CN111382910A - Analysis method of optimization model based on club-footed uplift pile - Google Patents

Analysis method of optimization model based on club-footed uplift pile Download PDF

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CN111382910A
CN111382910A CN202010184465.2A CN202010184465A CN111382910A CN 111382910 A CN111382910 A CN 111382910A CN 202010184465 A CN202010184465 A CN 202010184465A CN 111382910 A CN111382910 A CN 111382910A
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pile
uplift
uplift pile
expanded
formula
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姚文娟
肖路
顾毛亮
程泽坤
赵正山
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Beijing Transpacific Technology Development Ltd
University of Shanghai for Science and Technology
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
    • E—FIXED CONSTRUCTIONS
    • E02—HYDRAULIC ENGINEERING; FOUNDATIONS; SOIL SHIFTING
    • E02D—FOUNDATIONS; EXCAVATIONS; EMBANKMENTS; UNDERGROUND OR UNDERWATER STRUCTURES
    • E02D31/00—Protective arrangements for foundations or foundation structures; Ground foundation measures for protecting the soil or the subsoil water, e.g. preventing or counteracting oil pollution
    • E02D31/10—Protective arrangements for foundations or foundation structures; Ground foundation measures for protecting the soil or the subsoil water, e.g. preventing or counteracting oil pollution against soil pressure or hydraulic pressure
    • E02D31/12—Protective arrangements for foundations or foundation structures; Ground foundation measures for protecting the soil or the subsoil water, e.g. preventing or counteracting oil pollution against soil pressure or hydraulic pressure against upward hydraulic pressure
    • E—FIXED CONSTRUCTIONS
    • E02—HYDRAULIC ENGINEERING; FOUNDATIONS; SOIL SHIFTING
    • E02D—FOUNDATIONS; EXCAVATIONS; EMBANKMENTS; UNDERGROUND OR UNDERWATER STRUCTURES
    • E02D5/00—Bulkheads, piles, or other structural elements specially adapted to foundation engineering
    • E02D5/22—Piles
    • E02D5/34—Concrete or concrete-like piles cast in position ; Apparatus for making same
    • E02D5/38—Concrete or concrete-like piles cast in position ; Apparatus for making same making by use of mould-pipes or other moulds
    • E02D5/44—Concrete or concrete-like piles cast in position ; Apparatus for making same making by use of mould-pipes or other moulds with enlarged footing or enlargements at the bottom of the pile
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/12—Computing arrangements based on biological models using genetic models
    • G06N3/126—Evolutionary algorithms, e.g. genetic algorithms or genetic programming
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Systems or methods specially adapted for specific business sectors, e.g. utilities or tourism
    • G06Q50/08—Construction

Abstract

The invention discloses an analysis method of an optimization model based on an expanded-base uplift pile, which comprises the following steps of: firstly, establishing an optimal objective function and constraint conditions of the uplift pile by applying a genetic algorithm basic idea of an optimization theory to obtain an optimal mathematical model of the expanded-base uplift pile. And (3) calculating to obtain an optimized value of the variable through a self-programming program, thereby realizing that the pedestal-expanded uplift pile not only meets the safe and economic optimization target. The results show that: compared with the original design, the result obtained by the optimization model of the invention reduces the number of the club-footed uplift pile and the construction cost by 23 percent for the same actual project.

Description

Analysis method of optimization model based on club-footed uplift pile
Technical Field
The invention belongs to the technical field of geotechnical engineering, and particularly relates to an optimized computational analysis model for a club-footed uplift pile.
Background
With the vigorous development of urban underground spaces, the contradiction that the research and analysis of urban underground buildings and structures cannot meet the engineering standards required by the development of underground buildings at the present stage is more prominent. The method for effectively preventing the adverse effect of the water buoyancy on the underground buildings and structures becomes a hot point direction of academic research, and the uplift pile is widely applied as an effective measure for reducing the effect of the water buoyancy on the underground buildings. As the pedestal-expanded uplift pile has a larger vertical uplift bearing capacity level, a large amount of numerical simulation and experimental analysis are carried out by scholars at home and abroad on the interaction effect between the diameter expanding body and the soil body around the pile, and the conclusion shows that the diameter expanding body can effectively improve the uplift bearing capacity of the uplift pile. With the gradual widespread application of uplift piles in pile foundation engineering, the rational design of uplift piles becomes an important problem in civil engineering.
Disclosure of Invention
In order to solve the problems in the prior art, the invention aims to overcome the defects in the prior art and provide an analysis method of an optimization model based on a bottom-expanded uplift pile, so that the bottom-expanded uplift pile is optimized and can be effectively applied and popularized in engineering.
In order to achieve the purpose of the invention, the invention adopts the following conception:
on the basis of deeply researching the action mechanism between the uplift pile and the soil around the pile, the comprehensive optimization design of the whole uplift pile engineering is realized by applying the genetic algorithm in the optimization theory. On the basis of meeting the requirements of safety and stability, the construction cost is selected as an optimization target, so that the uplift pile achieves the relatively optimal indexes, and the effective application and popularization in the engineering are realized.
According to the inventive concept, the invention adopts the following technical scheme:
an analysis method of an optimization model based on an under-reamed uplift pile comprises the following steps:
1) by combining an optimization design theory, the mathematical function model expression which is expected by taking the minimum construction cost as a target in the pile foundation engineering is as follows:
Figure BDA0002412427870000011
in the formula, Q (x)i) The construction cost of the uplift pile is reduced; x is the number ofiThe constraint conditions of relevant parameters of the uplift pile are defined;
the main components of the construction cost of the single uplift pile are the consumption of pile body concrete, the consumption of pile body reinforcing steel bars and the excavation amount of pile holes of the uplift pile; taking the construction cost of the uplift pile foundation as a target expectation function, the target expectation function of the construction cost is expressed as the following items:
①, determining the concrete consumption of the pile body:
Figure BDA0002412427870000021
in the formula:
Qcthe cost of the concrete for the pile body of the single expanded-base uplift pile is reduced;
Ccthe unit price of the pile body concrete is;
Asthe maximum cross-sectional area of the stressed main reinforcement of the pedestal uplift pile is obtained;
d is the maximum diameter of the expanded section of the expanded-base uplift pile;
d is the diameter of the equal section of the club-footed uplift pile;
L1the length of the equal section part of the club-footed uplift pile is equal to that of the club-footed uplift pile;
L2the length of the expanded part of the expanded-base uplift pile is the length of the expanded base;
② determining the steel bar dosage of the pile body:
considering the main reinforcement of the uplift pile body and the related construction reinforcement, which is easily obtained by calculation and analysis, the related construction reinforcement can be approximately replaced by introducing an increase parameter α by the product of the increase parameter and the main reinforcement usage, and then the reinforcement usage of the uplift pile body is expressed as:
Figure BDA0002412427870000022
in the formula:
Qsthe cost of the steel bar of the single uplift pile body is reduced;
Csthe pile body of the uplift pile is stressed by a main reinforcement unit price;
d1is the equivalent diameter of the stress main rib of the uplift pile,
Figure BDA0002412427870000023
n is the number of the diameter of the reinforcing steel bars of the pile body of the uplift pile;
dithe diameter of the ith reinforcing steel bar of the pile body of the uplift pile is the same as the diameter of the ith reinforcing steel bar of the pile body of the uplift pile;
α is an increase parameter;
g is the nominal mass of the main reinforcement of the uplift pile;
③, determining the mechanical drilling engineering cost of the cast-in-situ bored pile:
Figure BDA0002412427870000024
in the formula:
Qtthe comprehensive cost of drilling the pile body of the single cast-in-situ bored pile is achieved;
Ctthe unit price of the excavation soil for mechanically drilling the uplift pile is determined;
therefore, the mathematical expression taking the construction cost of the uplift pile as the objective function is obtained as follows:
Figure BDA0002412427870000031
the above formula is a mathematical expression of the construction cost of a single expanded-base uplift pile, and the total cost of the whole pile foundation engineering is as follows:
Figure BDA0002412427870000032
in the formula:
s is the pile spacing of the uplift pile;
APthe total area of the uplift pile project;
2) the constraint conditions for determining the target expectation function of the uplift pile optimization are as follows:
(1) determining design variables of the uplift pile:
the uplift pile is used as a measure for reducing the influence of water buoyancy on an underground building, is applied to actual engineering, optimally selects and values each design variable under the condition of meeting the standard requirement, and is an effective way for meeting the safety, reliability and economic indexes of a structure;
the majority of uplift piles in engineering adopt the form of uplift grouped piles, and the design variables for describing the club-footed uplift grouped piles mainly comprise: maximum cross-sectional area A of stress main rib of uplift pilesWeighted average of frictional resistance f of pile side soilsLength-diameter ratio L of pile at non-expanded bottom part1D, the diameter ratio of pile body D/D, the diameter of pile body of expanded bottom part D, the length of pile of expanded bottom part L2And the pile spacing S of the club-footed uplift grouped piles;
the length-diameter ratio L of the pile at the non-expanded bottom part1β, and D/D is λ, the mathematical expression using the uplift pile cost as the target expectation function can be converted into:
Figure BDA0002412427870000041
(2) determining the constraint conditions of the design variables of the uplift pile:
the minimum reinforcement ratio of the longitudinal stress steel bar should satisfy the following formula:
Figure BDA0002412427870000042
ρminfor minimum reinforcement ratio of longitudinal stress steel bar, tension steel bar rho of axial tension memberminTake 0.2 and 45ft/fyThe larger of (a);
(2-1) when the uplift pile is damaged by tension, the concrete does not bear the action of tension, all the tension is borne by the steel bars by default, and therefore the vertical force of the top of the single pile in the pile group is calculated according to the following formula:
Figure BDA0002412427870000043
in the formula:
Nkvertical load applied to the top surface of the pile cap when the pile cap is combined with the standard of corresponding action;
Gkthe weight standard value of the soil on the bearing platform is added to the weight of the pile foundation bearing platform;
Nkwhen the vertical force is combined with the standard of corresponding action, the vertical force of any single pile is exerted under the action of the vertical force of the axis;
therefore, the tensile bearing strength requirement of the normal section of the uplift pile is as follows:
Figure BDA0002412427870000044
Figure BDA0002412427870000045
in the formula:
Tukthe standard value of the uplift limit bearing capacity of the foundation pile is obtained;
Gpthe self weight of the foundation pile, the floating weight below the underground water level and the pile length l of the club-footed uplift pileiWhen > (4-10 d), the perimeter u of the damaged surface of the pedestal uplift pile is brokeniCalculating the dead weight of the pile and the soil;
k is a safety factor taken during the design of the uplift pile, and generally K is 2;
fsthe weighted average value of the pile side soil frictional resistance of the pedestal uplift pile is obtained;
λitaking 0.70-0.80 of cohesive soil and silt and 0.50-0.70 of sandy soil as the anti-pulling coefficient;
(2-2) maximum crack width w of uplift pilemaxThe following requirements should be met by carrying out checking calculation according to load standard combination or quasi-permanent combination and considering long-term effect influence:
wmax≤wlim；
in the formula:
wlimfor maximum crack width limit, of uplift pilesThe value is 0.2 mm;
the maximum crack width can be calculated as follows:
Figure BDA0002412427870000051
in the formula:
Figure BDA0002412427870000052
Figure BDA0002412427870000053
Figure BDA0002412427870000054
(axial tension member);
in the formula:
αcrα is taken for axial tension member for member force characteristic coefficientcr＝2.7；
Psi is the uneven coefficient of strain of the longitudinal stress steel bar between the cracks, and when psi is less than 0.2, psi is taken to be 0.2; when psi is greater than 1.0, taking psi as 1.0;
Esis the modulus of elasticity of the steel bar;
deqthe equivalent diameter (mm) of the longitudinal steel bar in the tension area;
csthe distance (mm) from the outer edge of the corner rib at the outer side of the longitudinal tension steel bar to the bottom surface of the tension area; when c is going tosWhen the number is less than 20; get cs20; when c is going tosWhen > 65, take cs＝65；
ρteThe reinforcement ratio of the longitudinal tension steel bar is calculated according to the effective section area of the tension concrete, when rhoteWhen the value is less than 0.01, taking rhote＝0.01。
As a preferred technical scheme of the invention, the analysis method firstly encodes specific values of each variable through binary system to generate an initial population, and establishes a mapping relation between the genotype and the specific variable values; on the basis, the initial population of the code is subjected to initial evaluation, namely the minimum value of a fitness function is obtained, then individuals which are not suitable for the function are screened through a selection operator program, then a new generation of population is generated through a crossover operator and a mutation operator, the population is further subjected to selection, crossover and mutation again, population individuals which meet the adaptability requirement are generated through generation-by-generation evolution, the final population is decoded, the optimal solution of the problem is obtained, and a Matlab program is applied.
As a preferred technical scheme of the invention, the analysis method adopts a Genetic Algorithm (GA), has the capability of fast and random search regardless of the problem field, starts from a group, has potential parallelism, has high expandability, is easy to combine with other algorithms, can simultaneously search a plurality of areas of a solution space by the Genetic Algorithm, and avoids the Algorithm from falling into a local optimal solution; the method has strong robustness and can converge to the optimal solution with high possibility.
Compared with the prior art, the invention has the following obvious and prominent substantive characteristics and remarkable advantages:
1. firstly, establishing an optimal objective function and constraint conditions of the uplift pile by applying a genetic algorithm basic thought of an optimization theory to obtain an optimal mathematical model of the expanded-base uplift pile; the optimized value of the variable is obtained through calculation through a self-programming program, so that the expanded-base uplift pile can meet the optimized target of safety and economy; the results show that: compared with the original design, the result obtained by optimizing the model reduces the number of the club-footed uplift pile and the construction cost by 23 percent for the same actual project;
2. on the basis of meeting the requirements of safety and stability, the construction cost is selected as an optimization target, so that the uplift pile achieves the relatively optimal indexes, and the effective application and popularization in the engineering are realized.
Drawings
Fig. 1 is a mechanical principle schematic diagram of the pedestal uplift pile of the invention.
FIG. 2 is a block diagram of a genetic algorithm process described in the present invention.
Detailed Description
The above-described scheme is further illustrated below with reference to specific embodiments, which are detailed below:
the first embodiment is as follows:
in this embodiment, referring to fig. 1 and fig. 2, an analysis method based on an optimization model of a club-footed uplift pile includes the following steps:
1) by combining an optimization design theory, the mathematical function model expression which is expected by taking the minimum construction cost as a target in the pile foundation engineering is as follows:
Figure BDA0002412427870000071
in the formula, Q (x)i) The construction cost of the uplift pile is reduced; x is the number ofiThe constraint conditions of relevant parameters of the uplift pile are defined;
the main components of the construction cost of the single uplift pile are the consumption of pile body concrete, the consumption of pile body reinforcing steel bars and the excavation amount of pile holes of the uplift pile; taking the construction cost of the uplift pile foundation as a target expectation function, the target expectation function of the construction cost is expressed as the following items:
①, determining the concrete consumption of the pile body:
Figure BDA0002412427870000072
in the formula:
Qcthe cost of the concrete for the pile body of the single expanded-base uplift pile is reduced;
Ccthe unit price of the pile body concrete is;
Asthe maximum cross-sectional area of the stressed main reinforcement of the pedestal uplift pile is obtained;
d is the maximum diameter of the expanded section of the expanded-base uplift pile;
d is the diameter of the equal section of the club-footed uplift pile;
L1the length of the equal section part of the club-footed uplift pile is equal to that of the club-footed uplift pile;
L2the length of the expanded part of the expanded-base uplift pile is the length of the expanded base;
② determining the steel bar dosage of the pile body:
considering the main reinforcement of the uplift pile body and the related construction reinforcement, which is easily obtained by calculation and analysis, the related construction reinforcement can be approximately replaced by introducing an increase parameter α by the product of the increase parameter and the main reinforcement usage, and then the reinforcement usage of the uplift pile body is expressed as:
Figure BDA0002412427870000073
in the formula:
Qsthe cost of the steel bar of the single uplift pile body is reduced;
Csthe pile body of the uplift pile is stressed by a main reinforcement unit price;
d1is the equivalent diameter of the stress main rib of the uplift pile,
Figure BDA0002412427870000081
n is the number of the diameter of the reinforcing steel bars of the pile body of the uplift pile;
dithe diameter of the ith reinforcing steel bar of the pile body of the uplift pile is the same as the diameter of the ith reinforcing steel bar of the pile body of the uplift pile;
α is an increase parameter;
g is the nominal mass of the main reinforcement of the uplift pile;
③, determining the mechanical drilling engineering cost of the cast-in-situ bored pile:
Figure BDA0002412427870000082
in the formula:
Qtthe comprehensive cost of drilling the pile body of the single cast-in-situ bored pile is achieved;
Ctthe unit price of the excavation soil for mechanically drilling the uplift pile is determined;
therefore, the mathematical expression taking the construction cost of the uplift pile as the objective function is obtained as follows:
Figure BDA0002412427870000083
the above formula is a mathematical expression of the construction cost of a single expanded-base uplift pile, and the total cost of the whole pile foundation engineering is as follows:
Figure BDA0002412427870000084
in the formula:
s is the pile spacing of the uplift pile;
APthe total area of the uplift pile project;
2) the constraint conditions for determining the target expectation function of the uplift pile optimization are as follows:
(1) determining design variables of the uplift pile:
the uplift pile is used as a measure for reducing the influence of water buoyancy on an underground building, is applied to actual engineering, as shown in the following figure 1, and is an effective way for meeting safety, reliability and economic indexes of a structure by optimally selecting and valuing various design variables under the condition of meeting the standard requirement;
uplift piles have been widely used in practical engineering as an effective means for reducing the influence of water buoyancy on underground buildings, as shown in fig. 1 below; however, in the conventional concrete structure design method, an approximate value range is given no matter the section size, the reinforcement requirement and the like of the concrete structure. The specific values of all variables have great influence on the construction cost of the structure; the majority of uplift piles in engineering adopt the form of uplift grouped piles, and the design variables for describing the club-footed uplift grouped piles mainly comprise: maximum cross-sectional area A of stress main rib of uplift pilesWeighted average of frictional resistance f of pile side soilsLength-diameter ratio L of pile at non-expanded bottom part1D, the diameter ratio of pile body D/D, the diameter of pile body of expanded bottom part D, the length of pile of expanded bottom part L2And the pile spacing S of the club-footed uplift grouped piles;
the length-diameter ratio L of the pile at the non-expanded bottom part1β, and D/D is λ, the mathematical expression using the uplift pile cost as the target expectation function can be converted into:
Figure BDA0002412427870000091
(2) determining the constraint conditions of the design variables of the uplift pile:
the minimum reinforcement ratio of the longitudinal stress steel bar should satisfy the following formula:
Figure BDA0002412427870000092
ρminfor minimum reinforcement ratio of longitudinal stress steel bar, tension steel bar rho of axial tension memberminTake 0.2 and 45ft/fyThe larger of (a);
(2-1) when the uplift pile is damaged by tension, the concrete does not bear the action of tension, all the tension is borne by the steel bars by default, and therefore the vertical force of the top of the single pile in the pile group is calculated according to the following formula:
Figure BDA0002412427870000101
in the formula:
Nkvertical load applied to the top surface of the pile cap when the pile cap is combined with the standard of corresponding action;
Gkthe weight standard value of the soil on the bearing platform is added to the weight of the pile foundation bearing platform;
Nkwhen the vertical force is combined with the standard of corresponding action, the vertical force of any single pile is exerted under the action of the vertical force of the axis;
therefore, the tensile bearing strength requirement of the normal section of the uplift pile is as follows:
Figure BDA0002412427870000102
Figure BDA0002412427870000103
in the formula:
Tukthe standard value of the uplift limit bearing capacity of the foundation pile is obtained;
Gptaking the pile under the underground water level for the dead weight of the foundation pileBuoyancy, pile length l of club-footed uplift pileiWhen > (4-10 d), the perimeter u of the damaged surface of the pedestal uplift pile is brokeniCalculating the dead weight of the pile and the soil;
k is a safety factor taken during the design of the uplift pile, and generally K is 2;
fsthe weighted average value of the pile side soil frictional resistance of the pedestal uplift pile is obtained;
λitaking 0.70-0.80 of cohesive soil and silt and 0.50-0.70 of sandy soil as the anti-pulling coefficient;
(2-2) maximum crack width w of uplift pilemaxThe following requirements should be met by carrying out checking calculation according to load standard combination or quasi-permanent combination and considering long-term effect influence:
wmax≤wlim；
in the formula:
wlimthe maximum crack width limit value is set, and the value of the uplift pile is 0.2 mm;
the maximum crack width can be calculated as follows:
Figure BDA0002412427870000111
in the formula:
Figure BDA0002412427870000112
Figure BDA0002412427870000113
Figure BDA0002412427870000114
(axial tension member);
in the formula:
αcrα is taken for axial tension member for member force characteristic coefficientcr＝2.7；
Psi is the uneven coefficient of strain of the longitudinal stress steel bar between the cracks, and when psi is less than 0.2, psi is taken to be 0.2; when psi is greater than 1.0, taking psi as 1.0;
Esis the modulus of elasticity of the steel bar;
deqthe equivalent diameter (mm) of the longitudinal steel bar in the tension area;
csthe distance (mm) from the outer edge of the corner rib at the outer side of the longitudinal tension steel bar to the bottom surface of the tension area; when c is going tosWhen the number is less than 20; get cs20; when c is going tosWhen > 65, take cs＝65；
ρteThe reinforcement ratio of the longitudinal tension steel bar is calculated according to the effective section area of the tension concrete, when rhoteWhen the value is less than 0.01, taking rhote＝0.01。
Example two:
this embodiment is substantially the same as the first embodiment, and is characterized in that:
in this embodiment, the analysis method first encodes specific values of each variable through binary system to generate an initial population, and establishes a mapping relationship between a genotype and the specific variable values; on the basis, the initial population of the code is subjected to initial evaluation, namely the minimum value of a fitness function is obtained, then individuals which are not suitable for the function are screened through a selection operator program, then a new generation of population is generated through a crossover operator and a mutation operator, the population is further subjected to selection, crossover and mutation again, population individuals which meet the adaptability requirement are generated through generation-by-generation evolution, the final population is decoded, the optimal solution of the problem is obtained, and a Matlab program is applied.
In this embodiment, the analysis method adopts a Genetic Algorithm (GA), has a fast and random search capability regardless of the problem field, starts from a group, has potential parallelism, has high expandability, and is easy to combine with other algorithms, and meanwhile, the Genetic Algorithm can simultaneously search a plurality of areas of a solution space, thereby avoiding the Algorithm from falling into a local optimal solution; the method has strong robustness and can converge to the optimal solution with high possibility. Genetic Algorithm (GA) is a meta-heuristic natural selection process, belonging to the large class of Evolutionary Algorithms (EAs). Genetic algorithms are typically solutions to generate high quality optimization and search problems using biological heuristics such as mutation, crossover, and selection, and the present embodiment takes advantage of the use of genetic algorithms based on the presence of data analysis.
Example three:
this embodiment is substantially the same as the previous embodiment, and is characterized in that:
in this embodiment, a method for calculating an optimization model of a club-footed uplift pile is provided. The buried depth of the single-built underground garage of Rejin hospital in Shanghai city is 5.8m, and the total area is about 3500m2And covering soil about 1m deep above the top plate to serve as greening and leisure land. The distribution condition of soil layers within the depth range of 40m below the earth surface is shown in the following table 1, and the stable water level is 0.8-1.0 m because the shallow underground water of the engineering base belongs to a diving type. Because the garage of the project is located below the ground, the influence of the water buoyancy cannot be ignored. In order to meet the anti-floating requirement of the engineering, a large number of bottom-expanding uplift piles are applied to the garage foundation engineering to resist the influence of water buoyancy. Wherein the specification and the size of the adopted pedestal uplift pile are as follows: the maximum diameter of the diameter expanding part is 800mm, the diameter of the pile with the same cross section is 400mm, the length of the bottom expanding part is 1.5m, the effective pile length is 22m (the depth of the soil is about 29m), and the total number of the piles is 256.
TABLE 1 soil layer main physical mechanics parameter table
Figure BDA0002412427870000121
Comparing each optimization result of the design variable of the club-footed uplift pile obtained by adopting the optimization model calculation of the invention in the actual engineering with each index of the club-footed uplift pile of the original design scheme of the actual engineering, and taking the concrete unit price of 400 yuan/m3The unit price of the steel bar is 2300 yuan/m3Unit price of 100 yuan/m for earth and stone excavation3. The comparison result between the variable values of the optimization model and the original design scheme is shown in the following table 2:
TABLE 2 comparison of results of the optimization analysis with those of the original design
Figure BDA0002412427870000122
Figure BDA0002412427870000131
As can be seen from Table 2, after the model of the invention is optimized, compared with the original engineering design scheme, the total number of the bottom-expanded uplift piles is reduced by 9.38%, and the engineering cost is reduced by 23%.
The invention has the advantages of optimal design model, clear logic and easy operability, and fully displays the accuracy and the research potential of the optimal design research of the pedestal uplift pile. The requirements of the structure safety and the stability of the club-footed uplift pile are met, the optimal design model can enable the club-footed uplift pile to give full play to the structural potential, and greater economic value and social benefit are provided for the actual engineering.
The embodiments of the present invention have been described with reference to the accompanying drawings, but the present invention is not limited to the embodiments, and various changes and modifications may be made according to the purpose of the invention, and any changes, modifications, substitutions, combinations or simplifications made according to the spirit and principle of the technical solution of the present invention shall be equivalent substitutions, as long as the technical principle and the inventive concept of the analysis method based on the optimization model of the club-footed uplift pile according to the present invention are not departed from the technical principle and the inventive concept of the analysis method based on the optimization model of the club-footed uplift pile.

Claims (3)

1. An analysis method of an optimization model based on an expanded-base uplift pile is characterized by comprising the following steps: the analysis method comprises the following steps:
1) by combining an optimization design theory, the mathematical function model expression which is expected by taking the minimum construction cost as a target in the pile foundation engineering is as follows:
Figure FDA0002412427860000011
in the formula, Q (x)i) The construction cost of the uplift pile is reduced; x is the number ofiThe constraint conditions of relevant parameters of the uplift pile are defined;
the main components of the construction cost of the single uplift pile are the consumption of pile body concrete, the consumption of pile body reinforcing steel bars and the excavation amount of pile holes of the uplift pile; taking the construction cost of the uplift pile foundation as a target expectation function, the target expectation function of the construction cost is expressed as the following items:
①, determining the concrete consumption of the pile body:
Figure FDA0002412427860000012
in the formula:
Qcthe cost of the concrete for the pile body of the single expanded-base uplift pile is reduced;
Ccthe unit price of the pile body concrete is;
Asthe maximum cross-sectional area of the stressed main reinforcement of the pedestal uplift pile is obtained;
d is the maximum diameter of the expanded section of the expanded-base uplift pile;
d is the diameter of the equal section of the club-footed uplift pile;
L1the length of the equal section part of the club-footed uplift pile is equal to that of the club-footed uplift pile;
L2the length of the expanded part of the expanded-base uplift pile is the length of the expanded base;
② determining the steel bar dosage of the pile body:
considering the main reinforcement of the uplift pile body and the related construction reinforcement, which is easily obtained by calculation and analysis, the related construction reinforcement can be approximately replaced by introducing an increase parameter α by the product of the increase parameter and the main reinforcement usage, and then the reinforcement usage of the uplift pile body is expressed as:
Figure FDA0002412427860000013
in the formula:
Qsthe cost of the steel bar of the single uplift pile body is reduced;
Csthe pile body of the uplift pile is stressed by a main reinforcement unit price;
d1is the equivalent diameter of the stress main rib of the uplift pile,
Figure FDA0002412427860000021
n is the number of the diameter of the reinforcing steel bars of the pile body of the uplift pile;
dithe diameter of the ith reinforcing steel bar of the pile body of the uplift pile is the same as the diameter of the ith reinforcing steel bar of the pile body of the uplift pile;
α is an increase parameter;
g is the nominal mass of the main reinforcement of the uplift pile;
③, determining the mechanical drilling engineering cost of the cast-in-situ bored pile:
Figure FDA0002412427860000022
in the formula:
Qtthe comprehensive cost of drilling the pile body of the single cast-in-situ bored pile is achieved;
Ctthe unit price of the excavation soil for mechanically drilling the uplift pile is determined;
therefore, the mathematical expression taking the construction cost of the uplift pile as the objective function is obtained as follows:
Figure FDA0002412427860000023
the above formula is a mathematical expression of the construction cost of a single expanded-base uplift pile, and the total cost of the whole pile foundation engineering is as follows:
Figure FDA0002412427860000024
in the formula:
s is the pile spacing of the uplift pile;
APthe total area of the uplift pile project;
2) the constraint conditions for determining the target expectation function of the uplift pile optimization are as follows:
(1) determining design variables of the uplift pile:
the uplift pile is used as a measure for reducing the influence of water buoyancy on an underground building, is applied to actual engineering, optimally selects and values each design variable under the condition of meeting the standard requirement, and is an effective way for meeting the safety, reliability and economic indexes of a structure;
the majority of uplift piles in engineering adopt the form of uplift grouped piles, and the design variables for describing the club-footed uplift grouped piles mainly comprise: maximum cross-sectional area A of stress main rib of uplift pilesWeighted average of pile side soil frictional resistance
Figure FDA0002412427860000031
Length-diameter ratio L of pile of non-expanded bottom part1D, the diameter ratio of pile body D/D, the diameter of pile body of expanded bottom part D, the length of pile of expanded bottom part L2And the pile spacing S of the club-footed uplift grouped piles;
the length-diameter ratio L of the pile at the non-expanded bottom part1β, and D/D is λ, the mathematical expression using the uplift pile cost as the target expectation function can be converted into:
Figure FDA0002412427860000032
(2) determining the constraint conditions of the design variables of the uplift pile:
the minimum reinforcement ratio of the longitudinal stress steel bar should satisfy the following formula:
Figure FDA0002412427860000033
ρminfor minimum reinforcement ratio of longitudinal stress steel bar, tension steel bar rho of axial tension memberminTake 0.2 and 45ft/fyThe larger of (a);
(2-1) when the uplift pile is damaged by tension, the concrete does not bear the action of tension, all the tension is borne by the steel bars by default, and therefore the vertical force of the top of the single pile in the pile group is calculated according to the following formula:
Figure FDA0002412427860000034
in the formula:
Nkin the case of a standard combination of the respective effects,applying a vertical load on the top surface of the pile cap;
Gkthe weight standard value of the soil on the bearing platform is added to the weight of the pile foundation bearing platform;
Nkwhen the vertical force is combined with the standard of corresponding action, the vertical force of any single pile is exerted under the action of the vertical force of the axis;
therefore, the tensile bearing strength requirement of the normal section of the uplift pile is as follows:
Figure FDA0002412427860000041
Figure FDA0002412427860000042
in the formula:
Tukthe standard value of the uplift limit bearing capacity of the foundation pile is obtained;
Gpthe self weight of the foundation pile, the floating weight below the underground water level and the pile length l of the club-footed uplift pileiWhen > (4-10 d), the perimeter u of the damaged surface of the pedestal uplift pile is brokeniCalculating the dead weight of the pile and the soil;
k is a safety factor taken during the design of the uplift pile, and generally K is 2;
Figure FDA0002412427860000047
the weighted average value of the pile side soil frictional resistance of the pedestal uplift pile is obtained;
λitaking 0.70-0.80 of cohesive soil and silt and 0.50-0.70 of sandy soil as the anti-pulling coefficient;
(2-2) maximum crack width w of uplift pilemaxThe following requirements should be met by carrying out checking calculation according to load standard combination or quasi-permanent combination and considering long-term effect influence:
wmax≤wlim；
in the formula:
wlimthe maximum crack width limit value is set, and the value of the uplift pile is 0.2 mm;
the maximum crack width can be calculated as follows:
Figure FDA0002412427860000043
in the formula:
Figure FDA0002412427860000044
Figure FDA0002412427860000045
Figure FDA0002412427860000046
(axial tension member);
in the formula:
αcrα is taken for axial tension member for member force characteristic coefficientcr＝2.7；
Psi is the uneven coefficient of strain of the longitudinal stress steel bar between the cracks, and when psi is less than 0.2, psi is taken to be 0.2; when psi is greater than 1.0, taking psi as 1.0;
Esis the modulus of elasticity of the steel bar;
deqthe equivalent diameter (mm) of the longitudinal steel bar in the tension area;
csthe distance (mm) from the outer edge of the corner rib at the outer side of the longitudinal tension steel bar to the bottom surface of the tension area; when c is going tosWhen the number is less than 20; get cs20; when c is going tosWhen > 65, take cs＝65；
ρteThe reinforcement ratio of the longitudinal tension steel bar is calculated according to the effective section area of the tension concrete, when rhoteWhen the value is less than 0.01, taking rhote＝0.01。
2. The method for analyzing the optimization model based on the club-footed uplift pile according to claim 1, which is characterized in that: firstly, encoding specific values of all variables through a binary system to generate an initial population, and establishing a mapping relation between a genotype and the specific variable values; on the basis, the initial population of the code is subjected to initial evaluation, namely the minimum value of a fitness function is obtained, then individuals which are not suitable for the function are screened through a selection operator program, then a new generation of population is generated through a crossover operator and a mutation operator, the population is further subjected to selection, crossover and mutation again, population individuals which meet the adaptability requirement are generated through generation-by-generation evolution, the final population is decoded, the optimal solution of the problem is obtained, and a Matlab program is applied.
3. The method for analyzing the optimization model based on the club-footed uplift pile according to claim 1, which is characterized in that: the analysis method adopts Genetic Algorithm (GA), has quick and random search capability regardless of problem field, starts from group, has potential parallelism, has high expandability, is easy to combine with other algorithms, can simultaneously search a plurality of areas of solution space by the Genetic Algorithm, and avoids the Algorithm from falling into local optimal solution; the method has strong robustness and can converge to the optimal solution with high possibility.
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