A method for generating material point model of soil-rock mixed slope

Abstract

The present invention discloses a method for generating a material point method model of a soil-rock mixed slope, which is used to simulate the mechanical behavior of a soil-rock mixed slope. The method comprises the following steps: first, randomly dividing the slope area to generate polygonal units that meet the target area and shape distribution; then, based on the shape contours of the polygonal units, generating random block contours through polar coordinate sampling and Fourier series fitting, and controlling the size of the block by adjusting the area ratio; finally, mapping the generated block contours to a material point array, calibrating the material points belonging to the block, and completing the pre-processing of the material point method calculation. The present invention can truly reflect the size, shape, and spatial distribution characteristics of the blocks in the soil-rock mixed slope, effectively improve the efficiency of block placement, avoid overlapping problems, and overcome the defects of the existing technology in the simplification of block shape and insufficient randomness of distribution. At the same time, it is suitable for the numerical simulation of large deformation problems, has high calculation accuracy and broad engineering application prospects.

Description

Technical Field

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

[0002] Soil-rock slopes are common in nature and engineering practice, and their stability is profoundly influenced by the interaction between soil and rock. As a key component of slopes, the randomness of rock size, shape, and spatial distribution plays a key role in the slope's mechanical properties. However, existing research and simulation methods have significant limitations in describing and analyzing the complexity of soil-rock slopes.

[0003] The shape of the boulders has a significant impact on the stability of the slope. Considering the diversity and complexity of boulders' shapes, most existing simulation methods often use idealized simplified models such as circles and ellipses to represent boulders, which cannot accurately reflect the shape characteristics and complex contact relationships of boulders in real slopes. In existing simulation methods, the generation and placement of boulders are mostly done one by one to prevent overlap between boulders. When it is necessary to generate large-scale boulders, the placement efficiency is extremely low, and it is difficult to meet the requirements of statistical control of characteristics such as gradation 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 existing methods, there is an urgent need for a soil-rock mixed slope modeling method that can efficiently generate soil-rock mixed slopes that meet the random characteristics of rock blocks and are 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 existing technology of over-simplified simulated stone shapes, low stone placement efficiency, and difficulty in handling large deformation simulation. By accurately controlling the size, shape, and position distribution of the stones, the present invention can provide a more realistic and comprehensive calculation model for slope instability analysis.

[0006] The object of the present invention is achieved like this:

[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 rock 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;

[0009] S2. Based on the slope profile Ω and the number of rocks N, use the Voronoi method to partition the slope into N polygonal domains using 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 within 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. Randomly move a seed point X 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. Based on the final polygonal domain, 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 according to the stone content R to obtain the coordinates C of all block stone control points within the entire slope;

[0013] S6. Generate an equidistant material point array P based on the slope profile Ω and the material point spacing h, and calibrate the rock material point P in the material point array P based on the rock 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, based on the slope profile Ω and the number of rocks N, the Voronoi subdivision method is used to subdivide the slope into N polygonal domains using N seed points X randomly distributed within the slope profile Ω. The specific contents are as follows:

[0015] S21. Randomly generate N scattered points within the slope contour domain Ω, 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 decomposition method;

[0017] S23. Each generated Voronoi polygon is judged one by one to determine whether each vertex is outside the slope contour Ω. If no vertex is outside the slope contour Ω, no processing is performed and the judgment of other polygons is continued. 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, with 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 distance to 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 within the current slope is obtained. 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 content of calculating the error E between the current distribution and the target distribution is as follows:

[0023] S31. Calculate the long side M of the minimum circumscribed rectangle M of each polygon L and 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 within 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 probability density distribution curve of the target stone slenderness ratio L AR The root mean square error EAR , take E A and E AR The larger value is recorded as the error E.

[0025] In S4, the operation of randomly moving a seed point X multiple times is performed to re-divide the polygonal domain within 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 random numbers in the interval [-I, I]. I is the average size of the polygonal domain within the slope. I is calculated using the following formula:

[0027]

[0028] Where S Ω is the area of ​​the slope profile Ω, and N is the number of boulders. Determine whether the adjusted seed point X coordinate is within the soil-rock mixed slope profile Ω. If so, continue the current operation. If not, 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 decomposition method;

[0030] S43. Each generated Voronoi polygon is judged one by one to determine whether each vertex is outside the slope contour Ω. If no vertex is outside the slope contour Ω, no processing is performed and the judgment of other polygons is continued. 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, with 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 distance to 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, then abandon the operation of moving the point, restore the moved seed point to its original position, and repeat steps S41-S46; 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, all sampling points are expanded on the polar coordinate system with the polygon centroid as the origin, and then all sampling points are fitted with the Fourier series. N is equidistantly selected on the obtained fitting curve. n Sampling points, as the 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 S times the area of ​​the polygonal domain 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 soil-rock mixed slopes 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 rock, overcoming the limitation of the traditional method of simplifying the rock shape into a regular geometric shape, so that the model can more realistically reflect the complex shape of the rock in the actual slope.

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

[0044] (4) This method directly maps the generated stone block contours 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 computational complexity, and significantly improving the computational 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 decomposition of the 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 by an embodiment of the present invention;

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

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

[0051] Figure 7 A schematic diagram of the final polygonal decomposition result of the soil-rock mixed slope geometric model provided by an embodiment of the present invention;

[0052] Figure 8Schematic 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] Figure 9 A schematic diagram of the xth polygonal outline and rock block outline control points of the soil-rock mixed slope geometric model provided by an embodiment of the present invention;

[0054] Figure 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] Figure 11 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] Figure 12 A schematic diagram of calibrating rocks in a material point array in a soil-rock mixed slope geometric model provided in an embodiment of the present invention;

[0057] Figure 13 The horizontal displacement cloud map is obtained by importing the soil-rock mixed slope geometric model provided in the embodiment of the present invention into the material point method program for calculation. DETAILED DESCRIPTION

[0058] The present invention will be further described below with reference to the accompanying drawings and examples.

[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, rock content R, number of rocks N, and rock 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 is 20 meters. 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. Based on the slope profile Ω and the number of rocks N, the slope is subdivided into N polygonal domains using the Voronoi subdivision method using N seed points X randomly distributed within the slope profile Ω. Step 2 specifically includes:

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

[0062] S22. Using the N generated scattered points as seed points X, generate N Voronoi polygons using the Voronoi decomposition method. After the initial decomposition is completed, since the principle of Voronoi decomposition is based on the perpendicular bisector 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 slope contour boundary, requiring 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 no vertex is outside the slope contour Ω, no processing is performed and the judgment of other polygons is continued. 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 through judgment.

[0064] S24. Calculate each abnormal seed point X in turn * The distance to each edge Γ of the slope profile Ω, with 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 distance to 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 symmetrical based on the slope contour boundary, the polygons obtained this time are also symmetrical based on the boundary. Figure 4 As shown in the figure, the edge of the polygon coincides with the slope contour, avoiding the phenomenon of the polygon not being closed and the polygon vertex exceeding the slope contour boundary 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. Then, the polygon subdivision based on the original seed point can be obtained within the slope contour domain. 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 within 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 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 within 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 probability density distribution curve of the target stone slenderness ratio 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. Repeatedly randomly move a seed point X to re-divide the polygonal domain within the slope 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 random numbers in the interval [-I, I]. I is the average size of the polygonal domain within the slope. I is calculated using the following formula:

[0073]

[0074] Where S Ω The area of ​​the slope contour Ω and N is the number of boulders, so that the moved seed point is randomly moved within an average unit size area; determine whether the adjusted X coordinate of the seed point is within the soil-rock mixed slope contour Ω. If it is, continue the current operation; if it is outside the slope contour Ω, regenerate random numbers Δx and Δy until the adjusted X coordinate of the seed point is within the soil-rock mixed slope contour Ω; ensure that the seed point remains within the slope after moving to prevent the polygon obtained from the 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 no vertex is outside the slope contour Ω, no processing is performed and the judgment of other polygons is continued. 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, with 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 distance to 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, indicating that the current operation of moving the seed point fails to make the size and shape of the polygon in the entire slope closer to the target distribution, 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 the figure, it shows that the current operation of moving the seed point can make the similarity between the size and shape of the polygon in the entire slope and the target distribution less 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 domains finally segmented, a rock outline is generated within each polygonal domain according to the contour of the polygonal domain. The rock outline is scaled according to the rock content R to obtain the coordinates C of all rock outline control points within 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, all sampling points are expanded in the polar coordinate system with the polygon centroid as the origin, and then all sampling points are fitted with the Fourier series to generate a smooth block stone outline based on the polygon outline. Figure 9 As shown, N is selected equidistantly on the obtained fitting curve. n Sampling points, equidistant selection prevents excessive memory usage and excessive smoothness of the generated stone blocks, 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 Figure 10 As shown, the area of ​​the stone is scaled to the area of ​​the polygon domain S C times, S C The percentage of the stone content R is used. In this embodiment, the stone area is reduced to 30% of the polygon, so that the proportion of the stone area in the entire slope is controlled to be consistent with the set stone content. Figure 11 As shown in the figure, 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. In this embodiment, the material point spacing is 0.25m. Figure 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. Figure 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 pattern 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 enhances the computational 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. Determine the slope profile based on the slope's geometric shape and component characteristics , slope height H, stone content R, number of boulders N, probability density distribution curve of boulders area , probability density distribution curve of stone slenderness ratio , error threshold and the material point spacing h; S2. According to the slope contour and the number of rocks N, using the Voronoi method to pass N on the slope contour The randomly distributed seed points X divide the slope into N polygonal domains; S3. Based on the area probability density distribution curve of all polygonal domains within the current slope , Slenderness ratio probability density distribution curve , target rock area probability density distribution curve Probability density distribution curve of stone slenderness ratio , calculate the error between the current distribution and the target distribution ; S4. Repeatedly move a seed point X randomly to re-divide the polygonal domain within the slope until the error Less than the error threshold ; S5. Based on the final polygonal domain, a stone contour is generated within each polygonal domain according to the contour of the polygonal domain. The stone contour is scaled according to the stone content R to obtain the coordinates C of all stone contour control points within the entire slope. The specific contents of generating the stone outline according to the outline of the polygon domain are as follows: randomly select sampling points, According to the modeling accuracy requirements, all sampling points are expanded on the polar coordinate system with the polygon centroid as the origin, and then all sampling points are fitted with the Fourier series. The equidistant selection is made on the obtained fitting curve. Sampling points, as the stone contour control point C, Determined according to modeling accuracy requirements; S6. According to the slope contour And the material point spacing h, generate an equidistant material point array P, and mark the block stone material point in the material point array P according to the block stone contour control point coordinates C , the material points that are not calibrated are recorded as soil material points , and the material point method model of soil-rock mixed slope is obtained.

2. The method for generating a soil-rock mixed slope material point method model according to claim 1, characterized in that: S2 based on the slope profile and the number of rocks N, using the Voronoi method to pass N on the slope contour The specific content of dividing the slope into N polygonal domains by randomly distributed seed points X is as follows: S21. On the slope profile N scattered points are randomly generated in the domain, where N is the number of stones; S22. Using the generated N scattered points as seed points X, generate N Voronoi polygons using the Voronoi decomposition method. S23. Check each generated Voronoi polygon one by one to see if each vertex is on the slope contour. In addition, if each vertex is not on the slope contour If there is at least one vertex on the slope contour, no further processing is done and the judgment of other polygons is continued. If the polygon is not included, the seed point X corresponding to the polygon is marked as an abnormal seed point. ; S24. Calculate each abnormal seed point in turn To slope profile Each edge The distance to the nearest edge As the symmetry axis, the abnormal seed point Copy to get an auxiliary seed point ; If the difference between the second closest distance and the closest distance is not greater than , then the second closest edge As the symmetry axis, the abnormal seed point Copy again to get another auxiliary seed point , use the following formula to calculate the difference Perform the calculation: Where H is the slope height; S25. For each auxiliary seed point The position of the slope is judged and the slope contour is eliminated. Points within, with the remaining auxiliary seed points With the original seed point X as the base point, perform Voronoi subdivision again and delete the auxiliary seed point The corresponding polygon retains the polygon corresponding to the original seed point X.

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

4. The method for generating a soil-rock mixed slope material point method model according to claim 1, characterized in that: In S4, a seed point X is randomly moved multiple times to re-divide the polygonal domain within the slope until the error E is less than the error threshold. The specific contents are as follows: S41. Randomly select a seed point X and set the coordinates of the seed point X 、 Adjusted to, 、 , and All are value ranges The random number in the slope is I, which is the average size of the polygonal domain in the slope. I is calculated using the following formula: Where, Slope profile The area of ​​​​the soil-rock mixed slope is determined by the adjusted seed point X coordinate. If it is within the slope contour If it is within the slope contour, continue the current operation; Otherwise, regenerate the random number and , until the adjusted seed point X coordinate is located at the soil-rock mixed slope contour within; S42. Based on the seed point X, generate N Voronoi polygons using the Voronoi mesh method; S43. Check each generated Voronoi polygon one by one to see if each vertex is on the slope contour. In addition, if each vertex is not on the slope contour If there is at least one vertex on the slope contour, no further processing is done and the judgment of other polygons is continued. If the polygon is not included, the seed point X corresponding to the polygon is marked as an abnormal seed point. ; S44. Calculate each abnormal seed point in turn To slope profile Each edge The distance to the nearest edge As the symmetry axis, the abnormal seed point Copy to get an auxiliary seed point ; If the difference between the second closest distance and the closest distance is not greater than , then the second closest edge As the symmetry axis, the abnormal seed point Copy again to get another auxiliary seed point , use the following formula to calculate the difference Perform the calculation: Where H is the slope height; S45. For each auxiliary seed point The position of the slope is judged and the slope contour is eliminated. Points within, with the remaining auxiliary seed points With the original seed point X as the base point, perform Voronoi subdivision again and delete the auxiliary seed point The corresponding polygon retains the polygon corresponding to the original seed point X; S46. Calculate the error of the current polygon distribution , compare its size relationship with the error E, if , then abandon the operation of moving the point, restore the moved seed point to its original position, and repeat steps S41-S46; if , If the error threshold is set, the operation of moving the point is saved and steps S41-S46 are repeated; , then 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 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. times, is the percentage of stone content R.

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