A design method for slope anti-slide piles based on dual-objective optimization

Abstract

The present invention discloses a slope anti-slide pile design method based on dual-objective optimization, which belongs to the field of slope reinforcement technology. The method includes determining a slope finite element model based on the slope to be reinforced; formulating an alternative set of anti-slide pile design parameters to form an alternative plan; establishing a finite element model of the pile-reinforced slope; calculating the safety factor of the pile-reinforced slope and the response of the pile; calculating the economic cost of the anti-slide pile; screening and obtaining feasible alternative plans; and determining the optimal anti-slide pile parameters based on dual-objective optimization. The anti-slide pile design parameters obtained by the present invention not only meet the engineering safety requirements but also maximize economic benefits, achieving a balance between safety and economy. In addition, engineers can also select a design plan that is safer or more economical on the Pareto front based on actual engineering conditions such as accident consequences.

Description

Technical Field

[0001] The invention relates to a design method for slope anti-slide piles based on dual-objective optimization, and belongs to the technical field of slope reinforcement. Background Art

[0002] my country's widespread mountainous and hilly terrain creates numerous natural slopes. Furthermore, the construction of highways and railways has resulted in a significant number of engineered slopes. Slopes are often adjacent to structures such as buildings, bridges, and hydropower stations, making their stability and safety closely related to human life.

[0003] To improve slope stability and ensure the safety of people's lives and property, slopes are often reinforced. Rock slopes are often reinforced with anchor rods and cables, and steel mesh is used to prevent rockfall. Soil slopes are often reinforced with lattice slope protection and anti-slide piles. Anti-slide piles are piles used to reinforce unstable slopes or active landslides. They transfer part of the soil pressure from the upper unstable layer to the lower stable layer, thereby improving the stability of the soil behind the piles. Anti-slide piles have been widely used in actual projects since their introduction due to their simple structure, easy construction and significant reinforcement effect. For example, many active landslides and unstable slopes in the Three Gorges Reservoir area are reinforced with anti-slide piles.

[0004] The design of anti-slide piles should consider at least the following four aspects: First, the piles should be strong enough to bear the earth pressure of the upper unstable layer and ensure their own structural safety. This requires that the anti-slide piles have sufficient cross-sectional area. Second, the piles should be of sufficient length (or embedment depth) so that the depth of the piles embedded in the lower stable layer is sufficient to provide the required lateral resistance. Third, the location of the piles should significantly increase the safety factor of the reinforced slope or landslide, maximizing the reinforcement effect. Fourth, the spacing between piles should ensure that an effective soil arching effect is formed between adjacent piles, otherwise the soil may be squeezed out and damaged. In summary, in the design of piles, at least four parameters should be considered to ensure the reinforcement effect: the pile diameter D (or cross-sectional size), length L, pile location X, and pile spacing S.

[0005] Although some scholars have conducted similar research in the past, the vast majority of these studies were based on single-objective optimization, using the safety factor as the sole criterion for reinforcement effectiveness without prioritizing economic costs. While this is not a problem in terms of slope safety, it can sometimes lead to unnecessary financial expenditures. Design methods that minimize economic costs while achieving the target safety factor are worthy of further investigation. Summary of the Invention

[0006] The purpose of the present invention is to overcome the shortcomings of the existing technology and provide a design method for slope anti-slide piles based on dual-objective optimization to solve the problem that the existing technology cannot achieve a balance between maximizing the safety factor and minimizing the economic cost in designing slope anti-slide piles.

[0007] In order to achieve the above objectives / solve the above technical problems, the present invention is implemented by adopting the following technical solutions:

[0008] A slope anti-slide pile design method based on dual-objective optimization, the method comprising:

[0009] Determine the finite element model of the slope based on the slope to be reinforced;

[0010] Construct N anti-slide pile reinforcement alternative schemes based on the length alternative parameter set, position alternative parameter set, diameter alternative parameter set and spacing alternative parameter set of the anti-slide pile;

[0011] According to the slope finite element model and N anti-slide pile reinforcement alternatives, the anti-slide pile reinforcement slope finite element model corresponding to the N anti-slide pile reinforcement alternatives is established;

[0012] Based on the finite element model of the anti-slide pile reinforced slope, the strength reduction method is used to calculate the safety factors of N anti-slide pile reinforcement alternatives and the responses of the anti-slide piles.

[0013] According to the safety factors of N anti-slide pile reinforcement alternatives and the responses of the anti-slide piles, the N anti-slide pile reinforcement alternatives are screened to obtain a feasible anti-slide pile reinforcement alternative;

[0014] Calculate the economic costs of feasible anti-slide pile reinforcement alternatives;

[0015] Draw a scatter plot of feasible anti-slide pile reinforcement alternatives based on their safety factors and economic costs;

[0016] According to the scatter plot of feasible anti-slide pile reinforcement alternatives, the optimal anti-slide pile reinforcement alternative is obtained, and based on the optimal anti-slide pile reinforcement alternative, the parameters of the optimal anti-slide pile are determined;

[0017] Where N = n1 × n2 × n3 × n4, N is the number of anti-slide pile reinforcement alternatives, n1 is the number of length alternative parameters, n2 is the number of diameter alternative parameters, n3 is the number of spacing alternative parameters, and n4 is the number of location alternative parameters.

[0018] Optionally, determining a slope finite element model according to the slope to be reinforced includes:

[0019] The slope finite element model is determined based on the geometric shape, stress characteristics and material composition of the slope to be reinforced; wherein the slope finite element model includes two-dimensional or three-dimensional model selection, load and boundary conditions and material partitioning.

[0020] Optionally, the length candidate parameter set of the anti-slide pile is determined according to the initial sliding surface depth and slope height of the unreinforced slope, and the length candidate parameter set of the anti-slide pile is: L = (L+ΔL, L+2ΔL, ..., L+n1ΔL), where L is the minimum alternative length, ΔL is the increment of adjacent alternative lengths, and n1 is the number of length candidate parameters;

[0021] The diameter parameter set for the anti-slide pile is determined based on the slope scale, engineering experience, and the diameter characteristics of the construction machinery drilling drill bit. The diameter parameter set for the anti-slide pile is: D = (D+ΔD, L+2ΔD, ..., D+n2ΔD), where D is the minimum diameter, ΔD is the increment between adjacent diameters, and n2 is the number of diameter parameters.

[0022] The set of candidate anti-slide pile spacing parameters is determined based on the criteria that the soil between the piles can form a soil arching effect without extrusion failure. The set of candidate anti-slide pile spacing parameters is: S = (D, 2D, ..., n3D), where the spacing is an integer multiple of the pile diameter D, and n3 is the number of candidate spacing parameters.

[0023] The position of the anti-slip pile is represented by the distance X from the pile to the slope shoulder. The set of alternative position parameters for the anti-slip pile is: X = (X+ΔX, X+2ΔX, ..., X+n4ΔX), where X is the minimum alternative position, ΔX is the increment of adjacent alternative positions, and n4 is the number of alternative position parameters.

[0024] Optionally, the alternative scheme arranges and combines the length alternative parameter set, the position alternative parameter set, the diameter alternative parameter set and the spacing alternative parameter set of the anti-slide pile to form a total of N anti-slide pile reinforcement alternative schemes.

[0025] Alternatively, the strength reduction method can be used to calculate the safety factor of the anti-slide pile reinforcement solution as follows:

[0026] Where, φ is the effective internal friction angle of the slope soil, c is the effective cohesion of the slope soil; is the effective internal friction angle when the soil is reduced until the slope reaches the limit equilibrium state, It is the effective cohesion of the soil when it is reduced until the slope reaches the limit equilibrium state; FS is the safety factor of the reinforced slope.

[0027] Optionally, the anti-slide pile reinforcement alternatives are screened based on the safety factors of the anti-slide pile reinforcement alternatives and the responses of the anti-slide piles to obtain feasible anti-slide pile reinforcement alternatives, including:

[0028] First, a target safety factor is given, and alternatives whose safety factor after reinforcement is less than the target safety factor are eliminated;

[0029] Based on excluding alternative schemes whose safety factors after reinforcement are less than the target safety factors, the ultimate bending moment and shear force of the anti-slide piles are calculated according to the reinforced concrete structure theory, and the alternative reinforcement schemes whose actual bending moment or shear force of the anti-slide piles is greater than the ultimate bending moment and shear force are eliminated. The resulting scheme set is the feasible anti-slide pile reinforcement alternative scheme.

[0030] Optionally, the calculation of the economic cost of the anti-slide piles of the feasible anti-slide pile reinforcement solution includes:

[0031] Based on the length, diameter, spacing and reinforcement ratio of the anti-slide piles, the amount of concrete and steel bars used is calculated to obtain the economic cost of the anti-slide piles for a feasible anti-slide pile reinforcement scheme, where the economic cost of the anti-slide piles includes the costs of hole making and subsequent maintenance.

[0032] Optionally, determining the optimal anti-slide pile parameters based on the optimal anti-slide pile reinforcement alternative includes:

[0033] A dual-objective optimization was conducted to maximize the safety factor and minimize the economic cost, and the Pareto front of feasible anti-slide pile reinforcement alternatives was determined.

[0034] The normal boundary intersection method is used to normalize the Pareto front, determine the inflection point on the Pareto front, and obtain the optimal anti-slide pile reinforcement alternative, thereby determining the optimal anti-slide pile parameters.

[0035] Optionally, normalize the Pareto front using the normal frontier intersection method, including:

[0036] Taking the maximum and minimum values ​​of the safety factor and economic cost of the feasible anti-slide pile reinforcement alternatives as the boundary, the safety factor and economic cost of the anti-slide pile are normalized to the interval [0, 1]. The specific formula is as follows:

[0037]

[0038] Where, FS N is the normalized safety factor, C N is the normalized economic cost; FS max is the maximum safety factor of all feasible alternatives, FS min is the minimum safety factor of all feasible alternatives; C max is the maximum economic cost of all feasible alternatives, C minis the minimum economic cost of all feasible alternatives, is the economic cost of the feasible alternative, is the safety factor of the reinforced slope.

[0039] Optionally, the scatter plot of feasible anti-slide pile reinforcement alternatives is a scatter plot of all feasible anti-slide pile reinforcement alternatives plotted with economic cost as the horizontal axis and safety factor as the vertical axis.

[0040] Compared with the prior art, the present invention has the following beneficial effects:

[0041] The present invention formulates design parameters for four piles, namely pile length, pile diameter, pile position and pile spacing, based on the length alternative parameter set, position alternative parameter set, diameter alternative parameter set and spacing alternative parameter set of the anti-slide pile to form a design space. The present invention then screens feasible alternatives based on the target safety factor and pile body response. Finally, based on dual-objective optimization, the optimal design parameters for the anti-slide pile are obtained by maximizing the safety factor and minimizing the economic cost.

[0042] The anti-slide pile design parameters obtained by this method not only meet the engineering safety requirements but also maximize economic benefits, achieving a balance between safety and economy.

[0043] This method not only recommends the optimal design parameters, but also allows engineers to select other alternatives on the Pareto front based on the actual project. When the project is large or the consequences of an accident are serious, a design with a larger safety factor and relatively high economic cost can be selected; or when the project is small and no serious losses will be caused after an accident, the safety factor requirement can be appropriately reduced to save costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 A flow chart of a slope anti-slide pile design method based on dual-objective optimization provided by an embodiment of the present invention;

[0045] Figure 2 Schematic diagram of the finite element model of the slope to be reinforced in an embodiment of the present invention.

[0046] Figure 3 Schematic diagram of pile parameters of alternative anti-slide piles in an embodiment of the present invention;

[0047] Figure 4 Schematic diagram of the sliding surface of the slope to be reinforced in an embodiment of the present invention;

[0048] Figure 5 This is a diagram showing the relationship between the anti-slide pile diameter, ultimate bending moment, and shear force in an embodiment of the present invention;

[0049] Figure 6 A scatter plot and a Pareto front of feasible alternative solutions in an embodiment of the present invention;

[0050] Figure 7 is the normalized Pareto front of the feasible alternatives in the embodiment of the present invention. DETAILED DESCRIPTION

[0051] In order to make the technical means, creative features, objectives and effects achieved by the present invention easier to understand, the present invention is further described below in conjunction with specific implementation methods.

[0052] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, features defined as "first", "second", etc. may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0053] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "mounted," "connected," and "connected" should be understood in a broad sense. For example, they may refer to fixed connections, detachable connections, or integral connections; mechanical connections or electrical connections; direct connections or indirect connections through an intermediate medium; and internal communication between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0054] The embodiment of the present invention discloses a design method for slope anti-slide piles based on dual-objective optimization. This method proposes four pile design parameters, namely pile length, pile diameter, pile position and pile spacing, to form a design space, and screens feasible alternatives based on target safety and pile body response. Finally, based on dual-objective optimization, the optimal design parameters for anti-slide piles are obtained by maximizing the safety factor and minimizing the economic cost. This method not only meets the safety requirements of the project, but also achieves the greatest economic benefits, effectively achieving a balance between safety and economy, and has certain innovation and practical engineering significance. Figure 1 As shown, the specific steps include:

[0055] Step 1: determining a slope finite element model according to the slope to be reinforced;

[0056] Step 2: construct an alternative anti-slide pile reinforcement scheme based on the length alternative parameter set, position alternative parameter set, diameter alternative parameter set, and spacing alternative parameter set of the anti-slide pile;

[0057] Step 3: Based on the slope finite element model and the anti-slide pile reinforcement alternatives, a finite element model of the slope reinforced with anti-slide piles is established; a total of n1 × n2 × n3 × n4 finite element models of the slope reinforced with anti-slide piles are established;

[0058] Step 4: Based on the finite element model of the anti-slide pile reinforcement slope, the strength reduction method is used to calculate the safety factors and pile responses of n1 × n2 × n3 × n4 anti-slide pile reinforcement alternatives;

[0059] Step 5: Screening the anti-slide pile reinforcement alternatives based on their safety factors and responses of the anti-slide piles to obtain feasible anti-slide pile reinforcement alternatives;

[0060] Step 6, calculating the economic cost of the anti-slide piles for the feasible anti-slide pile reinforcement alternative;

[0061] Step 7, drawing a scatter plot of the feasible anti-slide pile reinforcement alternatives based on the safety factors of the feasible anti-slide pile reinforcement alternatives and the economic costs of the feasible anti-slide pile reinforcement alternatives;

[0062] Step 8: Based on the scatter plot of feasible anti-slide pile reinforcement alternatives, the optimal anti-slide pile reinforcement alternative is obtained. Based on this optimal anti-slide pile reinforcement alternative, the optimal anti-slide pile parameters are determined. The anti-slide pile reinforcement alternative includes four parameters: length, diameter, position, and spacing. These four parameters define the specific characteristics of a pile, or in other words, an anti-slide pile reinforcement alternative. Obtaining the optimal anti-slide pile reinforcement alternative means determining the optimal length, diameter, position, and spacing of the anti-slide piles.

[0063] In one embodiment, step 1, determining a slope finite element model based on the slope to be reinforced, specifically includes: taking a road embankment slope as an example, the slope is large enough in the longitudinal direction to meet the plane strain condition, so a two-dimensional slope plane strain finite element model is used for numerical simulation. The load only considers gravity, the bottom boundary is fixed, and the two side boundaries are normal constraints. The slope is homogeneous, the cohesion c = 20 kPa, and the friction angle φ = 30 ° , bulk density γ = 17 kN / m 3 , elastic modulus E = 100 MPa, Poisson's ratio v = 0.3. Slope height 20m, slope 45 ° , Figure 2 A schematic diagram of the finite element model of the slope to be reinforced is given.

[0064] In one embodiment, step 2 constructs an alternative anti-slide pile reinforcement scheme based on the length alternative parameter set, the position alternative parameter set, the diameter alternative parameter set, and the spacing alternative parameter set of the anti-slide pile, specifically including:

[0065] The design parameters of the anti-slide piles include the length of the anti-slide piles (L), the position of the anti-slide piles (X), the diameter of the anti-slide piles (D) and the spacing of the piles (S). Figure 3 A schematic diagram of various parameters of pile-reinforced slopes is provided, wherein the lateral spacing (S) of the piles is achieved by specifying the thickness of the plane strain. The embodiment of the present invention takes a single row of piles as an example.

[0066] The length parameter set of the anti-slide pile is determined based on the depth of the initial sliding surface of the unreinforced slope and the slope height, L = (L+ΔL, L+2ΔL, ..., L+n1ΔL). The embodiment of the present invention uses the K-means clustering partitioning method to extract the initial sliding surface. Figure 4 The initial sliding surface of the slope to be reinforced and the sliding surface depth at some locations are given. It can be seen that the maximum sliding surface depth is about 7m. Combined with the slope height of 20m, the proposed pile length parameter set here is: L = (5m, 7.5m, 10m, 12.5m, 15m, 17.5m, 20m), then n1 = 7.

[0067] Based on the slope size, project experience, and characteristics such as the diameter of the construction machinery's drill bit, we determined the candidate pile diameter parameter set D = (D + ΔD, L + 2ΔD, ..., D + n²ΔD). Here, the anti-slide pile diameter parameter set is proposed as D = (0.2m, 0.4m, 0.6m, 0.8m, 1.0m), resulting in n² = 5.

[0068] The set of candidate pile spacing parameters, S = (D, 2D, ..., n3D), is determined based on the principle that the soil between piles can effectively form a soil arching effect without extrusion failure. Researchers at home and abroad have studied the soil arching effect between piles and found that when the pile axis spacing S ≤ 4D, the soil arching effect can be effectively formed, avoiding soil extrusion failure between piles. To maximize economic benefits, the embodiment of the present invention adopts S = 4D, so n3 = 1.

[0069] The distance (X) from the anti-slide pile to the slope shoulder represents the pile position. The candidate parameter set for the anti-slide pile location is X = (X + ΔX, X + 2ΔX, ..., X + n4ΔX). Here, the candidate parameter set for X is X = (1m, 4m, 7m, 10m, 13m, 16m, 19m), so n4 = 7.

[0070] Finally, the above four parameters and their alternative parameter sets were combined to form a total of 200 pile reinforcement alternatives.

[0071] In one embodiment, step 3 is to establish a finite element model of the slope reinforced with anti-slide piles based on the slope finite element model and the anti-slide pile reinforcement alternative scheme. A total of n1 × n2 × n3 × n4 finite element models of the slope reinforced with anti-slide piles are established, specifically including:

[0072] Based on the finite element model of the slope to be reinforced and the 200 anti-slide pile reinforcement options, a finite element model of the slope reinforced with anti-slide piles was established in ABAQUS, resulting in a finite element model of the slope reinforced with 200 piles. This model can be efficiently established by writing an inp file.

[0073] In one embodiment, step 4, based on the finite element model of the anti-slide pile reinforced slope, uses the strength reduction method to calculate the safety factors of the n1 × n2 × n3 × n4 anti-slide pile reinforcement schemes and the pile responses, specifically including:

[0074] The strength reduction method was used to calculate the safety factor and pile response of 200 alternative pile reinforcement solutions. The safety factor is used to evaluate the reinforcement effect, and the pile response, including the bending moment and shear force, is used to evaluate the stability of the pile itself. The formula for calculating the slope safety factor using the strength reduction method is as follows:

[0075]

[0076] Where, φ and c are the effective internal friction angle and effective cohesion of the slope soil; φ f and c f represents the effective internal friction angle and effective cohesion of the soil when the slope reaches limit equilibrium; FS is the safety factor of the reinforced slope. In ABAQUS, strength reduction calculations are performed by defining initial and final field variables. Here, the initial field variable is defined as 0.5 and the final field variable is defined as 5, indicating that the computable safety factor range is 0.5 to 5.

[0077] In one embodiment, step 5, screening feasible alternatives, specifically includes:

[0078] Given a target safety factor (FS T ), excluding the alternatives whose safety factor after reinforcement is less than the target safety factor, here we take the target safety factor FS T = 1.2. Assuming that the anti-slide piles are made of C30 concrete, HRB400 steel bars, a reinforcement ratio of ρ = 1%, and a concrete cover thickness of 50 mm. Then, based on reinforced concrete structure theory, the ultimate bending moment and shear force of the anti-slide piles under various diameter conditions are calculated. The specific results are shown in Figure 5The maximum bending moment and maximum shear force values ​​of each alternative pile calculated by ABAQUS were extracted, and the alternatives whose maximum bending moment and maximum shear force were greater than the limit values ​​were eliminated; the remaining alternatives (with a safety factor greater than the target safety factor and the bending moment and shear force of the pile less than the limit values) were considered feasible alternatives.

[0079] In one embodiment, step 6, calculating the economic cost of the anti-slide pile, specifically includes:

[0080] According to the above, the economic cost should include the cost of hole making, concrete, steel bars and maintenance. In order to simplify the calculation, only the cost of hole making, concrete and steel bars is considered in the embodiment of the present invention. c It can be calculated as follows:

[0081]

[0082] The reinforcement ratio ρ is calculated as 1%, then the steel bar consumption V s = 0.01V c The cost of hole making is generally proportional to the volume of the hole. Therefore, the hole making cost (C1), concrete cost (C2) and steel cost (C3) are all proportional to the hole volume. Here, we assume that the total unit price of the three per unit volume is C0, C0 = C1 + C2 + C3, so the total economic cost can be calculated using V c ×C0 indicates that the economic cost is the same when the pile size parameters are the same despite different locations. The following table shows the economic cost of each alternative.

[0083] Table 1 Economic costs of each alternative (unit: C0 m 3 / m)

[0084] D = 0.2m D = 0.4m D = 0.6m D = 0.8m D = 1.0m L = 5m 0.196 0.393 0.589 0.785 0.982 L = 7.5m 0.294 0.589 0.884 1.178 1.473 L = 10m 0.393 0.785 1.178 1.571 1.963 L = 12.5m 0.491 0.982 1.473 1.963 2.454 L = 15m 0.589 1.178 1.767 2.356 2.945 L = 17.5m 0.687 1.374 2.062 2.749 3.436 L = 20m 0.785 1.571 2.356 3.141 3.927

[0085] In one embodiment, in step 7, the scatter plot of feasible anti-slide pile reinforcement alternatives is a scatter plot of all feasible anti-slide pile reinforcement alternatives plotted with economic cost as the abscissa and safety factor as the ordinate.

[0086] First, draw a two-dimensional scatter plot of the economic cost and safety factor of the feasible alternatives, see Figure 6 As shown; then according to the dual-objective optimization idea, the Pareto frontier of the design scheme is determined by maximizing the safety factor and minimizing the economic cost. Figure 6 As shown in , the Pareto front consists of a set of designs that are better than the other designs among the alternatives, but have no advantages or disadvantages over each other;

[0087] In step 8, the Pareto front is normalized using the normal frontier intersection method, including:

[0088] Taking the maximum and minimum values ​​of the safety factor and economic cost of the feasible anti-slide pile reinforcement alternatives as the boundary, the safety factor and economic cost of the anti-slide pile are normalized to the interval [0, 1]. The specific formula is as follows:

[0089]

[0090] Where, FS N is the normalized safety factor, C N is the normalized economic cost; FS max is the maximum safety factor of all feasible alternatives, FS min is the minimum safety factor of all feasible alternatives; C max is the maximum economic cost of all feasible alternatives, C min is the minimum economic cost of all feasible alternatives, is the economic cost of the feasible alternative, is the safety factor of the reinforced slope.

[0091] Finally, the Pareto front is normalized and the inflection point of the Pareto front is determined using the normal boundary intersection method. The normal boundary intersection method means that a straight line connects the two alternatives with the minimum economic cost and the maximum economic cost (or the minimum safety factor and the maximum safety factor) in the Pareto front. The design with the largest distance from the straight line on the Pareto front is the optimal design (inflection point). Figure 7 The distances from the points on the normalized Pareto preamble to the normal boundary in the embodiment of the present invention are 0, 0.001, 0.054, 0.222, 0.359, 0.353, 0.360, 0.407, 0.370, 0.282, 0.241, 0.174 and 0, respectively, and the maximum distance is 0.407. Therefore, the pile parameters corresponding to the optimal design scheme in the embodiment of the present invention are: L = 15m, X = 1m, D = 0.4m, S = 4D = 1.6m. The safety factor FS = 1.372, and the economic cost is 1.178 C0 m 3 / m.

[0092] The normal boundary intersection method means: connecting the two end points of the Pareto preamble to form the normal boundary. The point on the Pareto preamble with the maximum distance from the normal boundary is called the inflection point. The inflection point is the optimal anti-slide pile reinforcement alternative, and the corresponding parameters are the anti-slide pile design parameters.

[0093] It's worth noting that the optimal design described above isn't the only one. Engineers can choose other design points on the Pareto frontier based on actual project conditions and economic strength. For large-scale projects or where the consequences of a failure are severe, a design with a higher safety factor and relatively higher economic costs can be chosen. For smaller projects where a failure wouldn't cause significant losses, the safety factor can be appropriately reduced to save costs.

[0094] The present invention forms a design space with the design parameters of the four piles, namely pile length, pile diameter, pile position and pile spacing, and screens the schemes based on the target safety factor and pile body response to determine feasible alternative schemes. Finally, based on dual-objective optimization, the optimal design parameters of the anti-slip piles are obtained by maximizing the safety factor and minimizing the economic cost. The anti-slip pile design parameters obtained by the present invention not only meet the safety requirements of the project, but also maximize the economic benefits, achieving a balance between safety and economy. In addition, engineers can also choose a design scheme that is safer or more economical on the Pareto front according to the actual engineering conditions such as the consequences of the accident. When the scale of the project is large or the consequences of the accident are serious, a design scheme with a larger safety factor and a relatively high economic cost can be selected; or if the scale of the project is small and no serious losses will be caused after the accident, the safety factor requirement can be appropriately reduced to save costs.

[0095] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A design method for slope anti-slide piles based on dual-objective optimization, characterized in that: The method comprises: Determine the finite element model of the slope based on the slope to be reinforced; Construct N anti-slide pile reinforcement alternative schemes based on the length alternative parameter set, position alternative parameter set, diameter alternative parameter set and spacing alternative parameter set of the anti-slide pile; According to the slope finite element model and N anti-slide pile reinforcement alternatives, the anti-slide pile reinforcement slope finite element model corresponding to the N anti-slide pile reinforcement alternatives is established; Based on the finite element model of the anti-slide pile reinforced slope, the strength reduction method is used to calculate the safety factors of N anti-slide pile reinforcement alternatives and the responses of the anti-slide piles. According to the safety factors of N anti-slide pile reinforcement alternatives and the responses of the anti-slide piles, the N anti-slide pile reinforcement alternatives are screened to obtain a feasible anti-slide pile reinforcement alternative; Calculate the economic costs of feasible anti-slide pile reinforcement alternatives; Draw a scatter plot of feasible anti-slide pile reinforcement alternatives based on their safety factors and economic costs; According to the scatter plot of feasible anti-slide pile reinforcement alternatives, the optimal anti-slide pile reinforcement alternative is obtained, and based on the optimal anti-slide pile reinforcement alternative, the parameters of the optimal anti-slide pile are determined; Where N = n1 × n2 × n3 × n4, N is the number of anti-slide pile reinforcement alternatives, n1 is the number of length alternative parameters, n2 is the number of diameter alternative parameters, n3 is the number of spacing alternative parameters, and n4 is the number of location alternative parameters.

2. The slope anti-slide pile design method based on dual-objective optimization according to claim 1 is characterized in that: Determining the slope finite element model according to the slope to be reinforced includes: The slope finite element model is determined based on the geometric shape, stress characteristics and material composition of the slope to be reinforced; wherein the slope finite element model includes two-dimensional or three-dimensional model selection, load and boundary conditions and material partitioning.

3. The slope anti-slide pile design method based on dual-objective optimization according to claim 1, characterized in that: The length candidate parameter set of the anti-slide pile is determined according to the initial sliding surface depth and slope height of the unreinforced slope. The length candidate parameter set of the anti-slide pile is: L = ( L + ΔL, L +2 ΔL, ..., L +n1 ΔL ),in L For the alternative minimum length, ΔL is the adjacent candidate length increment, n1 is the number of length candidate parameters; The diameter parameter set of the anti-slide pile is determined based on the slope scale, engineering experience, and the diameter characteristics of the drilling bit of the construction machinery. The diameter parameter set of the anti-slide pile is as follows: D = ( D + ΔD, L +2 ΔD, ..., D +n2 ΔD ),in D For the alternative minimum diameter, ΔD is the adjacent alternative diameter increment, n2 is the number of diameter alternative parameters; The set of candidate parameters for the spacing of the anti-slide piles is determined based on the standard that the soil between the piles can form a soil arch effect without extrusion failure. The set of candidate parameters for the spacing of the anti-slide piles is: S = ( D, 2D, ..., n3 D ), the interval is taken as the pile diameter D An integer multiple of , n3 is the number of interval alternative parameters; The position of the anti-slide pile is the distance from the pile to the slope shoulder. X Indicates the location of the pile. The candidate parameter set for the location of the anti-slide pile is: X = ( X + ΔX, X +2 ΔX, ..., X +n4 ΔX ),in X is the alternative minimum position, ΔX is the increment of adjacent candidate positions, and n4 is the number of position candidate parameters.

4. The design method of slope anti-slide piles based on dual-objective optimization according to claim 3 is characterized in that: The alternative scheme arranges and combines the length alternative parameter set, the position alternative parameter set, the diameter alternative parameter set and the spacing alternative parameter set of the anti-slide pile to form a total of N anti-slide pile reinforcement alternative schemes.

5. The slope anti-slide pile design method based on dual-objective optimization according to claim 1 is characterized in that: The safety factor formula for the anti-slide pile reinforcement scheme using the strength reduction method is as follows: Where, φ is the effective internal friction angle of the slope soil, c is the effective cohesion of the slope soil; is the effective internal friction angle when the soil is reduced until the slope reaches the limit equilibrium state, The effective cohesion of the soil is reduced until the slope reaches the ultimate equilibrium state; FS is the safety factor of the reinforced slope.

6. The slope anti-slide pile design method based on dual-objective optimization according to claim 1 is characterized in that: The anti-slide pile reinforcement alternative schemes are screened based on the safety factors of the anti-slide pile reinforcement alternative schemes and the responses of the anti-slide piles to obtain feasible anti-slide pile reinforcement alternative schemes, including: First, a target safety factor is given, and alternatives whose safety factor after reinforcement is less than the target safety factor are eliminated; Based on excluding alternative schemes whose safety factors after reinforcement are less than the target safety factors, the ultimate bending moment and shear force of the anti-slide piles are calculated according to the reinforced concrete structure theory, and the alternative reinforcement schemes whose actual bending moment or shear force of the anti-slide piles is greater than the ultimate bending moment and shear force are eliminated. The resulting scheme set is the feasible anti-slide pile reinforcement alternative scheme.

7. The design method of slope anti-slide piles based on dual-objective optimization according to claim 1 is characterized in that: The calculation of the economic cost of the anti-slide piles of a feasible anti-slide pile reinforcement solution includes: Based on the length, diameter, spacing and reinforcement ratio of the anti-slide piles, the amount of concrete and steel bars used is calculated to obtain the economic cost of the anti-slide piles for a feasible anti-slide pile reinforcement scheme, where the economic cost of the anti-slide piles includes the costs of hole making and subsequent maintenance.

8. The slope anti-slide pile design method based on dual-objective optimization according to claim 1 is characterized in that: The method of determining the optimal anti-slide pile parameters based on the optimal anti-slide pile reinforcement alternative includes: A dual-objective optimization was conducted to maximize the safety factor and minimize the economic cost, and the Pareto front of feasible anti-slide pile reinforcement alternatives was determined. The normal boundary intersection method is used to normalize the Pareto front, determine the inflection point on the Pareto front, and obtain the optimal anti-slide pile reinforcement alternative, thereby determining the optimal anti-slide pile parameters.

9. The method for designing slope anti-slide piles based on dual-objective optimization according to claim 8, characterized in that: The Pareto front is normalized using the normal frontier intersection method, including: Taking the maximum and minimum values ​​of the safety factor and economic cost of the feasible anti-slide pile reinforcement alternatives as the boundary, the safety factor and economic cost of the anti-slide pile are normalized to the interval [0, 1]. The specific formula is as follows: Where, FS N is the normalized safety factor, C N is the normalized economic cost; FS max is the maximum safety factor of all feasible alternatives, FS min is the minimum safety factor of all feasible alternatives; C max is the maximum economic cost of all feasible alternatives, C min is the minimum economic cost of all feasible alternatives, is the economic cost of the feasible alternative, is the safety factor of the reinforced slope.

10. The slope anti-slide pile design method based on dual-objective optimization according to claim 1, characterized in that: The scatter plot of feasible anti-slide pile reinforcement alternatives is a scatter plot of all feasible anti-slide pile reinforcement alternatives plotted with economic cost as the horizontal axis and safety factor as the vertical axis.

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