Transmission line lattice tower design method based on genetic algorithm

Abstract

The application discloses a transmission line plate-type tower foundation design method based on a genetic algorithm, and has the following steps: a plurality of transmission line plate-type tower foundation structures are randomly generated, and a design parameter combination of each transmission line plate-type tower foundation structure is obtained; a comprehensive safety index and a comprehensive economic index of each transmission line plate-type tower foundation structure are obtained according to the design parameter combination; an actual bearing capacity of the transmission line plate-type tower foundation structure is obtained according to the design parameter combination, and an initial population composed of transmission line plate-type tower foundation structures with actual bearing capacities greater than design loads is obtained through filtering; a comprehensive evaluation function is obtained based on the comprehensive safety index and the comprehensive economic index of each transmission line plate-type tower foundation structure in the initial population; and after the initial population is optimized through a genetic algorithm, the design parameter combination of the transmission line plate-type tower foundation structure is selected according to the comprehensive evaluation function value. The application can improve the overall safety and economy of the transmission line tower foundation.

Description

Technical Field

[0001] This invention relates to the field of concrete structure optimization technology, specifically to a design method for slab tower foundations of power transmission lines based on genetic algorithms. Background Technology

[0002] In the design and construction of transmission line tower foundations, the load-bearing capacity and economy of concrete structural components have always been significant challenges for engineers. Traditional design methods often focus on assessing the load-bearing capacity of individual components, failing to fully consider the interactions between components and the overall structural safety. This one-sided design may lead to safety hazards in the tower foundation under load, such as insufficient load-bearing capacity in the base plate, columns, or anchorage areas, resulting in tower foundation instability. Furthermore, in terms of material usage, optimal configuration is often not achieved, leading to resource waste and increased project costs. Therefore, a systematic optimization method is urgently needed to improve the overall safety and economy of transmission line tower foundations. Summary of the Invention

[0003] This invention aims to at least solve one of the technical problems existing in the prior art. Therefore, one objective of this invention is to propose a design method for transmission line slab tower foundations based on genetic algorithms, thereby improving the overall safety and economy of transmission line tower foundations.

[0004] This invention discloses a method for designing slab tower foundations for transmission lines based on genetic algorithms, comprising the following steps:

[0005] Step S1: Randomly generate multiple transmission line slab tower base structures and obtain the design parameter combination for each transmission line slab tower base structure. Based on the design parameter combination, obtain the comprehensive safety index and comprehensive economic index for each transmission line slab tower base structure.

[0006] Step S2: Obtain the actual bearing capacity of the transmission line slab tower base structure according to the design parameter combination, and filter to obtain an initial population of transmission line slab tower base structures whose actual bearing capacity is greater than the design load;

[0007] Step S3: Obtain a comprehensive evaluation function based on the comprehensive safety index and comprehensive economic index of each transmission line slab tower foundation structure in the initial population;

[0008] Step S4: After selecting and optimizing the initial population using a genetic algorithm, select the combination of design parameters for the transmission line slab tower base structure based on the comprehensive evaluation function value.

[0009] Furthermore, the transmission line slab tower foundation structure includes a base plate, columns, and anchoring areas, and step S1 has the following sub-steps:

[0010] Step S11: Obtain the design parameter combination of the base plate, the design parameter combination of the column, and the design parameter combination of the anchorage area;

[0011] Step S12: Obtain the base plate safety index and base plate economic index based on the combination of base plate design parameters;

[0012] Step S13: Obtain the column safety index and column economic index based on the combination of column design parameters;

[0013] Step S14: Obtain the anchorage area safety index and anchorage area economic index based on the combination of anchorage area design parameters;

[0014] Step S15: Obtain the comprehensive safety index based on the base plate safety index, the column safety index, and the anchorage area safety index;

[0015] Step S16: Obtain the comprehensive economic index based on the base plate economic index, the column economic index, and the anchorage area economic index.

[0016] Furthermore, the combination of design parameters for the base plate includes the base plate thickness, base plate cross-sectional width, base plate cross-sectional length, height of the compression zone of the base plate concrete, effective height of the base plate cross-section, thickness of the protective layer for the tensile reinforcement in the base plate, tensile strength of the reinforcement, cross-sectional area of ​​the tensile reinforcement in the base plate, thickness of the protective layer for the compressive reinforcement, axial compressive strength of the concrete, axial tensile strength of the concrete, and reinforcement ratio of the base plate.

[0017] In step S12, obtaining the base plate safety index based on the base plate design parameter combination includes the following sub-steps:

[0018] Step S1211: Obtain the actual bearing capacity of the base plate based on the combination of base plate design parameters. The actual bearing capacity of the base plate includes the bending bearing capacity and the shear bearing capacity of the base plate. The calculation formula is as follows:

[0019] ;

[0020] ;

[0021] ;

[0022] ;

[0023] ;

[0024] Indicates the bending bearing capacity of the base plate. Indicates the axial compressive strength of concrete. Indicates the width of the base plate cross section. Indicates the height of the compression zone of the base slab concrete. Indicates the effective height of the base plate section. Indicates the thickness of the base plate. Indicates the thickness of the protective layer for the tensile reinforcement in the base slab. Indicates the tensile strength of the steel reinforcement. This indicates the cross-sectional area of ​​the tensile reinforcement in the base slab. Indicates the thickness of the protective layer for compressed steel bars. Indicates the shear bearing capacity of the base plate. Indicates the influence coefficient of section height. Indicates the axial tensile strength of concrete;

[0025] Step S1212: Based on the actual bearing capacity and design load of the base plate, obtain the safety index of the base plate. The design load of the base plate includes the bending design load and the shear design load.

[0026] , Indicates the safety index of the base plate. Indicates the bending design load of the base plate. Indicates the shear design load of the base plate;

[0027] Obtaining the economic index of the base plate based on the combination of base plate design parameters includes the following sub-steps:

[0028] Step S1221: Obtain the reference base plate design parameter combination that meets the reference base plate construction requirements. The reference base plate design parameter combination includes the reference base plate thickness, reference base plate cross-sectional width, reference base plate cross-sectional length, and reference base plate reinforcement ratio.

[0029] Step S1222: Obtain the economic index of the base plate based on the actual material cost and the benchmark material cost of the base plate;

[0030] The formula used to calculate the cost of the base plate's reference materials is:

[0031] ;

[0032] in, Indicates the base plate's baseline material cost. Indicates the thickness of the reference base plate. Indicates the width of the reference base plate section. Indicates the length of the reference base plate section. This indicates the price per unit volume of concrete. Indicates the reinforcement ratio of the base slab. This indicates the price per unit volume of steel reinforcement.

[0033] The formula used to calculate the actual material cost of the base plate is:

[0034] ;

[0035] in, This indicates the actual material cost of the base plate. Indicates the actual thickness of the base plate. Indicates the length of the base plate cross section. Indicates the reinforcement ratio of the base slab. This indicates the price per unit volume of steel reinforcement.

[0036] The formula used to calculate the aforementioned economic index is as follows:

[0037] ;

[0038] in, This serves as the baseline economic index.

[0039] Furthermore, the column design parameters include column cross-sectional width, column cross-sectional length, column cross-sectional height, longitudinal compression reinforcement area, concrete axial compressive strength, concrete axial tensile strength, stirrup spacing, and stirrup cross-sectional area;

[0040] In step S13, obtaining the column safety index based on the column design parameter combination includes the following sub-steps:

[0041] Step S1311: Obtain the actual bearing capacity of the column based on the combination of column design parameters. The actual bearing capacity of the column includes the axial compressive bearing capacity, the bending bearing capacity, and the shear bearing capacity. The calculation formulas for the axial compressive bearing capacity, the bending bearing capacity, and the shear bearing capacity are as follows:

[0042] ;

[0043] ;

[0044] ;

[0045] Indicates the axial compressive bearing capacity of the column. Represents the stability coefficient. Indicates the axial compressive strength of concrete. This indicates the cross-sectional area of ​​the column concrete. Indicates the compressive strength of longitudinal reinforcement. Indicates the area of ​​the reinforcing steel in the compression zone. Indicates the bending capacity of the column. Indicates the stress pattern coefficient in the compression zone. Indicates the width of the column cross-section. Indicates the height of the concrete compression zone of the column. Indicates the effective height of the concrete column. This represents the distance from the resultant force point of the compressed reinforcement to the compression edge. Indicates the shear bearing capacity of the column. Indicates the axial tensile strength of concrete. Indicates the tensile strength of concrete stirrups. Indicates the cross-sectional area of ​​the stirrups. Indicates the spacing between stirrups;

[0046] Step S1312: Based on the actual bearing capacity and design load of the column, obtain the safety index of the column. The design load of the column includes the axial compression design load, the bending design load, and the shear design load.

[0047] , This indicates the safety index of the pillar. This indicates the axial compression design load of the column. This indicates the design load for the column's bending resistance. Indicates the shear design load of the column;

[0048] Obtaining the economic index of the column based on the combination of column design parameters includes the following sub-steps:

[0049] Step S1321: Obtain the design parameter combination of the reference column that meets the structural requirements of the reference column. The design parameter combination of the reference column includes the reference cross-sectional dimensions, the reference concrete height of the column, and the reference reinforcement ratio.

[0050] Step S1322: Obtain the column economic index based on the actual material cost of the column and the reference material cost of the column;

[0051] The formula used to calculate the cost of the base material for the column is:

[0052] ;

[0053] in, Indicates the cost of the base materials for the column. Indicates the reference cross-sectional dimensions of the column. Indicates the reference concrete height of the column. This indicates the reference reinforcement ratio of the column. This indicates the price per unit volume of concrete. This indicates the price per unit volume of steel reinforcement.

[0054] The formula used to calculate the actual material cost of the column is as follows:

[0055] ;

[0056] in, This indicates the actual material cost of the column. This indicates the actual reinforcement ratio of the column;

[0057] The formula used to calculate the pillar economic index is as follows:

[0058] ;

[0059] in, It serves as a pillar economic index.

[0060] Furthermore, the design parameter combination for the anchorage area includes anchorage depth, number of bolts, cross-sectional area of ​​a single bolt, tensile strength of bolts, preload of bolts, and axial compressive strength of concrete.

[0061] In step S14, obtaining the anchorage area safety index based on the combination of anchorage area design parameters includes the following sub-steps:

[0062] Step S1411: Obtain the actual bearing capacity of the anchorage area based on the combination of design parameters of the anchorage area. The actual bearing capacity of the anchorage area includes the tensile bearing capacity and the shear bearing capacity of the anchorage area. The specific calculation formula is as follows:

[0063] ;

[0064] ;

[0065] ;

[0066] ;

[0067] in, Indicates the tensile bearing capacity of the anchorage area. Indicates the tensile bearing capacity of the bolt. Indicates the number of bolts. This represents the cross-sectional area of ​​a single bolt. Indicates the tensile strength of the bolt. Indicates the failure bearing capacity of the concrete cone. Represents the empirical coefficient. Indicates the anchorage depth. Indicates the shear bearing capacity of the anchorage zone. This represents the coefficient of friction between the bolt and the concrete. This indicates the preload of a single bolt. Indicates the axial compressive strength of concrete;

[0068] Step S1412: Based on the actual bearing capacity of the anchorage area and the design load of the anchorage area, obtain the safety index of the anchorage area. The design load of the anchorage area includes the tensile design load and the shear design load of the anchorage area.

[0069] , This indicates the safety index of the anchorage area. Indicates the tensile design load of the anchorage area. Indicates the shear design load of the anchorage zone;

[0070] Obtaining the economic index of the anchorage area based on the combination of design parameters includes the following sub-steps:

[0071] Step S1421: Obtain the design parameter combination of the reference anchorage area that meets the reference construction requirements of the anchorage area, wherein the design parameter combination of the reference anchorage area includes the number of reference bolts in the anchorage area;

[0072] Step S142: Obtain the economic index of the anchorage area based on the actual material cost of the anchorage area and the benchmark material cost of the anchorage area;

[0073] The formula used to calculate the cost of the reference material in the anchorage area is:

[0074]

[0075] in, This indicates the baseline material cost for the anchoring area. Indicates the number of reference bolts in the anchorage area. This indicates the unit price of the bolt;

[0076] The formula used to calculate the actual material cost of the anchorage area is as follows:

[0077] ;

[0078] in, This indicates the actual material cost of the anchoring area;

[0079] The formula used to calculate the economic index of the anchorage area is as follows:

[0080] ;

[0081] in, To anchor regional economic indices.

[0082] Further, in step S15: a comprehensive safety index is obtained based on the base plate safety index, the column safety index, and the anchorage area safety index, using the following formula:

[0083] ;

[0084] in, This indicates the overall safety index. Indicates the safety index of the base plate. This indicates the safety index of the pillar. Indicates the safety index of the anchorage area;

[0085] In step S16: A comprehensive economic index is obtained based on the base plate economic index, the column economic index, and the anchoring area economic index, using the following formula:

[0086] ;

[0087] in, This represents a comprehensive economic index. This serves as the baseline economic index. As a pillar economic index. To anchor regional economic indices.

[0088] Furthermore, in step S3, the formula used to obtain the comprehensive evaluation function is:

[0089] ;

[0090] in, This represents the comprehensive evaluation function. This indicates the overall safety index. This represents a comprehensive economic index. These represent the weighting coefficients of the comprehensive safety index and the comprehensive economic index, respectively. and .

[0091] Further, step S4 includes the following sub-steps:

[0092] Step S41: Sort the individuals in the initial population in descending order of the comprehensive evaluation function value, and select the top 50% of individuals as the parents;

[0093] Step S42: Perform crossover and mutation operations on each pair of adjacent parents to generate offspring. Determine the mutation amplitude and mutation probability based on the comprehensive evaluation function value of the parents and the values ​​of each gene in the parents.

[0094] Step S43: Combine the generated offspring with the parent generation to form a secondary population;

[0095] Step S44: Repeat steps S41-S43 until the termination condition is met, at which point the iteration terminates.

[0096] Step S45: Select the design parameter combination of the transmission line slab tower base structure with the highest current comprehensive evaluation function value.

[0097] Further, in step S42, the comprehensive evaluation function value of each individual in each iteration is recorded and sorted in descending order. Individuals with the highest comprehensive evaluation function values ​​(top 30%) are selected. For each gene in the selected individuals, the gene variation magnitude is calculated using the following formula:

[0098] ;

[0099] ;

[0100] ;

[0101] in, Indicates the first The baseline value for each gene, Indicates the number of individuals selected. Indicates the first Among the individuals, the first The values ​​of each gene, An index representing genes, and , This represents the number of genes in an individual. Indicates the selected individual index, and , Indicates the first Among the individuals, the first The deviation of each gene value from the benchmark value, Indicates the first Among the individuals, the first The magnitude of variation in each gene, This represents the scaling factor, and ;

[0102] The formula used to generate the individual's probability of variation based on the individual's comprehensive evaluation function value is:

[0103] ;

[0104] in, Indicates the first The probability of mutation for each individual. Represents the basic mutation probability, and , Indicates the first The comprehensive evaluation function value of each individual. This represents the maximum value of the overall evaluation function in the current population. This represents the baseline value of the comprehensive evaluation function in the current population.

[0105] Furthermore, the termination condition is that the number of iterations is preset or the increase in the highest comprehensive evaluation function value in 10 consecutive iterations is less than 5%.

[0106] As can be seen from the technical solution, the embodiments provided by the present invention have the following advantages:

[0107] Through an intelligent optimization process, a highly efficient synergy and balance between safety and economy is achieved. This method first generates a large number of design schemes randomly and performs preliminary safety screening based on design parameters, constructing an initial population that fully meets the load-bearing capacity requirements, thus ensuring the feasibility of the design schemes. Subsequently, by constructing a comprehensive evaluation function that integrates safety and economy, the traditional multi-objective decision-making problem, which relies on engineer experience and often overlooks certain aspects, is transformed into a quantifiable global optimization problem. The genetic algorithm, by simulating natural selection and genetic mechanisms, performs efficient parallel searches across multiple design parameter spaces, automatically and rapidly iterating and evolving high-quality solutions with high safety margins and low costs—solutions that are difficult to discover through traditional empirical design. This not only significantly improves design efficiency and shortens the design cycle, freeing engineers from tedious trial calculations, but also enables the handling of complex engineering problems with multiple variables and strong constraints, ensuring that the final design scheme achieves comprehensive performance optimization while strictly adhering to all specifications. Attached Figure Description

[0108] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0109] Figure 1 This is a schematic diagram of the method flow of an embodiment of the present invention;

[0110] Figure 2 This is a schematic diagram illustrating the variation of the base plate bearing capacity in an embodiment of the present invention;

[0111] Figure 3 This is a schematic diagram illustrating the variation in the column bearing capacity according to an embodiment of the present invention;

[0112] Figure 4 This is a schematic diagram illustrating the change in bearing capacity of the anchorage area according to an embodiment of the present invention. Detailed Implementation

[0113] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0114] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0115] Example 1

[0116] The following is combined with Figures 1-4 The present invention describes a method for designing slab tower foundations for power transmission lines based on genetic algorithms, comprising the following steps:

[0117] Step S1: Randomly generate multiple transmission line slab tower base structures and obtain the design parameter combination for each transmission line slab tower base structure. Based on the design parameter combination, obtain the comprehensive safety index and comprehensive economic index of each transmission line slab tower base structure.

[0118] Step S2: Obtain the actual bearing capacity of the transmission line slab tower base structure based on the design parameter combination, and filter to obtain the initial population of transmission line slab tower base structures whose actual bearing capacity is greater than the design load;

[0119] Step S3: Obtain the comprehensive evaluation function based on the comprehensive safety index and comprehensive economic index of each transmission line slab tower foundation structure in the initial population;

[0120] Step S4: After optimizing the initial population through a genetic algorithm, select the combination of design parameters for the transmission line slab tower base structure based on the comprehensive evaluation function value.

[0121] As can be seen from the technical solution, the embodiments provided by the present invention have the following advantages:

[0122] Through an intelligent optimization process, a highly efficient synergy and balance between safety and economy is achieved. This method first generates a large number of design schemes randomly and performs preliminary safety screening based on design parameters, constructing an initial population that fully meets the load-bearing capacity requirements, thus ensuring the feasibility of the design schemes. Subsequently, by constructing a comprehensive evaluation function that integrates safety and economy, the traditional multi-objective decision-making problem, which relies on engineer experience and often overlooks certain aspects, is transformed into a quantifiable global optimization problem. The genetic algorithm, by simulating natural selection and genetic mechanisms, performs efficient parallel searches across multiple design parameter spaces, automatically and rapidly iterating and evolving high-quality solutions with high safety margins and low costs—solutions that are difficult to discover through traditional empirical design. This not only significantly improves design efficiency and shortens the design cycle, freeing engineers from tedious trial calculations, but also enables the handling of complex engineering problems with multiple variables and strong constraints, ensuring that the final design scheme achieves comprehensive performance optimization while strictly adhering to all specifications.

[0123] Example 2

[0124] Furthermore, the transmission line slab tower foundation structure includes a base plate, columns, and anchorage areas, and step S1 has the following sub-steps:

[0125] Step S11: Obtain the design parameter combination of the base plate, the design parameter combination of the column, and the design parameter combination of the anchorage area;

[0126] Step S12: Obtain the base plate safety index and base plate economic index based on the combination of base plate design parameters;

[0127] Step S13: Obtain the column safety index and column economic index based on the combination of column design parameters;

[0128] Step S14: Obtain the safety index and economic index of the anchorage area based on the combination of design parameters of the anchorage area;

[0129] Step S15: Obtain the comprehensive safety index based on the base plate safety index, column safety index, and anchorage area safety index;

[0130] Step S16: Obtain the comprehensive economic index based on the base economic index, the pillar economic index, and the anchoring area economic index.

[0131] In this embodiment, the base plate is the load-bearing component of the entire structure, primarily responsible for transferring the superstructure load to the foundation and providing stability. The thickness and reinforcement configuration of the base plate directly affect its bending and shear resistance. The columns, as vertical load-bearing structures, mainly bear the compressive and bending loads from the superstructure. Therefore, the cross-sectional dimensions, material strength, and stirrup configuration of the columns are crucial to their load-bearing capacity. The anchorage zone is responsible for firmly connecting the structure to the foundation, ensuring no displacement or failure under various loads. The design of the anchorage zone, including the anchorage depth and bolt tensile strength, directly affects its load-bearing capacity and the overall stability of the structure. Dividing the structure into these three parts allows for independent analysis of the behavior of each part while reflecting the overall structural characteristics; different parts exhibit different characteristics in their load response and load-bearing capacity.

[0132] Example 3

[0133] Furthermore, the combination of design parameters for the base slab includes the base slab thickness, base slab cross-sectional width, base slab cross-sectional length, height of the compression zone of the base slab concrete, effective height of the base slab cross-section, thickness of the protective layer for the tensile reinforcement in the base slab, tensile strength of the reinforcement, cross-sectional area of ​​the tensile reinforcement in the base slab, thickness of the protective layer for the compressive reinforcement, axial compressive strength of the concrete, axial tensile strength of the concrete, and reinforcement ratio of the base slab.

[0134] Step S12, obtaining the base plate safety index based on the combination of base plate design parameters, includes the following sub-steps:

[0135] Step S1211: Obtain the actual bearing capacity of the base plate based on the combination of base plate design parameters. The actual bearing capacity of the base plate includes the bending bearing capacity and the shear bearing capacity of the base plate. The calculation formula is as follows:

[0136] ;

[0137] ;

[0138] ;

[0139] ;

[0140] ;

[0141] Indicates the bending bearing capacity of the base plate. Indicates the axial compressive strength of concrete. Indicates the width of the base plate cross section. Indicates the height of the compression zone of the base slab concrete. Indicates the effective height of the base plate section. Indicates the thickness of the base plate. Indicates the thickness of the protective layer for the tensile reinforcement in the base slab. Indicates the tensile strength of the steel reinforcement. This indicates the cross-sectional area of ​​the tensile reinforcement in the base slab. Indicates the thickness of the protective layer for compressed steel bars. Indicates the shear bearing capacity of the base plate. Indicates the influence coefficient of section height. Indicates the axial tensile strength of concrete;

[0142] Step S1212: Based on the actual bearing capacity and design load of the base slab, obtain the base slab safety index. The base slab design load includes the bending design load and the shear design load.

[0143] , Indicates the safety index of the base plate. Indicates the bending design load of the base plate. Indicates the shear design load of the base plate;

[0144] Obtaining the economic index of the foundation plate based on the combination of foundation plate design parameters includes the following sub-steps:

[0145] Step S1221: Obtain the design parameter combination of the reference base plate that meets the reference structural requirements of the base plate. The design parameter combination of the reference base plate includes the thickness of the reference base plate, the width of the reference base plate section, the length of the reference base plate section, and the reinforcement ratio of the reference base plate.

[0146] Step S1222: Obtain the economic index of the base plate based on the actual material cost and the benchmark material cost of the base plate;

[0147] The formula used to calculate the cost of the base plate's reference materials is:

[0148] ;

[0149] in, Indicates the base plate's baseline material cost. Indicates the thickness of the reference base plate. Indicates the width of the reference base plate section. Indicates the length of the reference base plate section. This indicates the price per unit volume of concrete. Indicates the reinforcement ratio of the base slab. This indicates the price per unit volume of steel reinforcement.

[0150] The formula used to calculate the actual material cost of the base plate is:

[0151] ;

[0152] in, This indicates the actual material cost of the base plate. Indicates the actual thickness of the base plate. This indicates the actual cross-sectional width of the base plate. Indicates the length of the base plate cross section. Indicates the reinforcement ratio of the base slab. This indicates the price per unit volume of steel reinforcement.

[0153] The formula used to calculate the economic index of the base plate is as follows:

[0154] ;

[0155] in, This serves as the baseline economic index.

[0156] The bearing capacity of the base plate reflects its ability to resist failure under load. The base plate is subjected to two main loads: bending bearing capacity, which represents the resistance to bending deformation and cracking caused by bending moment, and shear bearing capacity, which represents the resistance to diagonal cracks or shear failure caused by shear force. To ensure that neither of these two types of failure occurs, the shear bearing capacity is compared with the shear design load of the base plate, the bending bearing capacity is compared with the bending design load of the base plate, and the safety index is calculated for different load types. The benchmark value of the safety index is used as the comprehensive safety index of the base plate.

[0157] The calculation of flexural bearing capacity is based on the principles of internal force equilibrium and moment equilibrium within the cross-section. Under bending moment, the tensile force in the tension zone of the bottom slab section is borne by the steel reinforcement, while the compressive force in the compression zone is borne by the concrete. This reflects the moment contribution of the concrete compression zone. This refers to the total pressure in the compression zone of the concrete. The effective height of the base plate section represents the vertical distance from the outer edge of the compression zone concrete to the reasonable point of action of the tension reinforcement. It reflects the actual lever arm length of the coordinated work between the reinforcement and the concrete. This represents the distance from the point of application of the resultant compressive force to the center of the tensile reinforcement, i.e., the internal force arm. The greater the total compressive force and the internal force arm, the greater the required bearing capacity. It reflects the moment contribution of the tensile reinforcement, representing the moment generated by the tensile force on the tensile reinforcement. Its magnitude is determined by the strength of the reinforcement and the lever arm. The total tensile force of the tensioned steel bars. This represents the distance from the point of application of the resultant force of the tensile force on the steel reinforcement to the point of application of the resultant force in the compression zone. Shear bearing capacity This mainly reflects the shear strength of the concrete itself when the base slab is not cracked. This reflects the reduction in concrete shear strength, that is, the proportion of the reduction in actual shear capacity compared to theoretical tensile strength. The larger the effective cross-sectional area of ​​the base slab, the more significant the stress concentration effect of shear failure. This is determined by the influence coefficient of section height. This correction reflects that when the effective height of the section is less than or equal to 800mm, no correction is needed; when the effective height of the section is greater than 800mm, the shear bearing capacity increases accordingly. The effect of increasing load on the actual bearing capacity of the base slab is shown in Table 1 and 2. Figure 2 As shown;

[0158] Table 1. Variation of Actual Bearing Capacity of Base Plate

[0159]

[0160] The foundation slab safety index reflects the safety margin of the foundation slab under actual loads. The design load of the foundation slab is the maximum load that the foundation slab is expected to withstand. It is an externally given, fixed load value that reflects the maximum load that the foundation slab needs to withstand under all possible design conditions. The design load of the foundation slab is obtained through finite element analysis under the most unfavorable load combination. The design load of the foundation slab is divided into bending design load and shear design load according to the different forces on the foundation slab. The bending design load indicates that when the foundation slab is subjected to bending moment transmitted from the superstructure, it will undergo bending deformation, leading to cracking of the concrete in the tension zone at the bottom or yielding of the steel reinforcement. The critical stress value at which bending deformation occurs is D. 1,flex When the base plate is subjected to shear force, oblique section shear failure will occur. The critical stress value for shear failure is D. 1,shear The base plate may be bent due to excessive bending moment or sheared due to excessive shear force. These two failure modes are independent of each other. Therefore, the safety index of the base plate is calculated based on the actual bearing capacity and its corresponding maximum load. F1 is the actual bearing capacity of the base plate, i.e., the actual load it bears. The ratio of the two is the safety index of the base plate. Based on S1, the load bearing condition of the base plate is judged. When the actual bearing capacity is less than the design load, the actual load of the base plate cannot meet the design load requirements. Under the current parameters, the base plate does not have enough ability to resist the load it is expected to bear. The structure is unsafe and the base plate needs to be redesigned. When the actual bearing capacity is greater than or equal to the design load, the larger the safety index of the base plate, the greater the actual bearing capacity of the base plate relative to the design load. The base plate has the ability to bear the expected load. When the two are equal, it means that the actual bearing capacity of the base plate can just meet the design load requirements. At this time, the load limit is reached. The design load is obtained through finite element analysis. The specific process is as follows: establish a finite element model of the tower foundation concrete structure, apply various loads to the model, perform combined analysis of the loads to determine the most unfavorable working condition, extract the maximum bending moment at the control section of the base plate and establish the maximum value, and obtain the bending design load and the shear design load.

[0161] The baseline structural requirements for the base plate are baseline thickness and baseline reinforcement ratio, and the materials are concrete and steel bars; the baseline structural requirements for the column are baseline cross-sectional dimensions and baseline reinforcement ratio, and the materials are concrete and steel bars; the baseline structural requirements for the anchorage area are baseline anchorage depth and minimum number of bolts, and the materials are concrete and bolts.

[0162] The specific requirements for the baseline construction are as follows:

[0163] The base plate's reference thickness is The benchmark reinforcement ratio is ,in These represent the axial tensile strength of concrete and the tensile strength of steel reinforcement, respectively. The cantilever length of the base slab represents the horizontal distance from the edge of the column to the outer edge of the base slab. .

[0164] Example 4

[0165] Furthermore, the column design parameters include column section width, column section length, column section height, longitudinal compression reinforcement area, axial compressive strength of concrete, axial tensile strength of concrete, stirrup spacing, and stirrup cross-sectional area.

[0166] Step S13, obtaining the column safety index based on the combination of column design parameters, includes the following sub-steps:

[0167] Step S1311: Obtain the actual bearing capacity of the column based on the combination of column design parameters. The actual bearing capacity of the column includes the axial compressive bearing capacity, the bending bearing capacity, and the shear bearing capacity. The calculation formulas for the axial compressive bearing capacity, bending bearing capacity, and shear bearing capacity are as follows:

[0168] ;

[0169] ;

[0170] ;

[0171] Indicates the axial compressive bearing capacity of the column. Represents the stability coefficient. Indicates the axial compressive strength of concrete. This indicates the cross-sectional area of ​​the column concrete. Indicates the compressive strength of longitudinal reinforcement. Indicates the area of ​​the reinforcing steel in the compression zone. Indicates the bending capacity of the column. Indicates the stress pattern coefficient in the compression zone. Indicates the width of the column cross-section. Indicates the height of the concrete compression zone of the column. Indicates the effective height of the concrete column. This represents the distance from the resultant force point of the compressed reinforcement to the compression edge. Indicates the shear bearing capacity of the column. Indicates the axial tensile strength of concrete. Indicates the tensile strength of concrete stirrups. Indicates the cross-sectional area of ​​the stirrups. Indicates the spacing between stirrups;

[0172] Step S1312: Based on the actual bearing capacity of the column and the column design load, obtain the column safety index. The column design load includes the column axial compression design load, the column bending design load, and the column shear design load.

[0173] , This indicates the safety index of the pillar. This indicates the axial compression design load of the column. This indicates the design load for the column's bending resistance. Indicates the shear design load of the column;

[0174] Obtaining the economic index of a pillar based on a combination of pillar design parameters includes the following sub-steps:

[0175] Step S1321: Obtain the design parameter combination of the reference column that meets the structural requirements of the reference column. The design parameter combination of the reference column includes the reference cross-sectional dimensions, the reference concrete height of the column, and the reference reinforcement ratio. The materials used are concrete and steel bars.

[0176] Step S1322: Obtain the column economic index based on the actual material cost of the column and the benchmark material cost of the column;

[0177] The formula used to calculate the cost of the base material for the column is:

[0178] ;

[0179] in, Indicates the cost of the base materials for the column. Indicates the reference cross-sectional dimensions of the column. Indicates the reference concrete height of the column. This indicates the reference reinforcement ratio of the column. This indicates the price per unit volume of concrete. This indicates the price per unit volume of steel reinforcement.

[0180] The formula used to calculate the actual material cost of the column is as follows:

[0181] ;

[0182] in, This indicates the actual material cost of the column. This indicates the actual cross-sectional dimensions of the column. Indicates the actual concrete height of the column. This indicates the actual reinforcement ratio of the column;

[0183] The formula used to calculate the pillar economic index is as follows:

[0184] ;

[0185] in, It serves as a pillar economic index.

[0186] In actual operation, the column is mainly subjected to three types of loads: vertical axial force transmitted from the superstructure, such as the self-weight of the tower and the weight of the conductor, which may cause concrete crushing or steel bar yielding, as well as column instability and buckling; deformation or cracking caused by bending moment; and shearing action caused by horizontal force. The effective height of the column is the distance from the outer edge of the concrete in the compression zone to the point of application of the resultant force of the compression reinforcement. The effective height is the total height of the column after removing the influence of the protective layer and the position of the reinforcement. This indicates the axial bearing capacity of the column, reflecting its maximum bearing capacity under pure axial pressure, and helps prevent concrete crushing or steel bar buckling. This reflects the compressive strength contribution of the concrete portion. This reflects the compressive contribution of the reinforcing steel. This reflects the influence of the column's slenderness ratio on its axial bearing capacity; the larger the slenderness ratio, the greater the axial bearing capacity. The smaller the value, the easier it is for instability to occur, and the smaller the axial bearing capacity; the smaller the flexural bearing capacity... This reflects the column's bending resistance under the combined action of axial pressure and bending moment, preventing the tensile reinforcement from yielding or the concrete in the compression zone from crushing. Represents the equivalent rectangular stress block of the concrete compression zone, with graphical coefficients. , This indicates the flexural contribution provided by the compression zone of concrete. Table 2 reflects the flexural contribution provided by the compression reinforcement; the effects of column cross-sectional dimensions, stirrup spacing, and axial compressive strength of concrete on the axial compression, bending, and shear bearing capacity of the column are shown in Table 2 and... Figure 3 As shown;

[0187] Table 2. Variation of Axial Compression, Bending and Shear Bearing Capacity of Columns

[0188]

[0189] Column safety index This represents the ratio of the column's actual bearing capacity to the design load. The actual bearing capacity of the column may be one of the following: axial compression bearing capacity, bending bearing capacity, or shear bearing capacity. The design load is determined for each type of bearing capacity to avoid overall structural failure due to insufficient bearing capacity in any one of them. Axial compression bearing capacity is mainly caused by vertical loads, such as the structure's self-weight and the weight of conductors, which may lead to concrete crushing or steel bar buckling. This indicates the design axial force that the column must withstand under pure axial compression; the flexural bearing capacity is determined by the combined action of bending moment and axial force, reflecting the maximum bending moment the column can withstand. Exceeding the flexural bearing capacity may result in yielding of the tensile reinforcement or crushing of the concrete in the compression zone; the shear bearing capacity is caused by shear force, and loads exceeding the shear bearing capacity may lead to oblique section shear failure. Only when the benchmark values ​​of several bearing capacities meet the design loads of the column is the column structure considered safe. When the actual load-bearing capacity is less than the design load, the structure is unsafe and needs to be redesigned. When the theoretical load limit is reached, At that time, the actual bearing capacity is greater than the design load, and The larger the size, the greater the actual load-bearing capacity, and the safer the structure.

[0190] The reference cross-sectional dimensions of the column are The standard reinforcement ratio is: .

[0191] Example 5

[0192] Furthermore, the design parameter combination for the anchorage area includes anchorage depth, number of bolts, cross-sectional area of ​​a single bolt, tensile strength of bolts, preload of bolts, and axial compressive strength of concrete.

[0193] Step S14, obtaining the anchorage zone safety index based on the combination of anchorage zone design parameters, includes the following sub-steps:

[0194] Step S1411: Obtain the actual bearing capacity of the anchorage zone based on the combination of design parameters. The actual bearing capacity of the anchorage zone includes the tensile bearing capacity and the shear bearing capacity of the anchorage zone. The specific calculation formula is as follows:

[0195] ;

[0196] ;

[0197] ;

[0198] ;

[0199] in, Indicates the tensile bearing capacity of the anchorage area. Indicates the tensile bearing capacity of the bolt. Indicates the number of bolts. This represents the cross-sectional area of ​​a single bolt. Indicates the tensile strength of the bolt. Indicates the failure bearing capacity of the concrete cone. Represents the empirical coefficient. Indicates the anchorage depth. Indicates the shear bearing capacity of the anchorage zone. This represents the coefficient of friction between the bolt and the concrete. This indicates the preload of a single bolt. Indicates the axial compressive strength of concrete;

[0200] Step S1412: Based on the actual bearing capacity of the anchorage zone and the design load of the anchorage zone, obtain the safety index of the anchorage zone. The design load of the anchorage zone includes the tensile design load and the shear design load of the anchorage zone.

[0201] , This indicates the safety index of the anchorage area. Indicates the tensile design load of the anchorage area. Indicates the shear design load of the anchorage zone;

[0202] Obtaining the economic index of the anchorage area based on the combination of design parameters includes the following sub-steps:

[0203] Step S1421: Obtain the design parameter combination of the reference anchorage area that meets the reference construction requirements of the anchorage area. The design parameter combination of the reference anchorage area includes the number of reference bolts in the anchorage area.

[0204] Step S142: Obtain the economic index of the anchorage area based on the actual material cost of the anchorage area and the benchmark material cost of the anchorage area;

[0205] The formula used to calculate the cost of the reference material in the anchorage area is:

[0206]

[0207] in, This indicates the baseline material cost for the anchoring area. Indicates the number of reference bolts in the anchorage area. This indicates the unit price of the bolt;

[0208] The formula used to calculate the actual material cost of the anchorage area is as follows:

[0209] ;

[0210] in, This indicates the actual material cost of the anchoring area;

[0211] The formula used to calculate the economic index of the anchorage area is as follows:

[0212] ;

[0213] in, To anchor regional economic indices.

[0214] The tensile bearing capacity of the anchorage zone is determined by two parts, and the benchmark values ​​of the two are taken as the tensile bearing capacity. This indicates the tensile bearing capacity of a bolt, reflecting the tensile strength of the bolt material itself. A bolt may fracture or yield when under tension. The more bolts there are, the higher the total bearing capacity. The larger the cross-sectional area of ​​a single bolt, the greater the tensile force it can withstand. The higher the tensile strength of the bolt material, the higher the bearing capacity. This represents the bearing capacity of a concrete cone when bolts are anchored in it, reflecting the load-bearing capacity of the concrete under tension during cone-shaped failure. It mainly occurs when the anchorage depth is insufficient or the axial compressive strength of the concrete is low. Higher axial compressive strength of the concrete results in stronger resistance to cone failure; greater anchorage depth and larger concrete cone volume lead to higher bearing capacity. An empirical coefficient is also used. This reflects the influence of factors such as concrete cracking and edge effects. For cracked concrete, k decreases to reflect the reduced tensile strength of the concrete due to cracks. The shear capacity consists of two parts. Frictional shear resistance reflects the frictional shear resistance generated by the bolt preload on the contact surface. Essentially, frictional force = normal force × friction coefficient. The main normal force is the bolt preload, and the friction coefficient is related to the roughness of the concrete and bolt surfaces. The more bolts there are, the greater the total frictional force. This reflects the shear capacity of the bolt shank when directly subjected to shear. The larger the cross-sectional area of ​​the bolt, the stronger its shear resistance; the higher the strength of the bolt material, the stronger its shear resistance. This indicates that the shear strength is approximately 80% of the tensile strength. The shear bearing capacity is contributed by both friction and the bearing capacity of the bolt under direct shear, with both contributing simultaneously. The anchorage area may fail due to either tensile or shear forces, therefore, it is necessary to ensure safety under both loads. The influence of anchorage depth on the actual bearing capacity of the anchorage area is shown in Table 3. Figure 4 As shown;

[0215] Table 3. Variation of Actual Bearing Capacity in Anchorage Zone

[0216]

[0217] The anchorage zone safety index reflects the safety margin of the anchorage zone under actual loads. The anchorage zone safety index is calculated for both tensile and shear stress states. Considering overall safety, the baseline values ​​of both are taken as the comprehensive safety index of the anchorage zone. The tensile design load of the anchorage area is represented by the maximum design load that the anchorage area needs to withstand in the tensile direction. It is caused by the tensile force transmitted from the superstructure, wind load, etc., and reflects the safety requirements of the anchorage area under tension. The maximum pressure that the anchorage area can withstand is obtained through finite element analysis. This represents the shear design load of the anchorage region, i.e., the maximum design load that the anchorage region must withstand in the shear direction. It is caused by loads such as horizontal wind load and seismic horizontal force. The maximum shear force borne by the anchorage region under the most unfavorable load combination is obtained through finite element analysis. At that time, the actual bearing capacity was higher than the design load, the structure was safe, and The larger the size, the higher the safety margin. When this occurs, it means that the actual bearing capacity just meets the design load and reaches the theoretical load limit. If the actual load-bearing capacity is lower than the design load, the structure may fail and needs to be re-optimized.

[0218] The reference anchorage depth of the anchorage area is: ,in Where: is the bolt diameter; minimum number of bolts: ,in Indicates the tensile design load of the anchorage area. This indicates the shear design load in the anchorage zone. These represent the tensile bearing capacity of the bolt and the shear bearing capacity of the anchorage zone, respectively.

[0219] Example 6

[0220] Furthermore, in step S15: the comprehensive safety index is obtained based on the base plate safety index, the column safety index, and the anchorage area safety index, using the following formula:

[0221] ;

[0222] in, This indicates the overall safety index. Indicates the safety index of the base plate. This indicates the safety index of the pillar. Indicates the safety index of the anchorage area;

[0223] In step S16: The comprehensive economic index is obtained based on the base economic index, the pillar economic index, and the anchorage area economic index. The specific formula is as follows:

[0224] ;

[0225] in, This represents a comprehensive economic index. This serves as the baseline economic index. As a pillar economic index. To anchor regional economic indicators; This indicates the actual material cost of the base plate. This indicates the actual material cost of the column. This indicates the actual material cost of the anchoring area. Indicates the base plate's baseline material cost. Indicates the cost of the base materials for the column. This indicates the cost of the reference material for the anchoring area.

[0226] The comprehensive economic index reflects the economy and efficiency of material use while meeting design load requirements. It assesses whether materials are used efficiently by comparing actual material costs with benchmark material costs. The larger the value, the lower the actual material cost while meeting normal usage requirements, indicating higher economic efficiency. , , These reflect the economic index of each component, and the higher the value, the lower the actual material cost and the higher the economic efficiency.

[0227] Example 7

[0228] Furthermore, in step S3, the formula used to obtain the comprehensive evaluation function is:

[0229] ;

[0230] in, This represents the comprehensive evaluation function. This indicates the overall safety index. This represents a comprehensive economic index. These represent the weighting coefficients of the comprehensive safety index and the comprehensive economic index, respectively. and .

[0231] The comprehensive evaluation function reflects the overall optimization objective of structural components in terms of both safety and economy, by finding the maximum... The goal is to find the optimal solution between safety and economy. In actual production, safety is more important, therefore... , .

[0232] The thickness of the base slab and the cross-sectional area of ​​the tensile reinforcement directly determine the bending and shear bearing capacity of the base slab. The axial compressive strength of concrete affects the compressive, tensile, and shear properties of all components. The column cross-sectional dimensions determine the column's compressive, bending, and shear capabilities. The stirrup spacing affects the column's shear performance. The anchorage depth and the number of bolts determine the tensile and shear bearing capacity of the anchorage area. These materials interact with each other. For example, increasing the base slab thickness can improve the bearing capacity but increases material costs; increasing the reinforcement area can improve safety but reduces economy. Genetic algorithms are used to optimize these parameters to find the optimal solution that simultaneously satisfies both safety and economy.

[0233] Example 8

[0234] Further, step S4 includes the following sub-steps:

[0235] Step S41: Sort the individuals in the initial population in descending order of the comprehensive evaluation function value, and select the top 50% of individuals as the parents;

[0236] Step S42: Perform crossover and mutation operations on each pair of adjacent parents to generate offspring. Determine the mutation amplitude and mutation probability based on the comprehensive evaluation function value of the parents and the values ​​of each gene in the parents.

[0237] In step S42, the comprehensive evaluation function value of each individual in each iteration is recorded and sorted in descending order. Individuals with the top 30% comprehensive evaluation function values ​​are selected. For each gene in the selected individuals, the gene variation amplitude is calculated using the following formula:

[0238] ;

[0239] ;

[0240] ;

[0241] in, Indicates the first The baseline value for each gene, Indicates the number of individuals selected. Indicates the first Among the individuals, the first The values ​​of each gene, An index representing genes, and , This represents the number of genes in an individual. Indicates the selected individual index, and , Indicates the first Among the individuals, the first The deviation of each gene value from the benchmark value, Indicates the first Among the individuals, the first The magnitude of variation in each gene, This represents the scaling factor, and ;

[0242] The formula used to generate the individual's probability of variation based on the individual's comprehensive evaluation function value is:

[0243] ;

[0244] in, Indicates the first The probability of mutation for each individual. Represents the basic mutation probability, and , Indicates the first The comprehensive evaluation function value of each individual. This represents the maximum value of the overall evaluation function in the current population. This represents the baseline value of the comprehensive evaluation function in the current population;

[0245] Step S43: Combine the generated offspring with the parent generation to form a secondary population;

[0246] Step S44: Repeat steps S41-S43 until the termination condition is met, at which point the iteration terminates.

[0247] The termination condition is that the number of iterations is preset or the improvement of the highest comprehensive evaluation function value in 10 consecutive iterations is less than 5%.

[0248] Step S45: Select the design parameter combination of the transmission line slab tower base structure with the highest current comprehensive evaluation function value.

[0249] Here, "gene" refers to any value in the design parameter combination of the transmission line slab tower foundation. Based on the above embodiments, the gene includes the design parameter combination of the base plate, the design parameter combination of the columns, and the design parameter combination of the anchorage area. The base plate design parameter combination includes base plate thickness, base plate cross-sectional width, base plate cross-sectional length, height of the compression zone of the base plate concrete, effective height of the base plate cross-section, thickness of the protective layer for the tensile reinforcement, tensile strength of the reinforcement, cross-sectional area of ​​the tensile reinforcement, thickness of the protective layer for the compression reinforcement, axial compressive strength of the concrete, axial tensile strength of the concrete, and reinforcement ratio of the base plate. The column design parameter combination includes column cross-sectional width, column cross-sectional length, column cross-sectional height, area of ​​the longitudinal compression reinforcement of the column, axial compressive strength of the concrete, axial tensile strength of the concrete, stirrup spacing, and stirrup cross-sectional area. The anchorage area design parameter combination includes anchorage depth, number of bolts, cross-sectional area of ​​a single bolt, bolt tensile strength, bolt preload, and axial compressive strength of the concrete.

[0250] To simplify calculations, the axial tensile strength of concrete in the base plate design parameter combination and the axial tensile strength of concrete in the column design parameter combination are taken as the same value, belonging to the same gene.

[0251] To simplify calculations, the axial compressive strength of concrete in the base plate design parameter combination, the axial compressive strength of concrete in the column design parameter combination, and the axial compressive strength of concrete in the anchorage area design parameter combination are all taken as the same value, belonging to the same gene.

[0252] The baseline value of a gene is the average value of a specific gene among selected high-quality individuals. This reflects the ideal value of that gene in the current population. Relatively speaking, individuals with higher comprehensive evaluation function values ​​are considered higher quality. Individuals with the highest comprehensive evaluation function values ​​in the population are selected as high-quality individuals. The variation amplitude reflects the adjustment required when a gene undergoes mutation. A larger variation amplitude indicates that the gene needs greater adjustment to approach the optimal solution. If a gene deviates significantly from its baseline value, it indicates that the current gene is poor and the variation amplitude needs to be increased to accelerate exploration and move away from poorer genes. If a gene is close to its baseline value, it indicates that the current gene is close to its better solution and the variation amplitude needs to be reduced to approach the better gene. The search is then conducted near the better gene to obtain the optimal solution for the gene. The gene variation amplitude is proportional to the absolute value of the difference between the current gene value and the gene baseline value. The range of gene variation is... to .

[0253] The probability of individual variation is determined by the quality of the individual's solution; the larger the comprehensive evaluation function value of the individual, the better the individual's solution. The smaller the value, the lower the probability of mutation, thus protecting superior genes. The smaller the overall evaluation function value of an individual, the worse the individual's solution. The larger the value, the higher the mutation probability, which helps to escape local optima.

[0254] It is important to emphasize that this invention generates an initial population based on the parameters of structural components. By calculating the actual bearing capacity of the base plate, columns, and anchorage areas separately, it avoids the limitations of traditional methods that only consider a single type of load. It accurately assesses the actual bearing capacity of each component and more scientifically reflects the comprehensive performance of various components under actual working conditions. By generating a safety index for different components through the ratio of actual bearing capacity to design load, it intuitively quantifies the safety margin. Furthermore, it uses a geometric average of the safety indices of different components to generate a comprehensive safety index, which helps to quickly determine whether optimization design is needed, ensuring that the safety of various components is taken into account and avoiding localized damage.

[0255] This invention also measures the economic efficiency of actual costs by using a benchmark material usage as a baseline, comprehensively evaluating the material utilization efficiency of the base plate, columns, and anchorage areas, ensuring that material waste is reduced and engineering costs are lowered while meeting safety requirements. It also generates a comprehensive evaluation function to minimize costs while ensuring safety. Based on a genetic algorithm, it simultaneously adjusts parameters such as base plate thickness, rebar area, and anchorage depth, while considering the mutual influence of various components, enabling the solution to adapt to different engineering needs and site conditions, thus enhancing the flexibility of the solution. Furthermore, it adjusts the amplitude and frequency of individual mutations based on the comprehensive evaluation function value to improve the efficiency of finding the optimal solution.

[0256] Other components and operations of the transmission line slab tower foundation design method based on genetic algorithms according to embodiments of the present invention are known to those skilled in the art and will not be described in detail here. In the description of the present invention, "first feature" and "second feature" may include one or more of the features. The up-down direction, left-right direction, and front-back direction are defined according to the up-down direction, left-right direction, and front-back direction shown in the figures.

[0257] In the description of this invention, unless otherwise expressly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features not in direct contact but through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature.

[0258] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "illustrative embodiment," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0259] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A method for designing slab tower foundations for transmission lines based on genetic algorithms, characterized in that, It includes the following steps: Step S1: Randomly generate multiple transmission line slab tower base structures and obtain the design parameter combination for each transmission line slab tower base structure. Based on the design parameter combination, obtain the comprehensive safety index and comprehensive economic index for each transmission line slab tower base structure. Step S2: Obtain the actual bearing capacity of the transmission line slab tower base structure according to the design parameter combination, and filter to obtain an initial population of transmission line slab tower base structures whose actual bearing capacity is greater than the design load; Step S3: Obtain a comprehensive evaluation function based on the comprehensive safety index and comprehensive economic index of each transmission line slab tower foundation structure in the initial population; Step S4: After optimizing the initial population through a genetic algorithm, select the combination of design parameters for the transmission line slab tower foundation structure based on the comprehensive evaluation function value; The transmission line slab tower foundation structure includes a base plate, columns, and anchoring areas. Step S1 has the following sub-steps: Step S11: Obtain the design parameter combination of the base plate, the design parameter combination of the column, and the design parameter combination of the anchorage area; Step S12: Obtain the base plate safety index and base plate economic index based on the combination of base plate design parameters; Step S13: Obtain the column safety index and column economic index based on the combination of column design parameters; Step S14: Obtain the anchorage area safety index and anchorage area economic index based on the combination of anchorage area design parameters; Step S15: Obtain the comprehensive safety index based on the base plate safety index, the column safety index, and the anchorage area safety index; Step S16: Obtain the comprehensive economic index based on the base plate economic index, the column economic index, and the anchorage area economic index.

2. The design method for slab tower foundations of transmission lines according to claim 1, characterized in that, The design parameters of the base plate include the base plate thickness, base plate cross-sectional width, base plate cross-sectional length, height of the compression zone of the base plate concrete, effective height of the base plate cross-section, thickness of the protective layer for the tensile reinforcement, tensile strength of the reinforcement, cross-sectional area of ​​the tensile reinforcement, thickness of the protective layer for the compression reinforcement, axial compressive strength of the concrete, axial tensile strength of the concrete, and reinforcement ratio of the base plate. In step S12, obtaining the base plate safety index based on the base plate design parameter combination includes the following sub-steps: Step S1211: Obtain the actual bearing capacity of the base plate based on the combination of base plate design parameters. The actual bearing capacity of the base plate includes the bending bearing capacity and the shear bearing capacity of the base plate. The calculation formula is as follows: ； ； ； ； ； Indicates the bending bearing capacity of the base plate. Indicates the axial compressive strength of concrete. Indicates the width of the base plate cross section. Indicates the height of the compression zone of the base slab concrete. Indicates the effective height of the base plate section. Indicates the thickness of the base plate. Indicates the thickness of the protective layer for the tensile reinforcement in the base slab. Indicates the tensile strength of the steel reinforcement. This indicates the cross-sectional area of ​​the tensile reinforcement in the base slab. Indicates the thickness of the protective layer for compressed steel bars. Indicates the shear bearing capacity of the base plate. Indicates the influence coefficient of section height. Indicates the axial tensile strength of concrete; Step S1212: Based on the actual bearing capacity and design load of the base plate, obtain the safety index of the base plate. The design load of the base plate includes the bending design load and the shear design load. , Indicates the safety index of the base plate. Indicates the design load for bending resistance of the base plate. Indicates the shear design load of the base plate; Obtaining the economic index of the base plate based on the combination of base plate design parameters includes the following sub-steps: Step S1221: Obtain the reference base plate design parameter combination that meets the reference base plate construction requirements. The reference base plate design parameter combination includes the reference base plate thickness, reference base plate cross-sectional width, reference base plate cross-sectional length, and reference base plate reinforcement ratio. Step S1222: Obtain the economic index of the base plate based on the actual material cost and the benchmark material cost of the base plate; The formula used to calculate the cost of the base plate's reference materials is: ； in, Indicates the base plate's baseline material cost. Indicates the thickness of the reference base plate. Indicates the width of the reference base plate section. Indicates the length of the reference base plate section. This indicates the price per unit volume of concrete. Indicates the reinforcement ratio of the base slab. This indicates the price per unit volume of steel reinforcement. The formula used to calculate the actual material cost of the base plate is: ； in, This indicates the actual material cost of the base plate. Indicates the actual thickness of the base plate. Indicates the length of the base plate cross section. Indicates the reinforcement ratio of the base slab. This indicates the price per unit volume of steel reinforcement. The formula used to calculate the aforementioned economic index is as follows: ； in, This serves as the baseline economic index.

3. The design method for slab tower foundations of transmission lines according to claim 1, characterized in that, The column design parameters include column cross-sectional width, column cross-sectional length, column cross-sectional height, longitudinal compression reinforcement area, concrete axial compressive strength, concrete axial tensile strength, stirrup spacing, and stirrup cross-sectional area. In step S13, obtaining the column safety index based on the column design parameter combination includes the following sub-steps: Step S1311: Obtain the actual bearing capacity of the column based on the combination of column design parameters. The actual bearing capacity of the column includes the axial compressive bearing capacity, the bending bearing capacity, and the shear bearing capacity. The calculation formulas for the axial compressive bearing capacity, the bending bearing capacity, and the shear bearing capacity are as follows: ； ； ； Indicates the axial compressive bearing capacity of the column. Represents the stability coefficient. Indicates the axial compressive strength of concrete. This indicates the cross-sectional area of ​​the column concrete. Indicates the compressive strength of longitudinal reinforcement. Indicates the area of ​​the reinforcing steel in the compression zone. Indicates the bending capacity of the column. Indicates the stress pattern coefficient in the compression zone. Indicates the width of the column cross-section. Indicates the height of the concrete compression zone of the column. Indicates the effective height of the concrete column. This represents the distance from the resultant force point of the compressed reinforcement to the compression edge. Indicates the shear bearing capacity of the column. Indicates the axial tensile strength of concrete. Indicates the tensile strength of concrete stirrups. Indicates the cross-sectional area of ​​the stirrups. Indicates the spacing between stirrups; Step S1312: Based on the actual bearing capacity and design load of the column, obtain the safety index of the column. The design load of the column includes the axial compression design load, the bending design load, and the shear design load. , This indicates the safety index of the pillar. This indicates the axial compression design load of the column. This indicates the design load for the column's bending resistance. Indicates the shear design load of the column; Obtaining the economic index of the column based on the combination of column design parameters includes the following sub-steps: Step S1321: Obtain the design parameter combination of the reference column that meets the structural requirements of the reference column. The design parameter combination of the reference column includes the reference cross-sectional dimensions, the reference concrete height of the column, and the reference reinforcement ratio. Step S1322: Obtain the column economic index based on the actual material cost of the column and the reference material cost of the column; The formula used to calculate the cost of the base material for the column is: ； in, Indicates the cost of the base materials for the column. Indicates the reference cross-sectional dimensions of the column. Indicates the reference concrete height of the column. This indicates the reference reinforcement ratio of the column. This indicates the price per unit volume of concrete. This indicates the price per unit volume of steel reinforcement. The formula used to calculate the actual material cost of the column is as follows: ； in, This indicates the actual material cost of the column. This indicates the actual reinforcement ratio of the column; The formula used to calculate the pillar economic index is as follows: ； in, It serves as a pillar economic index.

4. The design method for slab tower foundations of transmission lines according to claim 1, characterized in that, The design parameter combination for the anchorage area includes anchorage depth, number of bolts, cross-sectional area of ​​a single bolt, bolt tensile strength, bolt preload, and axial compressive strength of concrete. In step S14, obtaining the anchorage area safety index based on the combination of anchorage area design parameters includes the following sub-steps: Step S1411: Obtain the actual bearing capacity of the anchorage area based on the combination of design parameters of the anchorage area. The actual bearing capacity of the anchorage area includes the tensile bearing capacity and the shear bearing capacity of the anchorage area. The specific calculation formula is as follows: ； ； ； ； in, Indicates the tensile bearing capacity of the anchorage area. Indicates the tensile bearing capacity of the bolt. Indicates the number of bolts. This represents the cross-sectional area of ​​a single bolt. Indicates the tensile strength of the bolt. Indicates the failure bearing capacity of the concrete cone. Represents the empirical coefficient. Indicates the anchorage depth. Indicates the shear bearing capacity of the anchorage zone. This represents the coefficient of friction between the bolt and the concrete. This indicates the preload of a single bolt. Indicates the axial compressive strength of concrete; Step S1412: Based on the actual bearing capacity of the anchorage area and the design load of the anchorage area, obtain the safety index of the anchorage area. The design load of the anchorage area includes the tensile design load and the shear design load of the anchorage area. , This indicates the safety index of the anchorage area. Indicates the tensile design load of the anchorage area. Indicates the shear design load of the anchorage zone; Obtaining the economic index of the anchorage area based on the combination of design parameters includes the following sub-steps: Step S1421: Obtain the design parameter combination of the reference anchorage area that meets the reference construction requirements of the anchorage area, wherein the design parameter combination of the reference anchorage area includes the number of reference bolts in the anchorage area; Step S142: Obtain the economic index of the anchorage area based on the actual material cost of the anchorage area and the benchmark material cost of the anchorage area; The formula used to calculate the cost of the reference material in the anchorage area is: in, This indicates the baseline material cost for the anchoring area. Indicates the number of reference bolts in the anchorage area. This indicates the unit price of the bolt; The formula used to calculate the actual material cost of the anchorage area is as follows: ； in, This indicates the actual material cost of the anchoring area; The formula used to calculate the economic index of the anchorage area is as follows: ； in, To anchor regional economic indices.

5. The design method for slab tower foundations of transmission lines according to claim 1, characterized in that, In step S15: A comprehensive safety index is obtained based on the safety index of the base plate, the safety index of the column, and the safety index of the anchorage area. The specific formula is as follows: ； in, This represents the overall safety index. Indicates the safety index of the base plate. This indicates the safety index of the pillar. Indicates the safety index of the anchorage area; In step S16: A comprehensive economic index is obtained based on the base plate economic index, the column economic index, and the anchoring area economic index, using the following formula: ； in, This represents the composite economic index. This serves as the baseline economic index. As a pillar economic index. To anchor regional economic indices.

6. The design method for slab tower foundations of transmission lines according to claim 1, characterized in that, In step S3, the formula used to obtain the comprehensive evaluation function is: ； in, This represents the comprehensive evaluation function. This represents the overall safety index. This represents the composite economic index. These represent the weighting coefficients of the comprehensive safety index and the comprehensive economic index, respectively. and .

7. The method for designing slab tower foundations for transmission lines according to claim 6, characterized in that, Step S4 includes the following sub-steps: Step S41: Sort the individuals in the initial population in descending order of the comprehensive evaluation function value, and select the top 50% of individuals as the parents; Step S42: Perform crossover and mutation operations on each pair of adjacent parents to generate offspring. Determine the mutation amplitude and mutation probability based on the comprehensive evaluation function value of the parents and the values ​​of each gene in the parents. Step S43: Combine the generated offspring with the parent generation to form a secondary population; Step S44: Repeat steps S41-S43 until the termination condition is met, at which point the iteration terminates. Step S45: Select the design parameter combination of the transmission line slab tower base structure with the highest current comprehensive evaluation function value.

8. The method for designing slab tower foundations for transmission lines according to claim 7, characterized in that, In step S42, the comprehensive evaluation function value of each individual in each iteration is recorded and sorted in descending order. Individuals with the top 30% comprehensive evaluation function values ​​are selected. For each gene in the selected individuals, the gene variation amplitude is calculated using the following formula: ； ； ； in, Indicates the first The baseline value for each gene, Indicates the number of individuals selected. Indicates the first Among the individuals, the first The values ​​of each gene, An index representing genes, and , This represents the number of genes in an individual. Indicates the selected individual index, and , Indicates the first Among the individuals, the first The deviation of each gene value from the benchmark value, Indicates the first Among the individuals, the first The magnitude of variation in each gene, This represents the scaling factor, and ; The formula used to generate the individual's probability of variation based on the individual's comprehensive evaluation function value is: ； in, Indicates the first The probability of mutation for each individual. Represents the basic mutation probability, and , Indicates the first The comprehensive evaluation function value of each individual. This represents the maximum value of the overall evaluation function in the current population. This represents the baseline value of the comprehensive evaluation function in the current population.

9. The design method for slab tower foundations of transmission lines according to claim 7, characterized in that, The termination condition is that the number of iterations is preset or the increase in the highest comprehensive evaluation function value in 10 consecutive iterations is less than 5%.

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