Slope angle optimization method of surface mine high slope based on differential evolution algorithm

Abstract

The invention discloses a slope angle optimization method of a surface mine high slope based on a differential evolution algorithm. The slope angle optimization method comprises the following steps: (1) counting a stable slope angle range as an initial population through geological survey; (2) setting an iteration target value N according to the slope height H; (3) selecting a mutation factor B and a cross factor C; (4) performing variation and crossover in the initial range to generate a new scheme; (5) establishing a stability model by using Slide software, calculating safety coefficients of different slope angles, and constructing a mapping set; (6) verifying whether the new scheme meets the constraint condition, and if not, returning to the step (4); (7) comparing new and old schemes through a fitness function, and reserving better schemes; and (8) iterating until conditions are met, and outputting an optimal slope angle scheme. According to the method, the safety and economy of strip mine slope design are enhanced.

Description

Technical Field

[0001] The invention belongs to the field of open-pit mine mining slope design and relates to a slope angle optimization method for high slopes in open-pit mines based on a differential evolution algorithm. Background Art

[0002] Optimizing slope angles in open-pit mines is a crucial technical approach for ensuring energy and resource security. Currently, my country positions mineral resources as a key material foundation for modernization and has explicitly called for strengthening strategic mineral security. Slope angle optimization directly impacts mining efficiency and resource intensiveness. According to statistical analysis, approximately 50 open-pit mines in my country have designed slopes exceeding 500 meters, posing significant pressure on open-pit mine safety in the future. Unstable slopes or those with potential landslide hazards account for approximately 15% to 20% of the total slope volume in large and medium-sized open-pit mines in my country, with this percentage reaching as high as 30% in some mines. In landslide cases, the ratio of overall slopes to step slopes is approximately 1:15, meaning that the majority of slope failures occur on step slopes or combined step slopes. Open-pit mine slope design is a systematic and dynamic process that considers both safety and economic efficiency. Current slope design methods often focus on analyzing the overall slope angle, reflecting the synergy between safety and economic efficiency. However, for large-scale open-pit mines, especially those with super-high slopes, there are many step slopes and combined step slopes, and safety issues are more prominent. In the future, the optimization design of open-pit mines with super-high slopes needs to comprehensively consider the overall slope, combined step slope, and step slope design to ensure the coordination of the safety of each level of slopes. The differential evolution algorithm is an artificial intelligence algorithm with the advantages of strong global search capabilities, simple parameter settings, strong robustness, and high computational efficiency. It can improve the scientificity and efficiency of large-scale mine slope angle optimization and solve the problem of super-high slope optimization design in large-scale open-pit mines. Therefore, it is necessary to propose a slope angle optimization method for super-high slopes in open-pit mines based on the differential evolution algorithm to achieve the unity of safety and efficient resource mining of super-high multi-level slopes in large-scale open-pit mines. Summary of the Invention

[0003] In order to overcome the shortcomings of the existing technology, the present invention provides a slope angle optimization method for high slopes in open-pit mines based on the differential evolution algorithm. It can avoid the problems of local optimum, low solution efficiency and low accuracy in the optimization design of slope angles in open-pit mines, achieve the coordination of the overall slope, combined step slope and step slope stability of the high slope, and solve the problem of high slope optimization design in large open-pit mines.

[0004] The technical solution adopted by the present invention to solve its technical problem is:

[0005] A slope angle optimization method for high slopes in open-pit mines based on a differential evolution algorithm comprises the following steps:

[0006] (1) Select large open-pit mines at home and abroad for engineering geological surveys, and statistically analyze the slope angles of overall slopes, combined bench slopes, and bench slopes that can maintain stability, so as to provide an initial population for the optimization of the slope angle of ultra-high slopes, that is, the initial range of reasonable slope angles;

[0007] (2) Use Excel software to calculate the end condition of the program, that is, the target value N of the number of iterations, according to the height H of the designed slope of the open-pit mine, as shown in formula ①;

[0008] N = roundup(H / 10) ①

[0009] (3) Select the mutation factor B and the crossover factor C according to the complexity of the slope geological conditions of the open-pit mine;

[0010] (4) Within the initial range of reasonable slope angles of the open-pit mine, select an initial design scheme of the slope angle for differential evolution operation. The process is as follows: first mutate the old scheme according to the mutation factor B, and then cross the old scheme and the mutated scheme according to the crossover factor C to obtain a new scheme;

[0011] (5) Use the geometric and mechanical parameters of the multi-level slope rock mass and joints of the open-pit mine to construct a slope stability analysis model, and use slide software to calculate the safety factors of the overall slope, combined bench slope, and bench slope at different slope angles respectively, and construct a mapping set of the slope angle and safety factor of the multi-level slope;

[0012] (6) Combine the mapping set in step (5) to judge whether the new scheme of the slope angle of the open-pit mine obtained in step (4) meets the constraint conditions, and make the following judgments:

[0013] If it is, then retain the new scheme of the slope angle and proceed to the next step;

[0014] If not, then discard the new scheme, return to step (4), and continue the differential evolution operation of the slope angle scheme;

[0015] (7) Construct a fitness function, calculate the fitness values of the new and old schemes of the slope angle, and make the following comparisons:

[0016] If f(new) < f(old), then the new scheme enters the next generation;

[0017] If f(new) ≥ f(old), then the old scheme enters the next generation;

[0018] (8) Whether the new or old scheme enters the next generation, the number of iterations increases by 1, and at the same time, return to the iteration number judgment condition until the program ends, and generate the optimal scheme of the slope angle of the ultra-high slope of the open-pit mine.

[0019] Furthermore, in step (1), when conducting engineering geological surveys of open-pit mine slopes, it is necessary to conduct hierarchical analysis of the overall slope, combined step slope, and step slope. According to the "double matching" principle, the slope rock mass and joints that match the slope scale are selected for analysis. It is also necessary to conduct statistical analysis of slopes of different levels according to the slope height.

[0020] Furthermore, in step (3), the values ​​of mutation factor B and variation factor C need to be determined according to the complexity of the slope rock mass and joints. The value range of mutation factor B is 0.4 to 0.9, and the value range of variation factor C is 0.1 to 1.

[0021] Furthermore, in step (5), when calculating the safety factors of various slopes at different slope angles, the range of slope angles must cover the reasonable range of slope angles obtained from engineering geological surveys.

[0022] In step (6), the constraints include platform parameter requirements and safety factor requirements, as follows:

[0023] ① The step slope height is fixed at 15m, the working platform width is ≥12m, and the transport platform width is ≥16m;

[0024] ②One combined step slope contains 3 to 4 step slopes;

[0025] ③ Overall slope safety factor F 总 ≥1.3, safety factor F of combined step slope 组 ≥1.2, step slope safety factor F 台 ≥1.1.

[0026] In step (7), the fitness function calculation formula is as follows:

[0027]

[0028] The beneficial effects of the present invention are mainly manifested in the following aspects: the method of the present invention is applicable to solving the safety problems of a large number of stepped slopes and combined stepped slopes; it comprehensively considers the optimization design of the overall slope, combined stepped slope and stepped slope, and can ensure the synergy of the safety of slopes at all levels; the differential evolution algorithm is an artificial intelligence algorithm with the advantages of strong global search capabilities, simple parameter setting, strong robustness, and high computational efficiency. It can improve the scientificity and efficiency of the optimization of slope angles in large mines and solve the problem of optimizing the super-high slopes in large open-pit mines. It is of great significance for reducing investment in the slopes of large open-pit mines, lowering production costs, and ensuring mining safety; at the same time, it is easy to operate, has high computational efficiency, and a wide range of applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1This is a flow chart of the slope angle optimization method for super-high slopes in open-pit mines based on differential evolution algorithm.

[0030] Figure 2 Schematic diagram of a slope of the Yunnan Beiya Gold Mine according to an embodiment. DETAILED DESCRIPTION

[0031] The present invention will be further described below with reference to the accompanying drawings.

[0032] Reference Figure 1 A slope angle optimization method for high slopes in open-pit mines based on differential evolution algorithm includes the following steps:

[0033] (1) Select large-scale open-pit mines at home and abroad for engineering geological surveys, and statistically analyze the overall slope, combined step slope, and step slope angles that can maintain stability, to provide an initial population for optimizing the slope angle of super-high slopes, that is, the initial range of reasonable slope angles;

[0034] When conducting engineering geological surveys on open-pit mine slopes, it is necessary to conduct graded analysis on the overall slope, combined step slope, and step slope. According to the "double matching" principle, the slope rock mass and joints that match the slope scale are selected for analysis. It is also necessary to conduct statistical analysis on slopes of different levels according to the slope height.

[0035] (2) Using Excel software, calculate the program end condition, i.e., the target value N of the number of iterations, according to the height H of the designed slope of the open-pit mine, as shown in formula ①;

[0036] N=roundup(H / 10) ①

[0037] (3) Select the mutation factor B and cross factor C according to the complexity of the geological conditions of the open-pit mine slope. The values ​​of mutation factor B and variation factor C need to be determined according to the complexity of the slope rock mass and joints. The value range of mutation factor B is 0.4-0.9, and the value range of variation factor C is 0.1-1.

[0038] (4) Within the initial range of reasonable slope angles for open-pit mines, an initial slope angle design scheme is selected for differential evolution. The process is as follows: first, the old scheme is mutated according to the mutation factor B, and then the old scheme and the mutated scheme are cross-processed according to the crossover factor C to obtain a new scheme.

[0039] (5) Using the geometric and mechanical parameters of the rock mass and joints of the multi-level slope of the open-pit mine, a slope stability analysis model was constructed. The safety factors of the overall slope, combined step slope, and step slope at different slope angles were calculated using Slide software, and a mapping set of slope angles and safety factors of the multi-level slope was constructed.

[0040] When calculating the safety factors of slopes at different slope angles, the range of slope angles should cover the reasonable slope angle range obtained from the engineering geological survey.

[0041] (6) Combining the mapping set in step (5), determine whether the new open-pit mine slope angle plan obtained in step (4) meets the constraint conditions, where the constraint conditions include platform parameter requirements and safety factor requirements, as follows:

[0042] ① The height of the bench slope is fixed at 15m, the width of the working platform ≥ 12m, and the width of the transportation platform ≥ 16m;

[0043] ② One combined bench slope contains 3 - 4 bench slopes;

[0044] ③ The overall slope safety factor F 总 ≥ 1.3, the safety factor of the combined bench slope F 组 ≥ 1.2, the safety factor of the bench slope F 台 ≥ 1.1;

[0045] Make the following judgment:

[0046] If so, retain the new slope angle plan and proceed to the next step;

[0047] If not, discard the new plan, return to step (4), and continue the differential evolution operation of the slope angle plan;

[0048] (7) Construct a fitness function, calculate the fitness values of the new and old slope angle plans, and the calculation formula of the fitness function is as follows: <00,001,11>

[0049]

[0050] And make the following comparison:

[0051] If f(new) < f(old), the new plan enters the next generation;

[0052] If f(new) ≥ f(old), the old plan enters the next generation;

[0053] (8) Whether the new plan or the old plan enters the next generation, the iteration count increases by 1, and at the same time, return the iteration count judgment condition until the program ends, generating the optimal slope angle plan for the open-pit mine's ultra-high slope.

[0054] This embodiment Figure 2 [[ID= 50]]As shown, taking a certain slope of the Beiya Gold Mine in Yunnan as an example, the total height of the slope is 180 meters, including 3 combined bench slopes, see combined bench slope 1, combined bench slope 2, and combined bench slope 3 in the figure; each combined bench slope contains 3 bench slopes, and the height of the bench slope is about 20m. The iteration count is 18 times.

[0055] Requirements: Optimize the slope angle design of this slope based on geological conditions.

[0056] Based on engineering geological surveys of large open-pit mines at home and abroad, a statistical analysis of the relationship between slope angle and safety factor was conducted. The reasonable slope angle ranges for maintaining self-stabilization for overall slopes, combined step slopes, and step slopes were determined to be: overall slope (25° to 55°), combined step slope (35° to 65°), and step slope (45° to 75°). The relationship between slope angle and safety factor for each slope level was calculated using SLIDE software, with slope angle values ​​taken at 0.5° intervals. The calculation results are shown in Table 1, forming a mapping relationship between slope angle and safety factor for each slope level.

[0057] Table 1 shows the settlement results of combined step 1;

[0058]

[0059]

[0060] Table 2 shows the settlement results of combined step 2;

[0061]

[0062] Table 3 shows the settlement results of combination step 3;

[0063]

[0064]

[0065] Within the reasonable slope angle range of each level of slope, a group of slope angles is selected to form a slope design scheme as the initial slope scheme of the slope angle optimization design program.

[0066] Based on the initial slope scheme, the evolutionary differential algorithm is used to generate a new slope angle scheme. The mapping set in Table 1 is called to calculate the safety factor corresponding to the new slope angle scheme. The constraint conditions are used for judgment, and the new slope angle schemes of each level of slopes with composite constraint conditions are retained.

[0067] The fitness function is used to calculate the fitness value of the new slope angle scheme, and the fitness values ​​of the new slope angle scheme and the old slope angle scheme are compared to select the slope angle scheme to enter the next round.

[0068] After 18 iterations, the optimal solution for the slope angle is obtained. The details are as follows:

[0069] The slope angles of the steps from top to bottom are: 65, 65, 65, 68, 68, 68, 71, 71, 71;

[0070] The combined step slope angles are: 54, 56, 58;

[0071] The overall slope angle is: 47.5°;

[0072] The solution of this embodiment ensures the safety of the overall slope, combined step slope, and step slope. It also ensures that the safety factors of the overall slope, combined step slope, and step slope are similar, avoiding the problem of the overall slope being safer and the step slope being unsafe. Based on the accurate calculation of the slope safety factor, it ensures that the safety reserves of slopes at all levels are not wasted, thus ensuring both safety and resource waste. The slope angle optimization design program is implemented using Python programming, which has a fast calculation speed and is highly efficient for slope angle optimization design in large open-pit mines with large data volumes. It is applicable to the slopes of various large, medium, and small open-pit mines and has a wide range of applications.

[0073] The embodiments of this specification are merely examples of implementations of the invention and are provided for illustrative purposes only. The scope of protection of the present invention should not be considered limited to the specific embodiments described in these embodiments. The scope of protection of the present invention also extends to equivalent technical means that can be conceived by a person of ordinary skill in the art based on the invention.

Claims

1. A slope angle optimization method for high slopes in open-pit mines based on differential evolution algorithm, characterized in that: It includes the following steps: (1) Select large domestic and foreign open-pit mines for engineering geological surveys, statistically analyze the slope angles of overall slopes, combined bench slopes, and bench slopes that can maintain stability, and provide an initial population for the optimization of the slope angle of ultra-high slopes, that is, the initial range of reasonable slope angles; (2) Use Excel software to calculate the end condition of the program, that is, the target value N of the number of iterations, according to the height H of the designed slope of the open-pit mine, as shown in formula ①; N = roundup(H / 10) ① (3) Select the mutation factor B and the crossover factor C according to the complexity of the slope geological conditions of the open-pit mine; (4) Within the initial range of reasonable slope angles of the open-pit mine, select an initial design scheme of the slope angle for differential evolution operation. The process is as follows: first mutate the old scheme according to the mutation factor B, and then cross the old scheme and the mutated scheme according to the crossover factor C to obtain a new scheme; (5) Use the geometric and mechanical parameters of the multi-level slope rock mass and joints of the open-pit mine to construct a slope stability analysis model, and use slide software to calculate the safety factors of the overall slope, combined bench slope, and bench slope at different slope angles respectively, and construct a mapping set of the slope angle and safety factor of the multi-level slope; (6) Combine the mapping set in step (5) to judge whether the new scheme of the slope angle of the open-pit mine obtained in step (4) meets the constraint conditions, and make the following judgments: If so, retain the new scheme of the slope angle and proceed to the next step; If not, discard the new scheme, return to step (4), and continue the differential evolution operation of the slope angle scheme; (7) Construct a fitness function, calculate the fitness values of the new and old schemes of the slope angle, and make the following comparisons: If f(new) < f(old), the new scheme enters the next generation; If f(new) ≥ f(old), the old scheme enters the next generation; (8) Whether the new or old scheme enters the next generation, the number of iterations increases by 1, and at the same time return to the iteration number judgment condition until the program ends, and generate the optimal scheme of the slope angle of the ultra-high slope of the open-pit mine.

2. The slope angle optimization method for high slopes in open-pit mines based on differential evolution algorithm according to claim 1, characterized in that: In step (1), when conducting the engineering geological survey of the open-pit mine slope, it is necessary to conduct hierarchical analysis on the overall slope, combined bench slope, and bench slope, and select slope rock masses and joints that match the slope scale for analysis according to the "double matching" principle; it is also necessary to conduct statistical analysis on different levels of slopes according to the slope height.

3. The slope angle optimization method for high slopes in open-pit mines based on differential evolution algorithm according to claim 1 or 2, characterized in that: In step (3), the values of the mutation factor B and the variation factor C need to be determined according to the complexity of the slope rock mass and joints. The value range of the mutation factor B is 0.4 - 0.9, and the value range of the variation factor C is 0.1 - 1.

4. The slope angle optimization method for high slopes in open-pit mines based on differential evolution algorithm according to claim 1 or 2, characterized in that: In step (5), when calculating the safety factors of each level of slope at different slope angles, the range of the slope angle should cover the range of reasonable slope angles obtained from the engineering geological survey.

5. The slope angle optimization method for high slopes in open-pit mines based on differential evolution algorithm according to claim 1 or 2, characterized in that: In step (6), the constraint conditions include platform parameter requirements and safety factor requirements, as follows: ① The height of the bench slope is fixed at 15m, the width of the working platform ≥ 12m, and the width of the transportation platform ≥ 16m; ③ Overall slope safety factor F 总 ≥1.3, safety factor F of combined step slope 组 ≥1.2, step slope safety factor F 台 ≥1.

1.

6. The slope angle optimization method for high slopes in open-pit mines based on differential evolution algorithm according to claim 5, characterized in that: ② One combined bench slope includes 3 - 4 bench slopes; In step (7), the calculation formula of the fitness function is as follows:

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