A method and system for optimizing closure jacking force of a multi-span continuous rigid frame bridge

Abstract

The present application relates to the field of bridge construction technology, in particular to a multi-span continuous rigid frame bridge closure jacking force optimization method and system, first according to the closure sequence scheme to determine the construction steps corresponding to the closure sequence scheme;Secondly, according to the closure sequence scheme and the corresponding construction steps are carried out soil constraint degradation simulation, the finite element model of the whole bridge is established;Then based on the finite element model, the parameters corresponding to each closure mouth are calculated respectively by applying unit jacking force and not applying unit jacking force, and the to-be-solved function is constructed based on the first parameter and the second parameter;Finally, the multi-objective optimization problem corresponding to the to-be-solved function is converted into a single objective linear programming problem by using fuzzy mathematics solution method, and the optimal solution of jacking force is obtained, the scheme disclosed in the present application simulates the soil constraint degradation effect comprehensively, and at the same time, the multi-objective problem under the deep water environment is converted into a single objective linear programming problem, which not only simplifies the solving process, but also accurately solves the optimal solution of jacking force.

Description

Technical Field

[0001] This invention relates to the field of bridge construction technology, and in particular to a method and system for optimizing the closure thrust of a multi-span continuous rigid frame bridge. Background Technology

[0002] Multi-span continuous rigid frame bridges face severe long-term stability challenges in deep-water, fast-flowing environments, especially in coastal and estuarine areas with complex hydrological conditions, such as Southeast Asia. The strong monsoon rainfall and tidal action cause a significantly higher scouring rate for bridge pier foundations compared to conventional land-based bridges. During operation, deep-water foundations are subjected to continuous water scouring, leading to a gradual degradation of the effective embedment depth of the piles and a significant decrease in the horizontal lateral stiffness of the soil. Simultaneously, the periodic water flow impact on the pier sections, combined with concrete shrinkage, creep, and temperature effects, creates a time-varying coupling effect, exacerbating cumulative pier displacement and stress concentration at the pier base. This long-term effect of multiple coupled factors severely tests traditional jacking design methods: insufficient jacking pre-deflection may result in pier top displacement exceeding limits ten years after bridge completion; excessive jacking can easily lead to tensile stress exceeding allowable values ​​during construction.

[0003] Current research on jacking force optimization is largely limited to conventional land-based bridge environments, exhibiting significant shortcomings: 1) It fails to consider the degradation effect of pile-soil constraint caused by deep-water scouring, still calculating soil spring stiffness based on the initial embedment depth, thus overestimating the pier constraint capacity; 2) It neglects the continuous impact of water flow loads on stress and bridge displacement during construction, especially under high-velocity conditions during the flood season, where the pier's water-blocking area increases with scouring depth, creating a positive feedback effect; 3) Existing trial-and-error methods struggle to quantify the cross-influence of jacking force combinations on the displacement of each pier in multi-span systems (n≥5). In deep-water environments, multiple displacement constraint objectives and stress control conditions form a high-dimensional nonlinear relationship, leading to a 20%-30% error in traditional trial-and-error methods. Therefore, establishing a multi-objective optimization system for jacking force that considers deep-water hydrological factors has become an urgent need for deep-water bridge construction in mountainous areas. Summary of the Invention

[0004] The purpose of this invention is to provide a method and system for optimizing the jacking thrust of a multi-span continuous rigid frame bridge during closure, so as to accurately solve for the optimal jacking thrust.

[0005] To achieve the above objectives, this invention provides a method for optimizing the closure thrust of a multi-span continuous rigid frame bridge, the method comprising:

[0006] Determine the closure sequence scheme for a multi-span continuous rigid frame bridge;

[0007] The construction steps corresponding to the closure sequence scheme are determined according to the closure sequence scheme.

[0008] Based on the closure sequence scheme and the corresponding construction steps, soil constraint degradation simulation was performed to establish a finite element model of the entire bridge;

[0009] Based on the finite element model, the parameters corresponding to applying a unit jacking force and not applying a unit jacking force to each closure joint are calculated respectively, and the first parameter and the second parameter are obtained respectively.

[0010] A function to be solved is constructed based on the first parameter and the second parameter; the function to be solved includes an objective function M and constraint equations;

[0011] By employing fuzzy mathematics, the multi-objective optimization problem corresponding to the function to be solved is transformed into a single-objective linear programming problem, thereby obtaining the optimal solution for the top thrust.

[0012] Optionally, the step of simulating soil constraint degradation based on the closure sequence and the corresponding construction steps to establish a finite element model of the entire bridge specifically includes:

[0013] According to the aforementioned closure sequence scheme and the corresponding construction steps, the deep-water foundation scour zone of the pile foundation is scoured according to the most unfavorable scour depth H. S Soil constraint degradation simulation was performed to obtain the effective embedment correction depth of the pile foundation;

[0014] Calculate the reduction degree of horizontal lateral stiffness of the soil based on the effective embedment correction depth of the pile foundation;

[0015] Establish the pile-soil interaction spring stiffness matrix based on the reduction of the horizontal lateral stiffness of the soil.

[0016] A finite element model of the entire bridge is constructed based on the pile-soil interaction spring stiffness matrix.

[0017] Optionally, the first parameter includes: the longitudinal horizontal displacement change of the top of the i-th pier caused by the unit thrust at the j-th closure joint after the scour state, ten years after the bridge's completion. The stress change value of the section of the i-th pier during the construction stage caused by the unit thrust of the j-th closure joint after scouring. ;

[0018] The second parameter includes: the self-weight of the main girder and the total displacement of the top of pier i caused by concrete shrinkage and creep ten years after the bridge's completion. Displacement of the top of pier i caused by water flow load ten years after the bridge's completion. The total displacement of the top of pier i caused by temperature difference ten years after the bridge's completion. Stress on the section of pier i caused by various loads during the construction phase .

[0019] Optionally, the step of employing fuzzy mathematics to transform the multi-objective optimization problem corresponding to the function to be solved into a single-objective linear programming problem to obtain the optimal solution for the top thrust specifically includes:

[0020] A multi-objective linear programming model is constructed based on the function to be solved. The multi-objective linear programming model includes a multi-objective objective function and multi-objective constraints.

[0021] The multi-objective linear programming model is standardized to obtain the standardized objective function and constraints.

[0022] By fuzzifying the standardized objective function and constraints, the multi-objective problem is transformed into a single-objective problem.

[0023] The single-objective problem was solved using MATLAB software to obtain the optimal solution for the top thrust of the entire bridge.

[0024] Optionally, the objective function M is specifically formulated as follows:

[0025] min

[0026] in, Let be the longitudinal horizontal displacement of the i-th pier. Apply a unit thrust to the j-th closure joint.

[0027] Optionally, the specific formula for the constraint condition equation is as follows:

[0028]

[0029] in, To allow tensile stress.

[0030] The present invention also provides a closure thrust optimization system for multi-span continuous rigid frame bridges, the system comprising:

[0031] The closure sequence determination module is used to determine the closure sequence scheme for multi-span continuous rigid frame bridges.

[0032] The construction step determination module is used to determine the construction steps corresponding to the closure sequence scheme based on the closure sequence scheme.

[0033] The finite element model building module is used to simulate soil constraint degradation based on the closure sequence scheme and the corresponding construction steps, and to build a finite element model of the entire bridge.

[0034] The parameter solving module is used to calculate the parameters corresponding to applying a unit jacking force and not applying a unit jacking force to each closure joint based on the finite element model, and obtain the first parameter and the second parameter respectively.

[0035] The module for constructing the function to be solved is used to construct the function to be solved based on the first parameter and the second parameter; the function to be solved includes an objective function M and constraint equations.

[0036] The top thrust optimal solution determination module is used to transform the multi-objective optimization problem corresponding to the function to be solved into a single-objective linear programming problem by using fuzzy mathematics to obtain the top thrust optimal solution.

[0037] Optionally, the finite element model building module specifically includes:

[0038] The soil constraint degradation simulation unit is used to simulate the scour zone of the deep water foundation of the pile foundation according to the closure sequence scheme and the corresponding construction steps, based on the most unfavorable scour depth H. S Soil constraint degradation simulation was performed to obtain the effective embedment correction depth of the pile foundation;

[0039] The soil horizontal lateral stiffness reduction calculation unit is used to calculate the soil horizontal lateral stiffness reduction based on the effective embedded correction depth of the pile foundation.

[0040] The spring stiffness matrix calculation unit is used to establish the pile-soil interaction spring stiffness matrix based on the reduction degree of the horizontal lateral stiffness of the soil.

[0041] The finite element model building unit is used to construct the finite element model of the entire bridge based on the pile-soil interaction spring stiffness matrix.

[0042] Optionally, the first parameter includes: the longitudinal horizontal displacement change of the top of the i-th pier caused by the unit thrust at the j-th closure joint after the scour state, ten years after the bridge's completion. The stress change value of the section of the i-th pier during the construction stage caused by the unit thrust of the j-th closure joint after scouring. ;

[0043] The second parameter includes: the self-weight of the main girder and the total displacement of the top of pier i caused by concrete shrinkage and creep ten years after the bridge's completion. Displacement of the top of pier i caused by water flow load ten years after the bridge's completion. The total displacement of the top of pier i caused by temperature difference ten years after the bridge's completion. Stress on the section of pier i caused by various loads during the construction phase .

[0044] Optionally, the module for determining the optimal solution of the top thrust specifically includes:

[0045] A multi-objective linear programming model building unit is used to construct a multi-objective linear programming model based on the function to be solved. The multi-objective linear programming model includes a multi-objective objective function and multi-objective constraints.

[0046] The standardization processing unit is used to standardize the multi-objective linear programming model to obtain the standardized objective function and constraints.

[0047] The problem transformation unit is used to transform a multi-objective problem into a single-objective problem by fuzzing the standardized objective function and constraints.

[0048] The solution unit is used to solve the single-objective problem using MATLAB software to obtain the optimal solution for the top thrust of the entire bridge.

[0049] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0050] This invention discloses a method and system for optimizing the jacking force of a multi-span continuous rigid frame bridge. First, the construction steps corresponding to the jacking sequence scheme are determined based on the jacking sequence scheme. Second, soil constraint degradation simulation is performed based on the jacking sequence scheme and the corresponding construction steps to establish a finite element model of the entire bridge. Then, based on the finite element model, parameters corresponding to applying a unit jacking force and not applying a unit jacking force at each jacking joint are calculated, and a solution function is constructed based on the first and second parameters. Finally, fuzzy mathematics is used to transform the multi-objective optimization problem corresponding to the solution function into a single-objective linear programming problem to obtain the optimal solution for the jacking force. The scheme disclosed in this invention comprehensively simulates the soil constraint degradation effect and transforms the multi-objective problem in deep-water environment into a single-objective linear programming problem, which not only simplifies the solution process but also accurately solves the optimal solution for the jacking force, reducing solution errors. Attached Figure Description

[0051] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0052] Figure 1 This is a flowchart of a method for optimizing the closure thrust of a multi-span continuous rigid frame bridge according to an embodiment of the present invention;

[0053] Figure 2 Elevation view of a multi-span continuous rigid frame bridge before its closure;

[0054] Figure 3 This is a schematic diagram showing the closure sequence of the side span, middle span, and secondary middle span. Detailed Implementation

[0055] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] The purpose of this invention is to provide a method and system for optimizing the jacking thrust of a multi-span continuous rigid frame bridge during closure, so as to accurately solve for the optimal jacking thrust.

[0057] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0058] like Figure 1 As shown, this invention discloses a method for optimizing the closure thrust of a multi-span continuous rigid frame bridge, the method comprising:

[0059] Step S1: Determine the closure sequence scheme for a multi-span continuous rigid frame bridge.

[0060] Step S2: Determine the construction steps corresponding to the closure sequence scheme according to the closure sequence scheme.

[0061] Step S3: Based on the closure sequence and corresponding construction steps, conduct soil constraint degradation simulation and establish a finite element model of the entire bridge.

[0062] Step S4: Based on the finite element model, calculate the parameters corresponding to applying a unit jacking force and not applying a unit jacking force to each closure joint, and obtain the first parameter and the second parameter respectively.

[0063] Step S5: Construct the function to be solved based on the first and second parameters; the function to be solved includes the objective function M and the constraint equations.

[0064] Step S6: Using fuzzy mathematics, the multi-objective optimization problem corresponding to the function to be solved is transformed into a single-objective linear programming problem, and the optimal solution for the top thrust is obtained.

[0065] The following is a detailed discussion of each step:

[0066] Step S1: Determine the closure sequence scheme for a multi-span continuous rigid frame bridge; the closure sequence scheme in this invention includes side span-middle span-secondary middle span, middle span-secondary middle span-side span, secondary middle span-side span-middle span, etc. The above is just an example and is not a specific limitation.

[0067] Step S3: Based on the closure sequence and corresponding construction steps, perform soil constraint degradation simulation and establish a finite element model of the entire bridge, specifically including:

[0068] Step S31: According to the closure sequence plan and corresponding construction steps, the deep water foundation scour zone of the pile foundation is scoured according to the most unfavorable scour depth H. S Soil constraint degradation simulation was performed to obtain the effective embedment correction depth of the pile foundation. The specific formula is as follows:

[0069] H 有效 = H 0- H s ;in, H s This represents the most unfavorable scour depth in the deep-water foundation scour zone. H 有效 To correct the effective embedment depth of the pile foundation. H 0 represents the total depth of the pile foundation.

[0070] Step S32: Calculate the reduction in horizontal lateral stiffness of the soil based on the effective embedment correction depth of the pile foundation. The specific calculation formula is as follows:

[0071] H 折减 = ab 1 mH 有效 ;in, a For the thickness of each soil layer, b 1 represents the calculated width of the pile, and m represents the proportionality coefficient of the foundation soil. H 有效 This refers to the effective embedment depth of the pile foundation, which is the distance from the midpoint of each soil layer to the layer with the greatest scour. H 折减 It represents the reduction degree of the horizontal lateral stiffness of the soil.

[0072] Step S33: Establish the pile-soil interaction spring stiffness matrix K based on the reduction of the horizontal lateral stiffness of the soil. S .

[0073] Step S34: Based on the pile-soil interaction spring stiffness matrix K S Construct a finite element model of the entire bridge.

[0074] In this embodiment, a deep-water scour simulation system was constructed through steps S31-S33 to correct the constraints on the pile-soil structure after riverbed scour, overcoming the limitations of traditional static soil models. Furthermore, water flow loads were embedded into the finite element model to quantify the instantaneous impact of water flow on pier stress during construction and the cumulative displacement effect ten years after bridge completion. The water flow load calculation was based on Article 4.3.9 of the "General Specifications for Design of Highway Bridges and Culverts" JTG D60-2015, and its expression is as follows:

[0075]

[0076] Where Fw is the water flow load, This is the cross-sectional shape factor of the bridge pier. The density of water, The design flow velocity is given by A, and the water-blocking area of ​​the bridge pier is given by A.

[0077] Step S4: Based on the finite element model, calculate the parameters corresponding to applying a unit jacking force and not applying a unit jacking force to each closure joint, and obtain the first parameter and the second parameter respectively; the first parameter is the corresponding parameter obtained by applying a unit jacking force to each closure joint, and the second parameter is the corresponding parameter obtained by not applying a unit jacking force to each closure joint.

[0078] The first parameter includes: the longitudinal horizontal displacement change of the top of the i-th pier ten years after the bridge is completed, caused by the unit thrust at the j-th closure joint after scouring. The stress change value of the section of the i-th pier during the construction stage caused by the unit thrust of the j-th closure joint after scouring. The stress variation value of the cross section during the construction stage includes the stress variation value of the cross section under water flow load. If the unit jacking force is 500KN, then The unit is mm / 500KN. The unit is MPa / 500KN.

[0079] The second parameter includes: the self-weight of the main girder and the total displacement of the top of pier i caused by concrete shrinkage and creep ten years after the bridge is completed. Displacement of the top of pier i caused by water flow load ten years after the bridge's completion. The total displacement of the top of pier i caused by temperature difference ten years after the bridge's completion. Stress on the section of pier i caused by various loads during the construction phase During the construction phase, various loads include water flow loads, permanent loads, variable loads, and accidental loads.

[0080] Step S5: Construct the function to be solved based on the first and second parameters; the function to be solved includes the objective function M and the constraint equations; the constraint equations are constructed to ensure that the stress at the top and bottom sections of each pier meets the requirements of the construction stage.

[0081] The specific formula for the objective function M is as follows:

[0082] min

[0083] in, Let be the longitudinal horizontal displacement of the i-th pier, where i = 1 to n, and there are a total of n piers. Apply a unit jacking force to the j-th closure joint. Apply a unit jacking force to the adjacent piers. like Figure 2 As shown.

[0084] The above method uses the pier top displacement 10 years after the bridge is completed as the objective function M. By controlling multiple objective values ​​and minimizing them, the alignment and stress of each pier can be effectively controlled.

[0085] The specific formula for the constraint equation is as follows:

[0086]

[0087] in, To allow tensile stress.

[0088] This invention aims to minimize the total displacement of the pier top (including self-weight, creep, temperature difference, and water flow load) 10 years after the bridge is completed, and establishes a matrix of influence coefficients for the jacking force, constrained by the tensile stress limit of the pier body during the construction stage. Using the displacement-stress transfer equation, a multi-objective optimization problem is transformed into an analytical single-objective linear programming problem through fuzzy membership weighting.

[0089] Step S6: Using fuzzy mathematics, the multi-objective optimization problem corresponding to the function to be solved is transformed into a single-objective linear programming problem, and the optimal solution for the top thrust is solved. Specifically, this includes:

[0090] Step S61: Construct a multi-objective linear programming model based on the function to be solved. The multi-objective linear programming model includes a multi-objective objective function and multi-objective constraints.

[0091] The multi-objective objective function is min , , , , , .

[0092] Multi-objective constraints are ; , , .

[0093] Step S62: Standardize the multi-objective linear programming model to obtain the standardized objective function and constraints; the standardized objective function is max ;in, , , , .

[0094] The standardized constraints are ; , , .

[0095] The specific derivation process is as follows: min ,make , ,have That is, max The constraints are .

[0096] Step S63: By fuzzifying the standardized objective function and constraints, the multi-objective problem is transformed into a single-objective problem. The specific formula is as follows:

[0097]

[0098] in, and Let the maximum and minimum values ​​of the i-th pier under the constraints be respectively. , This represents the change in longitudinal horizontal displacement of the top of pier i ten years after bridge completion, caused by the unit thrust at the j-th closure joint after scouring. Apply a unit thrust to the j-th closure joint. This represents the stress change in the cross-section of pier i during the construction stage caused by the unit jacking force at the j-th closure joint after scouring. For scaling indicators, i.e. = - , To quantify the overall degree of compromise, To quantify the maximum degree of overall compromise.

[0099] For single-objective problem formulas combination, , To quantify the overall degree of compromise, that is, to measure the overall satisfaction index that measures the simultaneous approximation of all pier top displacement targets to the ideal, its value range is [0,1] ( =1 indicates that all objectives are simultaneously optimized. =0 indicates that at least one objective cannot meet the minimum requirement.

[0100] Step S64: Use MATLAB software to solve the single-objective problem and obtain the optimal solution for the top thrust of the entire bridge. Specifically, use MATLAB software to solve the single-objective problem. ,in, This is the fuzzy optimal solution to the multi-objective linear programming problem, namely the optimal solution for the top thrust of the entire bridge.

[0101] The scheme disclosed in this invention comprehensively simulates the soil constraint degradation effect, and at the same time transforms the multi-objective problem in the deep water environment into a single-objective linear programming problem. This not only simplifies the solution process, but also accurately solves the optimal solution of the thrust force, reducing the solution error.

[0102] This invention establishes a full-bridge finite element model embedded with water flow loads, considering the continuous impact of water flow loads on stress during construction and displacement of the completed bridge. It quantifies multiple environmental factors affecting pier top displacement during construction and ten years after completion, including concrete shrinkage and creep, temperature difference effects, deep-water foundation scour, and dynamic water flow loads. By incorporating deep-water scour and water flow loads into the thrust optimization system, it significantly improves the long-term alignment control accuracy of multi-span continuous rigid frame bridges in complex hydrological environments.

[0103] This invention also discloses a closure thrust optimization system for a multi-span continuous rigid frame bridge, the system comprising:

[0104] The closure sequence determination module is used to determine the closure sequence scheme for multi-span continuous rigid frame bridges.

[0105] The construction step determination module is used to determine the construction steps corresponding to the closure sequence scheme based on the closure sequence scheme.

[0106] The finite element model building module is used to simulate soil constraint degradation based on the closure sequence scheme and the corresponding construction steps, and to build a finite element model of the entire bridge.

[0107] The parameter solving module is used to calculate the parameters corresponding to applying a unit jacking force and not applying a unit jacking force to each closure joint based on the finite element model, and obtain the first parameter and the second parameter respectively.

[0108] The module for constructing the function to be solved is used to construct the function to be solved based on the first parameter and the second parameter; the function to be solved includes the objective function M and the constraint equations.

[0109] The top thrust optimal solution determination module is used to transform the multi-objective optimization problem corresponding to the function to be solved into a single-objective linear programming problem by using fuzzy mathematics to obtain the top thrust optimal solution.

[0110] As an optional implementation, the finite element model establishment module of the present invention specifically includes:

[0111] The soil constraint degradation simulation unit is used to simulate the scour zone of the deep water foundation of the pile foundation according to the closure sequence scheme and the corresponding construction steps, based on the most unfavorable scour depth H. S Soil constraint degradation simulation was performed to obtain the effective embedment correction depth of the pile foundation.

[0112] The soil horizontal lateral stiffness reduction calculation unit is used to calculate the soil horizontal lateral stiffness reduction based on the effective embedded correction depth of the pile foundation.

[0113] The spring stiffness matrix calculation unit is used to establish the pile-soil interaction spring stiffness matrix based on the reduction degree of the horizontal lateral stiffness of the soil.

[0114] The finite element model building unit is used to construct the finite element model of the entire bridge based on the pile-soil interaction spring stiffness matrix.

[0115] As an optional implementation, the top thrust optimal solution determination module of the present invention specifically includes:

[0116] The multi-objective linear programming model building unit is used to construct a multi-objective linear programming model based on the function to be solved. The multi-objective linear programming model includes a multi-objective objective function and multi-objective constraints.

[0117] The standardization processing unit is used to standardize the multi-objective linear programming model to obtain the standardized objective function and constraints.

[0118] The problem transformation unit is used to transform a multi-objective problem into a single-objective problem by fuzzing the standardized objective function and constraints.

[0119] The solution unit is used to solve the single-objective problem using MATLAB software to obtain the optimal solution for the top thrust of the entire bridge.

[0120] For details on the same content as the method, please refer to the method section; it will not be repeated here.

[0121] For example, a major highway bridge located in the alluvial plain of the lower Mekong River in Cambodia has a total length of 3.7 km. The main bridge adopts a five-span, single-unit prestressed concrete continuous rigid frame bridge system (95+3×170+95) m. The main girder adopts a single-box, single-cell box section with a top slab width of 12.5 m and a bottom slab width of 7.0 m; the girder height at the root is 10.8 m, and the girder height at mid-span is 4.0 m. The main girder is constructed using the cantilever casting method with hanging baskets, and the design closure temperature is 20~30°C. The main piers of the continuous rigid frame bridge are piers 15-18, all of which are double-limb thin-walled piers. When single-limb, the cross-sectional dimensions are 7.0 m (transverse) × 2.0 m (longitudinal). The pier body is made of C50 concrete. The design flow velocity at the bridge site is 3.2 m / s, the 100-year flood level is 10.9 m, and the foundation is simulated based on the most unfavorable scour depth Hs=8.6 m.

[0122] The closure sequence is: side span - middle span - secondary middle span, and the closure steps are as follows: Figure 3 As shown.

[0123] The entire structure of this super-large bridge is symmetrical, with piers of similar height and symmetrical positions of the jacking force. According to structural mechanics principles, the horizontal displacement of the pier tops and the stress on the pier sections also exhibit symmetry at different stages. Therefore, only the right half of the bridge is analyzed. Specifically, the objective function is established using the horizontal displacements [z17, z18] of piers #17 and #18 10 years after bridge completion. The stresses at the pier top and bottom sections during construction are used as constraints to solve for the optimal jacking force combination [P1, P2]. The design tensile strength of the C50 concrete used in the main pier body is 1.89 MPa. Therefore, […]. The pressure is 1.89 MPa. Using the finite element model and taking a unit thrust of 500 kN, the calculation results are obtained from a multi-objective linear programming model, i.e.

[0124] The objective function is: min

[0125] The constraints are:

[0126] (1) During the mid-span jacking: only the jacking force P1 is involved, and only T-structures #16 and #17 are subjected to the jacking force. Therefore, the constraint conditions for the mid-span jacking are:

[0127] Pier top:

[0128] Pier bottom:

[0129] (2) During the jacking of the secondary mid-span: both jacking forces P1 and P2 are involved, and piers #15, #16, #17, and #18 are all subjected to jacking forces. Therefore, the constraint conditions for the jacking of the secondary mid-span are:

[0130] Pier top:

[0131] Pier bottom:

[0132] According to the fuzzy mathematical solution, the minimum and maximum values ​​of piers #17 and #18 under the constraints are respectively [z9] - ,z 10 - ] = [2.162,3.686] mm, [z9 * ,z 10 * Given [41.807, 243.125] mm, the scaling factor is [39.645, 239.439]. The model is then transformed into a single-objective linear programming problem, and the maximum satisfaction λ is obtained by solving it using MATLAB. *The value is 0.9455; the optimal jacking force combination [P1, P2] = [4.444, 5.802], which is a multiple of the unit jacking force, that is, the actual jacking force value is [P1, P2] = [2222, 2901] kN. According to the accuracy requirements of the construction equipment, the theoretical optimal solution [2222, 2901] kN is adjusted to [2200, 2900] kN, with an error of less than 1%, which meets the allowable range of the project.

[0133] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0134] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for optimizing the closure thrust of a multi-span continuous rigid frame bridge, characterized in that, The method includes: Determine the closure sequence scheme for a multi-span continuous rigid frame bridge; The construction steps corresponding to the closure sequence scheme are determined according to the closure sequence scheme. Based on the closure sequence scheme and the corresponding construction steps, soil constraint degradation simulation was performed to establish a finite element model of the entire bridge; Based on the finite element model, the parameters corresponding to applying a unit jacking force and not applying a unit jacking force to each closure section are calculated respectively, and the first parameter and the second parameter are obtained respectively; the first parameter includes: the longitudinal horizontal displacement change of the top of the i-th pier ten years after the completion of the bridge caused by the unit jacking force at the j-th closure section after the scour state. The stress change value of the section of the i-th pier during the construction stage caused by the unit thrust of the j-th closure joint after scouring. ; The second parameter includes: the self-weight of the main girder and the total displacement of the top of pier i caused by concrete shrinkage and creep ten years after the bridge's completion. Displacement of the top of pier i caused by water flow load ten years after the bridge's completion. The total displacement of the top of pier i caused by temperature difference ten years after the bridge's completion. Stress on the section of pier i caused by various loads during the construction phase ; A function to be solved is constructed based on the first parameter and the second parameter; the function to be solved includes an objective function M and constraint equations; the specific formula of the objective function M is: min ; in, Let be the longitudinal horizontal displacement of the i-th pier. Apply a unit jacking force to the j-th closure joint; The specific formula for the constraint condition equation is as follows: ； in, To allow tensile stress; By employing fuzzy mathematics, the multi-objective optimization problem corresponding to the function to be solved is transformed into a single-objective linear programming problem, thereby obtaining the optimal solution for the top thrust of the entire bridge. The step of simulating soil constraint degradation based on the closure sequence and corresponding construction steps to establish a finite element model of the entire bridge specifically includes: According to the aforementioned closure sequence scheme and the corresponding construction steps, the deep-water foundation scour zone of the pile foundation is scoured according to the most unfavorable scour depth H. S Soil constraint degradation simulation was performed to obtain the effective embedment correction depth of the pile foundation; Calculate the reduction degree of horizontal lateral stiffness of the soil based on the effective embedment correction depth of the pile foundation; Establish the pile-soil interaction spring stiffness matrix based on the reduction of the horizontal lateral stiffness of the soil. A finite element model of the entire bridge is constructed based on the pile-soil interaction spring stiffness matrix. The method employs fuzzy mathematics to transform the multi-objective optimization problem corresponding to the function to be solved into a single-objective linear programming problem, thereby obtaining the optimal solution for the top thrust of the entire bridge. Specifically, this includes: A multi-objective linear programming model is constructed based on the function to be solved. The multi-objective linear programming model includes a multi-objective objective function and multi-objective constraints. The multi-objective linear programming model is standardized to obtain the standardized objective function and constraints. By fuzzifying the standardized objective function and constraints, the multi-objective problem is transformed into a single-objective problem, as shown in the following formula: ； in, For scaling indicators, i.e. = - , and Let the maximum and minimum values ​​of the i-th pier under the constraints be respectively. , To quantify the overall degree of compromise, To quantify the maximum degree of overall compromise, ; Solve the single-objective problem using MATLAB software. ,in, This is the fuzzy optimal solution to the multi-objective linear programming problem, namely the optimal solution for the top thrust of the entire bridge.

2. A system for optimizing the closure thrust of a multi-span continuous rigid frame bridge, characterized in that, The system applies the closure thrust optimization method for a multi-span continuous rigid frame bridge as described in claim 1, and the system includes: The closure sequence determination module is used to determine the closure sequence scheme for multi-span continuous rigid frame bridges. The construction step determination module is used to determine the construction steps corresponding to the closure sequence scheme based on the closure sequence scheme. The finite element model building module is used to simulate soil constraint degradation based on the closure sequence scheme and the corresponding construction steps, and to build a finite element model of the entire bridge. The parameter solving module is used to calculate the parameters corresponding to applying a unit jacking force and not applying a unit jacking force to each closure joint based on the finite element model, and obtain the first parameter and the second parameter respectively. The module for constructing the function to be solved is used to construct the function to be solved based on the first parameter and the second parameter; the function to be solved includes an objective function M and constraint equations. The top thrust optimal solution determination module is used to transform the multi-objective optimization problem corresponding to the function to be solved into a single-objective linear programming problem using fuzzy mathematics, so as to obtain the top thrust optimal solution for the entire bridge.

3. The multi-span continuous rigid frame bridge closure thrust optimization system according to claim 2, characterized in that, The finite element model building module specifically includes: The soil constraint degradation simulation unit is used to simulate the scour zone of the deep water foundation of the pile foundation according to the closure sequence scheme and the corresponding construction steps, based on the most unfavorable scour depth H. S Soil constraint degradation simulation was performed to obtain the effective embedment correction depth of the pile foundation; The soil horizontal lateral stiffness reduction calculation unit is used to calculate the soil horizontal lateral stiffness reduction based on the effective embedded correction depth of the pile foundation. The spring stiffness matrix calculation unit is used to establish the pile-soil interaction spring stiffness matrix based on the reduction degree of the horizontal lateral stiffness of the soil. The finite element model building unit is used to construct the finite element model of the entire bridge based on the pile-soil interaction spring stiffness matrix.

4. The multi-span continuous rigid frame bridge closure thrust optimization system according to claim 2, characterized in that, The first parameter includes: the longitudinal horizontal displacement change of the top of the i-th pier caused by the unit thrust at the j-th closure joint after the bridge has been completed for ten years. The stress change value of the section of the i-th pier during the construction stage caused by the unit thrust of the j-th closure joint after scouring. ; The second parameter includes: the self-weight of the main girder and the total displacement of the top of pier i caused by concrete shrinkage and creep ten years after the bridge's completion. Displacement of the top of pier i caused by water flow load ten years after the bridge's completion. The total displacement of the top of pier i caused by temperature difference ten years after the bridge's completion. Stress on the section of pier i caused by various loads during the construction phase .

5. The multi-span continuous rigid frame bridge closure thrust optimization system according to claim 4, characterized in that, The module for determining the optimal solution of the top thrust specifically includes: A multi-objective linear programming model building unit is used to construct a multi-objective linear programming model based on the function to be solved. The multi-objective linear programming model includes a multi-objective objective function and multi-objective constraints. The standardization processing unit is used to standardize the multi-objective linear programming model to obtain the standardized objective function and constraints. The problem transformation unit is used to transform a multi-objective problem into a single-objective problem by fuzzing the standardized objective function and constraints. The solution unit is used to solve the single-objective problem using MATLAB software to obtain the optimal solution for the top thrust of the entire bridge.

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