A cost optimization calculation method for anchoring and supporting of a final slope of an open pit mine
By constructing mathematical models of the economic impact coefficient of anchoring units and the slope anchoring effect coefficient, and combining optimization algorithms and surrogate models, the problem of high cost in open-pit mine slope anchoring design was solved, achieving synergistic optimization of safety and cost, and significantly reducing support costs.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- 新疆葱岭能源有限公司
- Filing Date
- 2026-03-09
- Publication Date
- 2026-06-12
AI Technical Summary
The lack of existing optimization methods that directly and quantitatively link slope stability requirements with anchoring engineering costs leads to overly conservative open-pit mine slope anchoring designs, resulting in high engineering costs.
Mathematical models for the economic impact coefficient of anchoring units and the anchoring effect coefficient of slopes are constructed. By combining optimization algorithms and surrogate models, the anchoring parameters are systematically and quantitatively optimized. By defining the economic impact coefficient and the anchoring effect coefficient, parameters that are difficult to compare directly are transformed into quantifiable and comparable indicators, thereby achieving synergistic optimization of safety and cost.
It significantly reduces support costs while ensuring slope stability, realizing a shift from considering costs after ensuring safety. It is characterized by systematicness, quantification, and high efficiency, and can find more economical anchoring solutions than empirical designs.
Smart Images
Figure CN122199084A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the fields of open-pit mining slope engineering and engineering cost technology, and in particular to a method for optimizing the calculation of anchorage support costs for the final slope of an open-pit mine. Background Technology
[0002] As open-pit mining extends to deeper areas, the geological conditions of the final slope become increasingly complex, posing greater challenges to the safety requirements and cost control of anchoring support. Forming a stable and safe final slope is crucial during open-pit mining. Anchoring (including anchor bolts and cables) is one of the most commonly used techniques for reinforcing final slopes. Currently, slope anchoring design mainly relies on methods such as limit equilibrium and numerical simulation to determine the safety factor, and then design anchoring parameters (such as anchor bolt length, diameter, spacing, and prestress). However, this safety-first design approach often neglects economic efficiency, potentially leading to overly conservative anchoring schemes and high engineering costs.
[0003] Current technologies lack an optimization method that directly and quantitatively links slope stability requirements with anchoring costs. Designers typically conduct only a rough cost comparison of a few options after meeting safety standards, making it difficult to quickly find the optimal solution for a "safety-economy" balance from a vast array of possible parameter combinations. This is primarily because the relationship between the impact of anchoring parameters on stability (i.e., the "anchoring effect") and their impact on cost (i.e., the "economic impact") is complex and difficult to describe with a simple linear model. This disconnect between design and cost analysis further exacerbates cost waste in challenging projects like deep open-pit mine slope anchoring.
[0004] Therefore, there is an urgent need for a systematic and quantitative optimization method that can significantly reduce the anchoring support cost of the final slope while ensuring slope safety. Summary of the Invention
[0005] To address the aforementioned shortcomings in the existing technology, this application provides a method for optimizing the calculation of anchorage support costs for the final slope of an open-pit mine, which solves the problem that the slope stability requirements and anchorage engineering costs are difficult to describe using a simple linear model in the existing technology.
[0006] To achieve the aforementioned objectives, the technical solution adopted in this application is as follows: This application proposes a method for optimizing the calculation of anchorage support costs for the final slope of an open-pit mine, including: S1: Determine the anchorage design variables and their value ranges to form the parameter space; S2: Based on the anchorage design variables, construct an economic impact coefficient model for anchorage units based on the direct cost of anchorage materials and construction per unit support area, and obtain the economic impact coefficient of anchorage units. S3: Based on the relative improvement rate of the slope safety factor after reinforcement by anchoring parameters, construct a slope anchoring effect coefficient model to obtain the slope anchoring effect coefficient. S4: Based on the parameter space, establish the mathematical relationship between the economic impact coefficient of the anchoring unit, the slope anchoring effect coefficient and the anchoring design variables, and obtain the optimization problem with minimizing the economic impact coefficient of the anchoring unit as the objective and satisfying the slope anchoring effect coefficient corresponding to the target safety factor as the constraint. S5: Solve the optimization problem using optimization algorithms to obtain the optimal combination of anchorage parameters and the corresponding minimized economic impact coefficient of the anchorage unit under the slope safety requirements; S6: Verify the optimal combination of anchoring parameters and output the economic impact coefficient of the anchoring unit and the slope anchoring effect coefficient corresponding to the optimal combination of anchoring parameters.
[0007] The beneficial effects of the above scheme are: it places economy and safety within a unified mathematical model framework, realizing the transformation from considering cost after ensuring safety to synergistic optimization of safety and cost, and can significantly reduce support costs while ensuring slope stability. It has the characteristics of being systematic, quantitative and efficient.
[0008] Furthermore, the anchoring design variables include at least the length, diameter, prestress, lateral spacing, and longitudinal spacing of the anchoring unit, wherein the anchoring unit is an anchor rod, anchor cable, or soil nail.
[0009] The advantages of the above scheme are: the method framework is applicable to different geological conditions, different slope geometries, and different types of anchoring components (anchor rods, anchor cables, soil nails, etc.). Only the corresponding stability analysis model and cost calculation parameters need to be adjusted, making it highly versatile.
[0010] Furthermore, the economic impact coefficient model for the anchoring unit is as follows:
[0011]
[0012]
[0013]
[0014] in, The economic impact coefficient of the anchoring unit. This is the unit price of the grouting material. For single anchor grouting volume, The diameter of the borehole. For anchorage length, This refers to the unit price of steel. The weight of a single anchor steel piece. For the density of steel, The cross-sectional area of the steel in the anchoring unit. This is the unit price for the comprehensive installation of a single anchor. This is the construction cost coefficient per unit length. The aperture influence coefficient is... The influence coefficient of tension force. For prestressing, This is a fixed cost item. and These are the horizontal spacing and the vertical spacing, respectively.
[0015] The beneficial effects of the above scheme are: by defining the economic impact coefficient, anchoring parameters that are difficult to compare directly are transformed into quantifiable and comparable indicators, making the decision-making process more scientific and intuitive.
[0016] Furthermore, the slope anchorage effect coefficient model is as follows:
[0017] in, Anchorage design variables The corresponding slope anchorage effect coefficient, The safety factor for the unreinforced slope. To adopt anchorage design variables Safety factor of the reinforced slope.
[0018] The beneficial effects of the above scheme are: by using the anchoring effect coefficient, anchoring parameters that are difficult to compare directly are transformed into quantifiable and comparable indicators, making the decision-making process more scientific and intuitive.
[0019] Furthermore, the slope safety factor of the unreinforced slope or the slope safety factor of the reinforced slope is calculated using a slope stability analysis model, which includes the limit equilibrium method or a numerical analysis method based on strength reduction.
[0020] Furthermore, the numerical analysis method based on intensity reduction includes: A1: Establish a finite element model including slope geometry, mesh, material constitutive model and initial strength parameters, wherein the initial strength parameters include at least cohesion, internal friction angle and unit weight; A2: Apply gravity load to the finite element model and perform initial stress equilibrium calculation to obtain a stable initial stress state; A3: Establish structural elements of anchor bolts / anchor cables in the finite element model, set material properties and interactions with the soil, and apply prestress to the structural elements; A4: Based on the initial stress state and the structural elements after prestressing, strength reduction factors are defined respectively, and the soil strength parameters are reduced in each calculation step. The reduction calculation formula is as follows:
[0021]
[0022] in, The reduced cohesion, This is the reduced internal friction angle. The initial cohesion, The initial internal friction angle, This is the strength reduction factor; A5: Substitute the reduced strength parameters into the finite element model for finite element calculation, and gradually increase the strength reduction factor. Based on the calculation results, determine whether the instability criteria are met, and obtain the slope safety factor of the unreinforced slope and the slope safety factor of the reinforced slope.
[0023] The beneficial effects of the above scheme are: obtaining the slope safety factor of the unreinforced slope and the slope safety factor of the reinforced slope through the numerical analysis method based on strength reduction helps to obtain the slope anchorage effect coefficient and reduces the computational complexity.
[0024] Furthermore, the instability criteria include finite element calculation non-convergence, inability to find an equilibrium solution, complete penetration of the plastic strain zone on the sliding surface, and abrupt displacement of characteristic points at the toe or crest of the slope.
[0025] The beneficial effect of the above scheme is that it improves the accuracy of judgment by using multiple instability criteria to determine whether the slope is unstable.
[0026] Further, S4 includes: S401: In the parameter space, multiple sample points are generated using the Latin hypercube sampling method; S402: Calculate the economic impact coefficient of the anchoring unit and the slope anchoring effect coefficient for each sample point to obtain the dataset; S403: Using the anchorage design variables of the sample points as input and the corresponding slope anchorage effect coefficient as output, a regression model is trained using Gaussian process regression, multinomial regression, or artificial neural network methods to obtain a surrogate model for approximating the slope anchorage effect coefficient.
[0027]
[0028] in, A proxy model for the slope anchorage effect coefficient. Anchorage design variables The corresponding slope anchorage effect coefficient; S404: Determine the target value of the slope design safety factor, and based on the target value of the slope design safety factor, the surrogate model, and the economic impact coefficient of the anchoring unit, obtain an optimization problem with the objective of minimizing the economic impact coefficient of the anchoring unit and the constraint of satisfying the slope anchoring effect coefficient corresponding to the target safety factor. The expression for the constraint of satisfying the slope anchoring effect coefficient corresponding to the target safety factor is as follows:
[0029]
[0030] in, For the target safety factor, The target value for the safety factor is designed for the slope.
[0031] The advantages of the above scheme are: by using a surrogate model to approximate complex stability calculations and combining it with intelligent optimization algorithms, the optimal solution can be quickly located in a wide parameter space, avoiding the high time consumption and limitations of traditional trial-and-error methods.
[0032] Furthermore, the optimization algorithm is a sequential quadratic programming algorithm, a genetic algorithm, or a particle swarm optimization algorithm.
[0033] The beneficial effects of the above scheme are: intelligent optimization algorithms can quickly locate the optimal solution in a wide parameter space, avoiding the high time consumption and limitations of traditional trial and error methods.
[0034] Further, S6 includes: S601: Based on the optimal combination of anchorage parameters output by the optimization algorithm, a high-precision slope anchorage model is reconstructed in the selected professional slope stability analysis software. S602: In the high-precision slope anchorage model, the strength reduction principle is adopted to perform a complete strength reduction analysis, output the verification safety factor of the high-precision slope anchorage model when it becomes unstable, and calculate the economic impact coefficient of the anchorage unit corresponding to the optimal anchorage parameter combination corresponding to the verification safety factor. S603: Based on the economic impact coefficient of the anchoring unit and the verification safety coefficient, determine whether the safety coefficient is not less than the target safety coefficient and whether the economic impact coefficient of the anchoring unit is consistent with the output of the optimization algorithm; S604: Outputs the economic impact coefficient of the anchoring unit and the slope anchoring effect coefficient corresponding to the optimal anchoring parameter combination that satisfies the judgment.
[0035] The beneficial effects of the above scheme are: to verify the authenticity and reliability of the optimization results, independent verification is carried out to ensure that the optimal combination of anchoring parameters can save costs and improve economic efficiency while ensuring slope safety in complex geological and environmental conditions.
[0036] The beneficial effects of this application are: This application provides a method for optimizing the cost of anchorage support for the final slope of an open-pit mine. It places economy and safety within a unified mathematical model framework, shifting from considering cost only after ensuring safety to a synergistic optimization of safety and cost. This method significantly reduces support costs while maintaining slope stability, and is characterized by its systematic, quantitative, and efficient nature. Furthermore, by defining economic impact coefficients and anchorage effect coefficients, anchorage parameters that are difficult to compare directly are transformed into quantifiable and comparable indicators, making the decision-making process more scientific and intuitive. In addition, through global optimization, it is often possible to find anchorage schemes that are lower in cost and equally safe than empirical designs or local comparison schemes, contributing to a significant reduction in the total investment in open-pit mine slope support. Attached Figure Description
[0037] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other embodiments can be obtained based on these drawings.
[0038] Figure 1 An aerial photograph of an open-pit iron ore mine is provided as an embodiment of this application.
[0039] Figure 2 This is a real photograph of a slope in an open-pit iron ore mine, provided as an embodiment of this application.
[0040] Figure 3 This is a flowchart illustrating a method for optimizing the calculation of anchorage support costs for the final slope of an open-pit mine, as provided in an embodiment of this application.
[0041] Figure 4 This is a scatter plot and a schematic diagram of the fitted relationship curve between the economic impact coefficient and the anchoring effect coefficient provided in an embodiment of this application.
[0042] Figure 5 This is a convergence diagram of an optimization solution process provided in an embodiment of this application. Detailed Implementation
[0043] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art based on this application are within the scope of protection of this application.
[0044] Example 1: Taking the northern end slope of a large iron ore open-pit mine as an example, the mining area is located in a high-altitude area on the northern foothills of the West Kunlun Mountains. It is an erosion-type high-altitude landform with large topographic relief, and the slope is mostly between 20-30°, reaching 45° in some areas. Aerial photos of the mining area are available. Figure 1 See the actual photos of the slope on site. Figure 2 The open-pit mining depth exceeds 3847m. The slope is significantly affected by the bedding fractured geological conditions, exhibiting geological weaknesses such as cavities, fractures, and fissures, with slippage and dislocation traces already visible. Furthermore, the mining area is less than 10km from a popular highway, necessitating extremely high slope safety requirements. The slope height is 180m, and the rock mass is primarily composed of fractured diorite with unfavorable structural planes. The design requires a target slope safety factor of [value missing]. Calculations show that the safety factor for the unreinforced slope is... The value is 1.05. Based on this, this application provides a method for optimizing the calculation of anchorage support costs for the final slope of an open-pit mine. This method can be found in [reference needed]. Figure 3 , Figure 3 The diagram shown is a flowchart illustrating a method for optimizing the cost of anchorage support for the final slope of an open-pit mine, as provided in an embodiment of this application. The method includes: S1: Determine the anchorage design variables and their value ranges to form the parameter space: Determine the anchorage design variable, the anchor cable length of the anchorage unit. (15-40m), steel strand specifications (equivalent to diameter) (Corresponding to 1860 grade steel strand, 4-8 bundles) lateral spacing (3-6m), longitudinal spacing (3-6m) Prestressed (800-2000kN). Based on the scale of open-pit mining and the distribution of geological weak surfaces, reasonable value ranges are defined for each variable, forming a 5-dimensional parameter space.
[0045] S2: Construct an economic impact coefficient model for anchoring units.
[0046] The anchoring unit can be an anchor bolt, anchor cable, or soil nail. The economic impact coefficient of the anchoring unit is defined as the direct cost of anchoring materials and construction per unit support area. The specific process is as follows: collect local material and construction unit prices: grouting material unit price =450 yuan / cubic meter, unit price of steel strand =8500 yuan / ton, single anchor grouting volume Weight of a single anchor steel ( For the density of steel, (Cross-sectional area of the anchoring unit steel), comprehensive installation cost The cost includes direct costs of drilling, labor, and machinery, as well as indirect costs such as design and monitoring. A regression model is used for estimation. Based on historical cost data of similar projects in this region, the model is fitted as follows: ,in This is the construction cost coefficient per unit length, mainly reflecting the cost of drilling, grouting, and other processes that increase linearly with depth. This is the pore size influence coefficient, reflecting the difficulty of pore formation and slurry consumption. The tension force influence coefficient reflects the requirements of the tensioning equipment and process. , , Fixed costs The economic impact coefficient model for anchoring units can be obtained by fitting cost data from specific regions.
[0047] The economic impact coefficient of anchoring units under different parameter combinations was calculated based on the model. .
[0048] S3: Construct a slope anchorage effect coefficient model.
[0049] The slope anchorage effect coefficient is defined as the relative increase rate of the slope safety factor after reinforcement with specific anchorage parameters. This is determined using a pre-defined slope stability analysis model (such as the limit equilibrium method, which is a simplified version). The slope stability analysis model is based on the strength-reduced finite element method (FTEM) and calculated using the strength-reduced finite element method. This includes: firstly, establishing a baseline finite element model of the slope reflecting geological features such as strata and structural planes, including geometry, mesh, material constitutive model, and initial strengthening parameters (cohesion). internal friction angle Severe (etc.); apply gravity load to the finite element model, perform initial ground stress equilibrium calculation to obtain a stable initial stress state; define a strength reduction factor, and reduce the soil strength parameters in each calculation step, the calculation formula is:
[0050]
[0051] in, The reduced cohesion, This is the reduced internal friction angle. The initial cohesion, The initial internal friction angle, This is the strength reduction factor.
[0052] from Starting with a strength parameter of 1.0, finite element calculations are performed using the reduced strength parameters, gradually increasing the value. Repeated calculations are performed, and the slope is considered unstable when the following conditions occur: the finite element calculation fails to converge, an equilibrium solution cannot be found, the plastic strain zone on the sliding surface is completely connected, or the displacement of characteristic points at the toe or top of the slope changes abruptly. For unreinforced slopes, The value of is the critical strength reduction factor that just causes the slope to become unstable. That is, the safety factor of the slope. The safety factor in the unreinforced state was calculated. =1.05.
[0053] Secondly, for any set of anchoring parameters In the baseline model, according to the spacing and Arrange the structural units for anchor bolts / anchor cables, taking the anchor cable unit as an example, and set the corresponding length. Cross-sectional area (by Decision), prestressed Bond parameters with the rock mass. Then, a strength reduction analysis is performed: the strength reduction factor is gradually increased. and the strength parameters of the soil and rock mass (cohesion) internal friction angle Reduction: , ,in, The reduced cohesion, This is the reduced internal friction angle, calculated until the calculation fails to converge (slope instability), at which point the critical value is reached. That is, using anchorage design variables. Safety factor after reinforcement .
[0054] Finally, the slope anchorage effect coefficient model was obtained, including:
[0055] in, Anchorage design variables Corresponding slope anchorage effect coefficient, The safety factor for the unreinforced slope. To adopt anchorage design variables Safety factor of the reinforced slope.
[0056] Finally, the formula is used to calculate the corresponding parameter combination. value.
[0057] S4: Based on the parameter space, establish the mathematical relationship between the economic impact coefficient of the anchoring unit, the slope anchoring effect coefficient, and the anchoring design variables, and obtain the optimization problem with minimizing the economic impact coefficient of the anchoring unit as the objective and satisfying the slope anchoring effect coefficient corresponding to the target safety factor as the constraint.
[0058] In one embodiment of this application, such as Figure 4 As shown, within a given parameter space, sampling calculations (such as orthogonal experiments or Latin hypercube sampling) are performed to obtain a series of sample points corresponding to... Dataset. Utilize regression analysis (such as multi-Gaussian process regression, multinomial regression, or artificial neural network methods) to establish a dataset from anchoring parameters to... The proxy model is then used to construct an optimization problem with the objective of minimizing the economic impact coefficient of the anchoring unit and the constraint of satisfying the slope anchoring effect coefficient corresponding to the target safety factor. Specifically, this includes: S401: Generate using the Latin hypercube sampling method within the parameter space. There are 100 sample points. Let the number of design variables be 100. , No. The range of values for the variable is , and For the first The upper and lower bounds of a variable's value. First, divide the range of values for each variable into equal parts. There are n small intervals, each interval having a length of n. Then, for each variable Generate a number from 1 to 2. random arrangement Next, for each sample point , take variable The A range is defined, and a value is randomly selected from that range as the variable at the sample point. The values in the sample points are then determined, and finally, each variable is mapped to a different value at each sample point. The combination of values yields the first... 100 sample points. This generates 100 sample points. Groups of data, each group containing The specific values that each design variable can take.
[0059] In one embodiment of this application, for constructing The proxy model first requires acquiring a sufficient number of data pairs in a 5-dimensional parameter space. Latin hypercube sampling is used to generate 200 sample points. The specific steps are as follows: For each design variable, its value range is evenly divided into 200 intervals. A random permutation from 1 to 200 is generated for each variable, ensuring that each interval is selected once in the 200 samples. A value is randomly selected from each selected interval. The values randomly selected from the five variables under the same sample index are combined to form a sample point.
[0060] S402: Automatically substitute 200 sets of sample parameters by writing a script. The calculation formula and finite slope model were used to calculate 200 pairs of slopes in batches. data.
[0061] S403: With 5 anchorage design variables As input features, with the corresponding slope anchorage effect coefficient To achieve the desired output, a surrogate model for the slope anchorage effect coefficient is established using quadratic polynomial regression. :
[0062] in, A proxy model for the slope anchorage effect coefficient. Anchorage design variables The corresponding slope anchoring effect system.
[0063] S404: Safety factor target value according to design requirements ≥1.25, the target safety factor is calculated. Construct the following optimization problem: Decision variables: ; Objective function: ,in, Anchorage design variables The corresponding economic impact coefficient of the anchoring unit; Constraints: , , , , , .
[0064] S5: Solve the optimization problem using an optimization algorithm to obtain the optimal combination of anchorage parameters that meets the slope safety requirements and the corresponding minimum economic impact coefficient of the anchorage unit. The optimization algorithm can be a sequential quadratic programming algorithm, a genetic algorithm, or a particle swarm optimization algorithm.
[0065] In one embodiment of this application, a genetic algorithm is used for optimization, such as... Figure 5 As shown. Population size 50, 100 generations. During optimization, for each set of parameters evaluated, calculations are performed using a surrogate model. and simultaneous accounting The goal is The minimum optimal solution, i.e., the optimal combination of anchoring parameters. ,in, For optimal anchorage length, The optimal borehole diameter (equivalent to 6 bundles of steel strands). For optimal horizontal spacing, For optimal longitudinal spacing, For optimal prestress, the constraints are those predicted by the surrogate model. ≥0.19, ensuring the search for the optimal solution under complex geological and environmental constraints.
[0066] S6: Verify the optimal combination of anchoring parameters and output the economic impact coefficient of the anchoring unit and the slope anchoring effect coefficient corresponding to the optimal combination of anchoring parameters.
[0067] In one embodiment of this application, after the optimization algorithm converges, the optimal solution is obtained as follows: (6 bundles of steel strands) , , The predicted economic impact coefficient of the optimal anchoring unit The predicted optimal safety factor of the reinforced slope The proxy model predicts the optimal slope anchorage effect coefficient. To verify the authenticity and reliability of the optimization results, the following independent verification was conducted: Using the strength reduction principle, the analysis was re-executed in a more refined independent model. The core calculation formula is the reduction calculation formula. By continuously increasing the strength reduction coefficient until the model becomes unstable, the critical strength reduction coefficient at this point is the verification safety factor. The actual safety factor is calculated. ,Right now > If the design requirements are met, the verification is deemed a failure; otherwise, the process must return to the optimization steps to adjust the model or parameters, and the unit area cost must be recalculated based on the optimal combination of anchoring parameters. , To optimize the single-anchor grouting volume, To optimize the weight of a single anchor steel bar, and to optimize the output Verify the calculations to ensure accuracy. If all criteria are met, confirm the optimal parameter combination as the effective, feasible, and economical anchorage design scheme, and output the final key indicators: the economic impact coefficient of the anchorage unit and the slope anchorage effect coefficient. If any criterion is not met, analyze the reasons for failure (e.g., inaccurate surrogate model). Measures such as increasing sample density, correcting the surrogate model, and adjusting optimization algorithm parameters can be taken to re-execute the sampling and verification process until a validated optimal solution is obtained. Compared to the preliminary experience-based design scheme ( =35 7 bundles =4 , =4 , =1800 The cost is approximately RMB 1620 per square meter. It is evident that the optimized solution of this invention saves approximately 22.8% in cost while ensuring slope safety in complex geological and environmental conditions, demonstrating significant economic benefits. Furthermore, this method is applicable to different geological conditions, slope geometries, and different types of anchoring components (anchor bolts, anchor cables, soil nails, etc.), requiring only adjustments to the corresponding stability analysis model and cost calculation parameters.
[0068] This application provides a method for optimizing the cost of anchorage support for the final slope of an open-pit mine. It places economy and safety within a unified mathematical model framework, shifting from considering cost only after ensuring safety to a synergistic optimization of safety and cost. This method significantly reduces support costs while maintaining slope stability, exhibiting systematic, quantitative, and efficient characteristics. Furthermore, by defining economic impact coefficients and anchorage effect coefficients, anchorage parameters that are difficult to compare directly are transformed into quantifiable and comparable indicators, making the decision-making process more scientific and intuitive. Simultaneously, by employing a surrogate model to approximate complex stability calculations and combining it with intelligent optimization algorithms, the optimal solution can be quickly located in a broad parameter space, avoiding the high time consumption and limitations of traditional trial-and-error methods. Moreover, through global optimization, it can typically find anchorage schemes that are lower in cost and equally safe than empirical designs or local comparison schemes, contributing to a significant reduction in the total investment of open-pit mine slope support.
[0069] It should be noted that those skilled in the art will recognize that the embodiments described herein are for the purpose of helping readers understand the principles of this application, and should be understood as not limiting the scope of protection of this application to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this application without departing from the essence of this application, and these modifications and combinations are still within the scope of protection of this application.
Claims
1. A method for optimizing the calculation of anchorage support costs for the final slope of an open-pit mine, characterized in that, include: S1: Determine the anchorage design variables and their value ranges to form the parameter space; S2: Based on the anchorage design variables, construct an economic impact coefficient model for anchorage units based on the direct cost of anchorage materials and construction per unit support area, and obtain the economic impact coefficient of anchorage units. S3: Based on the relative improvement rate of the slope safety factor after reinforcement by anchoring parameters, construct a slope anchoring effect coefficient model to obtain the slope anchoring effect coefficient. S4: Based on the parameter space, establish the mathematical relationship between the economic impact coefficient of the anchoring unit, the slope anchoring effect coefficient and the anchoring design variables, and obtain the optimization problem with minimizing the economic impact coefficient of the anchoring unit as the objective and satisfying the slope anchoring effect coefficient corresponding to the target safety factor as the constraint. S5: Solve the optimization problem using optimization algorithms to obtain the optimal combination of anchorage parameters and the corresponding minimized economic impact coefficient of the anchorage unit under the slope safety requirements; S6: Verify the optimal combination of anchoring parameters and output the economic impact coefficient of the anchoring unit and the slope anchoring effect coefficient corresponding to the optimal combination of anchoring parameters.
2. The method for optimizing the calculation of anchorage support costs for the final slope of an open-pit mine according to claim 1, characterized in that, The anchorage design variables include at least the length, diameter, prestress, lateral spacing, and longitudinal spacing of the anchorage unit, wherein the anchorage unit is an anchor rod, anchor cable, or soil nail.
3. The method for optimizing the calculation of anchorage support costs for the final slope of an open-pit mine according to claim 2, characterized in that, The economic impact coefficient model for the anchoring unit is as follows: in, The economic impact coefficient of the anchoring unit. This is the unit price of the grouting material. For single anchor grouting volume, The diameter of the borehole. For anchorage length, This refers to the unit price of steel. The weight of a single anchor steel piece. For the density of steel, The cross-sectional area of the steel in the anchoring unit. This is the unit price for the comprehensive installation of a single anchor. This is the construction cost coefficient per unit length. The aperture influence coefficient is... The influence coefficient of tension force. For prestressing, This is a fixed cost item. and These are the horizontal spacing and the vertical spacing, respectively.
4. The method for optimizing the calculation of anchorage support costs for the final slope of an open-pit mine according to claim 3, characterized in that, The slope anchorage effect coefficient model is as follows: in, Anchorage design variables The corresponding slope anchorage effect coefficient, The safety factor for the unreinforced slope. To adopt anchorage design variables Safety factor of the reinforced slope.
5. The method for optimizing the calculation of anchorage support costs for the final slope of an open-pit mine according to claim 4, characterized in that, The slope safety factor of the unreinforced slope or the slope safety factor of the reinforced slope is calculated using a slope stability analysis model, which includes the limit equilibrium method or a numerical analysis method based on strength reduction.
6. The method for optimizing the calculation of anchorage support costs for the final slope of an open-pit mine according to claim 5, characterized in that, The numerical analysis method based on strength reduction includes: A1: Establish a finite element model including slope geometry, mesh, material constitutive model and initial strength parameters, wherein the initial strength parameters include at least cohesion, internal friction angle and unit weight; A2: Apply gravity load to the finite element model and perform initial stress equilibrium calculation to obtain a stable initial stress state; A3: Establish structural elements of anchor bolts / anchor cables in the finite element model, set material properties and interactions with the soil, and apply prestress to the structural elements; A4: Based on the initial stress state and the structural elements after prestressing, strength reduction factors are defined respectively, and the soil strength parameters are reduced in each calculation step. The reduction calculation formula is as follows: in, The reduced cohesion, This is the reduced internal friction angle. The initial cohesion, The initial internal friction angle, This is the strength reduction factor; A5: Substitute the reduced strength parameters into the finite element model for finite element calculation, and gradually increase the strength reduction factor. Based on the calculation results, determine whether the instability criteria are met, and obtain the slope safety factor of the unreinforced slope and the slope safety factor of the reinforced slope.
7. The method for optimizing the calculation of costs for anchorage support at the end of an open-pit mine as described in claim 6, characterized in that, The instability criteria include finite element calculation failure, inability to find an equilibrium solution, complete penetration of the plastic strain zone on the sliding surface, and abrupt changes in the displacement of characteristic points at the toe or crest of the slope.
8. The method for optimizing the calculation of costs for anchorage support at the end of an open-pit mine as described in claim 7, characterized in that, The S4 includes: S401: In the parameter space, multiple sample points are generated using the Latin hypercube sampling method; S402: Calculate the economic impact coefficient of the anchoring unit and the slope anchoring effect coefficient for each sample point to obtain the dataset; S403: Using the anchorage design variables of the sample points as input and the corresponding slope anchorage effect coefficient as output, a regression model is trained using Gaussian process regression, multinomial regression, or artificial neural network methods to obtain a surrogate model for approximating the slope anchorage effect coefficient. in, A proxy model for the slope anchorage effect coefficient. Anchorage design variables The corresponding slope anchorage effect coefficient; S404: Determine the target value of the slope design safety factor, and based on the target value of the slope design safety factor, the surrogate model, and the economic impact coefficient of the anchoring unit, obtain an optimization problem with the objective of minimizing the economic impact coefficient of the anchoring unit and the constraint of satisfying the slope anchoring effect coefficient corresponding to the target safety factor. The expression for the constraint of satisfying the slope anchoring effect coefficient corresponding to the target safety factor is as follows: in, For the target safety factor, The target value for the design safety factor of the slope.
9. The method for optimizing the calculation of costs for anchorage support of the final slope in open-pit mines according to claim 1, characterized in that, The optimization algorithm is a sequential quadratic programming algorithm, a genetic algorithm, or a particle swarm optimization algorithm.
10. The method for optimizing the calculation of anchorage support costs for the final slope of an open-pit mine according to claim 8, characterized in that, The S6 includes: S601: Based on the optimal combination of anchorage parameters output by the optimization algorithm, a high-precision slope anchorage model is reconstructed in the selected professional slope stability analysis software. S602: In the high-precision slope anchorage model, the strength reduction principle is adopted to perform a complete strength reduction analysis, output the verification safety factor of the high-precision slope anchorage model when it becomes unstable, and calculate the economic impact coefficient of the anchorage unit corresponding to the optimal anchorage parameter combination corresponding to the verification safety factor. S603: Based on the economic impact coefficient of the anchoring unit and the verification safety coefficient, determine whether the safety coefficient is not less than the target safety coefficient and whether the economic impact coefficient of the anchoring unit is consistent with the output of the optimization algorithm; S604: Outputs the economic impact coefficient of the anchoring unit and the slope anchoring effect coefficient corresponding to the optimal anchoring parameter combination that satisfies the judgment.