Soil-rock mixed slope material point method model generation method

Abstract

The invention discloses a method for generating a material point method model of a soil-rock mixed slope, which is used for simulating the mechanical behavior of the soil-rock mixed slope. The method comprises the following steps of: firstly, randomly dividing a slope region to generate polygonal units conforming to target area and shape distribution; then, according to the shape contour of the polygon unit, generating a random dimension stone contour through polar coordinate sampling and Fourier series fitting, and adjusting and controlling the dimension of the dimension stone through an area proportion; and finally, mapping the generated contour of the block stone into a substance point array, calibrating substance points belonging to the block stone, and completing pretreatment of substance point method calculation. The dimension, shape and spatial distribution characteristics of the rock blocks in the soil-rock mixed slope can be truly reflected, the rock block putting efficiency is effectively improved, the overlapping problem is avoided, the defects that in the prior art, the shape of the rock blocks is simplified, and the distribution randomness is insufficient are overcome, meanwhile, the method is suitable for numerical simulation of the large deformation problem, and the application prospect is wide. The method has high calculation precision and wide engineering application prospects.

Description

Technical Field

[0001] The invention relates to the field of civil engineering slope modeling, and in particular to a method for generating a material point method model of a soil-rock mixed slope. Background Art

[0002] Soil-rock slopes are widely found in nature and engineering practice, and their stability is deeply affected by the interaction between soil and rock. As an important component of the slope, the randomness of the size, shape and spatial distribution of rock plays a key role in the mechanical properties of the slope. However, existing research and simulation methods have many limitations in describing and analyzing the complexity of soil-rock slopes.

[0003] The shape of the rock blocks has a significant impact on the stability of the slope. Considering the diversity and complexity of the rock block shapes, most existing simulation methods often use idealized simplified models such as circles and ellipses to represent the rock blocks, which cannot accurately reflect the shape characteristics and complex contact relationships of the rock blocks in the real slope. In the existing simulation methods, the generation and placement of rock blocks are mostly carried out one by one to control the overlap between the rocks. When it is necessary to generate a large-scale group of rocks, the placement efficiency is extremely low, and it is difficult to meet the requirements of statistical control of characteristics such as grading and position distribution. The instability of soil-rock mixed slopes is usually accompanied by significant shear band formation and large deformation problems. The traditional research method, the finite element method, is difficult to effectively handle such large deformation scenarios due to grid distortion and other reasons.

[0004] In view of the shortcomings of the existing methods, there is an urgent need for a soil-rock mixed slope modeling method that can efficiently generate a model that meets the random characteristics of rock blocks and is suitable for large deformation calculation requirements. Summary of the invention

[0005] The present invention provides a method for generating a material point method model of a soil-rock mixed slope, which is used to solve the problems in the prior art that the shape of simulated stone blocks is too simplified, the efficiency of stone block placement is low, and large deformation simulation is difficult to handle. The present invention can provide a more realistic and comprehensive calculation model for slope instability analysis by accurately controlling the size, shape, and position distribution of the stone blocks.

[0006] The object of the present invention is achieved in that:

[0007] A method for generating a material point method model of a soil-rock mixed slope comprises the following steps:

[0008] S1. According to the geometric shape and component characteristics of the slope, determine the slope profile Ω, slope height H, rock content R, number of rocks N, and probability density distribution curve L of rock area A , probability density distribution curve of stone slenderness ratio L AR , error threshold ε and material point spacing h;

[0009] S2. According to the slope profile Ω and the number of rocks N, the slope is divided into N polygonal domains using the Voronoi partitioning method through N seed points X randomly distributed within the slope profile Ω;

[0010] S3. Based on the area probability density distribution curve L of all polygonal domains in the current slope A * , Slenderness ratio probability density distribution curve L AR * , target rock area probability density distribution curve L A And the probability density distribution curve of the stone slenderness ratio L AR , calculate the error E between the current distribution and the target distribution;

[0011] S4. The operation of randomly moving a seed point X is performed multiple times to re-divide the polygonal domain within the slope multiple times until the error E is less than the error threshold ε;

[0012] S5. According to the polygonal domain finally divided, a block stone outline is generated in each polygonal domain according to the outline of the polygonal domain, and the block stone outline is scaled and adjusted according to the stone content R to obtain the coordinates C of all block stone outline control points in the entire slope;

[0013] S6. Generate an equidistant material point array P according to the slope profile Ω and the material point spacing h, and calibrate the block stone material point P in the material point array P according to the block stone profile control point coordinates C rock , the uncalibrated material point is recorded as soil material point P soil , and the material point method model of soil-rock mixed slope is obtained.

[0014] In S2, according to the slope profile Ω and the number of rocks N, the Voronoi partitioning method is used to partition the slope into N polygonal domains through N seed points X randomly distributed within the slope profile Ω. The specific contents are as follows:

[0015] S21. randomly generate N scattered points in the slope profile Ω domain, where N is the number of boulders;

[0016] S22. Using the generated N scattered points as seed points X, generate N Voronoi polygons using the Voronoi partitioning method;

[0017] S23. Each generated Voronoi polygon is judged one by one to determine whether each vertex is outside the slope contour Ω. If each vertex is not outside the slope contour Ω, no processing is performed and other polygons are judged. If at least one vertex is outside the slope contour Ω, the seed point X corresponding to the polygon is marked as an abnormal seed point X. * ;

[0018] S24. Calculate each abnormal seed point X in turn* The distance to each edge Γ of the slope profile Ω is calculated by taking the distance to the nearest edge Γ nearest As the symmetry axis, the abnormal seed point X * Copy to get an auxiliary seed point X a ; If the difference between the second closest distance and the closest distance is not greater than Δd, then the second closest edge Γ second As the symmetry axis, the abnormal seed point X * Copy again to get another auxiliary seed point X a , use the following formula to calculate the difference Δd:

[0019] Δd=H / 2

[0020] Where H is the slope height;

[0021] S25. For each auxiliary seed point X a The position of the slope is judged, and the points within the slope contour Ω are eliminated, and the remaining auxiliary seed points X a With the original seed point X as the base point, perform Voronoi subdivision again and delete the auxiliary seed point X a The corresponding polygon retains the polygon corresponding to the original seed point X.

[0022] In S3, the area probability density distribution curve L of all polygonal domains in the current slope is A * , Slenderness ratio probability density distribution curve L AR * , target rock area probability density distribution curve L A And the probability density distribution curve of the stone slenderness ratio L AR , the specific contents of calculating the error E between the current distribution and the target distribution are as follows:

[0023] S31. Calculate the long side M of the minimum circumscribed rectangle M of each polygon L and the short side M S , the slenderness ratio R of the polygon is M L / M S ;

[0024] S32. Calculate the area probability density distribution curve L of all polygonal domains in the current slope A * and the target rock area probability density distribution curve L A The root mean square error E A , calculate the slenderness ratio probability density distribution curve L of all polygonal domains in the current slope AR * and the target stone slenderness ratio probability density distribution curve L AR The root mean square error EAR , take E A and E AR The larger value is recorded as error E.

[0025] In S4, the operation of randomly moving a seed point X is performed multiple times to re-divide the polygonal domain in the slope multiple times until the error E is less than the error threshold ε. The specific contents are as follows:

[0026] S41. Randomly select a seed point X and set the coordinates of the seed point X to X. x , X y Adjusted to, Δx and Δy are both random numbers in the interval [-I, I], I is the average size of the polygonal domain in the slope, and I is calculated using the following formula:

[0027]

[0028] In the formula, S Ω is the area of ​​the slope profile Ω, and N is the number of rocks; determine whether the adjusted seed point X coordinate is within the soil-rock mixed slope profile Ω. If it is within the slope profile Ω, continue the current operation; if it is outside the slope profile Ω, regenerate random numbers Δx and Δy until the adjusted seed point X coordinate is within the soil-rock mixed slope profile Ω;

[0029] S42. Based on the seed point X, generate N Voronoi polygons using the Voronoi partitioning method;

[0030] S43. Each generated Voronoi polygon is judged one by one to determine whether each vertex is outside the slope contour Ω. If each vertex is not outside the slope contour Ω, no processing is performed and other polygons are judged. If at least one vertex is outside the slope contour Ω, the seed point X corresponding to the polygon is marked as an abnormal seed point X. * ;

[0031] S44. Calculate each abnormal seed point X in turn * The distance to each edge Γ of the slope profile Ω is calculated by taking the distance to the nearest edge Γ nearest As the symmetry axis, the abnormal seed point X * Copy to get an auxiliary seed point X a ; If the difference between the second closest distance and the closest distance is not greater than Δd, then the second closest edge Γ second As the symmetry axis, the abnormal seed point X * Copy again to get another auxiliary seed point X a , use the following formula to calculate the difference Δd:

[0032] Δd=H / 2

[0033] Where H is the slope height;

[0034] S45. For each auxiliary seed point X a The position of the slope is judged, and the points within the slope contour Ω are eliminated, and the remaining auxiliary seed points X a With the original seed point X as the base point, perform Voronoi subdivision again and delete the auxiliary seed point X a The corresponding polygon retains the polygon corresponding to the original seed point X;

[0035] S46. Calculate the error E of the current polygon distribution new , compare its size relationship with the error E, if E new ≥E, the operation of moving the point is abandoned, the moved seed point is restored to its original position, and steps S41-S46 are repeated; if E new <E and E new >ε, where ε is the set error threshold, the operation of moving the point is saved and steps S41-S46 are repeated; if E new <E and E new ≤ε, continue the current operation.

[0036] The specific contents of generating the block stone outline according to the outline of the polygonal domain in S5 are as follows:

[0037] Randomly select N edges on the polygon m sampling points, N m According to the modeling accuracy requirements, take the centroid of the polygon as the origin, expand all sampling points in the polar coordinate system, and then use Fourier series to fit all sampling points. Select N equally spaced points on the obtained fitting curve. n sampling points, as the block stone contour control points C, N n Determined according to the modeling accuracy requirements.

[0038] The specific contents of scaling and adjusting the block stone outline according to the stone content R in S5 are as follows:

[0039] Calculate the area of ​​the polygonal domain and scale the area of ​​the stone to the area of ​​the polygonal domain S C times, S C is the percentage of stone content R.

[0040] The beneficial effects of the present invention are:

[0041] (1) The present invention randomly divides polygonal units and performs iterative optimization to make the area and shape of the polygons conform to the predetermined target distribution, thereby more accurately reflecting the size and distribution of boulders in the soil-rock mixed slope and improving the authenticity and applicability of the model.

[0042] (2) The random rock contour generation method based on Fourier series fitting can flexibly control the shape characteristics of the rocks, overcoming the limitation of the traditional method that the rock shape is simplified into a regular geometric shape, so that the model can more realistically reflect the complex shape of the rocks in the actual slope.

[0043] (3) Placing stones independently in each polygonal unit can efficiently generate a group of stones that meet the grading requirements, effectively avoid the problem of overlapping between stones, and significantly improve the efficiency of stone placement, which is particularly suitable for large-scale computing needs.

[0044] (4) This method directly maps the generated stone block contour to the material point array and automatically calibrates the stone material points at the corresponding positions, providing efficient and accurate pre-processing for the material point method calculation, reducing manual operations and calculation complexity, and significantly improving the calculation efficiency and accuracy of simulating the instability process of large deformation slopes. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 A flow chart of a method for generating a material point method model of a soil-rock mixed slope provided by the present invention;

[0046] Figure 2 The results of the initial polygonal subdivision of the soil-rock mixed slope geometric model before correction and the schematic diagram of the distribution of abnormal seed points provided by the embodiment of the present invention;

[0047] Figure 3 A schematic diagram of the distribution of auxiliary seed points for the initial polygonal subdivision of a soil-rock mixed slope geometric model provided by an embodiment of the present invention;

[0048] Figure 4 A schematic diagram of the results of the initial polygonal subdivision and correction of the soil-rock mixed slope geometric model provided in an embodiment of the present invention;

[0049] Figure 5 A comparison diagram of the polygon area and slenderness ratio probability density distribution curves obtained by the initial polygonal subdivision of the soil-rock mixed slope geometric model provided by the embodiment of the present invention and the target probability density distribution curve;

[0050] Figure 6 A comparison diagram of the polygon area and slenderness ratio probability density distribution curves obtained by final polygonal decomposition of the soil-rock mixed slope geometric model provided by the embodiment of the present invention and the target probability density distribution curve;

[0051] Figure 7 A schematic diagram of the result after the final polygonal subdivision and correction of the soil-rock mixed slope geometric model provided in an embodiment of the present invention;

[0052] Figure 8A schematic diagram of polar coordinate expansion and Fourier series fitting of the xth polygonal contour sampling point of the soil-rock mixed slope geometric model provided by an embodiment of the present invention;

[0053] Fig. 9 A schematic diagram of the xth polygonal contour and block stone contour control points of the soil-rock mixed slope geometric model provided in an embodiment of the present invention;

[0054] Fig.10 A schematic diagram of the xth polygonal outline of the soil-rock mixed slope geometric model and the block stone outline after scaling adjustment provided by an embodiment of the present invention;

[0055] Fig.11 A schematic diagram of the final polygonal decomposition and block stone placement results of the soil-rock mixed slope geometric model provided by an embodiment of the present invention;

[0056] Fig.12 A schematic diagram of calibrating rocks in a material point array for a soil-rock mixed slope geometric model provided in an embodiment of the present invention;

[0057] Fig.13 The soil-rock mixed slope geometric model provided in the embodiment of the present invention is imported into the material point method program to calculate the horizontal displacement cloud map. DETAILED DESCRIPTION

[0058] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0059] like Figure 1 As shown, S1. According to the geometric shape and component characteristics of the slope, determine the slope profile Ω, slope height H, stone content R, number of blocks N, and block area probability density distribution curve L A , probability density distribution curve of stone slenderness ratio L AR , error threshold ε and material point spacing h, the slope profile Ω in the embodiment is controlled by the control points (0,0), (100,0), (100,10), (60,10), (40,30), (0,30) and (0,0) in the two-dimensional coordinate system, the slope height H is 20 meters, the rock content R is 30%, the number of boulders N is 67, and the probability density distribution curve L of the boulders area A It is a log-normal distribution with a mean of 3.3 and a standard deviation of 0.5. The probability density distribution curve of the slenderness ratio of the stone is L AR It is a log-normal distribution with a mean of 0.43 and a standard deviation of 0.18. The error threshold ε is set to 0.00035, and the material point spacing h is 0.25 meters.

[0060] S2. According to the slope profile Ω and the number of rocks N, the slope is partitioned into N polygonal domains using the Voronoi partitioning method through N seed points X randomly distributed within the slope profile Ω; Step 2 specifically includes:

[0061] S21. Randomly generate N scattered points in the slope profile domain Ω, where N is the number of boulders.

[0062] S22. Using the generated N scattered points as seed points X, generate N Voronoi polygons using the Voronoi partitioning method. The initial partitioning is completed. Since the principle of Voronoi partitioning is based on perpendicular bisectors of adjacent seed points, the polygons generated based on seed points close to the edge of the slope contour may not be closed or the vertices may exceed the boundary of the slope contour, which requires further judgment and correction.

[0063] S23. Each generated Voronoi polygon is judged one by one to determine whether each vertex is outside the slope contour Ω. If each vertex is not outside the slope contour Ω, no processing is performed and other polygons are judged. If at least one vertex is outside the slope contour Ω, the seed point X corresponding to the polygon is marked as an abnormal seed point X. * ;reference Figure 2 As shown, the seed points corresponding to all unclosed polygons or polygons beyond the slope contour boundary are found out through judgment.

[0064] S24. Calculate each abnormal seed point X in turn * The distance to each edge Γ of the slope profile Ω is calculated by taking the distance to the nearest edge Γ nearest As the symmetry axis, the abnormal seed point X * Copy to get an auxiliary seed point X a ; If the difference between the second closest distance and the closest distance is not greater than Δd, then the second closest edge Γ second As the symmetry axis, the abnormal seed point X * Copy again to get another auxiliary seed point X a , use the following formula to calculate the difference Δd:

[0065] Δd=H / 2

[0066] Where H is the slope height.

[0067] S25. For each auxiliary seed point X a The position of the slope is judged, and the points within the slope contour Ω are eliminated, and the remaining auxiliary seed points X a With the original seed point X as the base point, Voronoi subdivision is performed again. Since the auxiliary seed points and the abnormal seed points are based on the symmetry of the slope contour boundary, the polygons obtained this time are also based on the symmetry of the boundary. Figure 4 As shown in the figure, the edge of the polygon coincides with the slope contour, avoiding the phenomenon that the polygon is not closed and the polygon vertices exceed the boundary of the slope contour during the initial segmentation. Delete the auxiliary seed point X aThe corresponding polygon is retained, and the polygon corresponding to the original seed point X is retained, so that the polygonal subdivision based on the original seed point can be obtained within the slope contour domain, and each polygon is completely closed and does not exceed the slope boundary.

[0068] S3. Based on the area probability density distribution curve L of all polygonal domains in the current slope A * , Slenderness ratio probability density distribution curve L AR * , target rock area probability density distribution curve L A And the probability density distribution curve of the stone slenderness ratio L AR , calculate the error E between the current distribution and the target distribution. S3 specifically includes:

[0069] S31. Calculate the long side M of the minimum circumscribed rectangle M of each polygon L and the short side M S , the long side and short side of the minimum circumscribed rectangle are the major axis and minor axis of the polygon, and the slenderness ratio R of the polygon is M L / M S .

[0070] S32. Reference Figure 5 As shown, calculate the area probability density distribution curve L of all polygonal domains in the current slope A * and the target rock area probability density distribution curve L A The root mean square error E A , calculate the slenderness ratio probability density distribution curve L of all polygonal domains in the current slope AR * and the target stone slenderness ratio probability density distribution curve L AR The root mean square error E AR , take E A and E AR The larger value is recorded as error E, and the error in the embodiment is 0.0064.

[0071] S4. The operation of randomly moving a seed point X is repeated multiple times to re-divide the polygonal domain within the slope multiple times until the error E is less than the error threshold ε; specifically, the operation includes:

[0072] S41. Randomly select a seed point X and set the coordinates of the seed point X to X. x , X y Adjusted to, Δx and Δy are both random numbers in the interval [-I, I], I is the average size of the polygonal domain in the slope, and I is calculated using the following formula:

[0073]

[0074] In the formula, S Ω is the area of ​​the slope contour Ω, N is the number of boulders, so that the moved seed point can be randomly moved within an average unit size area; determine whether the adjusted seed point X coordinate is within the soil-rock mixed slope contour Ω, if it is within the slope contour Ω, continue the current operation; if it is outside the slope contour Ω, regenerate random numbers Δx and Δy until the adjusted seed point X coordinate is within the soil-rock mixed slope contour Ω; ensure that the seed point is still within the slope after moving, so as to prevent the polygon obtained by segmentation from exceeding the slope boundary.

[0075] S42. Based on the seed point X, generate N Voronoi polygons using the Voronoi triangulation method.

[0076] S43. Each generated Voronoi polygon is judged one by one to determine whether each vertex is outside the slope contour Ω. If each vertex is not outside the slope contour Ω, no processing is performed and other polygons are judged. If at least one vertex is outside the slope contour Ω, the seed point X corresponding to the polygon is marked as an abnormal seed point X. * .

[0077] S44. Calculate each abnormal seed point X in turn * The distance to each edge Γ of the slope profile Ω is calculated by taking the distance to the nearest edge Γ nearest As the symmetry axis, the abnormal seed point X * Copy to get an auxiliary seed point X a ; If the difference between the second closest distance and the closest distance is not greater than Δd, then the second closest edge Γ second As the symmetry axis, the abnormal seed point X * Copy again to get another auxiliary seed point X a , use the following formula to calculate the difference Δd:

[0078] Δd=H / 2

[0079] Where H is the slope height.

[0080] S45. For each auxiliary seed point X a The position of the slope is judged, and the points within the slope contour Ω are eliminated, and the remaining auxiliary seed points X a With the original seed point X as the base point, perform Voronoi subdivision again and delete the auxiliary seed point X a The corresponding polygon retains the polygon corresponding to the original seed point X.

[0081] S46. Calculate the error E of the current polygon distribution new, compare its size relationship with the error E, if E new ≥E, it means that the current operation of moving the seed point has failed to make the size and shape of the polygon in the entire slope closer to the target distribution, then the operation of moving the point is abandoned, the moved seed point is restored to its original position, and steps S41-S46 are repeated; if E new <E and E new >ε, where ε is the set error threshold, indicating that the current operation of moving the seed point can make the size and shape of the polygon in the entire slope closer to the target distribution, then the operation of moving the point is saved and steps S41-S46 are repeated; if E new <E and E new ≤ε, refer to Figure 6 As shown in FIG. 1 , it is shown that the current operation of moving the seed point can make the size and shape of the polygon in the entire slope less similar to the target distribution than the set error threshold. The error in this embodiment is 0.0003499. Figure 7 As shown, if the polygonal subdivision result that meets the target requirements is obtained, continue the current operation.

[0082] S5. Based on the polygonal domain finally segmented, a block stone outline is generated in each polygonal domain according to the outline of the polygonal domain, and the block stone outline is scaled and adjusted according to the stone content R to obtain the coordinates C of all block stone outline control points in the entire slope, as follows:

[0083] S51 randomly selects N on the edge of the polygon m sampling points, N m Determined according to the modeling accuracy requirements, in this embodiment, it is taken as 1000, refer to Figure 8 As shown in the figure, taking the centroid of the polygon as the origin, all sampling points are expanded in the polar coordinate system, and then all sampling points are fitted with the Fourier series, so that a smooth block stone contour is generated based on the polygon contour. Fig. 9 As shown, N is selected equidistantly on the obtained fitting curve. n sampling points, equidistant point selection prevents excessive memory usage and the generated stone blocks are too smooth, as the stone block contour control points C, N n It is determined according to the modeling accuracy requirement and is set to 17 in this embodiment.

[0084] S52. Calculate the area of ​​the polygonal domain, refer to Fig.10 As shown, the area of ​​the block is scaled to the area of ​​the polygon domain S C times, S C is the percentage of the stone content R. In this embodiment, the area of ​​the block stone is reduced to 30% of the polygon, so as to control the proportion of the area occupied by the block stone in the entire slope to be consistent with the set stone content. Fig.11 As shown, the coordinates C of all the rock contour control points in the entire slope are obtained.

[0085] S6. Generate an equidistant material point array P according to the slope profile Ω and the material point spacing h. The material point spacing in this embodiment is 0.25m. Fig.12 As shown, the block stone material point P is calibrated in the material point array P according to the block stone contour control point coordinate C. rock , the uncalibrated material point is recorded as soil material point P soil , the material point method model of the soil-rock mixed slope is obtained, and the generated material point method model of the soil-rock mixed slope is imported into the material point method calculation program. In this embodiment, the open source material point method calculation program MPM3D-f90 is selected for calculation simulation, and the simulation result of the soil-rock mixed slope can be obtained. Fig.13 The horizontal displacement cloud diagram of the material point is shown.

[0086] In summary, the present invention realizes a method for generating a material point method model of a soil-rock mixed slope, which more accurately reflects the size and distribution law of boulders in the soil-rock mixed slope, more realistically reflects the complex shape of boulders in the actual slope, and at the same time significantly improves the efficiency of boulders placement, and improves the calculation efficiency and accuracy of simulating the instability process of large deformation slopes.

Claims

1. A method for generating a material point method model of a soil-rock mixed slope, characterized in that: The following steps are involved: S1. According to the geometric shape and component characteristics of the slope, determine the slope profile Ω, slope height H, rock content R, number of rocks N, and probability density distribution curve L of rock area A , probability density distribution curve of stone slenderness ratio L AR , error threshold ε and material point spacing h; S2. According to the slope profile Ω and the number of rocks N, the slope is divided into N polygonal domains using the Voronoi partitioning method through N seed points X randomly distributed within the slope profile Ω; S3. Based on the area probability density distribution curve L of all polygonal domains in the current slope A * , Slenderness ratio probability density distribution curve L AR * , target rock area probability density distribution curve L A And the probability density distribution curve of the stone slenderness ratio L AR , calculate the error E between the current distribution and the target distribution; S4. The operation of randomly moving a seed point X is performed multiple times to re-divide the polygonal domain within the slope multiple times until the error E is less than the error threshold ε; S5. According to the polygonal domain finally divided, a block stone outline is generated in each polygonal domain according to the outline of the polygonal domain, and the block stone outline is scaled and adjusted according to the stone content R to obtain the coordinates C of all block stone outline control points in the entire slope; S6. Generate an equidistant material point array P according to the slope profile Ω and the material point spacing h, and calibrate the block stone material point P in the material point array P according to the block stone profile control point coordinates C rock , the uncalibrated material point is recorded as soil material point P soil , and the material point method model of soil-rock mixed slope is obtained.

2. The method for generating a material point method model of a soil-rock mixed slope according to claim 1, characterized in that: In S2, according to the slope profile Ω and the number of rocks N, the Voronoi partitioning method is used to partition the slope into N polygonal domains through N seed points X randomly distributed within the slope profile Ω. The specific contents are as follows: S21. randomly generate N scattered points in the slope profile Ω domain, where N is the number of boulders; S22. Using the generated N scattered points as seed points X, generate N Voronoi polygons using the Voronoi partitioning method; S23. Each generated Voronoi polygon is judged one by one to determine whether each vertex is outside the slope contour Ω. If each vertex is not outside the slope contour Ω, no processing is performed and other polygons are judged. If at least one vertex is outside the slope contour Ω, the seed point X corresponding to the polygon is marked as an abnormal seed point X. * ; S24. Calculate each abnormal seed point X in turn * The distance to each edge Γ of the slope profile Ω is calculated by taking the distance to the nearest edge Γ nearest As the symmetry axis, the abnormal seed point X * Copy to get an auxiliary seed point X a ; If the difference between the second closest distance and the closest distance is not greater than Δd, then the second closest edge Γ second As the symmetry axis, the abnormal seed point X * Copy again to get another auxiliary seed point X a , use the following formula to calculate the difference Δd: Δd=H / 2 Where H is the slope height; S25. For each auxiliary seed point X a The position of the slope is judged, and the points within the slope contour Ω are eliminated, and the remaining auxiliary seed points X a With the original seed point X as the base point, perform Voronoi subdivision again and delete the auxiliary seed point X a The corresponding polygon retains the polygon corresponding to the original seed point X.

3. The method for generating a material point method model of a soil-rock mixed slope according to claim 1, characterized in that: In S3, the area probability density distribution curve L of all polygonal domains in the current slope is A * , Slenderness ratio probability density distribution curve L AR * , target rock area probability density distribution curve L A And the probability density distribution curve of the stone slenderness ratio L AR , the specific contents of calculating the error E between the current distribution and the target distribution are as follows: S31. Calculate the long side M of the minimum circumscribed rectangle M of each polygon L and the short side M S , the slenderness ratio R of the polygon is M L / M S ; S32. Calculate the area probability density distribution curve L of all polygonal domains in the current slope A * And the target rock area probability density distribution curve L A The root mean square error E A , calculate the slenderness ratio probability density distribution curve L of all polygonal domains in the current slope AR * and the target stone slenderness ratio probability density distribution curve L AR The root mean square error E AR , take E A and E AR The larger value is recorded as error E.

4. The method for generating a material point method model of a soil-rock mixed slope according to claim 1, characterized in that: In S4, the operation of randomly moving a seed point X is performed multiple times to re-divide the polygonal domain in the slope multiple times until the error E is less than the error threshold ε. The specific contents are as follows: S41. Randomly select a seed point X and set the coordinates of the seed point X to X. x , X y Adjusted to, Δx and Δy are both random numbers in the interval [-I, I], I is the average size of the polygonal domain in the slope, and I is calculated using the following formula: Where SΩ is the area of ​​the slope profile Ω, and N is the number of rocks. It is determined whether the adjusted seed point X coordinate is within the soil-rock mixed slope profile Ω. If it is within the slope profile Ω, the current operation is continued. If it is outside the slope profile Ω, random numbers Δx and Δy are regenerated until the adjusted seed point X coordinate is within the soil-rock mixed slope profile Ω. S42. Based on the seed point X, generate N Voronoi polygons using the Voronoi partitioning method; S43. Each generated Voronoi polygon is judged one by one to determine whether each vertex is outside the slope contour Ω. If each vertex is not outside the slope contour Ω, no processing is performed and other polygons are judged. If at least one vertex is outside the slope contour Ω, the seed point X corresponding to the polygon is marked as an abnormal seed point X. * ; S44. Calculate each abnormal seed point X in turn * The distance to each edge Γ of the slope profile Ω is calculated by taking the distance to the nearest edge Γ nearest As the symmetry axis, the abnormal seed point X * Copy to get an auxiliary seed point X a ; If the difference between the second closest distance and the closest distance is not greater than Δd, then the second closest edge Γ sceond As the symmetry axis, the abnormal seed point X * Copy again to get another auxiliary seed point X a , use the following formula to calculate the difference Δd: Δd=H / 2 Where H is the slope height; S45. For each auxiliary seed point X a The position of the slope is judged, and the points within the slope contour Ω are eliminated, and the remaining auxiliary seed points X a With the original seed point X as the base point, perform Voronoi subdivision again and delete the auxiliary seed point X a The corresponding polygon retains the polygon corresponding to the original seed point X; S46. Calculate the error E of the current polygon distribution new , compare its size relationship with the error E, if E new ≥E, the operation of moving the point is abandoned, the moved seed point is restored to its original position, and steps S41-S46 are repeated; if E new <E and E new >ε, where ε is the set error threshold, the operation of moving the point is saved and steps S41-S46 are repeated; if E new <E and E new ≤ε, continue the current operation.

5. The method for generating a soil-rock mixed slope material point method model according to claim 1, characterized in that: The specific contents of generating the block stone outline according to the outline of the polygonal domain in S5 are as follows: Randomly select N edges on the polygon m sampling points, N m According to the modeling accuracy requirements, take the centroid of the polygon as the origin, expand all the sampling points in the polar coordinate system, and then use the Fourier series to fit all the sampling points. Select N equally spaced points on the obtained fitting curve. n sampling points, as the block stone contour control points C, N n Determined according to the modeling accuracy requirements.

6. The method for generating a material point method model of a soil-rock mixed slope according to claim 1, characterized in that: The specific contents of scaling and adjusting the block stone outline according to the stone content R in S5 are as follows: Calculate the area of ​​the polygonal domain and scale the area of ​​the stone to the area of ​​the polygonal domain S C times, S C is the percentage of stone content R.

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