A computer-aided design method for the embedding depth of anti-slide piles and anchor cables

Abstract

The present invention proposes a computer-aided design method for the embedding depth of anti-slide piles and anchor cables, which relates to the technical field of anti-slide pile and anchor cable design, including: collecting drilling data of the engineering site, establishing a three-dimensional geological model including the spatial distribution of each soil layer; determining the feasible range of design parameters; establishing a slope stability analysis model considering the supporting effects of anti-slide piles and anchor cables according to the spatial distribution and parameters of the soil layers, which is used to calculate the slope stability safety factor under given design parameters; taking minimizing the engineering cost as the objective function, determining the optimization constraint conditions according to the slope stability analysis model, and using an optimization algorithm to iteratively optimize the design parameters within the feasible range until the optimization convergence conditions are met, and outputting the optimal design parameters. The present invention can overcome the problems of excessive reliance on experience, difficulty in considering multiple influencing factors, and low calculation efficiency of traditional design methods, and improve the design level of the embedding depth of anti-slide piles and anchor cables.

Description

Technical Field

[0001] The invention relates to the technical field of anti-slide pile and anchor cable design, and in particular to a computer-aided anti-slide pile and anchor cable embedding depth design method. Background Art

[0002] Anti-slide piles and anchor cables are commonly used support structures in slope engineering. Anti-slide piles provide anti-slide force through the bending resistance of the pile body and the interaction between the pile and the soil, while anchor cables provide support by using prestress and the anchoring effect of the rock and soil. As a composite support structure, the synergistic effect of anti-slide piles and anchor cables can effectively improve the stability of the slope. The embedded depth of the pile body and the embedded length of the anchor cable are the key parameters that affect the support effect, which directly determine the safety of the support structure and the engineering cost.

[0003] At present, the design of the embedding depth of anti-slide piles and anchor cables mainly adopts empirical methods, limit equilibrium methods and numerical analysis methods. The empirical method mainly determines the embedding parameters based on engineering analogy and design specifications; the limit equilibrium method is based on the principle of mechanical equilibrium and evaluates stability by calculating the ratio of sliding force to anti-slide force; the numerical analysis method uses numerical methods such as finite element to simulate the slope deformation process and analyze the stress state of the support structure. These methods have been widely used in actual engineering and provide important theoretical and technical support for the design of slope support structures.

[0004] However, the existing design methods still have some shortcomings: first, the traditional design methods rely too much on engineering experience and it is difficult to accurately reflect the interaction mechanism between pile-soil and anchor-soil under complex geological conditions; second, the existing methods often consider anti-slide piles and anchor cables as independent components, failing to fully reflect the synergistic effect of the two; third, it is difficult to take into account both the support effect and engineering economy in the design process, which often leads to over-design of the support structure or insufficient safety reserve; finally, the traditional design method has low calculation efficiency and it is difficult to quickly find the optimal solution among many design schemes, which restricts the improvement of the design level. Summary of the invention

[0005] In view of this, the present invention proposes a computer-aided design method for the embedding depth of anti-sliding piles and anchor cables. By establishing a three-dimensional geological model and a slope stability analysis model, an optimization algorithm is used to optimize the design of the embedding depth of anti-sliding piles and the embedding length of anchor cables, so as to achieve the goal of minimizing the project cost while ensuring the slope stability and structural strength requirements. This overcomes the problems of traditional design methods such as over-reliance on experience, difficulty in considering multiple influencing factors, and low calculation efficiency, and improves the design level of the embedding depth of anti-sliding piles and anchor cables.

[0006] The technical solution of the present invention is implemented as follows: The present invention provides a computer-aided anti-slide pile and anchor cable embedding depth design method, comprising:

[0007] S1. Collect drilling data of the project site and establish a three-dimensional geological model including the spatial distribution of each soil layer; extract the physical and mechanical parameters and groundwater level data of each soil layer, take the embedding depth of anti-slide piles and the embedding length of anchor cables as design parameters, and determine the feasible range of design parameters;

[0008] S2. According to the spatial distribution and parameters of soil layers, a slope stability analysis model considering the support effects of anti-slide piles and anchor cables is established to calculate the slope stability safety factor under given design parameters;

[0009] S3. Taking minimization of project cost as the objective function, the optimization constraints are determined according to the slope stability analysis model, and the optimization algorithm is used to iteratively optimize the design parameters within the feasible range until the optimization convergence conditions are met, and the optimal design parameters are output.

[0010] Based on the above technical solution, preferably, step S3 includes:

[0011] S31, according to the anti-slide pile embedding depth x 1 and anchor cable embedment length x 2 The feasible range [L 1 ,U 1 ] and [L 2 ,U 2 ], randomly generate the population using real number coding within the feasible range , where individual X i =[x 1i ,x 2i ], N is the population size; set the maximum number of iterations T;

[0012] S32, calculate the fitness value F(X) of each individual i ), determine the current optimal individual according to the fitness value ; The fitness function is as follows:

[0013] ;

[0014] ;

[0015] In the formula, f(X i ) is individual X i The objective function value; P(t) is the adaptive penalty function coefficient; G k (X i ) is the violation degree of the kth constraint; m is the number of constraints; δ is the exponent of the penalty function; P 0 is the initial penalty function coefficient; ψ is the growth exponent;

[0016] S33, using an adaptive shrinkage factor α(t) to adjust the search behavior, α(t) is dynamically updated with the number of iterations t;

[0017] S34, using the location update strategy to update the individual location X i (t+1);

[0018] S35, repeat steps S32-S34 to update the population;

[0019] S36, calculate the current fitness value of each individual and update the optimal solution ;

[0020] S37, judging whether the convergence condition is met, if so, outputting the optimal individual, that is, the optimal anti-sliding pile embedding depth and anchor cable embedding length; if not, after the adjustment step, returning to step S32 to continue iteration.

[0021] Based on the above technical solution, preferably, the objective function is:

[0022] f(X i )=C 1 (x 1i )+C 2 (x 2i );

[0023] Among them, C 1 (x 1i ) is the cost of the anti-slide pile project, C 2 (x 2i ) is the cost of anchor cable engineering, and the calculation formula is:

[0024] C 1 (x 1i )=c 1 ·x 1i ·n 1 ;

[0025] C 2 (x 2i )=c 2 ·x 2i ·n 2 ;

[0026] c 1 、c 2 are the cost of anti-slide piles and anchor cables per unit length, n 1 、n 2 are the number of anti-slide piles and anchor cables, respectively;

[0027] The constraints include:

[0028] Slope stability requirements:

[0029] G 1 (X i )=K req -K(X i);

[0030] Structural strength requirements for anti-slide piles:

[0031] G 2 (X i ) = σ pile (X i )-[σ] pile ;

[0032] Anchor cable structure strength requirements:

[0033] G 3 (X i ) = σ anchor (X i )-[σ] anchor ;

[0034] Among them, K req is the minimum safety factor required by the specification, K(X i ) is the slope stability safety factor corresponding to the i-th individual, σ pile (X i ),σ anchor (X i ) is the stress of the anti-sliding pile and anchor cable, [σ] pile , [σ] anchor is the allowable stress of the material.

[0035] On the basis of the above technical solution, preferably, when calculating the slope stability safety factor, the current individual X i =[x 1i ,x 2i ] is used as the design parameter to input into the slope stability analysis model, and the anti-slide pile resistance T of each block is calculated by block method. j and anchor cable axial force N j :

[0036] ;

[0037] ;

[0038] Where, T j (x 1i ) represents the anti-sliding pile resistance acting on the jth block; k p is the passive earth pressure coefficient; β j is the soil mass of the jth block; d 1 is the diameter of the anti-slide pile; n 1 is the number of anti-slide piles; f j is the distribution coefficient of the anti-sliding pile force; N j (x 2 i) represents the axial force of the anchor cable acting on the jth block; d 2is the anchor cable drilling diameter; is the ultimate bond strength between the anchor section and the rock-soil interface; n 2 is the number of anchor cables; is the angle between the anchor cable and the jth block sliding surface; g j is the distribution coefficient of the anchor force;

[0039] The slope stability safety factor is calculated based on the anti-slide pile resistance and anchor cable axial force of all blocks:

[0040] ;

[0041] Where n is the number of blocks; c j is the cohesion of the jth block; l j is the bottom length of the jth block; W j is the gravity of the jth block; α j is the angle between the bottom surface of the jth block and the horizontal plane; is the internal friction angle of the jth block.

[0042] Based on the above technical solution, preferably, the calculation formula of the adaptive shrinkage factor α(t) is:

[0043] ;

[0044] In the formula, α 0 is the initial shrinkage factor, is the adjustment parameter, γ is the adjustment index, and T is the maximum number of iterations.

[0045] Based on the above technical solution, preferably, step S34 includes:

[0046] When the probability of predation mechanism p<0.5, calculate the parameters A and C:

[0047] A = 2a·ra;

[0048] C = 2r';

[0049] Where a=2(1-(t / T) κ ), κ is the convergence acceleration coefficient, r, r' are random numbers between [0,1];

[0050] like , the surrounding predation mechanism is used to update the individual position:

[0051] ;

[0052] like , the searcher search mechanism is used to update the individual position:

[0053] ;

[0054] in, is the current optimal individual, X rand (t) is an individual randomly selected from the population;

[0055] When the predation mechanism probability p ≥ 0.5, the spiral position update strategy is used to update the individual position:

[0056] ;

[0057] ;

[0058] Where D represents the distance between the current individual and the current optimal individual, b is the spiral constant, q is a random number between -1, 1, l is the angle variable of the spiral trajectory, and α(t) is the adaptive contraction factor.

[0059] Based on the above technical solution, preferably, in step S37, when one of the following convergence conditions is met, the algorithm stops iterating:

[0060] The number of iterations reaches the maximum number of iterations T;

[0061] The relative change rate of the fitness value of the optimal individual in consecutive k iterations is less than the threshold ε:

[0062] ;

[0063] In the formula, F best (t) is the fitness value of the best individual in the tth iteration;

[0064] The diversity index Y(t) of the population is lower than the threshold ξ:

[0065] ;

[0066] In the formula, represents the Euclidean distance.

[0067] Based on the above technical solution, preferably, in step S37, the adjustment step includes:

[0068] Increase the adaptive shrinkage factor: α(t)=min{2α(t),α max}; where α max is the upper limit of the adaptive shrinkage factor;

[0069] Perform mutation operation on the population and introduce Gaussian distribution random perturbation: X i (t+1)=X i (t+1)+σ·N(0,1); where σ is the disturbance intensity and N(0,1) is a standard normal distribution random number;

[0070] Re-evaluate the adaptive penalty function coefficients: ; Where λ is the balance factor.

[0071] Based on the above technical solution, preferably, step S3 further includes using a mapping function to map individual X after randomly generating a population using real number coding. i =[x 1i ,x 2i ] decision variable x ji Preprocessing is performed and the preprocessed population is used as the initial population; the mapping function is as follows:

[0072] ;

[0073] In the formula, j=1,2, η is the nonlinear coefficient.

[0074] Based on the above technical solution, preferably, step S1 includes:

[0075] S11. Arrange the drilling points reasonably according to the requirements of the engineering survey specifications. The main section is arranged along the vertical direction of the slope, and the secondary section is arranged along the direction of the slope. The arrangement is denser in areas with weak structural surfaces. Drilling is carried out by combining rotary drilling and rotary drilling to find out the distribution depth and thickness of each soil layer, collect undisturbed soil and disturbed soil samples at different depths, and install inclinometer tubes and groundwater level observation tubes to record the dynamic change data of groundwater level.

[0076] S12. Use geological radar detection technology to detect shallow soil structure and identify the distribution characteristics of weak interlayers and cracks; at the same time, conduct high-density electrical exploration to obtain stratum electrical parameters to assist in determining the interface of soil layers; and carry out surface geological mapping, record surface outcrop characteristics, and measure structural surface occurrence data;

[0077] S13. Use geological modeling software to build a three-dimensional geological model, import drilling data and topographic survey data, set stratigraphic stratification standards, use spatial interpolation methods to generate stratigraphic interfaces, and build an aquifer distribution model; verify stratigraphic interfaces in combination with geophysical data and optimize interpolation results in abnormal areas;

[0078] S14. Conduct indoor geotechnical tests to determine soil physical indicators and strength parameters through compaction tests, direct shear tests and triaxial tests; conduct in-situ tests at the same time, using standard penetration tests, cross-plate shear tests and flat plate load tests to obtain soil engineering characteristic parameters;

[0079] S15. Determine the feasible range of the anti-slide pile embedding depth based on the depth of the bearing layer, the pile driver's drilling capacity and the requirements of the engineering specifications. 1 ,U 1]; Based on the strength characteristics of the rock and soil in the anchoring section and the drilling capacity of the drilling rig, determine the feasible range of the anchor cable embedding length [L 2 ,U 2 ].

[0080] Compared with the prior art, the present invention has the following beneficial effects:

[0081] The computer-aided design method provided by the present invention realizes the automation and intelligence of the support structure design by establishing a three-dimensional geological model and a slope stability analysis model, and optimizing the anti-sliding pile embedding depth and anchor cable embedding length in combination with an optimization algorithm, thereby minimizing the engineering cost while ensuring the slope stability requirements, and improving the design efficiency and solution quality.

[0082] The present invention adopts an adaptive penalty function to process constraint conditions, and by dynamically adjusting the penalty function coefficient, the penalty function value is gradually increased with the iteration process, which effectively avoids the occurrence of infeasible solutions in the optimization process, improves the processing effect of constraint conditions and the convergence performance of the algorithm;

[0083] The present invention adopts the block method to calculate the anti-slide pile resistance and anchor cable axial force, taking into account the influence of factors such as soil layer distribution and groundwater level on the force of the support structure, accurately reflects the pile-soil interaction and anchoring effect, and improves the accuracy of slope stability calculation;

[0084] The present invention introduces an adaptive shrinkage factor to adjust the search behavior, and adopts multiple position update strategies such as encirclement predation, searcher search and spiral update, which enhances the global search ability and local development ability of the algorithm and effectively avoids the optimization process from falling into the local optimum.

[0085] The present invention sets multiple convergence conditions based on the number of iterations, fitness change rate and population diversity, and ensures the reliability and stability of the optimization result by comprehensively judging the convergence state of the optimization process. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0087] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0088] Figure 2 The figure is a flow chart of an optimization algorithm according to an embodiment of the present invention. DETAILED DESCRIPTION

[0089] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0090] like Figure 1 As shown, the present invention provides a computer-aided anti-slide pile and anchor cable embedding depth design method, comprising:

[0091] S1. Collect drilling data of the project site and establish a three-dimensional geological model including the spatial distribution of each soil layer; extract the physical and mechanical parameters and groundwater level data of each soil layer, take the embedding depth of anti-slide piles and the embedding length of anchor cables as design parameters, and determine the feasible range of design parameters;

[0092] S2. According to the spatial distribution and parameters of soil layers, a slope stability analysis model considering the support effects of anti-slide piles and anchor cables is established to calculate the slope stability safety factor under given design parameters;

[0093] S3. Taking minimization of project cost as the objective function, the optimization constraints are determined according to the slope stability analysis model, and the optimization algorithm is used to iteratively optimize the design parameters within the feasible range until the optimization convergence conditions are met, and the optimal design parameters are output.

[0094] Specifically, in one embodiment of the present invention, step S1 includes:

[0095] S11. Arrange drilling points reasonably according to the requirements of engineering investigation specifications. The main section shall be arranged along the vertical direction of the slope, the secondary section shall be arranged along the direction of the slope, and the arrangement shall be denser in areas where weak structural surfaces exist. Drilling shall be carried out by combining rotary drilling with revolving drilling to determine the distribution depth and thickness of each soil layer, collect undisturbed soil and disturbed soil samples at different depths, and install inclinometer tubes and groundwater level observation tubes to record the dynamic change data of groundwater level.

[0096] Specifically, the drilling points are first arranged according to the requirements of the engineering survey specifications. A drilling point is arranged every 20-30 meters in the vertical direction of the slope of the main section, and a drilling point is arranged every 30-50 meters along the direction of the slope of the secondary section. In areas where weak structural surfaces are found, the spacing between drilling points is increased to 10-15 meters. The drilling is carried out using an XY-1 drilling rig, with rotary drilling for shallow layers and rotary drilling for deep layers. During the drilling process, the rock and soil stratification information is recorded in detail, double-tube drill bits are used for coring, and original soil samples and disturbed soil samples are collected at key locations. At the same time, ZX-1 inclinometer tubes and SW-1 groundwater level observation tubes are installed in the boreholes to observe and record groundwater level change data at regular intervals every day.

[0097] S12. Use geological radar detection technology to detect shallow soil structure and identify the distribution characteristics of weak interlayers and cracks; at the same time, carry out high-density electrical exploration to obtain stratum electrical parameters to assist in determining the interface of soil layers; and carry out surface geological mapping, record surface outcrop characteristics, and measure structural surface attitude data.

[0098] Specifically, SIR-3000 geological radar equipment was used for shallow detection with a detection depth of 0-6 meters and a survey line spacing of 2 meters. The distribution of weak interlayers and cracks was identified by the reflection characteristics of radar waves. DUK-2A high-density electrical method instrument was used for electrical depth and electrical profile measurements with a measurement point spacing of 5 meters to obtain electrical parameters such as formation resistivity. At the same time, surface geological mapping was carried out at a scale of 1:500, and a geological compass was used to measure the strike and inclination of the structural surface, and to record the lithological characteristics of the surface outcrops and the distribution of the structural surface.

[0099] S13. Use geological modeling software to construct a three-dimensional geological model, import drilling data and topographic survey data, set stratigraphic stratification standards, use spatial interpolation methods to generate stratigraphic interfaces, and simultaneously construct an aquifer distribution model; verify stratigraphic interfaces in combination with geophysical data and optimize interpolation results in abnormal areas.

[0100] Specifically, the geological model is constructed using CAD and other three-dimensional geological modeling software. First, the drilling data and 1:500 topographic survey data are imported into the software to establish a unified spatial coordinate system. The stratigraphic units are divided according to the lithological characteristics and engineering geological stratification standards, and the stratigraphic interface is generated using the Kriging interpolation method. At the same time, an aquifer distribution model is constructed based on the groundwater level observation data. The geological radar and high-density electrical data are superimposed on the model to correct and optimize the stratigraphic interface in the abnormal area.

[0101] S14. Conduct indoor geotechnical tests to determine soil physical indicators and strength parameters through compaction tests, direct shear tests and triaxial tests; conduct in-situ tests at the same time, using standard penetration tests, cross-plate shear tests and flat plate load tests to obtain soil engineering characteristic parameters.

[0102] Specifically, indoor tests were carried out on the collected soil samples, including compaction test (using heavy compaction standard), direct shear test (using ZJ-2 direct shear apparatus) and triaxial test (using TSZ-1 triaxial apparatus) to determine the physical and mechanical indicators of the soil, such as natural density, optimum water content, cohesion and internal friction angle. At the same time, in-situ tests were carried out, including standard penetration test (63.5kg hammer weight, 76cm drop distance), cross-plate shear test and φ30cm flat plate load test, to obtain the engineering characteristic parameters such as standard penetration number of soil layers, shear strength and deformation modulus of undisturbed soil.

[0103] S15. Determine the feasible range of the anti-slide pile embedding depth based on the depth of the bearing layer, the pile driver's drilling capacity and the requirements of the engineering specifications. 1 ,U 1 ]; Based on the strength characteristics of the rock and soil in the anchoring section and the drilling capacity of the drilling rig, determine the feasible range of the anchor cable embedding length [L 2 ,U 2 ].

[0104] Specifically, based on the bearing layer depth revealed by drilling, the maximum hole depth of the XR-150 rotary drilling rig (generally no more than 60 meters) and the requirements of the Technical Code for Building Slope Engineering, the feasible range of the anti-slide pile embedding depth is determined. 1 ,U 1 ]; According to the ultimate anchoring force per unit area of ​​the rock and soil in the anchoring section (determined by test) and the maximum drilling depth of the ZGYX-300 anchor drilling rig, combined with the requirements of the specification for the anchor inclination angle and free section length, determine the feasible range of the anchor cable embedding length [L 2 ,U 2 ].

[0105] Specifically, in one embodiment of the present invention, step S2 includes:

[0106] Based on the three-dimensional geological model, the calculation section is determined, and the Bishop simplification method is used to establish the slope stability analysis model. The sliding body is divided into n vertical strips along the most dangerous sliding surface. The width of each strip is no more than 5 meters. The stratum lithology mutation points and the support structure setting positions are appropriately encrypted; at the same time, unfavorable geological factors such as groundwater level and weak structural surface are included in the model to ensure that the model can accurately reflect the engineering geological conditions of the site. The deadweight load of each block is calculated, and the floating weight calculation is used for the soil below the groundwater level, considering the influence of groundwater on the slope stability; at the same time, the angle α between the bottom surface of each block and the horizontal plane is determined j , measure the length l of the bottom surface of each block j , and determine the cohesion c of each block based on the indoor test results j and internal friction angle . Construct the calculation formula of slope stability safety factor, that is, slope stability analysis model:

[0107] ;

[0108] Where n is the number of blocks; c j is the cohesion of the jth block; l j is the bottom length of the jth block; W j is the gravity of the jth block; α j is the angle between the bottom surface of the jth block and the horizontal plane; is the internal friction angle of the jth block.

[0109] According to the model, given the design parameters X i , the corresponding safety factor can be calculated.

[0110] In anti-slide pile and anchor cable support projects, the optimal design of embedding depth faces several typical challenges: first, there is a complex coupling relationship between the design variables. The embedding depth of the anti-slide pile will affect the stress state of the anchor cable, and vice versa; second, the constraints are highly nonlinear, including multiple constraints such as the overall stability of the slope, the bending strength of the anti-slide pile, and the axial force of the anchor cable; finally, the objective function (project cost) is highly sensitive to the design variables, and it is easy to form multiple local optimal solutions.

[0111] The optimization algorithm of the present invention is solved based on the improved whale optimization algorithm. The design of the algorithm fully considers the particularity of anti-slide pile and anchor cable support engineering, and makes many improvements on the limitations of traditional optimization algorithms in dealing with such problems.

[0112] The traditional whale optimization algorithm has limitations in many aspects. First, the traditional algorithm uses a fixed shrinkage factor to control the search behavior and cannot adaptively adjust the search range according to the needs of different optimization stages, resulting in either premature convergence to the local optimum or a search range that is too large and inefficient.

[0113] Secondly, the traditional simple penalty function method cannot effectively deal with the complex relationship between multiple nonlinear constraints in the slope support system, and the fixed penalty weights cannot reflect the dynamic importance of different constraints in the optimization process.

[0114] The algorithm lacks an effective mechanism for maintaining population diversity, and is prone to over-concentration of the population during the optimization process, resulting in missing out on potential high-quality solutions, especially in support structure design problems where there are multiple local optimal solutions.

[0115] Finally, the position of each design variable is updated independently, ignoring the coupling relationship between the embedding depth of the anti-slide pile and the embedding length of the anchor cable. At the same time, the boundary processing adopts a simple truncation method, which loses the valuable information that may be contained.

[0116] The present invention introduces the following improvements on the basis of the traditional whale optimization algorithm: first, an adaptive shrinkage factor α(t) is designed to dynamically adjust the global search and local development capabilities of the algorithm; second, an improved penalty function method is used to deal with constraints, and the feasibility and optimality are balanced by adaptively adjusting the penalty coefficient P(t); then an individual preprocessing mechanism based on a mapping function is introduced to make the population distribution better match the characteristics of the problem, thereby accelerating the convergence speed of the algorithm; finally, multiple convergence criteria are designed, including iteration number limit, optimal value improvement rate and population diversity index.

[0117] Specifically, Figure 2 As shown, in one embodiment of the present invention, step S3 includes:

[0118] S31, according to the anti-slide pile embedding depth x 1 and anchor cable embedment length x 2 The feasible range [L 1 ,U 1 ] and [L 2 ,U 2 ], randomly generate the population using real number coding within the feasible range , where individual X i =[x 1i ,x 2i ], N is the population size; set the maximum number of iterations T; specifically, the population size N can be 20, and T can be 200. The initialization method can adopt the Latin hypercube sampling method.

[0119] S32, calculate the fitness value F(X) of each individual i ), determine the current optimal individual according to the fitness value ; The fitness function is as follows:

[0120] ;

[0121] ;

[0122] In the formula, f(X i ) is individual X i The objective function value; P(t) is the adaptive penalty function coefficient; G k (X i ) is the violation degree of the kth constraint; m is the number of constraints; δ is the exponent of the penalty function; P 0 is the initial penalty function coefficient; ψ is the growth exponent; in this embodiment, ψ can be 1.5.

[0123] S33, using an adaptive shrinkage factor α(t) to adjust the search behavior, α(t) is dynamically updated with the number of iterations t;

[0124] S34, using the location update strategy to update the individual location X i (t+1);

[0125] S35, repeat steps S32-S34 to update the population;

[0126] S36, calculate the current fitness value of each individual and update the optimal solution ;

[0127] S37, judging whether the convergence condition is met, if so, outputting the optimal individual, that is, the optimal anti-sliding pile embedding depth and anchor cable embedding length; if not, after the adjustment step, returning to step S32 to continue iteration.

[0128] The present invention introduces an adaptive penalty function mechanism. The traditional fixed penalty coefficient method is difficult to balance the relationship between objective function optimization and constraint satisfaction. The present invention adopts a penalty coefficient P(t) that is dynamically adjusted with the iteration process, so that it increases with the increase in the number of iterations. This design idea is derived from the characteristics of engineering practice: in the early stage of optimization, the algorithm should be allowed to explore in a larger range, including a certain degree of constraint violation, so as not to exclude potential high-quality solutions too early; in the later stage of optimization, a larger penalty coefficient is needed to ensure the feasibility of the final solution. This improvement enables the algorithm to better handle multiple constraints in support engineering.

[0129] Specifically, in this embodiment, the objective function is:

[0130] f(X i )=C 1 (x 1i )+C 2 (x 2i );

[0131] Among them, C 1 (x 1i ) is the cost of the anti-slide pile project, C 2 (x 2i ) is the cost of anchor cable engineering, and the calculation formula is:

[0132] C 1 (x 1i )=c 1 ·x 1i ·n 1 ;

[0133] C 2 (x 2i )=c 2 ·x 2i ·n 2 ;

[0134] c 1 、c 2 are the cost of anti-slide piles and anchor cables per unit length, n 1 、n 2 are the number of anti-slide piles and anchor cables, respectively;

[0135] The constraints include:

[0136] Slope stability requirements:

[0137] G 1 (X i )=Kreq -K(X i );

[0138] Structural strength requirements for anti-slide piles:

[0139] G 2 (X i ) = σ pile (X i )-[σ] pile ;

[0140] Anchor cable structure strength requirements:

[0141] G 3 (X i ) = σ anchor (X i )-[σ] anchor ;

[0142] Among them, K req is the minimum safety factor required by the specification, K(X i ) is the slope stability safety factor corresponding to the i-th individual, σ pile (X i ),σ anchor (X i ) is the stress of the anti-sliding pile and anchor cable, [σ] pile , [σ] anchor is the allowable stress of the material.

[0143] When calculating the slope stability safety factor, the current individual X i =[x 1i ,x 2i ] is used as the design parameter to input into the slope stability analysis model, and the anti-slide pile resistance T of each block is calculated by block method. j and anchor cable axial force N j :

[0144] ;

[0145] ;

[0146] Where, T j (x 1i ) represents the anti-sliding pile resistance acting on the jth block; k p is the passive earth pressure coefficient; β j is the soil mass of the jth block; d 1 is the diameter of the anti-slide pile; n 1 is the number of anti-slide piles; f j is the distribution coefficient of the anti-sliding pile force; N j (x 2i ) represents the axial force of the anchor cable acting on the jth block; d2 is the anchor cable drilling diameter; is the ultimate bond strength between the anchor section and the rock-soil interface; n 2 is the number of anchor cables; is the angle between the anchor cable and the jth block sliding surface; g j is the distribution coefficient of the anchor force;

[0147] The slope stability safety factor is calculated based on the anti-slide pile resistance and anchor cable axial force of all blocks:

[0148] ;

[0149] Where n is the number of blocks; c j is the cohesion of the jth block; l j is the bottom length of the jth block; W j is the gravity of the jth block; α j is the angle between the bottom surface of the jth block and the horizontal plane; is the internal friction angle of the jth block.

[0150] The calculation formula of the adaptive shrinkage factor α(t) is:

[0151] ;

[0152] In the formula, α 0 is the initial shrinkage factor, is the adjustment parameter, γ is the adjustment index, and T is the maximum number of iterations.

[0153] In the optimization design of support structures, a small change in the design parameters (embedded depth) may lead to a significant change in the system response, which requires the algorithm to have the ability to dynamically adjust the search step size. The adaptive shrinkage factor designed in the present invention adopts the form of combining exponential decay with power function, which not only ensures a larger search range in the early stage, but also ensures the fine search capability in the later stage. When the algorithm stagnates, the shrinkage factor is increased to provide an opportunity to jump out of the local optimum.

[0154] In this embodiment, step S34 includes:

[0155] When the probability of predation mechanism p<0.5, calculate the parameters A and C:

[0156] A = 2a·ra;

[0157] C = 2r';

[0158] Where a=2(1-(t / T) κ ), κ is the convergence acceleration coefficient, r, r' are random numbers between [0,1];

[0159] like , the surrounding predation mechanism is used to update the individual position:

[0160] ;

[0161] like , the searcher search mechanism is used to update the individual position:

[0162] ;

[0163] in, is the current optimal individual, X rand (t) is an individual randomly selected from the population;

[0164] When the predation mechanism probability p ≥ 0.5, the spiral position update strategy is used to update the individual position:

[0165] ;

[0166] ;

[0167] Where D represents the distance between the current individual and the current optimal individual, b is the spiral constant, q is a random number between -1, 1, l is the angle variable of the spiral trajectory, and α(t) is the adaptive contraction factor.

[0168] Specifically, in this embodiment, when calculating the p value, an adaptive method is used: p=0.5+0.5·cos(π·t / T); so that the algorithm tends to global search in the early stage and gradually strengthens local search in the later stage.

[0169] The present invention designs a composite update strategy including three modes: encirclement predation, searcher search and spiral update. Through the dynamic regulation of probability p, the algorithm can adaptively switch between different search modes. In particular, an adaptive shrinkage factor is introduced in the spiral update mode, so that the search trajectory can better adapt to the nonlinear characteristics of the support system.

[0170] In step S37, the algorithm stops iterating when one of the following convergence conditions is met:

[0171] The number of iterations reaches the maximum number of iterations T;

[0172] The relative change rate of the fitness value of the optimal individual in consecutive k iterations is less than the threshold ε:

[0173] ;

[0174] In the formula, F best (t) is the fitness value of the best individual in the tth iteration;

[0175] The diversity index Y(t) of the population is lower than the threshold ξ:

[0176] ;

[0177] In the formula, represents the Euclidean distance.

[0178] In step S37, the adjustment step includes:

[0179] Increase the adaptive shrinkage factor: α(t)=min{2α(t),α max}; where α max is the upper limit of the adaptive shrinkage factor;

[0180] Perform mutation operation on the population and introduce Gaussian distribution random perturbation: X i (t+1)=X i (t+1)+σ·N(0,1); where σ is the disturbance intensity and N(0,1) is a standard normal distribution random number;

[0181] Re-evaluate the adaptive penalty function coefficients: ; Where λ is the balance factor.

[0182] In one embodiment of the present invention, step S3 further includes, after the real number coding randomly generates the population, using the mapping function to map the individual X i =[x 1i ,x 2i ] decision variable x ji Preprocessing is performed and the preprocessed population is used as the initial population; the mapping function is as follows:

[0183] ;

[0184] In the formula, j=1,2, η is the nonlinear coefficient.

[0185] The present invention uses a nonlinear mapping function to preprocess the initial population, and adjusts the nonlinear degree of the mapping through the parameter η, so that the population distribution better matches the characteristics of the problem.

[0186] Specifically, the optimization algorithm of the present invention adopts a hierarchical optimization strategy when setting various algorithm parameters: first, a larger search step size and a smaller population size are used for coarse optimization to quickly locate the approximate range of the optimal solution; then, on this basis, the parameters are refined for fine optimization.

[0187] There are many ways to verify the optimization results: first, make a preliminary judgment based on engineering experience to check whether the results are within a reasonable range; second, use professional finite element software to conduct a detailed analysis to verify the safety of the support structure; finally, compare the optimization results under different initial conditions to evaluate the stability of the solution.

[0188] In engineering practice, the optimization results are only used as a design reference, and the final plan also needs to consider practical factors such as construction technology, equipment conditions, and site restrictions.

[0189] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A computer-aided design method for the embedding depth of anti-slide piles and anchor cables, characterized in that: include: S1. Collect drilling data of the project site and establish a three-dimensional geological model including the spatial distribution of each soil layer; extract the physical and mechanical parameters and groundwater level data of each soil layer, take the embedding depth of anti-slide piles and the embedding length of anchor cables as design parameters, and determine the feasible range of design parameters; S2. According to the spatial distribution and parameters of soil layers, a slope stability analysis model considering the support effects of anti-slide piles and anchor cables is established to calculate the slope stability safety factor under given design parameters; S3, taking minimization of construction cost as the objective function, determining optimization constraints according to the slope stability analysis model, using the optimization algorithm to iteratively optimize the design parameters within the feasible range until the optimization convergence conditions are met, and outputting the optimal design parameters; Step S3 includes: S31, based on the feasible ranges [L1, U1] and [L2, U2] of the anti-slide pile embedding depth x1 and the anchor cable embedding length x2, a population is randomly generated within the feasible range using real number coding Among them, individual X i =[x 1i ,x 2i ], N is the population size; Set the maximum number of iterations T; S32, calculate the fitness value F(X) of each individual i ), determine the current optimal individual X according to the fitness value * (t); the fitness function is as follows: In the formula, f(X i ) is individual X i The objective function value; P(t) is the adaptive penalty function coefficient; G k (X i ) is the violation degree of the kth constraint; m is the number of constraints; δ is the exponent of the penalty function; P0 is the initial penalty function coefficient; ψ is the growth exponent; S33, using an adaptive shrinkage factor α(t) to adjust the search behavior, α(t) is dynamically updated with the number of iterations t; S34, using the location update strategy to update the individual location X i (t+1); S35, repeat steps S32-S34 to update the population; S36, calculate the fitness value of each individual at present and update the optimal solution X * (t+1); S37, judging whether the convergence condition is met, if so, outputting the optimal individual, that is, the optimal anti-sliding pile embedding depth and anchor cable embedding length; if not, after the adjustment step, returning to step S32 to continue iteration.

2. A computer-aided anti-slide pile and anchor cable embedding depth design method as claimed in claim 1, characterized in that: The objective function is: f(X i )=C1(x 1i )+C2(x 2i ); Among them, C1(x 1i ) is the cost of the anti-slide pile project, C2(x 2i ) is the cost of anchor cable engineering, and the calculation formula is: C1(x 1i )=c1·x 1i ·n1; C2(x 2i )=c2·x 2i ·n2; c1 and c2 are the cost of anti-slide piles and anchor cables per unit length, n1 and n2 are the number of anti-slide piles and anchor cables respectively; The constraints include: Slope stability requirements: G1(X i )=K req -K(X i ); Structural strength requirements for anti-slide piles: G2(X i )=σ pile (X i )-[σ] pile ; Anchor cable structure strength requirements: G3(X i )=s anchor (X i )-[s] anchor ; Among them, K req is the minimum safety factor required by the specification, K(X i ) is the slope stability safety factor corresponding to the i-th individual, σ pile (X i ),σ anchor (X i ) is the stress of the anti-sliding pile and anchor cable, [σ] pile , [σ] anchor is the allowable stress of the material.

3. A computer-aided design method for the embedding depth of anti-slide piles and anchor cables as claimed in claim 2, characterized in that: When calculating the slope stability safety factor, the current individual X i =[x 1i ,x 2i ] is used as the design parameter to input into the slope stability analysis model, and the anti-slide pile resistance T of each block is calculated by block method. j and anchor cable axial force N j : N j (x 2i )=π·d2·τ s ·x 2i ·n2·cosθ j ·g j ; Where, T j (x 1i ) represents the anti-sliding pile resistance acting on the jth block; k p is the passive earth pressure coefficient; β j is the soil mass of the jth block; d1 is the diameter of the anti-slide pile; n1 is the number of anti-slide piles; f j is the distribution coefficient of the anti-sliding pile force; N j (x 2i ) represents the axial force of the anchor cable acting on the jth block; d2 is the anchor cable drilling diameter; τ s is the ultimate bond strength between the anchor section and the rock-soil interface; n2 is the number of anchor cables; θ j is the angle between the anchor cable and the jth block sliding surface; g j is the distribution coefficient of the anchor force; The slope stability safety factor is calculated based on the anti-slide pile resistance and anchor cable axial force of all blocks: Where n is the number of blocks; c j is the cohesion of the jth block; l j is the bottom length of the jth block; W j is the gravity of the jth block; α j is the angle between the bottom surface of the jth block and the horizontal plane; is the internal friction angle of the jth block.

4. A computer-aided anti-slide pile and anchor cable embedding depth design method as claimed in claim 1, characterized in that: The calculation formula of the adaptive shrinkage factor α(t) is: Where α0 is the initial shrinkage factor, τ is the adjustment parameter, γ is the adjustment index, and T is the maximum number of iterations.

5. A computer-aided design method for the embedding depth of anti-slide piles and anchor cables as claimed in claim 1, characterized in that: Step S34 includes: When the probability of predation mechanism p<0.5, calculate the parameters A and C: A = 2a·ra; C＝2r'； Where a = 2(1-(t / T) κ ), κ is the convergence acceleration coefficient, r, r' are random numbers between [0,1]; If |A| < 1, the encirclement and predation mechanism is used to update the individual position: X i (t+1)=X * (t)-A·|C·X * (t)-X i (t)|; If |A|≥1, the searcher search mechanism is used to update the individual position: X i (t+1)=X rand (t)-A·|C·X rand (t)-X i (t)|; Among them, X * (t) is the current optimal individual, X rand (t) is an individual randomly selected from the population; When the predation mechanism probability p ≥ 0.5, the spiral position update strategy is used to update the individual position: D=|X * (t)-X i (t)|; X i (t+1)=D·e b·q ·cos(2πl)·α(t)+X * (t); Where D represents the distance between the current individual and the current optimal individual, b is the spiral constant, q is a random number between -1, 1, l is the angle variable of the spiral trajectory, and α(t) is the adaptive contraction factor.

6. A computer-aided anti-slide pile and anchor cable embedding depth design method as claimed in claim 1, characterized in that: In step S37, the algorithm stops iterating when one of the following convergence conditions is met: The number of iterations reaches the maximum number of iterations T; The relative change rate of the fitness value of the optimal individual in consecutive k iterations is less than the threshold ε: In the formula, F best (t) is the fitness value of the best individual in the tth iteration; The diversity index Y(t) of the population is lower than the threshold ξ: Here, ||·|| represents the Euclidean distance.

7. A computer-aided design method for the embedding depth of anti-slide piles and anchor cables as claimed in claim 1, characterized in that: In step S37, the adjustment step includes: Increase the adaptive shrinkage factor: α(t) = min{2α(t),α max }; where α max is the upper limit of the adaptive shrinkage factor; Perform mutation operation on the population and introduce Gaussian distribution random perturbation: X i (t+1)=X i (t+1)+σ·N(0,1); where σ is the disturbance intensity and N(0,1) is a standard normal distribution random number; Re-evaluate the adaptive penalty function coefficients: In the formula, λ is the balance factor.

8. A computer-aided design method for the embedding depth of anti-slide piles and anchor cables as claimed in claim 1, characterized in that: Step S3 also includes using a mapping function to map individual X after the real number code randomly generates a population. i =[x 1i ,x 2i ] decision variable x ji Preprocessing is performed and the preprocessed population is used as the initial population; the mapping function is as follows: In the formula, j=1,2, η is the nonlinear coefficient.

9. A computer-aided anti-slide pile and anchor cable embedding depth design method as claimed in claim 1, characterized in that: Step S1 includes: S11. Arrange the drilling points reasonably according to the requirements of the engineering survey specifications. The main section is arranged along the vertical direction of the slope, and the secondary section is arranged along the direction of the slope. The arrangement is denser in areas with weak structural surfaces. Drilling is carried out by combining rotary drilling and rotary drilling to find out the distribution depth and thickness of each soil layer, collect undisturbed soil and disturbed soil samples at different depths, and install inclinometer tubes and groundwater level observation tubes to record the dynamic change data of groundwater level. S12. Use geological radar detection technology to detect shallow soil structure and identify the distribution characteristics of weak interlayers and cracks; at the same time, conduct high-density electrical exploration to obtain stratum electrical parameters to assist in determining the interface of soil layers; and carry out surface geological mapping, record surface outcrop characteristics, and measure structural surface occurrence data; S13. Use geological modeling software to build a three-dimensional geological model, import drilling data and topographic survey data, set stratigraphic stratification standards, use spatial interpolation methods to generate stratigraphic interfaces, and build an aquifer distribution model; verify stratigraphic interfaces in combination with geophysical data and optimize interpolation results in abnormal areas; S14. Conduct indoor geotechnical tests to determine soil physical indicators and strength parameters through compaction tests, direct shear tests and triaxial tests; conduct in-situ tests at the same time, using standard penetration tests, cross-plate shear tests and flat plate load tests to obtain soil engineering characteristic parameters; S15. Determine the feasible range of the embedding depth of the anti-sliding piles [L1, U1] based on the depth of the bearing layer, the drilling capacity of the pile driver and the requirements of the engineering specifications; determine the feasible range of the embedding length of the anchor cable [L2, U2] based on the strength characteristics of the rock and soil in the anchoring section and the drilling capacity of the drilling rig.

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