Asphalt concrete core wall joint structure optimization method combining economical efficiency and safety

Abstract

The invention discloses an asphalt concrete core wall joint structure optimization method combining economical efficiency and safety, which comprises the following steps of: constructing an asphalt concrete core wall joint structure multi-objective optimization model by taking geometrical shape parameters of an asphalt concrete core wall joint structure as decision variables and taking the economical efficiency and the safety of an asphalt concrete core wall as objective functions; and fitting a second-order response surface regression model between the asphalt concrete core wall safety performance evaluation indexes and the decision variables, substituting the fitted second-order response surface regression model into the constructed multi-objective optimization model, and carrying out multi-objective optimization solution on the joint structure by adopting an NSGA-II algorithm to obtain joint optimal structure forms with different deviations. According to the method, the NSGA-II algorithm is adopted to solve the multi-objective optimization model, then the linear weighting method is adopted to compare and select the matching scheme, the optimal structural form of different deviation joints is obtained, and the engineering economy is considered while the structural stability of the asphalt concrete core wall is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of optimizing the joint structure of asphalt concrete core wall rock-fill dams, and relates to an optimization method for the joint structure of asphalt concrete core walls that combines economy and safety. Background Art

[0002] In recent years, asphalt concrete core wall rock-fill dams, which are known for their simple structure, small project quantity, fast construction speed, and good anti-seepage performance and deformation adaptability, have been increasingly widely used. Along with the start of construction of large-scale hydropower projects such as Changheba and Lianghekou, there are still certain safety problems with high core wall dams built in terrains with narrow river valleys and steep slopes. The steeper the slope, the stronger the shear force between the core wall and the slope, and shear failure will occur, which is the core issue that has been long concerned in engineering construction. The joint part between the asphalt concrete core wall and the concrete base is the key weak part of the asphalt concrete core wall dam. The connection performance between them is related to the overall anti-seepage safety of the dam, and its structural dimensions have a certain impact on the mechanical properties of the core wall and even the entire dam body. Therefore, optimizing the structural dimensions of the joint part between the asphalt concrete core wall and the concrete base, while reducing the amount of slope excavation and concrete filling in the project, and ensuring the safety and stability of the asphalt concrete core wall structure, has important engineering significance for the construction of asphalt concrete core wall rock-fill dams. Summary of the Invention

[0003] The purpose of the invention is to provide an optimization method for the joint structure of asphalt concrete core walls that combines economy and safety, and to obtain a safe and economic joint structure of asphalt concrete core walls by optimizing the shape parameters at the joint of the core wall.

[0004] The technical solution adopted by the invention is an optimization method for the joint structure of asphalt concrete core walls that combines economy and safety, including the following steps:

[0005] Step 1: Taking the geometric shape parameters of the asphalt concrete core wall joint structure as decision variables and the economy and safety of the asphalt concrete core wall as the objective function, construct a multi-objective optimization model for the asphalt concrete core wall joint structure;

[0006] Step 2: Fit a second-order response surface regression model between the safety performance evaluation index of the asphalt concrete core wall and the decision variables;

[0007] Step 3: Substitute the fitted second-order response surface regression model into the constructed multi-objective optimization model for the asphalt concrete core wall joint structure, and use the NSGA-II algorithm to perform multi-objective optimization and solution for the joint structure to obtain the optimal joint structure forms with different biases.

[0008] Among them, the specific process of Step 1 is as follows:

[0009] Step 1.1, select the enlarged angle θ, embedding depth h, and slope coefficient i of the asphalt concrete core wall joint structure as decision variables;

[0010] Step 1.2, select the shear stress τ, tensile stress σ, and arch effect coefficient R of the asphalt concrete core wall as safety performance evaluation indicators;

[0011] Step 1.3, determine the geometric constraint conditions of the asphalt concrete core wall joint structure as shown in Equation (1) and the stress constraint conditions as shown in Equation (2):

[0012]

[0013] In the formula, i min , θ min , h min are the lower limit values of the slope coefficient, enlarged angle, and embedding depth of the slope respectively, i max , θ max , h max are the upper limit values of the slope coefficient, enlarged angle, and embedding depth of the slope respectively, τ max , σ max , R min are the maximum shear stress, maximum tensile stress, and minimum arch effect coefficient of the asphalt concrete core wall respectively, [τ t , [σ t , [R t are the allowable values of the shear stress, tensile stress, and arch effect coefficient respectively;

[0014] Step 1.4, taking the economy and safety of the asphalt concrete core wall as the objective function, construct a multi-objective optimization model of the asphalt concrete core wall as shown in Equation (3) and Equation (4):

[0015] Obj{τ(i,θ,h),σ(i,θ,h),R(i,θ,h),V(i,θ,h)}→min (3)

[0016]

[0017] In the formula, V is the volume of the joint structure.

[0018] The specific process of Step 2 is as follows:

[0019] Step 2.1, adopt the central composite experimental design method, take the enlarged angle θ, embedding depth h, and slope coefficient i of the joint structure as design variables, take the shear stress τ, tensile stress σ, and arch effect coefficient R of the asphalt concrete core wall as response variables, determine the level values of the design variables according to the geometric constraint conditions of the core wall joint structure, and design a response surface regression test scheme;

[0020] Step 2.2, based on the designed response surface regression test scheme, successively conduct finite element numerical simulation calculations of the asphalt concrete core wall dam under each test scheme, and extract the corresponding response variable values;

[0021] Step 2.3, based on the response surface regression test scheme and the corresponding response variable values, fit the second-order response surface regression model between the safety performance evaluation index of the asphalt concrete core wall and the decision variables.

[0022] The specific process of Step 3 is as follows:

[0023] Step 3.1, substitute the fitted second-order response surface regression model into the constructed multi-objective optimization model of the asphalt concrete core wall joint structure, and use the NSGA-II algorithm to solve the multi-objective optimization model to obtain the Pareto optimal solution set of the optimized design of the asphalt concrete core wall joint structure;

[0024] Step 3.2, normalize the objective function values in the Pareto optimal solution set using Equation (5);

[0025]

[0026] In the formula, Y ij is the j-th normalized value of the i-th objective, x ij is the j-th attribute value of the i-th objective, is the maximum attribute value of the i-th objective, is the minimum attribute value of the i-th objective;

[0027] Step 3.3, obtain the comprehensive evaluation index of the mechanical properties of the core wall using Equation (6):

[0028]

[0029] In the formula, M j is the j-th normalized value of the comprehensive evaluation index of the mechanical properties of the core wall, and n is the number of evaluation indexes of the mechanical properties of the core wall;

[0030] Step 3.4, assign corresponding weight coefficients according to the importance of the objectives, and use Equation (7) to obtain the comprehensive evaluation index u j corresponding to the optimal structural form of the joint with different biases. The optimal solution with the smallest comprehensive evaluation index u j in the Pareto optimal solution set is the optimal solution scheme for the biased type;

[0031] u j = w m M j + w v V j (7)

[0032] In the formula, Vj is the j-th normalized value of the joint volume index, w m is the weight coefficient of the comprehensive evaluation index of the core wall mechanical properties, w v is the weight coefficient of the joint volume index.

[0033] In step 3.4, according to the importance degree of the objectives, the corresponding weight coefficients are assigned, and the linear weighted sum method is used to linearly combine the normalized values to obtain different mixing ratio schemes, and the mixing ratio schemes are compared and selected to obtain the optimal structural forms of joints with different biases.

[0034] The optimal structural forms of joints with different biases include safety-biased type, economy-biased type and balanced type joint structural forms.

[0035] In step 3.4, according to the importance degree of the objectives, the corresponding weight coefficients are assigned. For the safety-biased type, w m > w v , for the economy-biased type, w m < w v , for the balanced type, w m = w v .

[0036] In step 3.4, substitute the M j and V j corresponding to each group of optimal solutions in the Pareto optimal solution set into formula (7) to solve the comprehensive evaluation index u j minimum value of each biased joint. The optimal solution corresponding to the minimum u j is the optimal structural form of the corresponding biased joint.

[0037] The beneficial effects of the present invention are as follows: taking the geometric shape parameters of the asphalt concrete core wall joint structure as decision variables and the economy and safety of the asphalt concrete core wall as objective functions, a multi-objective optimization model considering the economy and safety of the asphalt concrete core wall is constructed. Based on the response surface method, the response surface regression relationship between the objective variables and the decision variables is fitted, and the NSGA-II algorithm is used to solve the multi-objective optimization model to obtain the Pareto optimal solution set of the core wall joint structure optimization design. Finally, the linear weighted legal method is used to compare and select the mixing ratio schemes to obtain the optimal structural forms of joints with different biases; while improving the structural stability of the asphalt concrete core wall, the present invention takes into account the economy of the project, and thus obtains the optimized asphalt concrete core wall joint structure. Description of the Drawings

[0038] Figure 1 is a schematic flow chart of the optimization method for the asphalt concrete core wall joint structure combining economy and safety of the present invention;

[0039] Figure 2It is a schematic diagram of the joint structure part of the asphalt concrete core wall foundation in Embodiment 6 of the present invention;

[0040] Figure 3 It is a scatter plot distribution diagram of the Pareto front between the shear stress evaluation index τ and the tensile stress evaluation index σ of the core wall in Embodiment 6 of the present invention;

[0041] Figure 4 It is a scatter plot distribution diagram of the Pareto front between the shear stress evaluation index τ and the arch effect coefficient evaluation index R of the core wall in Embodiment 6 of the present invention;

[0042] Figure 5 It is a scatter plot distribution diagram of the Pareto front between the shear stress evaluation index τ and the joint structure volume V of the core wall in Embodiment 6 of the present invention;

[0043] Figure 6 It is a scatter plot distribution diagram of the Pareto front between the tensile stress evaluation index σ and the arch effect coefficient evaluation index R of the core wall in Embodiment 6 of the present invention;

[0044] Figure 7 It is a scatter plot distribution diagram of the Pareto front between the tensile stress evaluation index σ and the joint structure volume V of the core wall in Embodiment 6 of the present invention;

[0045] Figure 8 It is a scatter plot distribution diagram of the Pareto front between the arch effect coefficient evaluation index R and the joint structure volume V of the core wall in Embodiment 6 of the present invention. Specific embodiments

[0046] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0047] Embodiment 1

[0048] An optimization method for the asphalt concrete core wall joint structure combining economy and safety includes the following steps:

[0049] Step 1: Taking the geometric shape parameters of the asphalt concrete core wall joint structure as decision variables and the economy and safety of the asphalt concrete core wall as objective functions, a multi-objective optimization model of the asphalt concrete core wall joint structure is constructed;

[0050] Step 2: Fitting a second-order response surface regression model between the safety performance evaluation index of the asphalt concrete core wall and the decision variables;

[0051] Step 3: Substitute the fitted second-order response surface regression model into the constructed multi-objective optimization model of the asphalt concrete core wall joint structure, and use the non-dominated sorting genetic algorithm NSGA-II (Nondominated Sorting Genetic Algorithm II, NSGA-II) to perform multi-objective optimization and solution of the joint structure to obtain the optimal joint structure forms with different biases.

[0052] Example 2

[0053] An optimization method for the asphalt concrete core wall joint structure combining economy and safety includes the following steps:

[0054] Step 1: Take the geometric shape parameters of the asphalt concrete core wall joint structure as decision variables, and take the economy and safety of the asphalt concrete core wall as objective functions to construct a multi-objective optimization model of the asphalt concrete core wall joint structure;

[0055] The specific process of Step 1 is as follows:

[0056] Step 1.1: According to the joint structure form of the asphalt concrete core wall, select the enlarged angle θ, the embedded depth h, and the slope coefficient i of the asphalt concrete core wall joint structure as decision variables;

[0057] Step 1.2: According to the stress characteristics of the asphalt concrete core wall, select the shear stress τ, the tensile stress σ, and the arch effect coefficient R of the asphalt concrete core wall as safety performance evaluation indicators;

[0058] Step 1.3: According to the "Design Code for Asphalt Concrete Face Slab and Core Wall of Earth-Rock Dam", determine the geometric constraint conditions of the asphalt concrete core wall joint structure as shown in Equation (1) and the stress constraint conditions as shown in Equation (2):

[0059]

[0060] In the formula, i min , θ min , h min are respectively the lower limit values of the slope coefficient of the bank slope, the enlarged angle, and the embedded depth, i max , θ max , h max are respectively the upper limit values of the slope coefficient of the bank slope, the enlarged angle, and the embedded depth, τ max , σ max , R min are respectively the maximum shear stress, the maximum tensile stress, and the minimum arch effect coefficient of the asphalt concrete core wall, [τ t , [σ t , [R t are respectively the allowable values of the shear stress, the tensile stress, and the arch effect coefficient;

[0061] Step 1.4: Construct a multi-objective optimization model for the asphalt concrete core wall with the economy and safety of the asphalt concrete core wall as the objective function, as shown in Equations (3) and (4):

[0062] Obj{τ(i,θ,h),σ(i,θ,h),R(i,θ,h),V(i,θ,h)}→min (3)

[0063]

[0064] In the formula, V is the volume of the joint structure.

[0065] Step 2: Fit a second-order response surface regression model between the safety performance evaluation index of the asphalt concrete core wall and the decision variables;

[0066] Step 3: Substitute the fitted second-order response surface regression model into the constructed multi-objective optimization model for the joint structure of the asphalt concrete core wall, and use the NSGA-II algorithm to perform multi-objective optimization solution for the joint structure to obtain the optimal joint structure forms with different biases.

[0067] Example 3

[0068] An optimization method for the joint structure of an asphalt concrete core wall combining economy and safety, comprising the following steps:

[0069] Step 1: Take the geometric shape parameters of the joint structure of the asphalt concrete core wall as decision variables, and take the economy and safety of the asphalt concrete core wall as the objective function to construct a multi-objective optimization model for the joint structure of the asphalt concrete core wall;

[0070] The specific process of Step 1 is as follows:

[0071] Step 1.1: Select the amplification angle θ, the embedding depth h, and the slope coefficient i of the joint structure of the asphalt concrete core wall as decision variables;

[0072] Step 1.2: Select the shear stress τ, the tensile stress σ, and the arch effect coefficient R of the asphalt concrete core wall as safety performance evaluation indicators;

[0073] Step 1.3: Determine the geometric constraint conditions of the joint structure of the asphalt concrete core wall as shown in Equation (1), and the stress constraint conditions as shown in Equation (2):

[0074]

[0075] In the formula, i min , θ min , h min are respectively the lower limit values of the slope coefficient of the bank slope, the amplification angle, and the embedding depth, i max , θ max , h maxThey are the upper limit values of the slope coefficient of the bank slope, the amplification angle, and the embedding depth, τ max , σ max , R min They are the maximum shear stress, the maximum tensile stress, and the minimum arch effect coefficient of the asphalt concrete core wall, respectively. [τ t , [σ t , [R t are the allowable values of the shear stress, the tensile stress, and the arch effect coefficient, respectively;

[0076] Step 1.4: Taking the economy and safety of the asphalt concrete core wall as the objective function, construct a multi-objective optimization model for the asphalt concrete core wall, as shown in Equations (3) and (4):

[0077] Obj{τ(i,θ,h),σ(i,θ,h),R(i,θ,h),V(i,θ,h)}→min (3)

[0078]

[0079] In the formula, V is the volume of the joint structure.

[0080] Step 2: Fit a second-order response surface regression model between the safety performance evaluation index of the asphalt concrete core wall and the decision variables;

[0081] The specific process of Step 2 is as follows:

[0082] Step 2.1: Adopt the Central Composite Design (CCD) method. Taking the amplification angle θ of the joint structure, the embedding depth h, and the slope coefficient i of the bank slope as the design variables, and taking the safety performance evaluation indexes of the shear stress τ, the tensile stress σ, and the arch effect coefficient R of the asphalt concrete core wall as the response variables, determine the horizontal values of the design variables according to the geometric constraint conditions of the core wall joint structure, and design a response surface regression test scheme;

[0083] Step 2.2: Based on the designed response surface regression test scheme, successively carry out finite element numerical simulation calculations of the asphalt concrete core wall dam under each test scheme, and extract the corresponding response variable values;

[0084] Step 2.3: Based on the response surface regression test scheme and the corresponding response variable values, fit a second-order response surface regression model between the safety performance evaluation index of the asphalt concrete core wall and the decision variables.

[0085] Step 3: Substitute the fitted second-order response surface regression model into the constructed multi-objective optimization model of the asphalt concrete core wall joint structure, and use the NSGA-II algorithm to perform multi-objective optimization solution of the joint structure to obtain the optimal joint structure forms with different biases.

[0086] Example 4

[0087] An optimization method for the joint structure of asphalt concrete core walls that combines economy and safety, comprising the following steps:

[0088] Step 1: Taking the geometric shape parameters of the asphalt concrete core wall joint structure as decision variables and the economy and safety of the asphalt concrete core wall as the objective function, construct a multi-objective optimization model for the asphalt concrete core wall joint structure;

[0089] The specific process of Step 1 is as follows:

[0090] Step 1.1: Select the enlarged angle θ, embedded depth h, and slope coefficient i of the asphalt concrete core wall joint structure as decision variables;

[0091] Step 1.2: Select the shear stress τ, tensile stress σ, and arch effect coefficient R of the asphalt concrete core wall as safety performance evaluation indicators;

[0092] Step 1.3: Determine the geometric constraint conditions of the asphalt concrete core wall joint structure as shown in Equation (1) and the stress constraint conditions as shown in Equation (2):

[0093]

[0094] In the formula, i min , θ min , h min are respectively the lower limit values of the slope coefficient, enlarged angle, and embedded depth of the bank slope, i max , θ max , h max are respectively the upper limit values of the slope coefficient, enlarged angle, and embedded depth of the bank slope, τ max , σ max , R min are respectively the maximum shear stress, maximum tensile stress, and minimum arch effect coefficient of the asphalt concrete core wall, [τ t , [σ t , [R t are respectively the allowable values of the shear stress, tensile stress, and arch effect coefficient;

[0095] Step 1.4: Taking the economy and safety of the asphalt concrete core wall as the objective function, construct a multi-objective optimization model for the asphalt concrete core wall, as shown in Equations (3) and (4):

[0096] Obj{τ(i,θ,h),σ(i,θ,h),R(i,θ,h),V(i,θ,h)}→min (3)

[0097]

[0098] In the formula, V is the volume of the joint structure.

[0099] Step 2: Fit a second-order response surface regression model between the safety performance evaluation indexes of the asphalt concrete core wall and the decision variables.

[0100] The specific process of Step 2 is as follows:

[0101] Step 2.1: Adopt the central composite experimental design method. Take the enlarged angle θ of the joint structure, the embedding depth h, and the bank slope coefficient i of the decision variables as the design variables, and take the shear stress τ, tensile stress σ, and arch effect coefficient R of the asphalt concrete core wall as the response variables of the safety performance evaluation indexes. Determine the horizontal values of the design variables according to the geometric constraint conditions of the core wall joint structure, and design a response surface regression test scheme.

[0102] Step 2.2: Based on the designed response surface regression test scheme, successively carry out finite element numerical simulation calculations of the asphalt concrete core wall dam under each test scheme, and extract the corresponding response variable values.

[0103] Step 2.3: Based on the response surface regression test scheme and the corresponding response variable values, fit a second-order response surface regression model between the safety performance evaluation indexes of the asphalt concrete core wall and the decision variables.

[0104] Step 3: Substitute the fitted second-order response surface regression model into the constructed multi-objective optimization model of the asphalt concrete core wall joint structure. Use the NSGA-II algorithm to solve the multi-objective optimization of the joint structure, and use the linear weighted sum method to compare the ratio schemes to obtain the optimal joint structure forms with different biases.

[0105] Example 5

[0106] An optimization method for the asphalt concrete core wall joint structure combining economy and safety, see Figure 1 , including the following steps:

[0107] Step 1: Take the geometric shape parameters of the asphalt concrete core wall joint structure as the decision variables, and take the economy and safety of the asphalt concrete core wall as the objective functions to construct a multi-objective optimization model of the asphalt concrete core wall joint structure.

[0108] The specific process of Step 1 is as follows:

[0109] Step 1.1: According to the joint structure form of the asphalt concrete core wall, select the enlarged angle θ of the joint structure, the embedding depth h, and the bank slope coefficient i as the decision variables.

[0110] Step 1.2: According to the stress characteristics of the asphalt concrete core wall, select the shear stress τ, tensile stress σ, and arch effect coefficient R of the asphalt concrete core wall as the safety performance evaluation indexes.

[0111] Step 1.3: According to the Design Code for Asphalt Concrete Face Slab and Core Wall of Earth-Rock Dam, determine the geometric constraint conditions of the asphalt concrete core wall joint structure as shown in Equation (1) and the stress constraint conditions as shown in Equation (2):

[0112]

[0113] In the formula, i min , θ min , h min are respectively the lower limit values of the slope coefficient of the bank slope, the magnification angle, and the embedding depth. i max , θ max , h max are respectively the upper limit values of the slope coefficient of the bank slope, the magnification angle, and the embedding depth. τ max , σ max , R min are respectively the maximum shear stress, the maximum tensile stress, and the minimum arch effect coefficient of the asphalt concrete core wall. [τ t , [σ t , [R t are respectively the allowable values of the shear stress, the tensile stress, and the arch effect coefficient;

[0114] Step 1.4: Taking the economy and safety of the asphalt concrete core wall as the objective function, construct a multi-objective optimization model of the asphalt concrete core wall as shown in Equation (3) and Equation (4):

[0115] Obj{τ(i, θ, h), σ(i, θ, h), R(i, θ, h), V(i, θ, h)} → min (3)

[0116]

[0117] In the formula, V is the volume of the joint structure.

[0118] Step 2: Fit the second-order response surface regression model between the safety performance evaluation index of the asphalt concrete core wall and the decision variables;

[0119] The specific process of Step 2 is as follows:

[0120] Step 2.1: Adopt the central composite experimental design method. Taking the magnification angle θ of the joint structure, the embedding depth h, and the slope coefficient i of the bank slope as the design variables, and taking the safety performance evaluation indexes of the shear stress τ, the tensile stress σ, and the arch effect coefficient R of the asphalt concrete core wall as the response variables, determine the horizontal values of the design variables according to the geometric constraint conditions of the core wall joint structure, and design the response surface regression test scheme;

[0121] Step 2.2: Based on the designed response surface regression test scheme, successively carry out the finite element numerical simulation calculations of the asphalt concrete core wall dam under each test scheme, and extract the corresponding response variable values;

[0122] Step 2.3: Based on the response surface regression test scheme and the corresponding response variable values, fit a second-order response surface regression model between the safety performance evaluation index of the asphalt concrete core wall and the decision variables.

[0123] Step 3: Substitute the fitted second-order response surface regression model into the multi-objective optimization model of the asphalt concrete core wall joint structure, and use the NSGA-II algorithm to solve the multi-objective optimization of the joint structure to obtain the optimal joint structure forms with different biases.

[0124] The specific process of Step 3 is as follows:

[0125] Step 3.1: Substitute the fitted second-order response surface regression model into the multi-objective optimization model of the asphalt concrete core wall joint structure, and use the NSGA-II algorithm to solve the multi-objective optimization model to obtain the Pareto optimal solution set of the optimized design of the asphalt concrete core wall joint structure.

[0126] Step 3.2: Normalize the objective function values in the Pareto optimal solution set using Equation (5).

[0127]

[0128] In the formula, Y ij is the j-th normalized value of the i-th objective, x ij is the j-th attribute value of the i-th objective, is the maximum attribute value of the i-th objective, is the minimum attribute value of the i-th objective;

[0129] Step 3.3: Obtain the comprehensive evaluation index M of the mechanical properties of the core wall using Equation (6). j ;

[0130]

[0131] In the formula, M j is the j-th normalized value of the comprehensive evaluation index of the mechanical properties of the core wall, and n is the number of evaluation indexes of the mechanical properties of the core wall;

[0132] Step 3.4: Assign corresponding weight coefficients according to the importance of the objectives, and use the linear weighted sum method to perform a linear combination of the normalized values to obtain different ratio schemes. Use the comprehensive evaluation index u j to compare and select the ratio schemes. The optimal solution scheme under the biased type is the one with the minimum comprehensive evaluation index u j in the Pareto optimal solution set:

[0133] u j = w m Mj +w v V j (7)

[0134] Wherein, V j is the j-th normalized value of the joint volume index, and w m is the weight coefficient of the comprehensive evaluation index of the core wall mechanical properties, and w v is the weight coefficient of the joint volume index.

[0135] The optimal structural forms of joints with different biases include safety-biased type, economy-biased type and balanced type joint structural forms. For the safety-biased type, w m > w v ; for the economy-biased type, w m < w v ; for the balanced type, w m = w v .

[0136] Example 6

[0137] An optimization method for the asphalt concrete core wall joint structure combining economy and safety includes the following steps:

[0138] Step 1, construct a multi-objective optimization model for the asphalt concrete core wall joint structure, and the specific process is as follows:

[0139] Step 1.1, according to the Figure 2 shown asphalt concrete core wall joint structure form, select the joint structure amplification angle θ, the embedding depth h, and the slope coefficient i of the bank slope as decision variables, Figure 2 where i = L / H, H is the core wall height, and L represents the horizontal distance between the top of the core wall and the base;

[0140] Step 1.2, according to the stress characteristics of the asphalt concrete core wall, select the shear stress τ, the tensile stress σ and the arch effect coefficient R of the asphalt concrete core wall as safety performance evaluation indicators;

[0141] Step 1.3, according to the "Design Code for Asphalt Concrete Face Slab and Core Wall of Earth-Rock Dam", determine the geometric constraint conditions of the asphalt concrete core wall joint structure as shown in Equation (1), and the stress constraint conditions as shown in Equation (2):

[0142]

[0143] Wherein, τ max , σ max , R min are respectively the maximum shear stress, the maximum tensile stress and the minimum arch effect coefficient of the asphalt concrete core wall;

[0144] Step 1.4: Taking the economy and safety of the asphalt concrete core wall as the objective function, a multi-objective optimization model of the asphalt concrete core wall is constructed, as shown in Equations (3) and (4):

[0145] Obj{τ(i,θ,h),σ(i,θ,h),R(i,θ,h),V(i,θ,h)}→min (3)

[0146]

[0147] In the formula, V is the volume of the joint structure, c is the axis length of the arc section at the bottom of the core wall, H is the height of the core wall, d is the height of the enlarged section of the joint structure, and l is the top width of the enlarged section of the joint structure;

[0148] Step 2: Fit the second-order response surface regression model between the safety performance evaluation index of the asphalt concrete core wall and the decision variables. The specific process is as follows:

[0149] Step 2.1: Using the Central Composite Design (CCD) method, taking the enlarged angle θ of the joint structure, the embedding depth h, and the slope coefficient i of the bank slope as the design variables, and taking the shear stress τ, tensile stress σ, and arch effect coefficient R of the asphalt concrete core wall as the response variables, determine the horizontal values of the design variables according to the geometric constraint conditions of the core wall joint structure, and design the response surface regression test scheme, as shown in Table 1;

[0150] Step 2.2: According to the designed test scheme, sequentially carry out the finite element numerical simulation calculation of the asphalt concrete core wall dam under each test scheme, and extract the corresponding response variable values, as shown in Table 1:

[0151] Table 1 CCD test design scheme and results

[0152]

[0153]

[0154] Step 2.3: Based on the response surface regression test scheme and the corresponding response variable values, fit the second-order response surface regression model between the safety performance evaluation index of the asphalt concrete core wall and the decision variables, as shown in Equations (6) - (8). Through variance analysis, the determination coefficient R of each second-order response surface regression model 2 is close to 90%, indicating that the regression model has good fitting accuracy.

[0155]

[0156] Step 3: Substitute the fitted second-order response surface regression model into the multi-objective optimization model of the asphalt concrete core wall joint structure, and use the NSGA-II algorithm to solve the multi-objective optimization of the joint structure to obtain the optimal joint structure forms with different biases. The specific process is as follows:

[0157] Step 3.1: Substitute the fitted second-order response surface regression models in Equations (6) - (8) into the multi-objective optimization model of the asphalt concrete core wall joint structure in Equation (3). Considering that for a specific project, the bank slope coefficient i is usually not a variable that can be optimized, based on the relevant engineering data of this asphalt concrete core wall dam, that is, the bank slope coefficient i is 0.33, the core wall height H is 132 m, the axis length c of the arc section at the bottom of the core wall is 122 m, the height d of the enlarged section of the joint structure is 3 m, and the top width l of the enlarged section of the joint structure is 1.5 m, the multi-objective optimization model is as shown in Equations (9) and (10).

[0158]

[0159] The constraint functions are as follows:

[0160]

[0161] Use the NSGA-II algorithm (Nondominated Sorting Genetic Algorithm II, NSGA-II) to solve the multi-objective optimization model. During the solution process, the population size of the NSGA-II algorithm is taken as 100, the number of genetic generations is taken as 200 generations, and the crossover probability is taken as 0.9. The obtained scatter plot of the optimized Pareto front is as Figures 3 to 8 shown. It can be seen that there are mutual constraints between each pair of indicators, and it is difficult to achieve the optimal goal simultaneously. Therefore, the optimal solution obtained by the multi-objective optimization algorithm is not unique, and a solution needs to be selected from the Pareto front as the optimal joint structure form according to the actual engineering requirements;

[0162] Step 3.2: Normalize the objective function values in the Pareto optimal solution set using Equation (11);

[0163]

[0164] where Y ij is the j-th normalized value of the i-th objective, x ij is the j-th attribute value of the i-th objective, is the maximum attribute value of the i-th objective, is the minimum attribute value of the i-th objective;

[0165] Step 3.3, considering the multiplicity of the mechanical property indexes of the core wall, the comprehensive evaluation index M of the mechanical properties of the core wall is obtained by using Equation (12). j ;

[0166]

[0167] where M j is the j-th normalized value of the comprehensive evaluation index of the mechanical properties of the core wall, and n is the number of evaluation indexes of the mechanical properties of the core wall;

[0168] Step 3.4, according to the importance degree of the objectives, the corresponding weight coefficients are assigned, and the linear weighted sum method is used to linearly combine the normalized values to obtain different proportioning schemes. The comprehensive evaluation index u j is used to compare and select the proportioning schemes. The minimum value of the comprehensive evaluation index u j in the Pareto optimal solution set is the optimal solution scheme under the biased type. That is, substitute M j and V j corresponding to each group of optimal solutions in the Pareto optimal solution set into Equation (13) to solve the minimum value of the comprehensive evaluation index u j of each biased joint. The optimal solution corresponding to the minimum u j is the optimal structural form of the biased joint:

[0169] uj = wmMj + wvVj (13)

[0170] where V j is the j-th normalized value of the joint volume index, w m is the weight coefficient of the comprehensive evaluation index of the mechanical properties of the core wall, and w v is the weight coefficient of the joint volume index.

[0171] In order to obtain the structural design schemes for the two objectives of structural safety and economy, the weights are allocated according to the importance degree of the two objectives. In the selection of the coefficients of the weight vector, the normalized mechanical property indexes of the core wall and the objective function values of the joint structure volume are magnified according to different biases for a certain biased objective. In the safety-biased type, the importance degree of the objective function of the mechanical property indexes of the core wall is set to be twice that of the joint structure volume, so its coefficient is 2 / 3, approximately regarded as 0.7, and the bias coefficient of the joint structure volume is 0.3. Similarly, finally, the weight vectors of the 3 types of joint structure design schemes of the safety-biased type, economy-biased type, and balanced type are taken as (0.7, 0.3), (0.3, 0.7), and (0.5, 0.5) in turn. The optimized design results of different biased joint structures are finally shown in Table 2.

[0172] It can be seen that compared with the existing joint form of this asphalt concrete core wall dam joint, the safety-biased joint form τ max is reduced by 14.10%, σmax Decrease by 1.28%, R min Increase by 3.82%, V increases by 10.06%; Economical-biased joint form τ max Decrease by 1.93%, σ max Decrease by 0.59%, minimum arch effect R min Increase by 0.85%, joint volume V increases by 1.57%; Balanced joint form τ max Decrease by 3.80%, σ max Increase by 0.62%, minimum arch effect R min Increase by 2.16%, joint volume V increases by 1.84%. It can be seen that the safety-biased joint structure has significant improvements in mechanical properties, but it will significantly increase the project investment. While the economical-biased and balanced joint structures have a relatively small degree of improvement in mechanical properties, the increase in project investment is also relatively small. Therefore, in the actual optimization design process of asphalt concrete core wall dam joints, various factors can be comprehensively considered to determine the final optimized design plan.

[0173] Table 2 Structural dimensions and performance indicators of the joint structure before and after optimization

[0174]

Claims

1. A method for optimizing the structure of asphalt concrete core-wall joints combining economy and safety, characterized in that: The following steps are involved: Step 1, taking the geometric shape parameters of the asphalt concrete core wall joint structure as decision variables and the economy and safety of the asphalt concrete core wall as objective functions, a multi-objective optimization model of the asphalt concrete core wall joint structure is constructed; Step 2, fitting a second-order response surface regression model between the asphalt concrete core wall safety performance evaluation index and the decision variables; Step 3: Substitute the fitted second-order response surface regression model into the constructed multi-objective optimization model of the asphalt concrete core-wall joint structure, and use the NSGA-II algorithm to solve the multi-objective optimization of the joint structure to obtain the optimal structural form of the joint with different biases.

2. The asphalt concrete core wall joint structure optimization method combining economy and safety according to claim 1 is characterized in that: The specific process of step 1 is as follows: Step 1.1, select the asphalt concrete core wall joint structure magnification angle θ, embedding depth h, and bank slope coefficient i as decision variables; Step 1.2, selecting asphalt concrete core wall shear stress τ, tensile stress σ and arch effect coefficient R as safety performance evaluation indicators; Step 1.3, determine the geometric constraints of the asphalt concrete core wall joint structure as shown in formula (1), and the stress constraints as shown in formula (2): In the formula, i min ,θ min 、h min are the lower limits of the slope coefficient, magnification angle, and embedding depth, respectively. max ,θ max 、h max are the upper limit of the bank slope coefficient, magnification angle, and embedding depth, respectively. max , σ max , R min are the maximum shear stress, maximum tensile stress and minimum arch effect coefficient of the asphalt concrete core wall, [τ t ]、[σ t ]、[R t ] are the allowable values ​​of shear stress, tensile stress and arch effect coefficient respectively; Step 1.4, taking the economy and safety of asphalt concrete core wall as the objective function, a multi-objective optimization model of asphalt concrete core wall is constructed, as shown in equations (3) and (4): Obj{τ(i,θ,h),σ(i,θ,h),R(i,θ,h),V(i,θ,h)}→min (3) Where V is the joint structure volume.

3. The asphalt concrete core wall joint structure optimization method combining economy and safety according to claim 2 is characterized in that: The specific process of step 2 is as follows: Step 2.1, adopt the central composite test design method, take the joint structure magnification angle θ, embedment depth h and bank slope coefficient i as the decision variables, take the asphalt concrete core wall shear stress τ, tensile stress σ and arch effect coefficient R safety performance evaluation index as the response variables, determine the horizontal value of the design variable according to the geometric constraints of the core wall joint structure, and design the response surface regression test plan; Step 2.2, based on the designed response surface regression test scheme, carry out the finite element numerical simulation calculation of the asphalt concrete core wall dam under each test scheme in turn, and extract the corresponding response variable value; Step 2.3, based on the response surface regression test plan and the corresponding response variable values, fit the second-order response surface regression model between the asphalt concrete core wall safety performance evaluation index and the decision variables.

4. The asphalt concrete core wall joint structure optimization method combining economy and safety according to claim 3 is characterized in that: The specific process of step 3 is as follows: Step 3.1, substitute the fitted second-order response surface regression model into the constructed multi-objective optimization model of asphalt concrete core-wall joint structure, use NSGA-II algorithm to solve the multi-objective optimization model, and obtain the Pareto optimal solution set of the asphalt concrete core-wall joint structure optimization design; Step 3.2, use formula (5) to normalize the objective function value in the Pareto optimal solution set; Where Y ij is the jth normalized value of the ith target, x ij is the jth attribute value of the ith target, is the maximum attribute value of the i-th target, is the minimum attribute value of the i-th target; Step 3.3, use formula (6) to obtain the comprehensive evaluation index of the core wall mechanical properties: Where M j is the jth normalized value of the comprehensive evaluation index of the core wall mechanical properties, and n is the number of evaluation indexes of the core wall mechanical properties; Step 3.4, assign corresponding weight coefficients according to the importance of the target, and obtain the comprehensive evaluation index u corresponding to the optimal structural form of the joint with different biases j , Pareto optimal solution centralized comprehensive evaluation index u j The smallest one is the optimal structural form of the biased joint; u j =w m M j +w v V j (7) Where V j is the jth normalized value of the joint volume index, w m is the weight coefficient of the comprehensive evaluation index of the core wall mechanical properties, w v is the weight coefficient of the joint volume index.

5. The asphalt concrete core wall joint structure optimization method combining economy and safety according to claim 4 is characterized in that: In step 3.4, corresponding weight coefficients are assigned according to the importance of the target, and the normalized values ​​are linearly combined using the linear weighted sum method to obtain different ratio schemes, and the ratio schemes are compared to obtain the optimal structural forms of joints with different biases.

6. The asphalt concrete core wall joint structure optimization method combining economy and safety according to claim 5 is characterized in that: The optimal structural forms of the joints with different inclinations include safety-oriented, economical-oriented and balanced joint structural forms.

7. The asphalt concrete core wall joint structure optimization method combining economy and safety according to claim 6 is characterized in that: In step 3.4, the corresponding weight coefficient is assigned according to the importance of the target. For the safety-oriented type, w m >w v , for the economic bias, w m <w v , for the balanced type, w m =w v .

8. The asphalt concrete core wall joint structure optimization method combining economy and safety according to claim 7 is characterized in that: In step 3.4, the M corresponding to each optimal solution in the Pareto optimal solution set is j and V j Substitute into formula (7) to solve the comprehensive evaluation index u of each deflection joint: j Minimum value, minimum u j The corresponding optimal solution is the optimal structural form of the offset joint.

Images