid.

[0073] S22 may specifically include:

[0074] S221. Determine multiple maximum value points of the energy dissipation rate on the regular grid model along the horizontal path and / or the vertical path according to the energy dissipation rate of each regular grid.

[0075] Specifically, in this embodiment, the energy dissipation rate is used as a discrimination index. On the regular grid model, multiple maximum points of the energy dissipation rate can be extracted along the horizontal search path to form point set A, or multiple maximum points of the energy dissipation rate can be extracted along the vertical search path to form point set B. In practice, since the extraction accuracy of the maximum points is higher when the search path intersects the potential sliding surface at a large angle, for the gently inclined sliding surface near the toe of the slope, it is advisable to use the vertical search path to extract the maximum points, while for the steeply inclined sliding surface at the rear edge of the landslide, it is advisable to use the horizontal search path to extract the maximum points. To integrate the advantages of both the horizontal search path and the vertical search path, this embodiment takes the union of point set A obtained by the horizontal search path and point set B obtained by the vertical search path to obtain the maximum point set C, that is, C = A ∪ B, which can effectively reduce the possibility of missing maximum points. The distribution of each point in the maximum point set C is as Figure 5 shown.

[0076] S222. Determine multiple maximum characteristic points of the energy dissipation rate on the longitudinal section of the slope according to multiple maximum points.

[0077] S222 may specifically include:

[0078] According to multiple maximum points and the boundary information of the longitudinal section of the slope, use the convex hull detection algorithm to determine multiple maximum characteristic points of the energy dissipation rate on the longitudinal section of the slope.

[0079] In this embodiment, since the area of the regular grid model is larger than that of the two-dimensional numerical model, the above interpolation algorithm will generate multiple external noise points outside the geometric boundary of the longitudinal section of the slope, and the process of searching and extracting the maximum points will also extract the maximum points among these external noise points. Therefore, the maximum point set C will also contain multiple external noise points, as Figure 5 shown. To eliminate the interference of these external noise points, this embodiment can filter out all the external noise points located outside the geometric boundary of the longitudinal section of the slope in the maximum point set C according to the boundary information of the longitudinal section of the slope by using the convex hull detection algorithm, and then use all the remaining maximum points as the maximum characteristic points. The distribution schematic diagram of multiple maximum characteristic points after filtering out the external noise points by using the convex hull detection algorithm is as Figure 6 shown.

[0080] S3. Determine the potential sliding surface of the slope according to multiple maximum characteristic points.

[0081] S3 may specifically include:

[0082] S31. Determine the clustering clusters according to multiple maximum characteristic points by using the clustering algorithm.

[0083] S31 may specifically include:

[0084] S311. Remove the maximum value feature points with an energy dissipation rate less than a preset threshold from multiple maximum value feature points to obtain a feature point set.

[0085] Specifically, there may still be internal noise points within the geometric boundary of the longitudinal section of the slope. Some of these internal noise points are numerical errors caused by the strong constraints on the boundary of the two-dimensional numerical model, and the other part is interference data generated by relatively dense low-energy dissipation regions inside the slope. To eliminate the interference of these internal noise points, in this embodiment, multiple maximum value feature points are arranged in descending order of the energy dissipation rate, and then the upper quartile is set as the preset threshold, and the maximum value feature points with an energy dissipation rate less than the upper quartile are removed, and then all the remaining maximum value feature points are used as the feature point set.

[0086] S312. According to the feature point set, use the density-based clustering algorithm to determine the clustering clusters.

[0087] Specifically, the density-based clustering algorithm can be Density-Based Spatial Clustering of Applications with Noise (abbreviated as DBSCAN algorithm). The DBSCAN algorithm can identify one or more high-density regions in the feature point set, and the high-density regions are the local failure regions inside the slope. The DBSCAN algorithm marks each high-density region as a clustering cluster, and some of these clustering clusters contain potential slip surfaces. At the same time, the DBSCAN algorithm can identify the sparse regions in the feature point set and mark the sparse regions as noise. The advantage of the DBSCAN algorithm is that it can complete the identification of clustering clusters without pre-specifying the number of clustering clusters, and at the same time can effectively identify non-convex clusters such as arc clusters. Therefore, it can realize the preliminary extraction of multiple potential slip surfaces under the condition that the number of potential slip surfaces is unknown.

[0088] Specifically, the hyperparameters of the DBSCAN algorithm include the neighborhood radius Eps and the minimum number of points MinPts. By adjusting the values of the above hyperparameters, the performance of the DBSCAN algorithm can be optimized. Usually, the values of the hyperparameters are adjusted manually. Exemplarily, in this embodiment, through manual adjustment, it is found that for the above-mentioned soft interlayer slope, when the neighborhood radius Eps = 0.5 and the minimum number of points MinPts = 3, the DBSCAN algorithm can achieve the most ideal clustering effect. As Figure 7 shown, when the DBSCAN algorithm performs ideal clustering on the feature point set of the above-mentioned soft interlayer slope based on the above hyperparameter values, a total of 11 high-density regions, that is, 11 clustering clusters, are identified. Among them, two clustering clusters each contain a potential slip surface. Among them, clustering cluster 1 contains the main slip surface, and clustering cluster 2 contains a secondary slip surface, presenting the most ideal performance of the DBSCAN algorithm.

[0089] It can be understood that the above ideal clustering effect of the DBSCAN algorithm is based on repeated manual adjustment of hyperparameters, so the dependence on manual work is relatively high. To improve the adjustment efficiency of hyperparameters and the automation degree of the DBSCAN algorithm, this embodiment can also use a hyperparameter optimization algorithm to automatically optimize the hyperparameter values of the DBSCAN algorithm.

[0090] S312 may specifically include:

[0091] Based on the silhouette score metric, and using a hyperparameter optimization algorithm to optimize multiple hyperparameters of the density-based clustering algorithm to obtain the best hyperparameter combination;

[0092] According to the best hyperparameter combination and the set of feature points, and using the density-based clustering algorithm to determine the clustering clusters.

[0093] Specifically, the hyperparameter optimization algorithm can be the grid search method. The grid search method is an exhaustive search method that finds the best hyperparameter combination by traversing all possible combinations of multiple hyperparameters.

[0094] Specifically, this embodiment uses the silhouette score as the evaluation metric to optimize multiple hyperparameters. First, use the grid search method to traverse all possible combinations of the neighborhood radius Eps and the minimum number of points MinPts; then, train the DBSCAN algorithm using each combination respectively, and calculate the silhouette score of the DBSCAN algorithm trained using each combination; finally, determine the combination corresponding to the best silhouette score as the best hyperparameter combination. The optimization result of this embodiment shows that when the neighborhood radius Eps = 1.2 and the minimum number of points MinPts = 19, the DBSCAN algorithm obtains the best silhouette score of 0.36. Therefore, the neighborhood radius Eps = 1.2 and the minimum number of points MinPts = 19 are the best hyperparameter combinations of this embodiment.

[0095] S32. According to the clustering clusters, use the random sample consensus algorithm to determine the potential sliding surface of the slope.

[0096] Specifically, this embodiment uses the Random Sample Consensus algorithm (RANSAC algorithm for short) to further separate discrete sliding surface feature points, that is, inliers, from the clustering clusters, and perform smooth fitting on the discrete inliers, and finally realize the automatic extraction of multiple potential sliding surfaces.

[0097] Specifically, this embodiment sequentially executes the RANSAC algorithm for each clustering cluster, sets the number of sampling times , the residual threshold , the minimum number of inliers MinInlier = 300. For a cluster with the number of points less than the minimum number of inliers MinInlier, the RANSAC algorithm directly skips it. For a cluster with the number of points greater than or equal to the minimum number of inliers MinInlier, the RANSAC algorithm separates the inliers and outliers in the cluster through iterative calculation, and then fits multiple discrete inliers to obtain the geometric model of the potential sliding surface .

[0098] Exemplarily, in this embodiment, the RANSAC algorithm is used to separate the inliers and outliers of the cluster 1 and the cluster 2 obtained by manually adjusting the hyperparameters above respectively, and determine the optimal number of inliers of a potential sliding surface , the optimal number of inliers of another potential sliding surface , and then smooth the inliers of the two potential sliding surfaces respectively for fitting, to obtain the fitting curve as shown in Figure 8 , and at the same time obtain the parameter vector of the geometric model of the two potential sliding surfaces , so as to obtain the geometric models of the two potential sliding surfaces and .

[0099] In practice, when the DBSCAN algorithm fails to achieve the ideal performance due to reasons such as hyperparameter selection, multiple potential sliding surfaces may be divided into the same cluster in the clustering. Exemplarily, as shown in Figure 9 , after the DBSCAN algorithm performs clustering based on the optimal hyperparameter combination (neighborhood radius Eps = 1.2 and minimum number of points MinPts = 19) obtained by the above automatic optimization, both the main sliding surface and the secondary sliding surface are divided into the same cluster 3. This is because there are local punching failure noise points along the extension line of the slope surface near the toe of the slope, and there are also X-shaped local shear failure noise points at the trailing edge of the secondary sliding surface. The existence of these noise points makes the point sets of the two potential sliding surfaces close to being connected, resulting in the DBSCAN algorithm misclassifying the two potential sliding surfaces into one category. To separate the two potential sliding surfaces, one method is to manually adjust the neighborhood radius Eps and the minimum number of points MinPts by combining prior knowledge, and the other method is to manually remove the above local punching failure noise points and local shear failure noise points to eliminate the influence of the noise on the clustering result. However, the above two methods cannot achieve the automatic extraction of the potential sliding surface, resulting in low extraction efficiency.

[0100] This embodiment can efficiently solve the problem that multiple potential sliding surfaces are divided into the same cluster by using the RANSAC algorithm in a nested manner.

[0101] Specifically, S32 may include:

[0102] S321. Use the Random Sample Consensus (RANSAC) algorithm to extract the current inlier set and the current outlier set from the clustering cluster, and fit the current inlier set to obtain the current potential sliding surface;

[0103] S322. Use the RANSAC algorithm to extract the next inlier set and the next outlier set from the current outlier set, and fit the next inlier set to obtain the next potential sliding surface;

[0104] S323. Take the next outlier set as the new current outlier set, and repeat S322 until the number of outliers in the current outlier set is less than the preset quantity.

[0105] Specifically, the preset quantity is the minimum number of inliers MinInlier.

[0106] Exemplarily, for Figure 9 the clustering cluster 3 containing two potential sliding surfaces, first use the RANSAC algorithm to perform multiple rounds of iteration to extract inliers in the clustering cluster 3 until the number of inliers of the main sliding surface is maximized, so as to obtain the inlier set of the main sliding surface, as Figure 10 shown. Figure 10 Iter-1 to Iter-13 in

[0107] respectively represent the best inlier fits obtained after each iteration in the process of extracting the inliers of the main sliding surface for 13 iterations. The colors of Iter-1 to Iter-13 from light to deep represent the change process of the best inlier fits during the iteration. It can be seen that the best inlier fits are initially distributed near the shallow sliding surface (Iter-1 to Iter-5), and then converge near the deeper sliding surface with more inliers after iteration (Iter-6 to Iter-13). Figure 11 shown. Figure 11 Iter-1 to Iter-9 in

[0108] respectively represent the best inlier fits obtained after each iteration in the process of extracting the inliers of the secondary sliding surface for 9 iterations. It can be seen that due to the reduction of the number of feature points in the outlier set, the extraction of the secondary sliding surface tends to converge starting from Iter-2. Subsequently, remove and fit the inlier set of the secondary sliding surface to obtain the geometric model of the secondary sliding surface. Finally, after judgment, since the number of remaining outliers is less than the minimum number of inliers MinInlier, the RANSAC algorithm stops extracting inliers.

[0109] Specifically, the implementation process of nested use of the RANSAC algorithm is as follows:

[0110] Step 1. Initialize the labels of potential slip surfaces and the best inlier count in . Define the number of samplings , the residual threshold , and the minimum inlier count MinInlier. Let the geometric model of the potential slip surface be , where represents the parameter vector of the geometric model . Exemplarily, in this embodiment, a quadratic curve is adopted, then , where and are respectively the abscissa and ordinate of the geometric model of the potential slip surface in the plane rectangular coordinate system, , and are respectively the control parameters of .

[0111] Step 2. Conduct times of repeated sampling in the clustering cluster :

[0112] 1) Randomly select 3 points to estimate the parameter vector of the potential slip surface . Since the potential slip surfaces of slopes in reality are all convex downward, if , then directly skip this sampling.

[0113] 2) For the th point , , where and are respectively the abscissa and ordinate of the point in the plane rectangular coordinate system. Calculate the ordinate of when the parameter vector is and the abscissa is , and then calculate the residual between and the ordinate of the point .

[0114] 3) If , then the point is called is an inlier. Calculate the residuals of all points and count the number of inliers , which means that the total number of all points satisfying is the number of inliers.

[0115] 4) If and , then , and the optimal parameter vector .

[0116] Step 3, Data output:

[0117] 1) Obtain the geometric model of the potential sliding surface and its parameter vector and its inlier set .

[0118] 2) Remove the inlier set of the potential sliding surface from the clustering cluster , that is .

[0119] 3) If the remaining number of feature points in the clustering cluster is still greater than MinInlier, then repeat Step 2 (let , ); otherwise, stop the extraction of the potential sliding surface.

[0120] Considering that the DBSCAN algorithm is sensitive to the two hyperparameters of the neighborhood radius Eps and the minimum number of points MinPts, the present invention only uses the DBSCAN algorithm to preliminarily cluster the feature point set to reduce the probability of failure in extracting the potential sliding surface and ensure the robustness of the extraction program. Then, the RANSAC algorithm is used to further extract inliers and fit from the clustering clusters obtained by the DBSCAN algorithm to achieve the accurate extraction of the potential sliding surface. At the same time, through the nested use of the RANSAC algorithm, even if the DBSCAN algorithm fails to achieve accurate clustering in the case of multiple potential sliding surfaces coexisting, the RANSAC algorithm can still accurately lock multiple potential sliding surfaces in the background of dense noise, demonstrating the advantages of the present invention in the recognition of complex failure modes of slopes.

[0121] The above are only several embodiments of the present application, and do not impose any form of limitation on the present application. Although the present application is disclosed above with preferred embodiments, it is not intended to limit the present application. Any person skilled in the art, without departing from the scope of the technical solution of the present application, makes some changes or modifications using the disclosed technical content, which are equivalent to equivalent implementation cases and all belong to the scope of the technical solution.​

Claims

1. A method for extracting potential sliding surface of slope based on energy dissipation rate, characterized in that: The method comprises: S1. Determine the centroid coordinates of each grid cell on the two-dimensional numerical model of the slope longitudinal section and predict the energy dissipation rate of each grid cell; S2. Determine multiple maximum characteristic points of the energy dissipation rate on the longitudinal section of the slope according to the centroid coordinates and energy dissipation rate of each grid cell; S3, determining the potential sliding surface of the slope based on multiple maximum feature points; The energy dissipation rate of each grid unit is predicted in S1, specifically including: Obtain the elastic-plastic parameters and creep parameters of different material partitions of the slope; Based on the elastic-viscoplastic creep damage model, the energy dissipation rate of each grid unit is predicted according to the elastic-plastic parameter and the creep parameter; The S2 specifically includes: S21, constructing a regular grid model according to the two-dimensional numerical model, and determining the energy dissipation rate of each regular grid on the regular grid model according to the centroid coordinates and energy dissipation rate of each grid unit on the two-dimensional numerical model; S22, determining a plurality of maximum characteristic points of the energy dissipation rate on the longitudinal section of the slope according to the energy dissipation rate of each regular grid; Determining the energy dissipation rate of each regular grid on the regular grid model in S21 specifically includes: Determine the energy dissipation rate of each regular grid on the regular grid model by using an interpolation algorithm; The S22 specifically includes: S221, according to the energy dissipation rate of each regular grid, determining a plurality of maximum points of the energy dissipation rate along a horizontal path and / or a vertical path on the regular grid model; S222. Determine multiple maximum characteristic points of the energy dissipation rate on the longitudinal section of the slope based on the multiple maximum points.

2. The method according to claim 1, characterized in that The S222 specifically includes: According to the multiple maximum value points and the boundary information of the slope longitudinal section, a convex hull detection algorithm is used to determine the multiple maximum value characteristic points of the energy dissipation rate on the slope longitudinal section.

3. The method according to claim 1, characterized in that The S3 specifically includes: S31, determining clusters using a clustering algorithm based on multiple maximum feature points; S32. Determine the potential sliding surface of the slope using a random sample consensus algorithm based on the clusters.

4. The method according to claim 3, characterized in that The S31 specifically includes: S311, removing the maximum value feature points whose energy dissipation rate is less than a preset threshold from the multiple maximum value feature points to obtain a feature point set; S312: Determine clusters according to the feature point set using a density-based clustering algorithm.

5. The method according to claim 4, characterized in that The S312 specifically includes: Based on the silhouette score indicator, the hyperparameter optimization algorithm is used to optimize multiple hyperparameters of the density-based clustering algorithm to obtain the best hyperparameter combination; A cluster is determined according to the optimal hyperparameter combination and the feature point set and using the density-based clustering algorithm.

6. The method according to claim 3, characterized in that The S32 specifically includes: S321, extracting a current inner point set and a current outer point set from the cluster using a random sample consensus algorithm, and fitting the current inner point set to obtain a current potential sliding surface; S322, extracting the next inner point set and the next outer point set from the current outer point set by using the random sample consensus algorithm, and fitting the next inner point set to obtain the next potential sliding surface; S323: Take the next external point set as the new current external point set, and repeat S322 until the number of external points in the current external point set is less than a preset number.

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