Construction linear control method for cantilever casting bridge

Abstract

The present invention discloses a method for controlling the construction alignment of a cantilever casting bridge, that is, dividing the influencing factors of the displacement of the cantilever casting bridge into four categories, respectively determining the theoretical calculated values and measured values of these four types of displacements, recording the ratio of the measured value to the theoretical calculated value as the error deviation coefficient, and using the modified grey theory to predict the error deviation coefficient of the subsequent construction; providing a method for measuring the elastic deformation of a hanging basket, that is, by using the final displacement of the hanging basket and deducting the self-deformation of the bridge structure and the inclined displacement of the hanging basket caused by the deformation of the bridge structure, the elastic deformation of the hanging basket can be obtained; proposing a modified grey theory prediction method, that is, using a linear optimization algorithm to replace the traditional least squares method to determine the calculation parameters of the grey theory. Using the modified grey theory to predict the state of the bridge has the characteristics of higher accuracy and clearer calculation.

Description

Technical Field

[0001] The present invention belongs to the technical field of bridge construction, and particularly relates to a method for controlling the construction alignment of a cantilever casting bridge. Background Art

[0002] For a cantilever casting bridge, the design unit gives a reasonable alignment of the completed bridge as the goal of bridge construction. During the bridge construction process, the bridge alignment is affected by many aspects such as the self-weight deformation of the bridge structure, construction accuracy, and environmental factors. The purpose of controlling the construction alignment of the bridge is to use a reasonable construction method to ensure that the alignment of the completed bridge meets the design requirements under the condition of considering the above influencing factors.

[0003] Conventional technical solutions widely use the method of setting cambers to control the alignment of cantilever casting bridges. Usually, the camber is determined by finite element calculation. This method is simple to operate and highly practical, but it does not consider the errors of the structural state and system measurement, and there are certain limitations in the construction control of long-span bridges; existing solutions also have a method of using traditional grey theory to determine the construction errors of cantilever casting bridges, but there are disadvantages such as large prediction deviations and low accuracy in implementation, and the method is mostly used to determine the errors of a single working condition and a single measuring point, and a complete system of construction alignment control method for cantilever casting bridges has not been formed. Summary of the Invention

[0004] The main object of the present invention is to provide a method for controlling the construction alignment of a cantilever casting bridge, which establishes a complete bridge alignment control system, effectively reduces the influence of various errors on the construction alignment of the bridge, and ensures that the alignment of the completed bridge meets the design requirements.

[0005] To achieve the above object, the present invention provides the following technical solutions: A method for predicting the construction errors of a cantilever casting bridge, that is, dividing the influencing factors of the displacement of the cantilever casting bridge into four categories, respectively determining the theoretical calculated values and measured values of these four types of displacements, recording the ratio of the measured value to the theoretical calculated value as the error deviation coefficient, and using the modified grey theory to predict the error deviation coefficient of subsequent construction; providing a method for measuring the elastic deformation of the hanging basket, that is, using the final displacement of the hanging basket, subtracting the self-deformation of the bridge structure and the inclined displacement of the hanging basket caused by the deformation of the bridge structure, and the elastic deformation of the hanging basket can be obtained; proposing a modified grey theory prediction method, that is, using a linear optimization algorithm to replace the traditional least squares method to determine the calculation parameters of the grey theory, and using the modified grey theory to predict the state of the bridge has the characteristics of higher accuracy and clearer calculation. Specifically, it includes the following steps:

[0006] S1: Divide the main girder of the cantilever casting bridge into 1 0# block, n normal casting segments and 1 closure segment, a total of n + 2 segments;

[0007] S2: Divide the factors affecting the alignment of cantilever - cast bridges into four categories: self - weight of the structure, prestress tensioning, deformation of the hanging basket, and shrinkage and creep.

[0008] S3: Discretize the box girder into beam elements by segment, and use the finite - element software Midas / Civil to calculate the vertical displacements \(f\) of each segment under the conditions of self - weight of the structure, prestress tensioning, and shrinkage and creep. 砼i and \(f\) 预i ;

[0009] S4: For the \(i\) - th segment under construction, when assembling the hanging basket, arrange elevation measuring points on the bottom formwork, simulate the pre - pressing of the hanging basket, and measure and record the vertical displacement \(f\) of the bottom - formwork measuring points under the pre - pressing load. 挂i ;

[0010] S5: Carry out the concrete pouring construction of the \(i\) - th segment. The construction process includes steel - bar binding, installation of prestress ducts, and concrete pouring. Measure and record the elevation changes of the top slabs of the segments that have been formed before and after construction (denoted as \(\Delta\) 砼ji , representing the displacement generated by the concrete pouring of the \(i\) - th segment at the forefront of the \(j\) - th segment), measure and record the elevation changes of the bottom - formwork measuring points before and after concrete pouring (denoted as \(\Delta\) 挂i ', representing the displacement generated by the concrete pouring of the \(i\) - th segment on the hanging basket of the \(i\) - th segment). After construction, arrange elevation measuring points on the top slab of the \(i\) - th segment.

[0011] S6: Carry out the prestress tensioning construction of the \(i\) - th segment, and measure and record the elevation changes of the top slabs of the segments that have been formed before and after prestress tensioning (denoted as \(\Delta\) 预ji , representing the displacement generated by the prestress tensioning of the \(i\) - th segment at the forefront of the \(j\) - th segment).

[0012] S7: Denote the ratio of the measured value to the theoretical calculated value of the displacement generated by the concrete pouring of the \(i\) - th segment on the \(j\) - th segment as the self - weight error deviation coefficient \(\delta\) 砼ji , and use the self - weight error deviation coefficient as the original sequence to predict the self - weight error deviation coefficient of subsequent construction by using the modified grey theory.

[0013] S8: Denote the ratio of the measured value to the theoretical calculated value of the displacement generated by the prestress tensioning of the \(i\) - th segment on the \(j\) - th segment as the prestress - tensioning error deviation coefficient \(\delta\) 预ji , and use the prestress - tensioning error deviation coefficient as the original sequence to predict the prestress - tensioning error deviation coefficient of subsequent construction by using the modified grey theory.

[0014] S9: Calculate the measured deformation \(\Delta\) 挂i " of the hanging basket during the concrete pouring of the \(i\) - th segment, and denote the ratio of \(\Delta\) 挂i " and \(f\) 挂i as the elastic - deformation error deviation coefficient \(\delta\) 挂i, taking the deviation coefficient of the elastic deformation error of the hanging basket as the original sequence, the deviation coefficient of the deformation error of the hanging basket in the subsequent construction is predicted by using the modified grey theory;

[0015] S10: Multiply the predicted deviation coefficient by the corresponding theoretical calculated value to determine the displacement values of each section in each subsequent working condition. Determine the pre-camber line shape of the bridge according to the obtained displacement values, and set out the elevation of the formwork during the subsequent construction.

[0016] As a preferred embodiment of the present invention, in steps S7, S8, S9, and S10, the modified grey theory predicts the error deviation coefficient in each subsequent working condition by the following steps:

[0017] Denote the error deviation coefficient in each stage of the cantilever casting bridge as:

[0018] X (0) ={X (0) (s)|s = 1, 2, 3...m} (1)

[0019] In the formula, s represents the construction stage;

[0020] The original data is processed by using the first-order cumulative generation, that is:

[0021]

[0022] In the formula, k represents the construction stage number after the cumulative summation of s1, s2, s3...;

[0023] From the sequence X (1) construct the background sequence Z (1) , that is:

[0024]

[0025] The whitenized differential equation can be obtained:

[0026]

[0027] Discretize formula (4) to obtain the GM(1, 1) model as:

[0028] X (0) (m)+aZ (1) (m)=b (5)

[0029] where m is the construction stage number in the discrete state;

[0030] Define ε s as the error of the predicted value, and there is

[0031] |ε s |=|X (0) (s)-X' (0) (s)| (6)

[0032] Wherein X (0) (s), X' (0) (s) are the measured values and predicted values obtained by using the grey theory of the error deviation coefficient under working condition s;

[0033] The average relative error of bridge state prediction using the grey theory is:

[0034]

[0035] Equation (5) uses b - aZ (1) (s) to predict the original sequence X (0) (s), and its prediction error is:

[0036] ε s = X (0) (s) - b + aZ (1) (s) (8)

[0037] Substituting equation (8) into equation (7) gives:

[0038]

[0039] To minimize the average relative error, that is

[0040]

[0041] Using linear optimization to find the parameters a and b and substituting them into equation (10), taking the initial value as X (1) (t)| t＝1 = X (0) (1), solving the differential equation gives:

[0042]

[0043] Taking the s and s + 1 stages for analysis gives:

[0044]

[0045]

[0046] Subtracting the two gives:

[0047]

[0048] When s ≥ m, the prediction of the error deviation coefficient can be realized.

[0049] As a preferred embodiment of the present invention, in steps S7 and S8, the error deviation coefficients of concrete pouring and prestress tensioning are predicted according to the following steps:

[0050] List the vertical displacement influence of the i-th segment under construction on the j-th segment under the self-weight of the segment and the prestress tensioning condition;

[0051] When the bridge construction reaches a certain segment k, the displacement prediction for all subsequent segments is carried out;

[0052] For a cantilever casting bridge with a total number of construction segments of n and without considering the closure segment, since the number of original data m required for grey theory prediction should satisfy m > 2, when the construction reaches the k-th segment, the number of segments l that can completely predict the displacement data at this time is:

[0053] l = min{n - k, k - 2} (14)

[0054] To predict the complete displacement data of as many beam segments as possible, there should be:

[0055] n - k = k - 2 (15)

[0056] It can be obtained that:

[0057]

[0058] When n is odd, take or Both are acceptable.

[0059] As a preferred embodiment of the present invention, in steps S4 and S9, the following method is used to calculate the measured elastic deformation of the hanging basket during the preloading of the hanging basket or the concrete pouring process:

[0060] When pouring the concrete of the i-th segment, the already constructed segments will have vertical displacement and vertical rotation. The total vertical displacement of the i-th segment includes the vertical displacement of the already constructed i - 1-th segment, the vertical displacement of this segment caused by the rotation of the i-th segment, and the elastic deformation of the hanging basket of the i-th segment;

[0061] Denote the vertical displacement generated in the i-th segment during the construction of the i-th segment as Δ ii , and the vertical displacement generated in the i - 1-th segment during the construction of the i-th segment as Δ ii and Both can be directly measured;

[0062] When pouring the concrete of the i-th segment, it is approximately considered that the rotations of the i-th segment and the i - 1-th segment are equal, and the average rotation value of the i - 1-th segment is approximately taken as the rotation of the i-th segment, that is:

[0063]

[0064] The vertical displacement generated at the front end of the i-th segment by this rotation is:

[0065]

[0066] wherein l i is the length of the main girder of the i-th segment in the longitudinal direction of the bridge;

[0067] At this time, the measured elastic deformation Δ” of the hanging basket 挂i is: Δ” 挂i = Δ ii - Δ (i-1)i - Δ 转ii (19).

[0068] As a preferred embodiment of the present invention, in step S10, the following method is used to calculate the formwork erection elevation of the bridge construction:

[0069] The formwork erection elevation of each segment during the box girder pouring consists of several parts: H 施 = H 设 + f (20)

[0070] wherein, H 施 is the formwork erection elevation at the front end of the bottom plate of the box girder; H 设 is the design elevation of the point in the completed bridge state; f is the pre-camber value of the beam segment, and is calculated by the following formula:

[0071] f = ∑f 砼ji × δ 砼ji + ∑f 预ji × δ 预ji + f 挂i × δ 挂i + f 二期i + f 时i (21)

[0072] wherein, f 砼ij is the theoretical calculated value of the vertical displacement generated by the concrete pouring; f 预ij is the theoretical calculated value of the vertical displacement generated by the prestress tensioning; f 挂i is the elastic deformation value generated by the simulation and preloading of the hanging basket of the i-th segment; f 二期i is the theoretical calculated value of the vertical displacement generated by the secondary dead load in the i-th segment; f 时i is the theoretical calculated value of the vertical displacement generated by the shrinkage and creep in the i-th segment.

[0073] Due to the adoption of the above technical solution, the present invention has the following beneficial effects:

[0074] The present invention establishes a complete set of linear control methods for the cantilever casting bridge construction. The method classifies the influencing factors of the bridge alignment, decouples the mutual influence between errors, respectively elaborates the accurate acquisition methods of the measured displacements of the bridge under the action of various influencing factors, proposes a calculation method for the theoretical displacement value considering the action of errors. When using this method to control the bridge alignment, the influence of various errors on the bridge alignment can be considered to ensure the completed bridge quality and safety. Brief Description of the Drawings

[0075] To more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0076] Figure 1 It is a schematic diagram of the segment division distribution of the method in the embodiments of the present invention.

[0077] Figure 2 It is a schematic diagram of the distribution of measuring points on the top plate and bottom formwork in the embodiments of the present invention.

[0078] Figure 3 It is a schematic diagram of the elevation change before and after concrete pouring in the embodiments of the present invention.

[0079] Figure 4 It is a schematic diagram of the elevation change of the measuring points on the bottom formwork in the embodiments of the present invention. Detailed Embodiments

[0080] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. The embodiments described below by referring to the drawings are exemplary and are only used to explain the present invention and should not be construed as a limitation of the present invention.

[0081] The cantilever construction method refers to a construction method in which working platforms are set on both sides of the pier, and beam segments are cast or assembled cantilever by cantilever towards the mid-span in a balanced manner until the bridge span structure is closed. It can be divided into two categories: cantilever casting and cantilever assembly. Its working principle can be illustrated by three main working links: working platform displacement (hanging basket or crane), construction beam segment positioning (casting or assembly), and construction beam segment connection (strong tension prestress).

[0082] The construction technology of cantilever casting is relatively complex. From the construction process, it includes four parts: the construction of the 0# block, the construction of the hanging basket, the construction of the side span, and the construction of the closure section. Among them, the first two processes are particularly important and complex. The 0# block is the first step of the overall cantilever casting construction and also the basis of the overall construction. Its construction is similar to that of the basic concrete bridge pier. The construction of the hanging basket is the basis for the subsequent construction such as the side span construction. The hanging basket is assembled with Bailey trusses. One set of Bailey beams is used at the top of each web, and each set of Bailey beams is composed of four upper and lower strengthened Bailey trusses. The foundation of the side span construction site is treated. After completion, the support is erected and preloaded. After the support preloading is completed, the permanent bearings are installed, the steel bars are tied, the formwork is installed, and the concrete of the cast-in-place section is poured. The construction technology is mature. After the straight section is prestressed, grouted and reaches the designed strength as required, the side formwork of the straight section is removed to reduce part of the weight. At the same time, about 1.0 m of the bottom formwork and part of the support are removed at the closure end to facilitate the hanging basket of the closure section to extend over the closure section. The construction of the continuous beam closure section is the key process to control the stress state and linear shape of the whole bridge and must be strictly controlled. The sequence of first closing the side span and then closing the middle span is adopted to finally complete the system transformation of the whole bridge and form a continuous rigid frame.

[0083] Therefore, for a cantilever-cast bridge, during the bridge construction process, the bridge alignment is affected by many factors such as the self-deformation of the bridge structure, construction accuracy, and environmental factors. The purpose of bridge construction alignment control is to use a reasonable construction method to ensure that the alignment of the completed bridge meets the design requirements under the condition of considering the above influencing factors. Based on the technical background of reasonably and accurately realizing the alignment requirements of the completed bridge state, the present invention provides a method for controlling the construction alignment of a cantilever-cast bridge, establishes a complete set of bridge alignment control systems, effectively reduces the influence of various errors on the bridge construction alignment, and ensures that the alignment of the completed bridge meets the design requirements.

[0084] A method for predicting construction errors of a cantilever-cast bridge according to the present invention divides the influencing factors of the displacement of the cantilever-cast bridge into four categories, determines the theoretical calculated values and measured values of these four types of displacements respectively, records the ratio of the measured value to the theoretical calculated value as the error deviation coefficient, and uses the modified grey theory to predict the error deviation coefficient of the subsequent construction; provides a method for measuring the elastic deformation of the hanging basket, that is, by using the final displacement of the hanging basket and deducting the self-deformation of the bridge structure and the inclined displacement of the hanging basket caused by the deformation of the bridge structure, the elastic deformation of the hanging basket can be obtained; proposes a modified grey theory prediction method, that is, using the linear optimization algorithm to replace the traditional least square method to determine the calculation parameters of the grey theory. Using the modified grey theory to predict the state of the bridge has the characteristics of higher accuracy and clearer calculation. Specifically, it includes the following steps:

[0085] S1: Divide the main beam of the cantilever-cast bridge into 1 0# block, n normal casting segments and 1 closure segment, a total of n + 2 segments;

[0086] S2: Classify the factors affecting the alignment of cantilever - cast bridges into four categories: self - weight of the structure, prestress tensioning, deformation of the hanging basket, and shrinkage and creep.

[0087] S3: Discretize the box girder into beam elements by segment, and use the finite - element software Midas / Civil to calculate the vertical displacements \(f\) of each segment under the working conditions of self - weight of the structure, prestress tensioning, and shrinkage and creep. 砼i and \(f\) 预i ; Among them, Midas / Civil is a general - purpose spatial finite - element analysis software, which can be applied to the analysis and design of structures such as bridge structures, underground structures, industrial buildings, airports, dams, ports, etc.

[0088] S4: For the \(i\) - th segment under construction, when assembling the hanging basket, arrange elevation measuring points on the bottom formwork, conduct simulated pre - pressing on the hanging basket, and measure and record the vertical displacement \(f\) of the bottom - formwork measuring points under the pre - pressing load. 挂i ;

[0089] S5: Carry out the concrete pouring construction of the \(i\) - th segment. The construction process includes steel - bar binding, installation of prestress ducts, and concrete pouring. Measure and record the elevation change of the top slabs of the segments that have been formed before and after construction (denoted as \(\Delta\) 砼ji , representing the displacement generated by the concrete pouring of the \(i\) - th segment at the forefront of the \(j\) - th segment), measure and record the elevation change of the bottom - formwork measuring points before and after concrete pouring (denoted as \(\Delta\) 挂i ', representing the displacement generated by the concrete pouring of the \(i\) - th segment on the hanging basket of the \(i\) - th segment). After the construction is completed, arrange elevation measuring points on the top slab of the \(i\) - th segment.

[0090] S6: Carry out the prestress tensioning construction of the \(i\) - th segment, and measure and record the elevation change of the top slabs of the segments that have been formed before and after prestress tensioning (denoted as \(\Delta\) 预ji , representing the displacement generated by the prestress tensioning of the \(i\) - th segment at the forefront of the \(j\) - th segment).

[0091] S7: Denote the ratio of the measured value to the theoretical calculated value of the displacement generated by the concrete pouring of the \(i\) - th segment on the \(j\) - th segment as the self - weight error deviation coefficient \(\delta\) 砼ji , and use the self - weight error deviation coefficient as the original sequence to predict the self - weight error deviation coefficient of subsequent construction by using the modified grey theory.

[0092] S8: Denote the ratio of the measured value to the theoretical calculated value of the displacement generated by the prestress tensioning of the \(i\) - th segment on the \(j\) - th segment as the prestress - tensioning error deviation coefficient \(\delta\) 预ji , and use the prestress - tensioning error deviation coefficient as the original sequence to predict the prestress - tensioning error deviation coefficient of subsequent construction by using the modified grey theory.

[0093] S9: Calculate the measured deformation \(\Delta\) of the hanging basket during the concrete pouring of the \(i\) - th segment挂i ", the ratio of Δ 挂i " and f 挂i is denoted as the deviation coefficient δ of the elastic deformation error of the hanging basket 挂i . Taking the deviation coefficient of the elastic deformation error of the hanging basket as the original sequence, the deviation coefficient of the deformation error of the hanging basket in the subsequent construction is predicted by using the modified grey theory;

[0094] S10: Multiply the predicted deviation coefficient by the corresponding theoretical calculated value to determine the displacement values of each section in each subsequent working condition, and determine the pre-camber line shape of the bridge according to the obtained displacement values. During the subsequent construction, set out the elevation of the formwork.

[0095] Furthermore, in the embodiment of the present invention, in the above steps S4 and S5, the section division is as Figure 1 shown. For the i-th section, the elevation measuring points arranged are as Figure 2 shown. In the figure, i represents the section number.

[0096] Furthermore, in the embodiment of the present invention, in the above step S5, for the i-th section, measure the elevation change Δ 砼ji of the top slab of each cast section before and after the concrete pouring as Figure 3 shown. In the figure, i represents the construction section, j represents the section number, and the displacement test position is the front end of the section. The elevation change Δ 挂i ' of the bottom formwork measuring point is as Figure 4 shown. In the figure, Δ 挂i ' represents the displacement generated by the concrete pouring of the i-th section in the hanging basket of the i-th section.

[0097] Furthermore, in the embodiment of the present invention, in the above steps S7, S8, S9, and S10, the modified grey theory predicts the error deviation coefficient of each subsequent working condition by the following steps:

[0098] Denote the error deviation coefficient of each stage of the cantilever casting bridge as:

[0099] X (0) ={X (0) (s)|s = 1, 2, 3...m} (1)

[0100] In the formula, s represents the construction stage.

[0101] Use the first-order cumulative generation to process these original data, that is:

[0102]

[0103] In the formula, k represents the construction stage number after the cumulative summation of s1, s2, s3...

[0104] Construct the background sequence Z from the sequence X(1) (1) , that is:

[0105]

[0106] The whitening differential equation can be obtained as follows:

[0107]

[0108] Where t represents the identification of the data series after continuous processing, and a and b respectively represent the fitting parameters of the gray theory prediction model.

[0109] Discretizing Equation (4), the GM(1,1) gray theory model is obtained as:

[0110] X (0) (m) + aZ (1) (m) = b (5)

[0111] Where m is the construction stage number in the discrete state.

[0112] Define ε s as the error of the predicted value, and we have

[0113] |ε s | = |X (0) (s) - X' (0) (s)| (6)

[0114] Where X (0) (s) and X' (0) (s) are the measured value and the predicted value obtained by the gray theory of the error deviation coefficient under working condition s;

[0115] The average relative error of bridge state prediction using the gray theory is:

[0116]

[0117] Where εs represents the error of the predicted value.

[0118] Equation (5) uses b - aZ (1) (s) to predict the original sequence X (0) (s), and its prediction error is:

[0119] ε s = X (0) (s) - b + aZ (1) (s) (8)

[0120] Substituting Equation (8) into Equation (7), we get:

[0121]

[0122] To minimize the average relative error, that is

[0123]

[0124] Use linear optimization to find the parameters a and b and substitute them into Equation (10), taking the initial value as X (1) (t)| t＝1 = X (0) (1), solve the differential equation to obtain:

[0125]

[0126] Taking the s and s + 1 stages for analysis, it can be obtained that:

[0127]

[0128]

[0129] In the formula, m represents the construction stage number in the discrete state.

[0130] Subtract the two to obtain:

[0131]

[0132] When s ≥ m, the prediction of the error deviation coefficient can be realized.

[0133] Furthermore, in the example of the present invention, in the above steps S7 and S8, the error deviation coefficients of concrete pouring and prestress tensioning are predicted according to the following steps:

[0134] The influence of the self-weight of the segment and the vertical displacement of the i-th segment under construction on the j-th segment under the prestress tensioning condition is shown in Table 1:

[0135] Table 1 Schematic diagram of the calculation of the vertical displacement of each beam segment

[0136]

[0137] The first row in the table represents the currently predicted beam segment number i, the first column represents the currently constructed segment number, and the beam segment number is denoted as j. √ in the table indicates that the influence of this beam segment needs to be considered, and the influence value is denoted as Δ ij (influence of the construction of the j-th beam segment on the i-th beam segment).

[0138] When the bridge is constructed to a certain segment k, the displacement prediction for all subsequent segments can be carried out, which is manifested in Table 1 as using the data of each diagonal row to predict the corresponding error deviation coefficient of the next segment.

[0139] For a cantilever casting bridge with a total number of construction segments of n and without considering the closure segment, since the number of original data m required for grey theory prediction should satisfy m > 2, when it is constructed to the k-th segment, the number of segments l that can completely predict the displacement data at this time is:

[0140] l = min{n - k, k - 2} (14)

[0141] To predict the complete displacement data of as many beam segments as possible, there should be:

[0142] n - k = k - 2 (15)

[0143] It can be obtained that:

[0144]

[0145] When n is odd, take or Both are acceptable.

[0146] Furthermore, in the embodiment of the present invention, in the above steps S4 and S9, the following method is used to calculate the measured elastic deformation of the hanging basket during the preloading of the hanging basket or the concrete pouring process (taking the concrete pouring of the i-th segment as an example):

[0147] When the concrete of the i-th segment is poured, the already constructed segments (segments 0 to i - 1) will have vertical displacements and vertical rotations. The total vertical displacement of the i-th segment includes the vertical displacement of the already constructed i - 1 segment, the vertical displacement of this segment caused by the rotation of the i-th segment, and the elastic deformation of the hanging basket of the i-th segment;

[0148] Denote the vertical displacement generated in the i-th segment during the construction of the i-th segment as Δ ii , and the vertical displacement generated in the i - 1 segment during the construction of the i-th segment as Δ ii and Both can be directly measured;

[0149] When the concrete of the i-th segment is poured, it is approximately considered that the rotations of the i-th segment and the i - 1 segment are equal, and the average rotation of the i - 1 segment is approximately taken as the rotation of the i-th segment, that is:

[0150]

[0151] The vertical displacement generated at the front end of the i-th segment by this rotation is:

[0152]

[0153] where l i is the length of the main beam of the i-th segment in the longitudinal direction of the bridge;

[0154] At this time, the measured elastic deformation Δ” 挂i of the hanging basket is: Δ” 挂i = Δ ii - Δ (i-1)i - Δ 转ii (19).

[0155] Further, in the embodiments of the present invention, in the above step S10, the following method is used to calculate the formwork elevation for bridge construction:

[0156] The formwork elevation of each segment during the casting of the box girder consists of several parts: H 施 = H 设 + f(20)

[0157] Wherein, H 施 is the formwork elevation at the front end of the bottom slab of the box girder; H 设 is the designed elevation of this point in the completed bridge state; f is the pre-camber value of the beam segment, and is calculated using the following formula:

[0158] f = ∑f 砼ji × δ 砼ji + ∑f 预ji × δ 预ji + f 挂i × δ 挂i + f 二期i + f 时i (21)

[0159] Wherein, f 砼ij is the theoretical calculated value of the vertical displacement generated by concrete pouring; f 预ij is the theoretical calculated value of the vertical displacement generated by prestress tensioning; f 挂i is the elastic deformation value generated by the simulated preloading of the hanging basket for the i-th segment; f 二期i is the theoretical calculated value of the vertical displacement generated by the secondary permanent load in the i-th segment; f when i is the theoretical calculated value of the vertical displacement generated by shrinkage and creep in the i-th segment.

[0160] The beneficial effects of the present invention are: to establish a complete set of linear control methods for cantilever casting bridge construction, the method classifies the influencing factors of the bridge alignment, decouples the mutual influence between errors, respectively elaborates the accurate acquisition methods of the measured displacements of the bridge under the action of various influencing factors, proposes a calculation method for the theoretical displacement value considering the action of errors, when using this method to control the bridge alignment, the influence of various errors on the bridge alignment can be considered to ensure the completed bridge quality and safety.

[0161] 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 spirit of the present invention, and the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A construction linear control method for cantilever casting bridges, characterized in that, It includes the following steps: S1: Divide the main girder of the cantilever casting bridge into 1 0# block, n normal casting segments and 1 closure segment, a total of n + 2 segments; S2: Divide the factors affecting the alignment of the cantilever casting bridge into four categories: self-weight of the structure, prestress tensioning, deformation of the hanging basket, shrinkage and creep; S3: Discretize the box girder into beam elements by segment, and use the finite element software Midas / Civil to calculate the vertical displacements f of each segment under the conditions of self-weight of the structure, prestress tension, shrinkage and creep 砼i and f 预i ; S4: For the i-th segment under construction, elevation measurement points are arranged on the bottom formwork during the erection of the hanging basket. The hanging basket is simulated and preloaded, and the vertical displacement f of the measurement points on the bottom formwork under the preloading load is measured and recorded. 挂i ; S5: Carry out the concrete pouring construction of the i-th segment. The construction process includes steel bar binding, prestressed duct installation, and concrete pouring. Measure and record the elevation change of the top slab of each segment generated before and after construction, denoted as Δ 砼ji , representing the displacement generated by the concrete pouring of the i-th segment at the forefront of the j-th segment. Measure and record the elevation change of the bottom formwork measuring points before and after concrete pouring, denoted as Δ 挂i ', representing the displacement generated by the concrete pouring of the i-th segment on the hanging basket of the i-th segment. After construction, arrange elevation measuring points on the top slab of the i-th segment; S6: Carry out the prestressed tension construction for the i-th segment, measure and record the elevation change of the top slab of each segment that has been formed before and after the prestressed tension, denoted as Δ 预ji , representing the displacement generated by the prestressed tension of the i-th segment at the forefront of the j-th segment; S7: Denote the ratio of the measured value to the theoretical calculated value of the displacement generated by the concrete pouring of the i-th segment on the j-th segment as the structural self-weight error deviation coefficient δ 砼ji Take the self-weight error deviation coefficient as the original sequence and adopt the modified grey theory to predict the structural self-weight error deviation coefficient of subsequent construction; S8: Denote the ratio of the measured value to the theoretical calculated value of the displacement generated by the prestress tension of the i-th segment on the j-th segment as the prestress tension error deviation coefficient δ 预ji ; Take the prestress tension error deviation coefficient as the original sequence and use the modified grey theory to predict the prestress tension error deviation coefficient of subsequent construction S9: Calculate the measured deformation Δ of the hanging basket during the concrete pouring of the i-th segment 挂i ", and record the ratio of Δ 挂i " and f 挂i as the deviation coefficient δ of the elastic deformation error of the hanging basket 挂i ; take the deviation coefficient of the elastic deformation error of the hanging basket as the original sequence and use the modified grey theory to predict the deviation coefficient of the deformation error of the hanging basket in the subsequent construction. S10: Multiply the deviation coefficients predicted in steps S7, S8, and S9 by the corresponding theoretical calculation values to determine the displacement values of each segment under each subsequent working condition. Determine the pre-camber alignment of the bridge based on the obtained displacement values, and set the formwork elevation during subsequent construction.

2. The cantilever casting bridge construction alignment control method according to claim 1, wherein In steps S7, S8, S9, and S10, the modified grey theory uses the following steps to predict the error deviation coefficients of each subsequent working condition: Record the error deviation coefficient of each stage of the cantilever casting bridge as: X (0) = {X (0) (s) | s = 1, 2, 3... m} (1) In the formula, s represents the construction stage; Use the first-order cumulative generation to process the original data, that is: In the formula, k represents the construction stage number after cumulative summation of s1, s2, s3...; From the sequence X (1) Construct the background sequence Z (1) , namely: The whitenized differential equation can be obtained: Discretize formula (4) to obtain the GM(1,1) model as: X (0) (m)+aZ (1) (m) = b (5) In the formula, m represents the construction stage number in the discrete state; Define ε s as the error of the predicted value, where |ε s | = | X (0) (s)-X' (0) (s)| (6) where X (0) (s), X' (0) (s) are the measured value of the error deviation coefficient and the predicted value obtained by using the grey theory under condition s; The average relative error of using grey theory to predict the bridge state is: Equation (5) uses b - aZ (1) (s) predicts the original sequence X (0) (s), and its prediction error is: ε s = X (0) (s) - b + aZ (1) (s) (8) Substitute formula (8) into formula (7) to obtain: To make the average relative error minimum, that is Use linear optimization to find the parameters a and b and substitute them into Equation (10), taking the initial value as X (1) (t)| t＝1 =X (0) (1), solve the differential equation to obtain: Take the s and s + 1 stages for analysis to obtain: Subtract the two to get: When s ≥ m, the prediction of the error deviation coefficient can be realized.

3. The linear control method for cantilever casting bridge construction according to claim 1, characterized in that In steps S7 and S8, predict the error deviation coefficients of concrete pouring and prestress tensioning according to the following steps: List the vertical displacement influence of the currently constructed i-th segment on the j-th segment under the conditions of segment self-weight and prestress tensioning; When the bridge is constructed to a certain segment k, start predicting the displacements of all subsequent segments; For a cantilever casting bridge with a total number of construction segments of n, without considering the closure segment, since the number of original data m required for grey theory prediction should satisfy m > 2, when the construction reaches the k-th segment, the number of segments l that can completely predict the displacement data at this time is: l = min{n - k, k - 2} (14) To predict the complete displacement data of as many beam segments as possible, there should be: n - k = k - 2 (15) It can be obtained: When n is odd, take or Both are acceptable.

4. The linear control method for cantilever casting bridge construction according to claim 1, characterized in that, In steps S4 and S9, use the following method to calculate the measured elastic deformation of the hanging basket during hanging basket preloading or concrete pouring: When pouring concrete for the i-th segment, the already constructed segments will have vertical displacements and vertical rotations. The total vertical displacement of the i-th segment includes the vertical displacement of the already constructed i - 1-th segment, the vertical displacement of this segment caused by the rotation of the i-th segment, and the elastic deformation of the hanging basket of the i-th segment; Denote the vertical displacement generated in the \(i\)-th segment during the construction of the \(i\)-th segment as \(\Delta\) ii and the vertical displacement generated in the \((i - 1)\)-th segment during the construction of the \(i\)-th segment as \(\Delta\) (i-1)i \(\Delta\) ii and \(\Delta\) (i-1)i can both be directly measured; When pouring concrete for the i-th segment, it is approximately considered that the rotations of the i-th segment and the i - 1-th segment are equal. Take the average value of the rotations of the i - 1-th segment as the rotation of the i-th segment approximately, that is: The vertical displacement generated by this rotation at the front end of the i-th segment is: where l i is the length of the i-th segment of the main girder in the longitudinal direction of the bridge; At this time, the measured elastic deformation Δ” of the hanging basket 挂i is: Δ” 挂i = Δ ii - Δ (i-1)i - Δ 转ii (19).

5. The linear control method for cantilever casting bridge construction according to claim 1, characterized in that In step S10, calculate the formwork elevation of the bridge construction using the following method: The erection elevation of each segment during the casting of the box girder consists of several parts: H 施 = H 设 + f(18) Among them, H 施 is the formwork erection elevation at the front end of the box girder bottom slab; H 设 is the designed elevation at the completed bridge state of this point; f is the camber value of the beam segment, and is calculated using the following formula: f = ∑f 砼ji ×δ 砼ji +∑f 预ji ×δ 预ji +f 挂i ×δ 挂i +f 二期i +f 时i (19) Among them, f 砼ij is the theoretical calculated value of the vertical displacement generated by concrete pouring; f 预ij is the theoretical calculated value of the vertical displacement generated by prestress tensioning; f 挂i is the elastic deformation value generated by the simulation preloading of the hanging basket in the i-th segment; f 二期i is the theoretical calculated value of the vertical displacement generated by the secondary dead load in the i-th segment; f 时i is the theoretical calculated value of the vertical displacement generated by shrinkage and creep in the i-th segment.

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