Cable-supported railway bridge track alignment construction control method

Abstract

The application discloses a cable-supported railway bridge track alignment construction control method, and belongs to the track ballast and track construction technical field of the cable-supported railway bridge, and comprises the following steps: obtaining a steel beam reference alignment under a reference temperature condition; establishing a sensitivity matrix of the influence of unit track ballast thickness distribution on the alignment of the whole bridge steel beam, and then obtaining the steel beam deformation caused by the track ballast load based on the final track ballast thickness distribution and the sensitivity matrix; obtaining the bridge completion rail bottom predicted alignment based on the steel beam reference alignment, the final track ballast thickness distribution and the steel beam deformation caused by the track ballast load; and establishing a planning solution model with the minimum deviation between the bridge completion rail bottom predicted alignment and the bridge completion rail bottom design alignment as the target, solving the optimal track ballast thickness distribution, and then determining the specific adjustment amount of the track ballast on the bottom surface and the track ballast on the top surface of each section. The application is suitable for the cable-supported bridge and the track ballast thickness adjustment, can comprehensively consider the coupling action between the track ballast thickness and the main beam alignment, and effectively improves the final precision of the bridge completion track alignment.

Description

Technical Field

[0001] This invention relates to a method for controlling the track alignment during construction of cable-stayed railway bridges, belonging to the technical field of ballast and track construction for cable-stayed railway bridges. Background Technology

[0002] During the construction of long-span cable-stayed bridges, temporary loads, environmental factors, and variations in material parameters often lead to deviations in the main girder alignment during the completed bridge phase. For railway bridges, the accuracy of the track alignment directly affects train ride smoothness and operational safety. To meet the high standards for track alignment, the main girder alignment needs to be adjusted using stay cables or suspenders. However, the adjustment range of the stay cables is limited, making it difficult to achieve zero-deviation control of the main girder alignment entirely through cable adjustment. Therefore, auxiliary adjustments are also necessary using appropriate settings for ballast thickness and ballast weight.

[0003] Depending on the ballast layout on the bridge deck, ballast adjustments can be placed in two areas: ① the bottom surface of the original ballast design, corresponding to... Figure 1 ① The bottom surface of the ballast, ② the top surface of the original ballast design, corresponding to Figure 1 The top surface of the ballast. If only the bottom surface of the ballast is adjusted, the ballast will not only affect the overall alignment of the main beam, but also, due to the change in the thickness of the ballast at the bottom of the sleepers, will have a local optimization adjustment on the track alignment; if only the top surface of the ballast is adjusted, the ballast will only serve as a load counterweight and will not have any additional adjustment on the track alignment.

[0004] Because long-span cable-stayed bridges have relatively low structural stiffness, changes in ballast thickness can further alter the main girder alignment. Therefore, for long-span cable-stayed bridge systems, the coupling effect between ballast thickness adjustment and main girder alignment must be considered. Furthermore, the uneven distribution of alignment errors across different main girder segments necessitates determining the ballast thickness separately for each segment. Existing technologies urgently require a track alignment construction method that comprehensively considers the coupling effect between ballast thickness and main girder alignment, effectively improving the final accuracy of the completed bridge track alignment. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the defects of the prior art and provide a construction control method for the track alignment of cable-stayed railway bridges. This method is applicable to cable-stayed bridges and is based on ballast thickness adjustment. It can comprehensively consider the coupling effect between ballast thickness and main beam alignment, and effectively improve the final accuracy of the track alignment of the completed bridge.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0007] A method for controlling the track alignment during construction of cable-stayed railway bridges includes the following steps:

[0008] Elevation data and structural temperature data at the measurement time are obtained from various alignment measurement points on the steel beams of long-span cable-stayed bridges. The actual alignment of the steel beams under the measured temperature conditions is obtained by combining the elevation data and structural temperature data.

[0009] After calculating the temperature difference between the design reference temperature and the measured temperature, the temperature difference is substituted into the finite element simulation analysis model to analyze the change in the steel beam profile caused by the temperature effect. Then, based on the change in the steel beam profile, the actual profile of the steel beam is converted to obtain the reference profile of the steel beam under the reference temperature condition.

[0010] Based on the finite element model, a sensitivity matrix is ​​established to the influence of unit ballast thickness distribution on the overall steel beam alignment. Then, based on the final ballast thickness distribution and the sensitivity matrix, the steel beam deformation caused by ballast load is obtained.

[0011] The predicted alignment of the bridge track bottom is obtained based on the baseline shape of the steel beam, the final ballast thickness distribution, and the deformation of the steel beam caused by the ballast load.

[0012] With the objective of minimizing the deviation between the predicted alignment of the completed bridge track bottom and the designed alignment of the completed bridge track bottom, and satisfying the adjustment boundary conditions for the top and bottom ballast, a planning and solution model is established:

[0013] The optimal ballast thickness distribution that satisfies the overall bridge alignment control objective is obtained by solving the planning solution model. Then, the specific adjustment amount of the bottom and top ballast of each segment is determined based on the optimal ballast thickness distribution.

[0014] The expression for the actual linear shape of the steel beam under measured temperature conditions is:

[0015] (1);

[0016] In the formula, Let n be the set of actual elevations of all linear measuring points on the steel beam, where n is the number of linear measuring points on the steel beam. This represents the actual elevation of the steel beam corresponding to the first linear measuring point. This represents the actual elevation of the steel beam corresponding to the second linear measuring point. This represents the actual elevation of the steel beam corresponding to the nth linear measuring point.

[0017] The conversion formula between the actual alignment of the steel beam and the baseline alignment of the steel beam is as follows:

[0018] (2);

[0019] In the formula, This is a set of reference elevations for various linear measuring points on the steel beam. This is the set of changes in the steel beam's shape caused by temperature effects, where T is the difference between the design reference temperature and the measured temperature.

[0020] (3);

[0021] In the formula, The reference elevation of the steel beam corresponding to the first linear measuring point. The reference elevation of the steel beam corresponding to the second linear measuring point. This is the reference elevation of the steel beam corresponding to the nth linear measuring point.

[0022] The sensitivity matrix established based on the finite element model to the influence of the final ballast thickness distribution on the overall bridge steel beam alignment includes:

[0023] In the finite element model, calculate the influence of the ballast weight per unit thickness of the i-th steel beam segment on the j-th linear measuring point. This will affect the amount The sensitivity matrix is ​​obtained by arranging the matrix. The sensitivity matrix expression is as follows:

[0024] (4);

[0025] In the formula, i = 1, 2, ..., n, j = 1, 2, ..., n, and n represents the number of measuring points for the steel beam alignment and the number of steel beam segments.

[0026] The final expression for the ballast thickness distribution is:

[0027] (5);

[0028] In the formula, This is a set of final ballast thicknesses for each segment. This refers to the final ballast thickness of the first segment. This refers to the final ballast thickness of the first segment. The final ballast thickness for the nth segment;

[0029] (6);

[0030] In the formula, Let j be the final ballast thickness of the j-th segment. Design the ballast thickness for the j-th segment. The adjustment amount for the bottom ballast of the j-th segment is... This is the adjustment amount for the top surface ballast of the j-th segment.

[0031] The calculation method for steel beam deformation caused by ballast load based on the final ballast thickness distribution and sensitivity matrix is ​​as follows:

[0032] (7);

[0033] In the formula, This refers to the set of steel beam deformations caused by ballast loads. The deformation of the steel beam at the first linear measuring point caused by ballast load. The deformation of the steel beam at the second linear measuring point caused by the ballast load. The deformation of the steel beam at the nth linear measuring point caused by the ballast load.

[0034] The calculation method for obtaining the predicted track bottom alignment of the completed bridge based on the steel beam baseline shape, the final ballast thickness distribution, and the steel beam deformation caused by the ballast load is as follows:

[0035] (8);

[0036] In the formula, This is a set of predicted elevations for the bottom of the bridge tracks.

[0037] The specific boundary conditions for adjusting the top and bottom ballast are as follows:

[0038] (9);

[0039] (10);

[0040] In the formula, Design elevation for rail top. Design elevation for the top surface of ballast.

[0041] The expression for the planning and solving model is:

[0042] (11);

[0043] In the formula, The design elevation of the bottom of the bridge track is given by the i-th linear measuring point.

[0044] In determining the specific adjustment amounts of the bottom and top ballast of each segment based on the optimal ballast thickness distribution, the bottom ballast is adjusted first, and the top ballast is adjusted only when the bottom ballast adjustment reaches its upper limit.

[0045] The beneficial effects of this invention are as follows: This invention provides a method for controlling the track alignment during construction of cable-stayed railway bridges. Specifically for long-span cable-stayed railway bridges, considering the strong coupling effect between ballast thickness adjustment and main beam alignment changes, a two-way mapping mechanism of "ballast-alignment" is constructed. With the track acceptance alignment as the final control target, the coupling relationship between ballast adjustment and main beam alignment is established, clarifying the range of ballast placement and the boundary conditions for ballast adjustment, and determining the final total amount of ballast on the bridge. This effectively solves the problem of passive response of the main beam alignment caused by active ballast thickness adjustment, achieving precise control of track geometry. Attached Figure Description

[0046] Figure 1 This is a schematic diagram of the arrangement of ballast on the bridge deck in this invention. Detailed Implementation

[0047] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to illustrate the technical solution of the present invention more clearly, and should not be used to limit the scope of protection of the present invention.

[0048] This invention discloses a method for controlling the track alignment during construction of cable-stayed railway bridges, comprising the following steps:

[0049] Step 1: Obtain the elevation data and structural temperature data at the measurement time of each alignment measuring point on the steel beam of the long-span cable-stayed bridge. Combine the elevation data and structural temperature data to obtain the actual alignment of the steel beam under the measured temperature conditions.

[0050] Step two: After calculating the temperature difference between the design reference temperature and the measured temperature, the temperature difference is substituted into the finite element simulation analysis model to analyze the change in the steel beam profile caused by the temperature effect. Then, based on the change in the steel beam profile, the actual profile of the steel beam is converted to obtain the reference profile of the steel beam under the reference temperature condition.

[0051] Step 3: Based on the finite element model, establish the sensitivity matrix of the influence of unit ballast thickness distribution on the overall steel beam alignment, and then obtain the steel beam deformation caused by ballast load based on the final ballast thickness distribution and sensitivity matrix.

[0052] Step four: Based on the baseline shape of the steel beam, the final ballast thickness distribution, and the deformation of the steel beam caused by the ballast load, the predicted shape of the track bottom of the completed bridge is obtained.

[0053] Step 5: With the goal of minimizing the deviation between the predicted alignment of the completed bridge track bottom and the designed alignment of the completed bridge track bottom, and satisfying the boundary conditions for adjusting the top and bottom ballast, establish a planning solution model.

[0054] Step 6: Solve the planning model to obtain the optimal ballast thickness distribution that satisfies the overall bridge alignment control objective, and then determine the specific adjustment amount of the bottom and top ballast of each segment based on the optimal ballast thickness distribution.

[0055] This invention targets long-span cable-stayed railway bridges, considering the strong coupling effect between ballast thickness adjustment and main beam alignment changes. By constructing a two-way mapping mechanism of "ballast-alignment," and taking the track acceptance alignment as the final control target, it establishes the coupling relationship between ballast adjustment and main beam alignment, clarifies the range of ballast placement and boundary conditions for ballast adjustment, and determines the final total amount of ballast on the bridge. This effectively solves the problem of passive response of main beam alignment caused by active ballast thickness adjustment, and achieves precise control of track geometry.

[0056] Example 2

[0057] This invention discloses a method for controlling the track alignment during construction of cable-stayed railway bridges, comprising the following steps:

[0058] Step one: After the bridge is closed, the steel beam alignment measurement points are determined based on the bridge's structural characteristics. For long-span cable-stayed bridges, measurement points are generally set at major nodes of the steel beams. By acquiring the elevation data and structural temperature data at the measurement time of each alignment measurement point on the steel beam of the long-span cable-stayed bridge, the actual alignment of the steel beam under the measured temperature conditions is obtained by combining the elevation data and structural temperature data. The expression for the actual alignment of the steel beam under the measured temperature conditions is:

[0059] (1);

[0060] In the formula, Let n be the set of actual elevations of all linear measuring points on the steel beam, where n is the number of linear measuring points on the steel beam. This represents the actual elevation of the steel beam corresponding to the first linear measuring point. This represents the actual elevation of the steel beam corresponding to the second linear measuring point. This represents the actual elevation of the steel beam corresponding to the nth linear measuring point.

[0061] Step two: After calculating the temperature difference between the design reference temperature and the measured temperature, the temperature difference is substituted into the finite element simulation analysis model to analyze the change in the steel beam profile caused by the temperature effect. Then, based on the change in the steel beam profile, the actual profile of the steel beam is converted to obtain the reference profile of the steel beam under the reference temperature condition.

[0062] The conversion formula between the actual alignment of the steel beam and the baseline alignment of the steel beam is as follows:

[0063] (2);

[0064] In the formula, This is a set of reference elevations for various linear measuring points on the steel beam. This is the set of changes in the steel beam's shape caused by temperature effects, where T is the difference between the design reference temperature and the measured temperature.

[0065] (3);

[0066] In the formula, The reference elevation of the steel beam corresponding to the first linear measuring point. The reference elevation of the steel beam corresponding to the second linear measuring point. This is the reference elevation of the steel beam corresponding to the nth linear measuring point.

[0067] Step 3: Based on the finite element model, establish the sensitivity matrix of the influence of unit ballast thickness distribution on the overall steel beam alignment, and then obtain the steel beam deformation caused by ballast load based on the final ballast thickness distribution and sensitivity matrix.

[0068] Among them, based on the finite element model, the sensitivity matrix of the influence of unit ballast thickness distribution on the overall bridge steel beam alignment is established, including:

[0069] In the finite element model, calculate the influence of the ballast weight per unit thickness of the i-th steel beam segment on the j-th linear measuring point. This will affect the amount The sensitivity matrix is ​​obtained by arranging the matrix. The sensitivity matrix expression is as follows:

[0070] (4);

[0071] In the formula, i = 1, 2, ..., n, j = 1, 2, ..., n, where n represents the number of steel beam alignment measuring points and the number of steel beam segments. In this invention, steel beam segments and steel beam alignment measuring points are corresponding, with one steel beam alignment measuring point set for each steel beam segment; therefore, the total number of both is the same.

[0072] The final expression for the ballast thickness distribution is:

[0073] (5);

[0074] In the formula, This is a set of final ballast thicknesses for each segment. This refers to the final ballast thickness of the first segment. This refers to the final ballast thickness of the first segment. The final ballast thickness of the nth segment;

[0075] This invention requires determining the boundary conditions for ballast thickness adjustment. The total adjusted ballast thickness consists of the adjustment amount of the bottom ballast and the adjustment amount of the top ballast of the segment, i.e.

[0076] (6);

[0077] The final expression for the ballast thickness is:

[0078] (7);

[0079] In the formula, The total ballast thickness is adjusted for the j-th segment. Let j be the final ballast thickness of the j-th segment. Design the ballast thickness for the j-th segment. The adjustment amount for the bottom ballast of the j-th segment is... This is the adjustment amount for the top surface ballast of the j-th segment.

[0080] This invention determines the boundary conditions for the final ballast thickness by adjusting the bottom and top ballast surfaces. The adjustment range for the bottom ballast surface should meet the requirements of specifications and allowable construction deviations, and can generally be taken as follows:

[0081] (8);

[0082] The adjustment range for the top ballast should be determined based on the design elevation of the rail top and the design elevation of the top ballast surface, and can be taken as follows:

[0083] (9);

[0084] In the formula, Design elevation for rail top. Design elevation for the top surface of ballast.

[0085] The calculation method for the steel beam deformation caused by ballast load, based on the final ballast thickness distribution and sensitivity matrix, is as follows:

[0086] (10);

[0087] In the formula, This refers to the set of steel beam deformations caused by ballast loads. The deformation of the steel beam at the first linear measuring point caused by ballast load. The deformation of the steel beam at the second linear measuring point caused by the ballast load. The deformation of the steel beam at the nth linear measuring point caused by the ballast load.

[0088] Step four: Based on the baseline shape of the steel beam, the final ballast thickness distribution, and the deformation of the steel beam caused by the ballast load, the predicted track bottom shape of the completed bridge is obtained. The specific calculation method is as follows:

[0089] (11);

[0090] In the formula, This is a set of predicted elevations for the bottom of the bridge tracks.

[0091] Step 5: With the objective of minimizing the deviation between the predicted alignment of the completed bridge track bottom and the designed alignment, and satisfying the boundary conditions for adjusting the top and bottom ballast, establish a planning and solution model. The designed alignment of the completed bridge track bottom is denoted as:

[0092] (12);

[0093] In the formula, The set of design elevations for the track bottom of the completed bridge. The design elevation of the first completed bridge track bottom. The second completed bridge track bottom design alignment elevation. The design elevation of the track bottom of the nth completed bridge.

[0094] The expression for the planning and solving model is:

[0095] (13);

[0096] In the formula, The design elevation of the bottom of the bridge track is given by the i-th linear measuring point.

[0097] Step six: Solve the planning model to obtain the optimal ballast thickness distribution that satisfies the overall bridge alignment control objective. Then, determine the specific adjustment amounts for the bottom and top ballast of each segment based on the optimal ballast thickness distribution. Prioritize adjusting the bottom ballast; only activate top ballast adjustment when the bottom ballast adjustment reaches its upper limit.

[0098] During the phased construction of the second-stage dead load or ballast, the steel beam alignment should be re-measured in a timely manner according to the construction progress, and the structural temperature should be recorded simultaneously. Based on the latest measured alignment, temperature correction, alignment prediction, and ballast thickness optimization calculations should be performed again, and the total ballast adjustment amount should be dynamically updated to form a closed-loop control process of "measurement-correction-prediction-optimization-feedback" to ensure that the track alignment of the completed bridge meets the design requirements.

[0099] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0100] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0101] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0102] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for controlling the track alignment during construction of cable-stayed railway bridges, characterized in that: Includes the following steps: Elevation data and structural temperature data at the measurement time are obtained from various alignment measurement points on the steel beams of long-span cable-stayed bridges. The actual alignment of the steel beams under the measured temperature conditions is obtained by combining the elevation data and structural temperature data. After calculating the temperature difference between the design reference temperature and the measured temperature, the temperature difference is substituted into the finite element simulation analysis model to analyze the change in the steel beam profile caused by the temperature effect. Then, based on the change in the steel beam profile, the actual profile of the steel beam is converted to obtain the reference profile of the steel beam under the reference temperature condition. Based on the finite element model, a sensitivity matrix is ​​established to the influence of unit ballast thickness distribution on the overall steel beam alignment. Then, based on the final ballast thickness distribution and the sensitivity matrix, the steel beam deformation caused by ballast load is obtained. The predicted alignment of the bridge track bottom is obtained based on the baseline shape of the steel beam, the final ballast thickness distribution, and the deformation of the steel beam caused by the ballast load. With the objective of minimizing the deviation between the predicted alignment of the completed bridge track bottom and the designed alignment of the completed bridge track bottom, and satisfying the adjustment boundary conditions for the top and bottom ballast, a planning and solution model is established: The optimal ballast thickness distribution that satisfies the overall bridge alignment control objective is obtained by solving the planning solution model. Then, the specific adjustment amount of the bottom and top ballast of each segment is determined based on the optimal ballast thickness distribution.

2. The method for controlling the track alignment during construction of cable-stayed railway bridges according to claim 1, characterized in that: The expression for the actual alignment of the steel beam under measured temperature conditions is as follows: （1）； In the formula, Let n be the set of actual elevations of all linear measuring points on the steel beam, where n is the number of linear measuring points on the steel beam. This represents the actual elevation of the steel beam corresponding to the first linear measuring point. This represents the actual elevation of the steel beam corresponding to the second linear measuring point. This represents the actual elevation of the steel beam corresponding to the nth linear measuring point.

3. The method for controlling the track alignment during construction of cable-stayed railway bridges according to claim 2, characterized in that: The conversion formula between the actual alignment of the steel beam and the baseline alignment of the steel beam is as follows: （2）； In the formula, This is a set of reference elevations for various linear measuring points on the steel beam. This is the set of changes in the steel beam's shape caused by temperature effects, where T is the difference between the design reference temperature and the measured temperature. （3）； In the formula, The reference elevation of the steel beam corresponding to the first linear measuring point. The reference elevation of the steel beam corresponding to the second linear measuring point. This is the reference elevation of the steel beam corresponding to the nth linear measuring point.

4. The method for controlling the track alignment during construction of cable-stayed railway bridges according to claim 1, characterized in that: The sensitivity matrix established based on the finite element model to the influence of unit ballast thickness distribution on the overall bridge steel beam alignment includes: In the finite element model, calculate the influence of the ballast weight per unit thickness of the i-th steel beam segment on the j-th linear measuring point. This will affect the amount The sensitivity matrix is ​​obtained by arranging the matrix. The sensitivity matrix expression is as follows: （4）； In the formula, i = 1, 2, ..., n, j = 1, 2, ..., n, and n represents the number of measuring points for the steel beam alignment and the number of steel beam segments.

5. The method for controlling the track alignment during construction of cable-stayed railway bridges according to claim 4, characterized in that: The final expression for the ballast thickness distribution is: （5）； In the formula, This is a collection of the final ballast thicknesses for each segment. This refers to the final ballast thickness of the first segment. This refers to the final ballast thickness of the first segment. The final ballast thickness for the nth segment; （6）； In the formula, Let the final ballast thickness be the j-th segment. Design the ballast thickness for the j-th segment. The adjustment amount for the bottom ballast of the j-th segment is... This is the adjustment amount for the top surface ballast of the j-th segment.

6. The method for controlling the track alignment during construction of cable-stayed railway bridges according to claim 5, characterized in that: The calculation method for steel beam deformation caused by ballast load based on the final ballast thickness distribution and sensitivity matrix is ​​as follows: （7）； In the formula, This refers to the set of steel beam deformations caused by ballast loads. The deformation of the steel beam at the first linear measuring point caused by ballast load. The deformation of the steel beam at the second linear measuring point caused by the ballast load. The deformation of the steel beam at the nth linear measuring point caused by the ballast load.

7. The method for controlling the track alignment during construction of cable-stayed railway bridges according to claim 6, characterized in that: The calculation method for obtaining the predicted track bottom alignment of the completed bridge based on the steel beam baseline shape, the final ballast thickness distribution, and the steel beam deformation caused by the ballast load is as follows: （8）； In the formula, This is a set of predicted elevations for the bottom of the bridge track.

8. The method for controlling the track alignment during construction of cable-stayed railway bridges according to claim 5, characterized in that: The specific boundary conditions for adjusting the top and bottom ballast are as follows: （9）； （10）； In the formula, Design elevation for rail top. Design elevation for the top surface of ballast.

9. The method for controlling the track alignment during construction of cable-stayed railway bridges according to claim 7, characterized in that: The expression for the planning and solving model is: （11）； In the formula, The design elevation of the bottom of the bridge track is given by the i-th linear measuring point.

10. The method for controlling the track alignment during construction of cable-stayed railway bridges according to claim 7, characterized in that: In determining the specific adjustment amounts of the bottom and top ballast of each segment based on the optimal ballast thickness distribution, the bottom ballast is adjusted first, and the top ballast is adjusted only when the bottom ballast adjustment reaches its upper limit.

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