Deep foundation pit supporting structure design method based on system reliability analysis

Abstract

A deep foundation pit supporting structure design method based on system reliability analysis relates to the technical field of foundation pit structures, and obtains a supporting structure design method with high safety coefficient and low supporting cost through calculation and analysis, and comprises the following steps: S1, obtaining an engineering exploration report and a preliminary design scheme corresponding to a deep foundation pit; s2, determining a value range of a design variable x and statistical characteristics of a random variable y; s3, determining a failure mode of a deep foundation pit support design system according to engineering characteristics of the support corresponding to the deep foundation pit; s4, constructing a limit state function of each failure mode; s5, constructing a system reliability model through the system failure probability of the series system in the step S4, fusing a multi-objective optimization model into the system reliability model, and setting an objective function and a constraint condition; and S6, setting a multi-objective optimization algorithm in the deep foundation pit support design system, calculating the safety and cost of different support structures by using the algorithm, obtaining a Pareto solution set, and obtaining the corresponding deep foundation pit support structure design through comparison and selection.

Description

Technical Field

[0001] The present invention relates to the technical field of foundation pit structures, and particularly relates to a design method for deep foundation pit support structures based on system reliability analysis. Background Art

[0002] In recent years, due to the rapid development of urban subway projects, subway stations, open-cut sections of local intervals, etc. also involve a large number of foundation pit projects. In double-track intersection subway stations, the foundation pits are as deep as 20 - 30m. Foundation pit excavations for underground workshops and underground pump houses also exist in water conservancy and electric power.

[0003] Whether it is a deep foundation pit project for high-rise buildings or subways, since the excavation is carried out in the city, there are usually various structures such as traffic arteries, existing buildings or pipelines around the foundation pit. This involves a very important content of foundation pit excavation, which is to protect the safe use of the surrounding structures.

[0004] Generally, most foundation pit supports are temporary structures, with large investment and easy to cause waste. However, if the support structure is not safe, it is bound to cause engineering accidents. Therefore, how to safely and reasonably select a suitable support structure and conduct scientific design according to the characteristics of foundation pit projects is the main content to be solved in foundation pit projects. Summary of the Invention

[0005] I. Technical Problems to be Solved

[0006] In view of the deficiencies of the prior art, the present invention proposes a design method for deep foundation pit support structures based on system reliability analysis. By analyzing the engineering exploration reports and multiple preliminary design schemes of the deep foundation pit to be excavated, a support structure design method with high safety factor and low support cost is obtained.

[0007] II. Specific Technical Solutions

[0008] A design method for deep foundation pit support structures based on system reliability analysis includes the following steps:

[0009] S1. Obtain the engineering exploration report and preliminary design scheme corresponding to the deep foundation pit; and obtain the design variables x and random variables y corresponding to the deep foundation pit according to the engineering exploration report and preliminary design scheme, and construct a deep foundation pit support design system by using the design variables x and random variables y; where the design variables x include the parameters of structural members, and the random variables y include exploration data;

[0010] S2. Determine the value range of the design variables x and the statistical characteristics of the random variables y;

[0011] S3. According to the engineering characteristics of the corresponding support of the deep foundation pit, determine the failure criterion and failure threshold of the failure mode of the deep foundation pit support design system;

[0012] S4. Construct the limit state function for each failure mode; connect each failure mode in series through a series system, and calculate the failure probability of the deep foundation pit support design system through this series system;

[0013] S5. Construct a system reliability model based on the system failure probability of the series system described in step S4, incorporate a multi-objective optimization model into the system reliability model, and set the objective function and constraint conditions;

[0014] S6. Set a multi-objective optimization algorithm in the deep foundation pit support design system, use this multi-objective optimization algorithm to calculate the safety and cost of different support structures, obtain the Pareto solution set (Pareto solution set), and obtain the support structure design corresponding to the deep foundation pit through comparison and selection.

[0015] Implementation principle, working principle:

[0016] In this solution, indicators such as the horizontal displacement of the support structure, ground settlement, and deformation of adjacent pipelines are used as the basis for evaluating the safety of the deep foundation pit system. Compared with the traditional optimization design theory, this method will consider the overall safety of the deep foundation pit support structure and surrounding facilities, and at the same time use safety and cost as the objective function, which can obtain a series of optimal solutions, facilitating designers to make convenient comparisons and selections, and choosing different design schemes according to different safety levels.

[0017] Preferably, in step S1, the design variable x is determined through the preliminary design scheme. The preliminary design scheme includes the preliminary selection of the foundation pit support system, and the parameters of the structural members are the parameters of the structural members required for the corresponding foundation pit support system. The beneficial effect of this preference is that for deep foundation pits, the cost of the corresponding support structure is relatively fixed and within an estimable range. Therefore, the design variable x effectively represents the construction cost of the corresponding support structure.

[0018] Preferably, in step S1, the random variable y is determined through the engineering exploration report. The random variable y includes the physical and mechanical parameters of the rock and soil mass, specifically including the cohesion, internal friction angle, and compression modulus of each soil layer; it also includes using the sensitivity analysis method to determine the random variable y. When determining the random variable y, triple standard deviation sampling is also included. The beneficial effect of this preference is that the value range of the random variable can be well covered by the 3-fold standard deviation principle of statistics. The most influential unstable factors on the deep foundation pit support structure can be selected through the sensitivity analysis method, and the safety factor of the support method selected through this method is better.

[0019] Preferably, in S2.1, determine the value range of the design variable x, or the upper and lower limits of the value of the design variable x; in S2.2, use the exploration data and the corresponding design variable x to perform deep foundation pit system calculations to obtain the system responses under different combinations of the design variable x and the exploration data; in S2.3, calculate the relative sensitivity of the deep foundation pit system to the exploration data under different combinations according to the different deep foundation pit system responses, and select the exploration data with a relative sensitivity exceeding the preset value as the random variable y; in S2.4, the deep foundation pit system responses correspond one by one to the failure modes of the deep foundation pit system. The beneficial effect of this preference is that through the correspondence between the system response and the failure mode, the suitability of the random variable and the corresponding foundation pit can be judged, and among them, through the relative sensitivity, the influence of specific parts of the exploration data on the safety of the foundation pit can be judged.

[0020] Preferably, in step S2.1, it is determined that the design variable x is a continuous value or several discrete values within the upper and lower limits; the random characteristics of the random variable y include the statistical distributions of the parameters in the exploration report. If the number of exploration points is less than the set value, it is assumed that each parameter conforms to the logarithmic state distribution, and this distribution satisfies that the physical and mechanical parameters of the rock and soil mass are greater than 0, and this distribution can be transformed into the standard normal distribution. The beneficial effect of this preference is that through the setting of the design variable x and the random variable y, the amount of calculation is smaller and the calculation difficulty is lower.

[0021] Preferably, in S4.1, define the failure modes, where the failure modes include the horizontal displacement of the support structure, the ground settlement, the axial force of the internal support, and the deformation of the adjacent pipelines, and determine the failure thresholds corresponding to each failure mode; in this step, by determining the failure thresholds of each failure mode, it is convenient to intuitively evaluate the safety of the corresponding structure. In S4.2, define the failure criteria, where the failure criteria are selected from one or both of the bearing capacity check and the deformation check. The bearing capacity check includes the overall stability check of the foundation pit and the anti-heave check; the deformation check includes the deep horizontal displacement of the foundation pit support structure, the ground settlement, and the additional settlement of the surrounding buildings; through the setting of the failure criteria, it is convenient to comprehensively evaluate the factors affecting the support structure, and it is more comprehensive and has better quantifiability; in S4.3, use the command stream to batch establish a finite element model, execute the calculation, and record the soil properties of the deep foundation pit in the finite element model and the thresholds required to determine the failure thresholds; use the recorded soil properties and deformation values, and then use the soil properties as the input and the failure thresholds as the output to construct and train a backpropagation neural network model (BPNN); when calculating the failure probability, first set the number of samples, sample in the preset statistical distribution by the Monte Carlo method, and then substitute it into the BPNN model to calculate the failure probability and the system reliability index of the deep foundation pit support design system.

[0022] Preferably, the limit state function described in step S4 has the following expression:

[0023] Gi (x,y 0 ) = f i (x,y 0 ) - T i (1)

[0024] In (1), x is a random variable, and y 0 is a certain design scheme. G i (x, y 0 ) represents the limit state function of the i-th failure mode, f i (x, y 0 ) represents the bearing capacity calculation function or the deformation calculation function, and T i represents the failure threshold of the i-th failure mode;

[0025] In step S4.3, the failure probability calculation for a single failure mode is as follows:

[0026]

[0027] In (2), I[G i (x)] is an indicator function used to count the number of failure samples, and N is the sample size;

[0028] Among them, to ensure the accuracy of the failure probability calculation in (2), a certain sample size should be guaranteed, and the sample size should satisfy the following expression:

[0029]

[0030] The failure probability calculation for multiple failure modes is the same as that for a single failure mode, but the system failure criterion needs to be defined through a series-parallel system. For a series system, the indicator function I[Gi(x)] should be:

[0031]

[0032] Preferably, the objective function includes the construction cost and overall safety of the deep foundation pit support structure; the constraint conditions are continuous values or several discrete values within the upper and lower limits of the design variable x, and the statistical distributions of various parameters in the exploration report.

[0033] Preferably, the multi-objective optimization algorithm includes one or both of the second-generation non-dominated genetic algorithm or the third-generation non-dominated genetic algorithm. When using the multi-objective optimization algorithm to solve the multi-objective optimization model, it includes generating initial samples within the set domain, performing non-dominated sorting, performing iterative search within the set domain, and updating the non-dominated solution set.

[0034] A deep foundation pit support structure design device includes a computer program. Using the above-mentioned deep foundation pit support structure design method based on system reliability analysis, it also includes an input unit, a processing unit, and an output unit. The input unit is used to input data, and the input data includes the type of deep foundation pit and the preliminary support design plan corresponding to the deep foundation pit. The processing unit has the computer program built in. The processing unit processes the input data to obtain the support structure design plan for the corresponding deep foundation pit. The output unit is used to output the support structure design plan, and the support structure design plan includes construction cost and safety

[0035] The beneficial effects of the present invention are as follows:

[0036] In this solution, indicators such as the horizontal displacement of the support structure, ground settlement, and deformation of adjacent pipelines are used as the basis for evaluating the safety of the deep foundation pit system. Compared with the traditional optimization design theory, this method will consider the overall safety of the deep foundation pit support structure and surrounding facilities, and at the same time take safety and cost as the objective function, and can obtain a series of optimal solutions, which is convenient for designers to make comparisons. According to different safety levels, different design plans can be selected, and then a support structure design method with high safety factor and low support cost can be obtained Description of the Drawings

[0037] Figure 1 It is a flowchart of the deep foundation pit support structure optimization design method according to the embodiment of the present invention

[0038] Figure 2 It is a flowchart of the multi-objective optimization model solving algorithm according to the embodiment of the present invention

[0039] Figure 3 It is a schematic diagram of the finite element model according to the embodiment of the present invention

[0040] Figure 4 It is the prediction effect diagram of the backpropagation neural network model according to the embodiment of the present invention

[0041] Figure 5 It is the first-generation Pareto solution set obtained by solving the multi-objective optimization model according to the embodiment of the present invention

[0042] Figure 6 It is the fifth-generation Pareto solution set obtained by solving the multi-objective optimization model according to the embodiment of the present invention

[0043] Figure 7 It is the fiftieth-generation Pareto solution set obtained by solving the multi-objective optimization model according to the embodiment of the present invention Detailed Embodiments

[0044] The following elaborates on the preferred embodiments of the present invention in conjunction with the accompanying drawings, so that the advantages and features of the present invention can be more easily understood by those skilled in the art, thereby making a clearer and more definite definition of the protection scope of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0045] As Figure 1-7 shown:

[0046] A design method for deep foundation pit support structures based on system reliability analysis includes the following steps:

[0047] S1. Obtain the engineering exploration report and preliminary design plan for the corresponding deep foundation pit; and obtain the design variables x and random variables y for the corresponding deep foundation pit according to the engineering exploration report and preliminary design plan, and construct a deep foundation pit support design system using the design variables x and random variables y; where the design variables x include the parameters of structural members, and the random variables y include exploration data.

[0048] Among them, in step S1, through the preliminary design of the to-be-constructed deep foundation pit, the design variables x are determined through the preliminary design plan. The preliminary design plan includes selecting different foundation pit support systems, and the structural members selected in different foundation pit support systems are different. Selecting the structural member parameters required for the corresponding foundation pit support system can accurately estimate the cost range of the corresponding support structure. Therefore, the design variables x effectively represent the construction cost of the corresponding support structure; for example, when selecting the diaphragm wall - internal support support system, the corresponding parameters to be optimized are the thickness, depth of the diaphragm wall, cross-sectional area of the internal support, spacing of the internal support, etc.; for the row pile - anchor support system, the corresponding set of parameters to be optimized can be the cross-sectional area, spacing, depth of the row pile, cross-sectional area of the anchor, and length of the anchor.

[0049] In step S1, the random variable y is determined through the engineering exploration report. The random variable y includes the physical and mechanical parameters of the rock and soil mass, specifically including the cohesion, internal friction angle, and compression modulus of each soil layer. It also includes determining the random variable y using the sensitivity analysis method. Among them, determining the random variable y according to the exploration report is equivalent to determining the natural characteristics with relatively high uncertainty related to the physical and mechanical parameters of the rock and soil mass, and then selecting the random variable y that has an obvious impact on safety to participate in the subsequent reliability analysis and optimization calculation. Specifically, it includes the cohesion, internal friction angle, and compression modulus of each soil layer. If the subsequent limit state function is mainly for bearing capacity calculation, the compression modulus may not be considered. If the limit state function involves seepage calculation, the permeability coefficient of each soil layer should be included. When there are many soil layers on the site, important parameters should be screened out as the random variable y through single-factor sensitivity analysis. Through the sensitivity analysis method, the most unstable factors that have the greatest impact on the deep foundation pit support structure can be selected, and the safety factor of the support method selected by this method is better.

[0050] S2. Determine the value range of the design variable x and the statistical characteristics of the random variable y. Among them, the design variable x in step S2.1 is a continuous value or several discrete values within the upper and lower limits. The statistical characteristics of the random variable y include the statistical distribution of each parameter in the exploration report. If the number of exploration points is less than the set value, it is assumed that each parameter conforms to the logarithmic normal distribution. This distribution satisfies that the physical and mechanical parameters of the rock and soil mass are greater than 0, and this distribution can be transformed into the standard normal distribution, which is convenient for subsequent reliability analysis.

[0051] Specifically, step S2 includes the following steps:

[0052] S2.1. Determine the value range of the design variable x, or the upper and lower limits of the value of the design variable x. The design variable x is a continuous value or several discrete values within the upper and lower limits. The general characteristics of the random variable y include the statistical distribution of each parameter in the exploration report. If the number of exploration points is less than the set value, it is assumed that each parameter conforms to the logarithmic normal distribution. This distribution satisfies that the physical and mechanical parameters of the rock and soil mass are greater than 0, and this distribution can be transformed into the standard normal distribution. The beneficial effect of this optimization is that through the setting of the design variable x and the random variable y, the calculation amount is smaller and the calculation difficulty is lower.

[0053] S2.2. Use the exploration data and the corresponding design variable x to perform calculations on the deep foundation pit system, and obtain the system response under different combinations of the design variable x and the exploration data.

[0054] S2.3. According to different deep foundation pit system responses, calculate the relative sensitivity of the deep foundation pit system to the exploration data under different combinations, and select the exploration data with a relative sensitivity exceeding the preset value as the random variable y.

[0055] S2.4. The responses of the deep foundation pit system correspond one-to-one with the failure modes of the deep foundation pit system. Among them, the 3-fold standard deviation principle of statistics can well cover the value range of the random variable y. Through the correspondence between the system response and the failure mode, the fitness between the random variable y and the corresponding foundation pit can be judged. Among them, through relative sensitivity, the influence of specific parts in the exploration data on the safety of the foundation pit can be judged.

[0056] During implementation, in step S3, according to the engineering characteristics of the corresponding support of the deep foundation pit, determine the failure criterion and failure threshold of the failure mode of the deep foundation pit support design system. Through the failure criterion and failure threshold, it is convenient to determine the selection and calculation of the support scheme.

[0057] During implementation, in step S4, construct the limit state function of each failure mode; connect each failure mode in series through a series system, and calculate the failure probability of the deep foundation pit support design system through this series system. The specific steps are as follows:

[0058] S4.1. Define the failure mode. The failure mode includes the horizontal displacement of the support structure, the ground settlement, the axial force of the internal support, and the deformation of adjacent pipelines, and determine the failure threshold corresponding to each failure mode; in this step, through the determination of the failure threshold of each failure mode, it is convenient to intuitively evaluate the safety of the corresponding structure in each failure mode.

[0059] S4.2. Define the failure criterion. Among them, the failure criterion selects one or two of the bearing capacity check and the deformation check. The bearing capacity check includes the overall stability check of the foundation pit and the anti-heave check; the deformation check includes the deep horizontal displacement of the foundation pit support structure, the ground settlement, and the additional settlement of surrounding buildings; through the setting of the failure criterion, it is convenient to comprehensively evaluate the factors affecting the safety of the support structure, and the degree of quantification is better;

[0060] S4.3. Use the command stream to batch establish a finite element model, execute the calculation, and record the soil properties of the deep foundation pit in the finite element model and the thresholds required to determine the failure threshold; use the recorded soil properties and deformation values, and then use the soil properties as the input and the failure threshold as the output to construct and train a backpropagation neural network model (BPNN); when calculating the failure probability, first set the number of samples, sample in the preset statistical distribution through the Monte Carlo method, and then substitute it into the BPNN model to calculate the failure probability and system reliability index of the deep foundation pit support design system.

[0061] Specifically, the limit state function described in step S4 has the following expression:

[0062] G i (x, y 0 ) = f i (x, y 0 )—Ti (1)

[0063] In (1), x is a random variable, and y 0 is a certain design scheme, and G i (x, y 0 ) represents the limit state function of the i-th failure mode, and f i (x, y 0 ) represents the bearing capacity calculation function or the deformation calculation function, and T i represents the failure threshold of the i-th failure mode;

[0064] In step S4.3, the failure probability calculation for a single failure mode is as follows:

[0065]

[0066] In (2), is the failure probability, I[G i (x)] is the indicator function, which is used to count the number of failure samples, and N is the sample size;

[0067] Among them, to ensure the accuracy of the failure probability calculation in (2), a certain sample size should be ensured, and the sample size should satisfy the following expression:

[0068]

[0069] The failure probability calculation for multiple failure modes is the same as that for a single failure mode, but the system failure criterion needs to be defined through a series-parallel system. For the failure probability of a series system, the indicator function I[G i (x)] should be:

[0070]

[0071] Among them, m is the number of failure modes. For a series system, as long as any one failure mode occurs, the entire system is considered to have failed.

[0072] S5. Construct a system reliability model through the system failure probability of the series system described in step S4. Incorporate a multi-objective optimization model into the system reliability model, and set the objective function and constraint conditions. The constraint conditions are continuous values or several discrete values within the upper and lower limits of the design variable x, and the statistical distributions of the parameters in the exploration report; among them, the objective function includes the construction cost and overall safety of the deep foundation pit support structure; among them, the component cost is mainly determined by the support form. For example, for the diaphragm wall - internal support support system, it is mainly the concrete material and steel support material; for the pile-anchor support system, it is mainly the anchor rod steel bar material and the pile body concrete or cement soil material; for the overall safety, it is expressed by the system failure probability or the system reliability index, and there is the following conversion relationship between the reliability index and the failure probability:

[0073] βsys = Φ(1 - P f ) (5)

[0074] Wherein, βsys is the system reliability index, Φ is the cumulative distribution function of the standard normal distribution, and P f is the system failure probability; for the value ranges of the above-mentioned design variable x and random variable y, appropriate constraint conditions can also be set according to the actual engineering situation, such as restricting the building material cost or the overall structural safety within a certain range. If the on-site conditions make some design solutions impossible to implement, those design solutions are prohibited from participating in the solution of the optimization model to improve the calculation efficiency.

[0075] S6. Set a multi-objective optimization algorithm in the deep foundation pit support design system, and use this multi-objective optimization algorithm to calculate the safety and cost of different support structures to obtain the Pareto solution set, and obtain the support structure design corresponding to the deep foundation pit through comparison and selection; specifically, the multi-objective optimization algorithm includes one or both of the second-generation non-dominated genetic algorithm and the third-generation non-dominated genetic algorithm. When using the multi-objective optimization algorithm to solve the multi-objective optimization model, it includes generating an initial sample within the set domain, performing non-dominated sorting, performing iterative search within the set domain, and updating the non-dominated solution set.

[0076] Specifically, the multi-objective optimization model is as follows:

[0077] Objectives:

[0078] Find: x

[0079] Constraints:

[0080] Wherein, x is the design variable, D is the sampling space corresponding to the random variable, y is the random variable, S is the value range corresponding to the design variable, and βsys > β L means that the system reliability shall not be less than the preset lower limit value to ensure the overall safety of the system and avoid iterative solution in invalid design solutions; the purpose of this model is to find the design solution with the highest overall safety under the minimum building material cost.

[0081] The specific implementation method is as follows:

[0082] In step S1 during specific implementation, it further includes:

[0083] Since the engineering site involves multiple strata, it is often simplified into several soil layers in the calculation. Therefore, the physical and mechanical parameters of each soil layer can be regarded as random variables y. When there are many soil layers, the parameters that have a greater impact on the calculation results are selected as random variables y. Specifically, the parameters are screened through single-factor sensitivity analysis. For a foundation pit project with k parameters, the single-factor sensitivity analysis can be carried out with reference to the parameter values in Table 1 below:

[0084]

[0085] Table 1 Parameter Values for Single-Factor Sensitivity Analysis

[0086] As can be seen from Table 1, for an engineering problem with k variables, a total of 2k + 1 sample points are required. Among them, L represents the lower limit value of the corresponding variable, and U represents the upper limit value of the corresponding variable;

[0087] If there are the sample mean μ and sample standard deviation σ of this variable, the upper and lower limits of the random variable y can be determined according to the 3-fold standard deviation principle. The upper limit is U = μ + 3σ, and the lower limit is L = μ - 3σ.

[0088] After determining the 2k + 1 samples and the corresponding parameter values, the relative sensitivity of each parameter should be calculated according to the following formula (7):

[0089]

[0090]

[0091] When there are multiple response indicators (such as the deformation of a deep foundation pit, the surface settlement deformation, etc., which are all important bases for the selection of the support structure type), further calculations should be carried out according to the above formula (8). Specifically, the parameters with a relative sensitivity greater than 5% are selected as random variables y;

[0092] Among them, in formulas (7) and (8), n represents the number of variables, m represents the number of failure modes. When there are multiple failure modes, each failure mode corresponds to a system response. λ ik 、ω ik respectively represent the absolute sensitivity and relative sensitivity of the kth variable to the ith system response, and g i (x) represents the ith system response. respectively represent the upper limit combination, lower limit combination, and mean combination in the value combination of the random variable. ω k represents the relative sensitivity of the kth variable to the overall system.

[0093] In an embodiment, taking the diaphragm wall - internal bracing support system as an example, the first - layer bracing is generally a concrete bracing, and the remaining layers are steel bracings. The design variables x are the thickness of the diaphragm wall, the depth of the diaphragm wall, the cross - sectional area of the steel bracing, and the cross - sectional area of the concrete bracing. For a row of round piles as the support structure, it can be converted into an equivalent thickness according to the following formula (9);

[0094]

[0095] where d is the diameter of the round pile, t is the net spacing between two round piles, and h is the equivalent thickness of the row of piles.

[0096] The thickness of the diaphragm wall, the depth of the diaphragm wall, the cross - sectional area of the steel bracing, and the cross - sectional area of the concrete bracing are all set as several discrete values, as shown in Table 2 below. When the value range of the design variable is several discrete values, the solution of the subsequent optimization model is "quasi - integer optimization".

[0097]

[0098]

[0099] Table 2 Value range of design variables

[0100] In this embodiment, according to the characteristics of deep foundation pit engineering, the maximum deep - layer horizontal displacement of the diaphragm wall, the maximum surface settlement deformation, and the axial compression ratio of the steel bracing are respectively selected as the evaluation indexes of the overall safety of the support structure, that is, the failure threshold. The values of the failure threshold refer to the "Code for Design of Building Foundation" (GB50007 - 2011) and the "Technical Code for Monitoring of Building Foundation Pit Engineering" (GB50497 - 2019), and the specific values are shown in Table 3 below:

[0101]

[0102] Table 3 Values of failure threshold

[0103] a The failure threshold is denoted as the vector δ = [δx1, δx2, δy,F NS ,ρ N ,ρ S . b H represents the excavation depth of the foundation pit.

[0104] When performing step S4 in this embodiment, it further includes establishing a limit state function as shown in formula (1), establishing a deep foundation pit model by finite element analysis, and extracting three data items including the maximum deep horizontal displacement of the diaphragm wall, the maximum surface settlement deformation, and the axial compression ratio of the steel support. The single-mode failure probability and the system failure probability can be obtained through the Monte Carlo simulation method. Since the finite element calculation is repeatedly performed, the calculation cost is relatively high. Within the value ranges of the design variables and random variables, 600-1000 groups of finite element models can be randomly generated for training the backpropagation neural network model, but attention should be paid to ensuring the accuracy of the neural network model, and generally control its coefficient of determination R 2 > 0.95. The deep foundation pit finite element model in this embodiment is as shown in Figure 3 ; the prediction effect of the backpropagation neural network model is as shown in Figure 4 .

[0105] Specifically, further, the S5 includes: according to the characteristics of the deep foundation pit model, respectively setting the objective function, parameters to be optimized, constraint conditions, etc. of the optimization model, as shown in formula (10) below;

[0106]

[0107] In the formula, β sys represents the system reliability index, which can be obtained from the backpropagation neural network; the building material cost calculation function Q is composed of the concrete material cost Q w of the diaphragm wall and the steel support material cost Q s ; the value range of the design variable x is the same as that in Table 2, and the random variable y is assumed to follow a lognormal distribution; setting the system reliability βsys > 2.0 as a constraint condition to ensure the overall safety of the support structure. B and L are the length and width of the foundation pit respectively; N h , N v respectively represent the arrangement numbers of the steel supports in the horizontal and vertical directions of the deep foundation pit; U C , U S , ρ respectively represent the unit volume cost of concrete, the unit mass cost of steel support, and the steel density.

[0108] The non-dominated genetic algorithm is used for solution, setting the Pareto solution set to 30 and the number of iterations to 50 generations to solve the multi-objective optimization model. Among them, the Pareto solution sets after the 1st, 5th, and 30th iterations are as shown in Figure 5 .

[0109] When the number of Pareto solution sets is set too large, the number of solutions that meet the constraint conditions may be less than the number of solution sets, which affects the solution efficiency. When the number of solution sets is too small, the boundary line of the Pareto solution set may not be depicted. Therefore, for integer programming-like problems, the number of solution sets can be set to 2-3% of the total number of solutions. For this embodiment, as can be seen from Table 2, the total number of solutions is 11×5×5×6 = 1650 design solutions. Setting the number of iterations to 50 generations can meet the requirements.

[0110] This solution also provides a deep foundation pit support structure design device, including a computer program, adopting the above-mentioned deep foundation pit support structure design method based on system reliability analysis, and further including an input unit, a processing unit, and an output unit. The input unit is used to input data, and the input data includes the type of deep foundation pit and the preliminary support design solution corresponding to the deep foundation pit. The processing unit has the computer program built in, and the processing unit processes the input data to obtain the support structure design solution corresponding to the deep foundation pit. The output unit is used to output the support structure design solution, and the support structure design solution includes construction cost and safety.

[0111] The beneficial effects of the present invention are as follows:

[0112] In this solution, indicators such as the horizontal displacement of the support structure, ground settlement, and deformation of adjacent pipelines are used as the basis for evaluating the safety of the deep foundation pit system. Compared with the traditional optimization design theory, this method will consider the overall safety of the deep foundation pit support structure and surrounding facilities, and at the same time take safety and cost as the objective functions, and can obtain a series of optimal solutions, which is convenient for designers to make comparisons and selections. According to different safety levels, different design solutions can be selected, and then a support structure design method with high safety factor and low support cost can be obtained.

[0113] Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirits of the present invention. The scope of the present invention is defined by the appended claims.

Claims

1. A deep foundation pit support structure design method based on system reliability analysis, characterized in that: The following steps are involved: S1. Obtain an engineering survey report and a plurality of preliminary design schemes corresponding to a deep foundation pit; obtain a design variable x and a random variable y corresponding to the deep foundation pit according to the engineering survey report and the preliminary design scheme, and construct a deep foundation pit support design system using the design variable x and the random variable y; The design variables x include the parameters of the structural components, and the random variables y include the exploration data; S2, determine the value range of the design variable x and the statistical characteristics of the random variable y; S3. According to the engineering characteristics of the deep foundation pit support, determine the failure criteria and failure threshold of the failure mode of the deep foundation pit support design system; S4, constructing the limit state function of each failure mode; connecting each failure mode in series through a series system, and calculating the failure probability of the deep foundation pit support design system through the series system; S5, constructing a system reliability model through the system failure probability of the series system described in step S4, integrating a multi-objective optimization model into the system reliability model, and setting objective functions and constraints; S6. A multi-objective optimization algorithm is set up in the deep foundation pit support design system, and the multi-objective optimization algorithm is used to calculate the safety and cost of different support structures to obtain the Pareto solution set, and the support structure design of the corresponding deep foundation pit is obtained through comparison.

2. The deep foundation pit support structure design method based on system reliability analysis according to claim 1 is characterized in that: In step S1, the design variable x is determined through the preliminary design scheme, the preliminary design scheme includes the preliminary selection of the foundation pit support system, and the parameters of the structural components are the structural component parameters required for the corresponding foundation pit support system.

3. The deep foundation pit support structure design method based on system reliability analysis according to claim 2 is characterized in that: In step S1, the random variable y is determined through the engineering exploration report, and the random variable y includes the physical and mechanical parameters of the rock and soil mass, specifically including the cohesion, internal friction angle, and compression modulus of each soil layer; it also includes using a sensitivity analysis method to determine the random variable y, and when determining the random variable y, it also includes using three times standard deviation sampling.

4. The deep foundation pit support structure design method based on system reliability analysis according to claim 3 is characterized in that: include: S2.

1. Determine the range of the design variable x, or the upper and lower limits of the design variable x; S2.2, using the exploration data and the corresponding design variables x to perform deep foundation pit system calculations, and obtaining the system response under the combination of design variables x and different exploration data; S2.

3. According to different responses of the deep foundation pit system, the relative sensitivity of the deep foundation pit system to the exploration data under different combinations is calculated, and the exploration data with relative sensitivity exceeding the preset value is selected as the random variable y; S2.

4. The response of the deep foundation pit system corresponds one to one with the failure mode of the deep foundation pit system.

5. The deep foundation pit support structure design method based on system reliability analysis according to claim 4 is characterized in that: In determining step S2.1, the design variable x is a continuous value or a plurality of discrete values ​​within the range of the upper limit and the lower limit; The general characteristics of the random variable y include the statistical distribution of each parameter in the survey report. If the number of survey points is less than the set value, the parameters are assumed to conform to the logarithmic distribution, which satisfies the physical and mechanical parameters of the rock and soil mass greater than 0, and the distribution can be transformed into the standard normal distribution.

6. The deep foundation pit support structure design method based on system reliability analysis according to claim 1 is characterized in that: include: S4.

1. Define failure modes, including horizontal displacement of support structure, ground settlement, internal support axial force, and deformation of adjacent pipelines, and determine the failure threshold corresponding to each failure mode; S4.

2. Define failure criteria, where the failure criteria are selected from one or both of bearing capacity verification and deformation verification. Bearing capacity verification includes overall stability verification of foundation pit and anti-uplift verification; deformation verification includes deep horizontal displacement of foundation pit support structure, surface settlement, and additional settlement of surrounding buildings; S4.

3. Use command stream to batch establish finite element models, perform calculations, and record the soil parameters of the deep foundation pit in the finite element model and the thresholds required to determine the failure threshold; use the recorded soil parameters and deformation values, and then use the soil parameters as input and the failure threshold as output to build and train a back propagation network model (BPNN); when calculating the failure probability, first set the number of samples, sample in the preset statistical distribution through the Monte Carlo method, and then substitute it into the BPNN model to calculate the failure probability of the deep foundation pit support design system and the system reliability index.

7. The deep foundation pit support structure design method based on system reliability analysis according to claim 6 is characterized in that: The limit state function described in step S4 is expressed as follows: G i (x,y0)=f i (x,y0)-T i (1) In (1), x is a random variable, y0 is a design solution, and G i (x, y0) represents the limit state function of the ith failure mode, f i (x, y0) represents the bearing capacity calculation function or deformation calculation function, T i represents the failure threshold of the i-th failure mode; In step S4.3, the failure probability for a single failure mode is calculated as follows: In (2), I[G i (x)] is the indicator function, which is used to count the number of failed samples, and N is the number of samples; In order to ensure the accuracy of the failure probability calculation in (2), a certain number of samples should be guaranteed, and the number of samples should satisfy the following expression: The failure probability calculation of multiple failure modes is the same as that of single failure mode, but the system failure criterion needs to be defined by the series-parallel system. For the series system, the indicator function I[G i (x)] should read:

8. The deep foundation pit support structure design method based on system reliability analysis according to claim 1 is characterized by: The objective function includes the construction cost and overall safety of the deep foundation pit support structure; the constraint conditions are continuous values ​​or several discrete values ​​within the upper and lower limits of the design variable x, and the statistical distribution of each parameter in the survey report.

9. The method for designing a deep foundation pit support structure based on system reliability analysis according to claim 1, characterized in that: The multi-objective optimization algorithm includes one or both of a second-generation non-dominated genetic algorithm or a third-generation non-dominated genetic algorithm. When using the multi-objective optimization algorithm to solve a multi-objective optimization model, it includes generating an initial sample within a set domain, performing non-dominated sorting, performing iterative search within the set domain, and updating a non-dominated solution set.

10. A deep foundation pit support structure design device, characterized in that: It includes a computer program, which includes the deep foundation pit support structure design method based on system reliability analysis as described in claims 1-9, and also includes an input unit, a processing unit and an output unit. The input unit is used to input data, and the input data includes the deep foundation pit type and the preliminary support design plan corresponding to the deep foundation pit. The processing unit has the computer program built in. The processing unit performs data processing according to the input data to obtain the support structure design plan corresponding to the deep foundation pit. The output unit is used to output the support structure design plan, and the support structure design plan includes construction cost and safety.

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