Cable-stayed bridge ballastless track cushion thickness determination method and system

Abstract

A method and system for determining the thickness of a cushion layer of a ballastless track of a cable-stayed bridge, the method comprising: after closure of the bridge, measuring the beam surface elevation of each preset measuring point under the condition that the bridge deck is free of temporary load; formulating the target value of the top surface elevation of the cushion layer of each preset measuring point according to the bridge secondary dead load, the target track alignment and the cable adjustment scheme; applying a uniform load at each preset measuring point, and constructing a top surface elevation calculation matrix of the cushion layer in combination with the uniform load, the design thickness of the cushion layer and the corrected finite element model; calculating the thickness coefficient of the cushion layer of each preset measuring point according to the top surface elevation calculation matrix of the cushion layer, the beam surface elevation of each preset measuring point, the target value of the top surface elevation of the cushion layer of each preset measuring point and the preset allowable error of the top surface elevation of the cushion layer; and multiplying the thickness coefficient of the cushion layer of each preset measuring point by the design thickness of the cushion layer to obtain the pouring thickness of the cushion layer of each preset measuring point. The method can improve the accuracy of the pouring thickness of the cushion layer and the precision and effect of the alignment adjustment of the bridge.

Description

Technical Field

[0001] This application relates to the field of track bridge technology, specifically to a method and system for determining the thickness of the ballastless track cushion layer for cable-stayed bridges. Background Technology

[0002] Today, ballastless track structures are widely used in high-speed railways due to their advantages such as robustness, cleanliness, durability, and low maintenance costs. However, compared to ballasted tracks which use crushed stone ballast as the track bed, ballastless track structures are primarily concrete, making them generally difficult to adjust after construction. Therefore, ballastless tracks require extremely high precision in alignment control during construction. The application of ballastless tracks in roadbeds or short-span cable-stayed bridges in high-speed railways is very mature. However, when applied to long-span cable-stayed bridges, the alignment is significantly affected by factors such as cable force, temperature, and load, resulting in substantial deviations and posing significant challenges to the alignment control of ballastless tracks. Therefore, during the construction of long-span cable-stayed bridges, a concrete bedding layer of a certain thickness is typically installed as a leveling layer. This serves two purposes: firstly, to eliminate local manufacturing errors in the bridge deck, and secondly, to act as counterweight to adjust the load-bearing deformation of the cable-stayed bridge.

[0003] In existing ballastless track bridge alignment adjustment technologies, the concrete cushion layer thickness is often laid uniformly according to the design thickness. Although this can play a role in adjusting the bridge alignment to a certain extent, the uniform laying of the cushion layer according to the design thickness results in low accuracy of bridge alignment adjustment. Summary of the Invention

[0004] This application provides a method and system for determining the thickness of the ballastless track cushion layer for cable-stayed bridges, which can solve the technical problem of low bridge alignment adjustment accuracy in current ballastless track bridge alignment adjustment technology.

[0005] To achieve the above objectives, in a first aspect, this application provides a method for determining the thickness of the ballastless track cushion layer for cable-stayed bridges, the method comprising:

[0006] After the bridge is closed, and under the condition that there is no temporary load on the bridge deck, the elevation of the beam surface at each preset measuring point is measured.

[0007] Based on the bridge's second-phase dead load, target track alignment, and cable adjustment plan, target elevation values ​​for the top surface of the subgrade at each pre-set measuring point were determined.

[0008] A uniformly distributed load is applied at each preset measuring point. The elevation calculation matrix of the top surface of the subgrade is constructed by combining the uniformly distributed load, the design thickness of the subgrade, and the corrected finite element model.

[0009] Based on the elevation calculation matrix of the top surface of the subgrade, the beam surface elevation of each preset measuring point, the target elevation value of the top surface of the subgrade at each preset measuring point, and the preset allowable error of the top surface elevation of the subgrade, the subgrade thickness coefficient of each preset measuring point is calculated.

[0010] The thickness coefficient of the subgrade at each preset measuring point is multiplied by the design thickness of the subgrade to obtain the subgrade pouring thickness at each preset measuring point.

[0011] Furthermore, in one embodiment, before measuring the beam surface elevation at each preset measuring point, the method further includes:

[0012] According to the preset measurement point spacing, preset measurement points are arranged on the center line of each ballastless track of the cable-stayed bridge, and the measurement point arrangement method is the same for each ballastless track.

[0013] Furthermore, in one embodiment, the step of applying a uniformly distributed load at each preset measuring point, and constructing a matrix for estimating the elevation of the top surface of the subgrade by combining the uniformly distributed load, the design thickness of the subgrade, and the corrected finite element model, includes:

[0014] Uniformly distributed loads are applied one by one at each preset measuring point. Based on the modified finite element model, the elevation increment of the first beam surface at each preset measuring point is calculated, and the elevation increment matrix of the first beam surface is constructed. The uniformly distributed load at one preset measuring point corresponds to one working condition, and the elements of the elevation increment matrix of the first beam surface are the elevation increments of the first beam surface at each preset measuring point under each working condition.

[0015] Construct the second beam surface elevation increment matrix based on the design thickness of the subbase.

[0016] The elevation increment matrix of the first beam surface and the elevation increment matrix of the second beam surface are added together to form the elevation calculation matrix of the top surface of the cushion layer.

[0017] Furthermore, in one embodiment, the uniformly distributed load is obtained by multiplying the design thickness of the cushion layer, the cushion layer density, and the gravitational acceleration.

[0018] Furthermore, in one embodiment, the uniformly distributed load is a surface uniformly distributed load, the longitudinal range of which is the distance between two adjacent measuring points, and the lateral range is the width of the ballastless track cushion layer.

[0019] Furthermore, in one embodiment, the modified finite element model refers to the modification of the stiffness parameters of the main tower, main beam, and stay cables in the existing finite element model.

[0020] Furthermore, in one embodiment, a constrained optimization problem is constructed based on the elevation calculation matrix of the top surface of the subgrade, the beam surface elevation of each preset measuring point, the target elevation value of the top surface of the subgrade at each preset measuring point, and the preset allowable error of the top surface elevation of the subgrade. By solving the constrained optimization problem, the subgrade thickness coefficient of each preset measuring point is obtained.

[0021] Furthermore, in one embodiment, after obtaining the thickness of the subbase pouring at each preset measuring point, the method further includes:

[0022] The pouring control points are set according to the number of ballastless tracks between two adjacent retaining walls of the bridge.

[0023] Based on the thickness of the subbase pouring at each preset measuring point, the elevation of the pouring control point is determined, and the subbase is poured on the pouring control network formed by the pouring control points.

[0024] Furthermore, in one embodiment, the step of setting pouring control points based on the number of ballastless tracks between two adjacent retaining walls of the bridge includes:

[0025] When there is a single ballastless track between two adjacent retaining walls of a bridge, the pouring control points are set at each preset measuring point and on both sides of the retaining wall of the ballastless track. The pouring control points on the retaining wall are determined by drawing a perpendicular line from each preset measuring point to the retaining wall that is perpendicular to the center line of the ballastless track. The intersection of the perpendicular line and the retaining wall is the pouring control point.

[0026] When there are multiple ballastless tracks between two adjacent retaining walls of a bridge, the pouring control points are set at each preset measuring point, on both sides of the retaining walls of the ballastless tracks, and at the midpoint between two adjacent ballastless tracks. The method for determining the pouring control points on the retaining walls is the same as when there is a single ballastless track between two adjacent retaining walls of a bridge. The midpoint of two adjacent ballastless tracks is the midpoint of the line connecting the preset measuring points of the two adjacent ballastless tracks, and this line is perpendicular to the retaining wall.

[0027] Secondly, based on the above-mentioned method for determining the thickness of the ballastless track cushion layer in cable-stayed bridges, this application provides a cushion layer thickness determination system for the method of determining the thickness of the ballastless track cushion layer in cable-stayed bridges, the system comprising:

[0028] The beam elevation module is used to measure the beam elevation at each preset measuring point after the bridge is closed, under conditions where there is no temporary load on the bridge deck.

[0029] The target value module is used to determine the target elevation of the top surface of the subgrade at each preset measuring point based on the bridge's second-phase dead load, target track alignment, and cable adjustment scheme.

[0030] The matrix module is used to apply a uniformly distributed load at each preset measuring point, and combine the uniformly distributed load, the design thickness of the subgrade, and the corrected finite element model to construct a matrix for calculating the elevation of the top surface of the subgrade.

[0031] The coefficient module is used to calculate the thickness coefficient of the subgrade at each preset measuring point based on the subgrade top surface elevation calculation matrix, the beam surface elevation of each preset measuring point, the target value of the subgrade top surface elevation of each preset measuring point, and the preset allowable error of the subgrade top surface elevation.

[0032] The thickness module is used to multiply the thickness coefficient of the subbase at each preset measuring point by the design thickness of the subbase to obtain the subbase pouring thickness at each preset measuring point.

[0033] The beneficial effects of the technical solutions provided in this application include:

[0034] This application, after bridge closure and under conditions of no temporary load on the bridge deck, measures the beam elevation at each pre-set measuring point. Based on the bridge's second-phase dead load, target track alignment, and cable adjustment scheme, it sets target values ​​for the top surface elevation of the subgrade at each pre-set measuring point. By applying a uniformly distributed load at each pre-set measuring point, and combining the uniformly distributed load, the design thickness of the subgrade, and a modified finite element model, it constructs a subgrade top surface elevation estimation matrix. Then, based on the subgrade top surface elevation estimation matrix, the beam elevation at each pre-set measuring point, the target values ​​for the subgrade top surface elevation at each pre-set measuring point, and the pre-set allowable error for the subgrade top surface elevation, it calculates the subgrade thickness coefficient for each pre-set measuring point. Finally, it multiplies the subgrade thickness coefficient at each pre-set measuring point by the design thickness of the subgrade to obtain the subgrade pouring thickness at each pre-set measuring point. By calculating the subgrade thickness coefficient at each pre-set measuring point and determining the subgrade pouring thickness accordingly, it achieves precise control of the subgrade pouring thickness at the measuring point level. During the construction of the alignment adjustment of the cable-stayed bridge with ballastless track, the subbase is poured according to the thickness of each preset measuring point, rather than simply pouring it uniformly according to the design thickness. This can effectively improve the accuracy of the subbase pouring thickness, thereby improving the precision of the bridge alignment adjustment and enhancing the effect of the bridge alignment adjustment. Attached Figure Description

[0035] Figure 1 This is a flowchart illustrating the method for determining the thickness of the ballastless track cushion layer in a cable-stayed bridge according to an embodiment of this application.

[0036] Figure 2 This is a schematic diagram showing the transverse arrangement of measuring points on a steel truss cable-stayed bridge.

[0037] Figure 3 This is a simulation diagram of the thickness of the subbase at some measuring points of the four ballastless track lines obtained by solving the constraint optimization problem in step S402 of the embodiment of this application.

[0038] Figure 4 This is a simulation diagram of the elevation deviation of the top surface of the ballastless track layer at some measuring points on four ballastless track lines, obtained based on the method for determining the thickness of the ballastless track layer in the embodiments of this application.

[0039] Figure 5 This is a simulation diagram of the elevation deviation of the top surface of the subgrade at some measuring points of four ballastless track lines, obtained based on the design thickness of the subgrade and the equal thickness casting method.

[0040] Figure 6 This is a schematic diagram of the half-span bridge deck in the embodiment of the four-track long-span cable-stayed bridge of this application.

[0041] Figure 7 This is a block diagram of the system for determining the thickness of the ballastless track cushion layer in a cable-stayed bridge, as described in this application.

[0042] In the picture:

[0043] 1. Steel truss beam; 2. Ballastless track subbase to be poured; 3. Measuring points of the centerline of the first ballastless track line; 4. Measuring points of the centerline of the second ballastless track line; 5. Measuring points of the centerline of the third ballastless track line; 6. Measuring points of the centerline of the fourth ballastless track line. Detailed Implementation

[0044] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present application.

[0045] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described in further detail below with reference to the accompanying drawings.

[0046] In a first aspect, embodiments of this application provide a method for determining the thickness of the ballastless track cushion layer for cable-stayed bridges.

[0047] In one embodiment, see Figure 1 As shown, the above-mentioned method for determining the thickness of the cushion layer includes:

[0048] S1. After the bridge is closed, under the condition that there is no temporary load on the bridge deck, measure the elevation of the beam surface at each preset measuring point.

[0049] S2. Based on the bridge's second-phase dead load, target track alignment, and cable adjustment plan, formulate the target elevation values ​​for the top surface of the subgrade at each preset measuring point.

[0050] S3. Apply a uniformly distributed load at each preset measuring point, and construct a matrix for estimating the elevation of the top surface of the subgrade by combining the uniformly distributed load, the design thickness of the subgrade, and the corrected finite element model.

[0051] S4. Based on the elevation calculation matrix of the top surface of the subgrade, the beam elevation of each preset measuring point, the target elevation of the top surface of the subgrade at each preset measuring point, and the preset allowable error of the top surface elevation of the subgrade, the subgrade thickness coefficient of each preset measuring point is calculated.

[0052] S5. Multiply the thickness coefficient of the subbase at each preset measuring point by the design thickness of the subbase to obtain the subbase pouring thickness at each preset measuring point.

[0053] In this embodiment, after the bridge is closed and without temporary loads, the elevation of the beam surface at preset measuring points is measured. Combined with the secondary dead load, target alignment, and cable adjustment scheme, the target elevation value of the top surface of the subbase is determined. By applying a uniformly distributed load, an elevation calculation matrix is ​​constructed using a finite element model to calculate the subbase thickness coefficient at each measuring point. Based on this, the subbase pouring thickness is determined, achieving precise control at the measuring point level. This effectively improves the accuracy of the subbase pouring thickness, enhances the precision and effect of bridge alignment adjustment, and thus solves the technical problem of low bridge alignment adjustment precision in current ballastless track bridge alignment adjustment technology.

[0054] Furthermore, in one embodiment, before measuring the beam surface elevation of each preset measuring point in step S1 above, each preset measuring point is arranged on the center line of each ballastless track of the cable-stayed bridge according to the preset measuring point spacing, and the measuring points of each ballastless track are arranged in the same way.

[0055] In this embodiment, the preset spacing between measuring points is less than or equal to 10m. The cable-stayed bridge contains m tracks, and n measuring points are arranged on the center line of each track. A total of m×n measuring points are measured for the entire cable-stayed bridge.

[0056] Furthermore, in one embodiment, in step S3 above, a uniformly distributed load is applied at each preset measuring point. Combining the uniformly distributed load, the design thickness of the cushion layer, and the corrected finite element model, a matrix for calculating the elevation of the top surface of the cushion layer is constructed. The specific steps are as follows:

[0057] S301. Apply uniformly distributed loads one by one at each preset measuring point. Based on the modified finite element model, calculate the first beam surface elevation increment at each preset measuring point and construct the first beam surface elevation increment matrix. Here, the uniformly distributed load at one preset measuring point corresponds to one working condition. The elements of the first beam surface elevation increment matrix are the first beam surface elevation increments at each preset measuring point under each working condition, and the first beam surface elevation increment is caused by the uniformly distributed load.

[0058] In this embodiment, the aforementioned uniformly distributed load is a surface uniformly distributed load. Its longitudinal range is the distance between two adjacent measuring points, and its transverse range is the width of the ballastless track cushion layer. The surface uniformly distributed load is obtained by multiplying the design thickness of the cushion layer, the cushion layer density, and the gravitational acceleration. The calculation formula is as follows:

[0059] ,

[0060] in, Indicates a uniformly distributed load on the surface. Indicates the density of the subbase layer. Represents gravitational acceleration. This indicates the design thickness of the underlayment.

[0061] The aforementioned revised finite element model refers to the modification of the stiffness parameters of the main tower, main beam, and stay cables in the existing finite element model.

[0062] S302. Construct the second beam surface elevation increment matrix based on the design thickness of the subbase.

[0063] In this embodiment, the second beam surface elevation increment matrix is ​​a diagonal matrix. In this diagonal matrix, the elements on the diagonal are all the design thickness of the cushion layer, and the elements off the diagonal are all 0.

[0064] S303. Add the elevation increment matrix of the first beam surface and the elevation increment matrix of the second beam surface to obtain the elevation calculation matrix of the top surface of the cushion layer, that is:

[0065] ,

[0066] in, This represents the elevation increment matrix of the first beam surface. This represents the elevation increment matrix of the second beam surface. This represents the matrix for estimating the elevation of the top surface of the subbase. mn Indicates the number of operating conditions.

[0067] Furthermore, in one embodiment, in step S4 above, the subgrade thickness coefficient for each preset measuring point is calculated based on the subgrade top surface elevation calculation matrix, the beam surface elevation of each preset measuring point, the target value of the subgrade top surface elevation of each preset measuring point, and the preset allowable error of the subgrade top surface elevation. The specific steps are as follows:

[0068] S401. Based on the elevation calculation matrix of the top surface of the subgrade, the beam surface elevation of each preset measuring point, the target elevation value of the top surface of the subgrade at each preset measuring point, and the preset allowable error of the top surface elevation of the subgrade, a constrained optimization problem is constructed. The formula for constructing the constrained optimization problem is as follows:

[0069] ,

[0070] in, This represents the vector of subbase thickness coefficients to be solved, where the elements of the vector are the subbase thickness coefficients at each measuring point on the cable-stayed bridge. express m×n An identity matrix of order 1. Indicates that all elements are 1 m× n dimensional vector, This represents the vector of target elevation values ​​for the top surface of the subgrade at each preset measuring point. This represents the beam surface elevation vector for each preset measuring point. This indicates the preset allowable error in the elevation of the top surface of the subbase.

[0071] The above-mentioned constrained optimization problem means that when the elevation of the top surface of the subgrade does not exceed the preset allowable error of the top surface elevation of the subgrade, the subgrade thickness coefficient at each measuring point is calculated to minimize the relative variance of the subgrade thickness coefficient.

[0072] S402. Solve the constraint optimization problem constructed in step S401 to obtain the thickness coefficient of the cushion layer at each preset measuring point.

[0073] In this embodiment, a constrained optimization problem is constructed by using the elevation calculation matrix of the top surface of the subbase, the beam surface elevation of each preset measuring point, the target elevation value of the top surface of the subbase at each preset measuring point, and the preset allowable error of the top surface of the subbase. Solving this problem yields the subbase thickness coefficient at each preset measuring point, which can effectively improve the calculation accuracy of the thickness of the thick subbase and further improve the calculation accuracy of the top surface elevation of the subbase, thereby enhancing the alignment adjustment accuracy and alignment adjustment effect of the ballastless track.

[0074] Furthermore, in one embodiment, in step S5 above, the thickness coefficient of the cushion layer at each preset measuring point is multiplied by the design thickness of the cushion layer to obtain the casting thickness of the cushion layer at each preset measuring point. The calculation formula is as follows:

[0075] ,

[0076] in, H i Indicates the first i The thickness of the subbase pouring at each preset measuring point x i Indicates the first i The thickness of the subgrade at each preset measuring point h This indicates the design thickness of the underlayment.

[0077] Furthermore, in one embodiment, after obtaining the foundation layer thickness at each preset measuring point in step S5 above, the foundation layer of the ballastless track is poured according to the foundation layer thickness at each preset measuring point. The specific steps are as follows:

[0078] A101. Set pouring control points according to the number of tracks between two adjacent retaining walls of the bridge. The bridge must have at least two retaining walls, and there must be at least one ballastless track between every two adjacent retaining walls. The specific method for setting pouring control points is as follows:

[0079] When there is a single ballastless track between two adjacent retaining walls of the bridge, the pouring control points are set at each preset measuring point and on the retaining walls on both sides of the track. The pouring control points on the retaining walls are determined by drawing a perpendicular line from each preset measuring point to the retaining wall that is perpendicular to the center line of the track. The intersection of the perpendicular line and the retaining wall is the pouring control point.

[0080] When there are multiple ballastless tracks between two adjacent retaining walls of a bridge, the pouring control points are set at each preset measuring point, on the retaining walls on both sides of the track, and at the midpoint between two adjacent ballastless tracks. The method for determining the pouring control points on the retaining walls is the same as when there is a single ballastless track between two adjacent retaining walls of a bridge. The midpoint of two adjacent ballastless tracks is the midpoint of the line connecting the preset measuring points of the two adjacent ballastless tracks, and this line is perpendicular to the retaining wall.

[0081] A102. Based on the thickness of the subbase pouring at each preset measuring point, determine the elevation of the pouring control points, and pour the subbase using the pouring control network formed by the pouring control points. The elevation of each pouring control point is determined as follows:

[0082] When the bridge has a single ballastless track between two adjacent retaining walls, the elevations of the pouring control points set at each preset measuring point and the elevations of the pouring control points set on the retaining walls on both sides of the track are both the thickness of the subbase pouring at the corresponding preset measuring points, that is:

[0083] ,

[0084] Among them, G i G represents the elevation of the pouring control point at the i-th preset measuring point. i1 G represents the elevation of the pouring control point of the retaining wall on one side corresponding to the i-th preset measuring point. i2 The elevation of the pouring control point of the retaining wall on the other side corresponding to the i-th preset measuring point is indicated, and m represents the number of preset measuring points on a single ballastless track.

[0085] When there are multiple ballastless tracks between two adjacent retaining walls of a bridge, the elevation of the pouring control points set at each preset measuring point is the corresponding thickness of the subbase pouring at the preset measuring point, that is:

[0086] ,

[0087] in, G j,i Indicates the first j The first ballastless track i Elevation of the pouring control points at each preset measuring point n This indicates the number of ballastless tracks between two adjacent retaining walls of a bridge. H j,i Indicates the first j The first ballastless track i The thickness of the subbase pouring at each preset measuring point.

[0088] The elevation of the pouring control points set on the retaining walls on both sides of the track is determined based on the elevation of the pouring control point at the i-th measuring point of each ballastless track, the elevation of the midpoint of the two adjacent tracks corresponding to that measuring point, the lateral spacing of the i-th measuring points of each ballastless track, and the distance between the retaining walls on both sides and the i-th measuring point closest to them.

[0089] The elevation set at the midpoint between two adjacent ballastless tracks is the average value of the preset measuring points of the two adjacent ballastless tracks corresponding to that midpoint, that is:

[0090] ,

[0091] in, G cj_j+1,i Indicates the first j The ballastless track and the first j+1 The first ballastless track i The elevation at the midpoint between the two ballastless tracks corresponding to each preset measuring point represents... H j+1,i Indicates the first j+1 The first ballastless track i The thickness of the subbase pouring at each preset measuring point.

[0092] Furthermore, in one embodiment, see [reference needed]. Figure 2 As shown, taking a four-track cable-stayed bridge with a main span of 392m as an example, the method for determining the thickness of the ballastless track cushion layer of the above-mentioned cable-stayed bridge is explained. This cable-stayed bridge is a double-layer steel truss structure, with a six-lane highway on the upper layer and a four-track railway on the lower layer. It includes four ballastless tracks, with two ballastless tracks set in a group within two adjacent retaining walls. During the cantilever construction of the cable-stayed bridge, the stiffness of the main tower, main beam, and cable stays in the calculation model has been corrected to be consistent with the actual values. The specific method for determining the thickness of the ballastless track cushion layer and the cushion layer pouring steps are as follows:

[0093] (1) After the cable-stayed bridge is closed, remove excess temporary loads on the bridge deck, such as cranes, maintenance vehicles, transport vehicles, girder erecting cranes, closure counterweights, and uninstalled ancillary facilities. Measure the elevation of the beam surface on the centerline of each ballastless track, and arrange measuring points on the centerline of each ballastless track, with the transverse arrangement as follows: Figure 2 The measuring points 3, 4, 5, and 6 along the centerline of the first, second, third, and fourth ballastless track lines were used. The steel truss girder span is 14m long, with a pre-set measuring point spacing of 7m. The bridge comprises four tracks, with 121 measuring points along each track's centerline, totaling 484 measuring points for the beam surface elevation. .

[0094] (2) Accurately calculate the weight of the bridge's second-phase dead load. Based on the final target track alignment and cable adjustment plan, determine the target elevation values ​​of the top surface of the subgrade corresponding to each measuring point on the track centerline when the subgrade pouring is completed, denoted as... The second phase of the bridge's permanent load includes the ballastless track structure layer, the overhead contact line, and the guardrails.

[0095] (3) Apply a uniform surface load at each measuring point. The measuring points are all located at the center of the uniform surface load. The longitudinal range of a single uniform surface load is the distance between two adjacent measuring points, and the transverse range is the width of the ballastless track cushion layer. A total of 4×121 working conditions are calculated.

[0096] (4) Based on the uniformly distributed load and the corrected finite element model, construct the first beam surface elevation increment matrix, denoted as A uniformly distributed load at a measuring point corresponds to a working condition, and the elements of the first beam surface elevation increment matrix are the first beam surface elevation increments at each measuring point under each working condition.

[0097] (5) Construct the second beam surface elevation increment matrix based on the design thickness of the subbase, denoted as This matrix is ​​a diagonal matrix, and the elements on the diagonal are the design thickness of the padding layer.

[0098] (6) Add the elevation increment matrix of the first beam surface and the elevation increment matrix of the second beam surface to obtain the elevation calculation matrix of the top surface of the cushion layer, that is: .

[0099] (7) Set the allowable error for the elevation of the top surface of the cushion layer as follows: In this embodiment, the value is taken as 2mm. Based on the elevation calculation matrix of the top surface of the subgrade, the beam surface elevation at each measuring point, the target elevation value of the top surface of the subgrade at each measuring point, and the preset allowable error of the top surface elevation of the subgrade, a constrained optimization problem is constructed, as follows:

[0100] ,

[0101] in, This represents the vector of subbase thickness coefficients to be solved, where the elements of the vector are the subbase thickness coefficients at each measuring point on the cable-stayed bridge. This represents a 484×484 identity matrix. This represents a 484×484-dimensional vector with all elements being 1. This represents the target elevation vector of the top surface of the subgrade at each measuring point. This represents the beam surface elevation vector at each measuring point. This indicates the preset allowable error in the elevation of the top surface of the subbase.

[0102] Solving the above constrained optimization problem yields the subbase thickness coefficient at each measuring point. Multiplying this coefficient by the design thickness of the subbase gives the subbase pouring thickness at each measuring point, denoted as . .

[0103] See Figure 3 As shown, Figure 3 The simulation diagram shows the thickness of the subbase (i.e., the casting thickness of the subbase) at some measuring points of the four ballastless track lines obtained by solving the constrained optimization problem in step S402 above. In this embodiment, the designed thickness of the subbase is 165mm, while the calculated casting thickness of the subbase at each measuring point is 133mm~210mm, with a range of 77mm. This indicates that the smoothness of the bridge deck alignment is poor, and the track alignment needs to be optimized by adjusting the subbase thickness. This proves the necessity of the method for determining the subbase thickness of the ballastless track in this application. If it is not controlled, the subsequent alignment adjustment capability of the ballastless track structure will be small, making it difficult to adjust the track alignment deviation and failing to meet the acceptance requirements of the specifications.

[0104] Secondly, see Figure 4 and Figure 5 As shown, Figure 4 The images show simulations of the elevation deviation of the top surface of the subgrade at some measuring points on four ballastless track lines, obtained based on the subgrade thickness determination method provided in this application. Figure 5 The simulation diagram shows the elevation deviation of the top surface of the subgrade at some measuring points of four ballastless track lines, obtained by the equal-thickness casting method based on the design thickness of the subgrade. The elevation deviation of the top surface of the subgrade calculated according to this application is much smaller than the elevation deviation of the top surface of the subgrade when casting according to the design thickness of the subgrade. It can be seen that this application has a more prominent advantage in the accuracy of subgrade casting thickness calculation.

[0105] (8) Set up pouring control points at each measuring point, on the retaining walls on both sides of the track, and at the midpoint between two adjacent ballastless tracks. Determine the elevation of each pouring control point. See [reference needed]. Figure 6 As shown, the calculation process is illustrated using the first longitudinal measuring point and the half of the bridge deck where measuring points one and two are located in the transverse direction as an example.

[0106] The elevation of the pouring control point at the measuring point is the thickness of the subbase pouring at the corresponding measuring point, that is:

[0107] ,

[0108] ,

[0109] in, This indicates the elevation of the pouring control point at the first measuring point on the left track. This indicates the thickness of the subbase at the measuring point. This indicates the elevation of the pouring control point of the first measuring point on the right track. This indicates the thickness of the subbase at the measuring point.

[0110] The formula for calculating the elevation of the pouring control points on the retaining walls on both sides of the track is:

[0111] ,

[0112] ,

[0113] in, This indicates the elevation of the pouring control point on the left retaining wall. This indicates the lateral distance between the first measuring points of the two ballastless tracks. This indicates the distance between the left retaining wall and the first measuring point on the left track. This indicates the elevation of the pouring control point on the right retaining wall. This indicates the distance between the right retaining wall and the first measuring point on the right track.

[0114] (9) According to the above calculation, the pouring control points are set up, the subbase pouring instructions are prepared, and the subbase pouring construction is carried out on the subbase 2 of the ballastless track to be poured.

[0115] During the actual construction of the subbase, in addition to taking into account the measurement error of the spacing between the measuring points, the difference between the distances of the lines connecting each measuring point to the measuring points before and after it should be controlled within the preset difference range. This can, to a certain extent, make the top surface of the subbase relatively smooth, laying a good foundation for the subsequent track structure construction.

[0116] Secondly, based on the above-mentioned method for determining the thickness of the ballastless track cushion layer in cable-stayed bridges, an embodiment of a cushion layer thickness determination system for this method is provided. See also... Figure 7 As shown, the system includes a beam surface elevation module, a target value module, a matrix module, a coefficient module, and a thickness module, specifically:

[0117] The beam elevation module is used to measure the beam elevation at each preset measuring point after the bridge is closed, under conditions where there is no temporary load on the bridge deck.

[0118] The target value module is used to determine the target elevation of the top surface of the subgrade at each preset measuring point based on the bridge's second-phase dead load, target track alignment, and cable adjustment scheme.

[0119] The matrix module is used to apply a uniformly distributed load at each preset measuring point, and combine the uniformly distributed load, the design thickness of the subgrade, and the corrected finite element model to construct a matrix for calculating the elevation of the top surface of the subgrade.

[0120] The coefficient module is used to calculate the thickness coefficient of the subgrade at each preset measuring point based on the subgrade top surface elevation calculation matrix, the beam surface elevation of each preset measuring point, the target value of the subgrade top surface elevation of each preset measuring point, and the preset allowable error of the subgrade top surface elevation.

[0121] The thickness module is used to multiply the thickness coefficient of the subbase at each preset measuring point by the design thickness of the subbase to obtain the subbase pouring thickness at each preset measuring point.

[0122] This application allows for precise control of the subbase thickness down to the measuring point level. A dense subbase pouring control network can be formed based on the subbase pouring control points, simultaneously controlling the overall and local alignment to the optimal level. Furthermore, considering the errors in actual construction and measurement, local deviations can be adjusted as appropriate according to the on-site pouring conditions, providing a certain degree of flexibility for on-site construction.

[0123] It should be noted that the sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0124] The terms "comprising" and "having," and any variations thereof, in the specification, claims, and accompanying drawings of this application are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to such process, method, product, or apparatus. The terms "first," "second," and "third," etc., are used to distinguish different objects, etc., and do not indicate a sequence, nor do they limit "first," "second," and "third" to different types.

[0125] In the description of the embodiments of this application, terms such as "exemplary," "for example," or "for instance" are used to indicate examples, illustrations, or explanations. Any embodiment or design described as "exemplary," "for example," or "for instance" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of terms such as "exemplary," "for example," or "for instance" is intended to present the relevant concepts in a concrete manner.

[0126] In the description of the embodiments of this application, unless otherwise stated, " / " means "or". For example, A / B can mean A or B. The "and / or" in the text is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can mean: A exists alone, A and B exist simultaneously, and B exists alone. In addition, in the description of the embodiments of this application, "multiple" means two or more.

[0127] In some processes described in the embodiments of this application, multiple operations or steps are included in a specific order. However, it should be understood that these operations or steps may not be executed in the order they appear in the embodiments of this application, or they may be executed in parallel. The sequence number of the operation is only used to distinguish different operations, and the sequence number itself does not represent any execution order. In addition, these processes may include more or fewer operations, and these operations or steps may be executed sequentially or in parallel, and these operations or steps may be combined.

[0128] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) as described above, and includes several instructions to cause a terminal device to execute the methods described in the various embodiments of this application.

[0129] The above are merely preferred embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A method for determining the thickness of the ballastless track pad layer in a cable-stayed bridge, characterized in that, The method includes: After the bridge is closed, under the condition that there is no temporary load on the bridge deck, measure the beam surface elevation at each preset measuring point; Based on the bridge's second-phase dead load, target track alignment, and cable adjustment plan, the target elevation values ​​for the top surface of the subgrade at each pre-set measuring point are determined. A uniformly distributed load is applied at each preset measuring point. The elevation calculation matrix of the top surface of the subgrade is constructed by combining the uniformly distributed load, the design thickness of the subgrade, and the corrected finite element model. Based on the elevation calculation matrix of the top surface of the subbase, the beam surface elevation of each preset measuring point, the target elevation value of the top surface of the subbase at each preset measuring point, and the preset allowable error of the top surface of the subbase, the subbase thickness coefficient of each preset measuring point is calculated. The thickness coefficient of the subbase at each preset measuring point is multiplied by the design thickness of the subbase to obtain the subbase pouring thickness at each preset measuring point. The process involves applying a uniformly distributed load at each preset measuring point, and then, based on the uniformly distributed load, the design thickness of the subgrade, and the corrected finite element model, constructing a matrix for estimating the elevation of the top surface of the subgrade. This includes: Uniformly distributed loads are applied one by one at each preset measuring point. Based on the modified finite element model, the elevation increment of the first beam surface at each preset measuring point is calculated, and the elevation increment matrix of the first beam surface is constructed. The uniformly distributed load at one preset measuring point corresponds to one working condition, and the elements of the elevation increment matrix of the first beam surface are the elevation increments of the first beam surface at each preset measuring point under each working condition. Construct the second beam surface elevation increment matrix based on the design thickness of the subbase; The elevation increment matrix of the first beam surface and the elevation increment matrix of the second beam surface are added together to obtain the elevation calculation matrix of the top surface of the cushion layer. The method for calculating the subgrade thickness coefficient at each preset measuring point based on the subgrade top surface elevation calculation matrix, the beam surface elevation at each preset measuring point, the target subgrade top surface elevation at each preset measuring point, and the preset allowable error for the subgrade top surface elevation is as follows: Based on the elevation calculation matrix of the top surface of the subgrade, the beam surface elevation of each preset measuring point, the target elevation value of the top surface of the subgrade at each preset measuring point, and the preset allowable error of the top surface elevation of the subgrade, a constrained optimization problem is constructed. The formula for constructing the constrained optimization problem is as follows: ， in, This represents the vector of subbase thickness coefficients to be solved, where the elements of the vector are the subbase thickness coefficients at each measuring point on the cable-stayed bridge. express m×n An identity matrix of order 1. Indicates that all elements are 1 m×n dimensional vector, This represents the vector of target elevation values ​​for the top surface of the subgrade at each preset measuring point. This represents the beam surface elevation vector for each preset measuring point. This indicates the preset allowable error in the elevation of the top surface of the subbase; The constrained optimization problem is solved to obtain the thickness coefficient of the cushion layer at each preset measuring point.

2. The method for determining the thickness of the ballastless track pad layer for cable-stayed bridges as described in claim 1, characterized in that, Before measuring the beam surface elevation at each preset measuring point, the method further includes: According to the preset measurement point spacing, preset measurement points are arranged on the center line of each ballastless track of the cable-stayed bridge, and the measurement point arrangement method is the same for each ballastless track.

3. The method for determining the thickness of the ballastless track pad layer for cable-stayed bridges as described in claim 1, characterized in that, The uniformly distributed load is obtained by multiplying the design thickness of the cushion layer, the density of the cushion layer, and the gravitational acceleration.

4. The method for determining the thickness of the ballastless track pad layer for cable-stayed bridges as described in claim 1, characterized in that, The uniformly distributed load is a surface uniformly distributed load, the longitudinal range of which is the distance between two adjacent measuring points, and the lateral range is the width of the ballastless track cushion layer.

5. The method for determining the thickness of the ballastless track pad layer for cable-stayed bridges as described in claim 1, characterized in that, The modified finite element model refers to the modification of the stiffness parameters of the main tower, main beam, and stay cables in the existing finite element model.

6. The method for determining the thickness of the ballastless track pad layer for cable-stayed bridges as described in claim 1, characterized in that, After obtaining the thickness of the subbase pouring at each preset measuring point, the process further includes: Set pouring control points according to the number of ballastless tracks between two adjacent retaining walls of the bridge; Based on the thickness of the subbase pouring at each preset measuring point, the elevation of the pouring control point is determined, and the subbase is poured on the pouring control network formed by the pouring control points.

7. The method for determining the thickness of the ballastless track pad layer for cable-stayed bridges as described in claim 6, characterized in that, The step of setting pouring control points based on the number of ballastless tracks between two adjacent retaining walls of the bridge includes: When there is a single ballastless track between two adjacent retaining walls of the bridge, the pouring control points are set at each preset measuring point and on both sides of the retaining wall of the ballastless track. The pouring control points on the retaining wall are determined by drawing a perpendicular line from each preset measuring point to the retaining wall that is perpendicular to the center line of the ballastless track. The intersection of the perpendicular line and the retaining wall is the pouring control point. When there are multiple ballastless tracks between two adjacent retaining walls of a bridge, the pouring control points are set at each preset measuring point, on both sides of the retaining walls of the ballastless tracks, and at the midpoint between two adjacent ballastless tracks. The method for determining the pouring control points on the retaining walls is the same as when there is a single ballastless track between two adjacent retaining walls of a bridge. The midpoint of two adjacent ballastless tracks is the midpoint of the line connecting the preset measuring points of the two adjacent ballastless tracks, and this line is perpendicular to the retaining wall.

8. A system for determining the thickness of the ballastless track ballast layer for cable-stayed bridges based on the method for determining the thickness of the ballastless track ballast layer according to any one of claims 1-7, characterized in that, The system includes: The beam elevation module is used to measure the beam elevation at each preset measuring point after the bridge is closed, under the condition that there is no temporary load on the bridge deck. The target value module is used to determine the target elevation of the top surface of the subgrade at each preset measuring point based on the bridge's second-phase dead load, target track alignment, and cable adjustment scheme. The matrix module is used to apply a uniformly distributed load at each preset measuring point, and combine the uniformly distributed load, the design thickness of the subbase, and the corrected finite element model to construct a matrix for calculating the elevation of the top surface of the subbase. The coefficient module is used to calculate the thickness coefficient of the subgrade at each preset measuring point based on the subgrade top surface elevation calculation matrix, the beam surface elevation of each preset measuring point, the target value of the subgrade top surface elevation of each preset measuring point, and the preset allowable error of the subgrade top surface elevation. The thickness module is used to multiply the thickness coefficient of the subbase at each preset measuring point by the design thickness of the subbase to obtain the subbase pouring thickness at each preset measuring point.

Images