Design method and application of variable-length pile groups for vibration control along railway lines

Abstract

The present invention belongs to the technical field of railway traffic vibration control and relates to a variable-length pile group design method and application for vibration control along railway traffic. The method comprises the following steps: clarifying the stratum parameters of the vibration control area and determining the geometric position; establishing a three-dimensional vehicle-track coupling analytical model to calculate the standard vibration source intensity load; determining the value range of the parameter that satisfies the requirement of avoiding underground pipelines; establishing a three-dimensional finite element simulation calculation model to calculate the effective value of the vibration acceleration response of the vibration-sensitive building under the action of the load. ； The method uses fitting to obtain the coefficient values in the variable-length pile group structure parameter selection formula; randomly combines each parameter to form multiple candidate design conditions; calculates the effective value of the vibration acceleration response at sensitive buildings under all conditions; and determines the parameters of the variable-length pile group structure to be implemented in the project. This method effectively controls vibrations at sensitive points along the railway caused by railway operations, while avoiding municipal pipelines.

Description

Technical Field

[0001] The invention belongs to the technical field of railway traffic vibration control, and relates to a variable-length pile group design method for vibration control along railway traffic and its application. Background Art

[0002] As railway networks become increasingly dense, lines inevitably pass through areas densely populated with precision instruments, such as universities, research institutes, and high-tech industrial zones. Train vibrations can affect the proper functioning of these instruments. Therefore, effectively and efficiently controlling ground vibrations along lines caused by train operations is of great technological value.

[0003] Currently, there are three main methods for controlling the vibration caused by railway train operation. First, using vibration-damping pads on rails to reduce vibration energy at the source; second, installing isolation trenches and pile structures along the vibration transmission path to block the outward propagation of vibration energy; and third, installing isolation supports at vibration-sensitive targets to reduce the impact of vibration energy. Pile groups, among other methods, offer advantages such as easy construction, low cost, and effective vibration control, and therefore hold great promise for future application.

[0004] However, when rail lines are close to sensitive targets and there are unavoidable municipal pipelines in the ground, traditional equal-length upright pile groups cannot meet on-site construction layout requirements. Variable-length pile groups are needed to avoid the municipal pipelines. Existing pile group design technologies and methods do not yet include a variable-length pile group design method specifically designed for vibration control along railway lines. Summary of the Invention

[0005] The purpose of the present invention is to provide an efficient design method for variable-length pile group structures for vibration-sensitive areas around railway lines with underground pipelines, thereby filling the current research gap in the engineering field for variable-length pile group design methods for vibration control along railway traffic lines, so as to more fully serve the field of controlling environmental vibration caused by railway train operation.

[0006] The technical solution of the present invention is to first clarify the specific locations of railway lines, vibration-sensitive points and underground municipal pipelines, and then set reasonable value ranges for parameters such as pile length increment, pile diameter, and layout position of the variable-length pile group structure based on the specific positional relationship of the three, and provide multiple parameter combination working conditions; then establish a roadbed-pile group-stratum-building finite element analysis model, and at the same time use the vehicle-track coupling analytical model to calculate the vibration source load under the train operation condition, calculate the effective value of vibration acceleration at the vibration-sensitive building position under the action of different variable-length pile group structures, and substitute it into the fitting formula of the vibration reduction effect of the variable-length pile group structure to determine the parameter value, and finally design a large number of feasible variable-length pile group working conditions based on the actual situation on site, use the fitting formula to calculate the effective value of vibration acceleration under each working condition, select the working condition with the smallest effective value of vibration acceleration as the actual engineering layout working condition of the variable-length pile group, and achieve the purpose of optimizing the pile row design parameters. The specific design method is carried out in the following steps:

[0007] S1: Based on actual project requirements, clarify the ground parameters of the vibration control area and determine the geometric locations of railway lines, vibration-sensitive buildings, and underground pipelines;

[0008] S2: Establish a three-dimensional vehicle-track coupling analytical model to calculate the standard vibration source strength load; specifically: use the three-dimensional vehicle-track coupling analytical model to calculate the standard vibration source strength load of railway train operation. The standard source strength load refers to the fastener support reaction force calculated using an EMU train with a train speed of 120 km / h, a train axle weight of 14t, and an 8-car train formation.

[0009] S3: Determine the value ranges of pile length increment parameters, pile group layout position parameters, and pile diameter parameters that meet the requirements of avoiding underground pipelines; specifically, set the maximum length of the pile group structure based on the geometric positions of the railway line, vibration-sensitive buildings, and underground pipelines determined in step S1. L max , and then determine the pile length increment parameter to avoid underground pipelines , pile group layout position parameters , pile diameter parameters The pile group structure is preferably arranged in three rows, and the pile spacing is consistent with the pile diameter parameter.

[0010] S4: Use the orthogonal design method to design and calculate working conditions within the value range of the parameters in step S3, establish a three-dimensional roadbed-stratum-variable length pile group structure-sensitive building finite element simulation calculation model, and calculate the effective value of the vibration acceleration response at the vibration-sensitive building under the load obtained in step S2; specifically: according to the value range of the pile group and pile group structure parameters (pile length increment parameter, pile group layout position parameter, pile diameter parameter) determined in S3, use the orthogonal design method to design at least 10 groups of working conditions, and establish a three-dimensional roadbed-stratum-variable length pile group structure-sensitive building finite element simulation calculation model, and calculate the effective value of the vibration acceleration response at the vibration-sensitive building under the strong load of the standard vibration source calculated in S2 under each working condition a rms,B .

[0011] S5: Using the calculation results of step S4, fitting the coefficient values in the variable length pile group structure parameter selection formula; specifically: using the calculation results of step S4 to calculate the working condition and the effective value of the vibration acceleration response under each working condition a rms,B , according to the formula for selecting the parameters of variable length pile group structure, the coefficients in the formula A 1. A 2. A 3. A 4 Perform fitting calculations to obtain the definite values of each coefficient.

[0012] The formula for selecting the structural parameters of variable-length pile groups is as follows:

[0013] Formula (1)

[0014] Where, a rms,B (Unit: mm / s 2 ) represents the effective value of the vibration acceleration response at the vibration-sensitive building; Δ (unit: m) is the increment of pile length between each row of piles in the pile group structure; is the pile group layout parameter, where d 线桩距 (Unit: m) is the distance from the railway line to the center point of the pile group structure, d 线建距 (Unit: m) is the distance from the railway line to the vibration-sensitive building, d 桩建距 (Unit: m) is the distance from the center of the pile group structure to the vibration-sensitive building. d 线建距 = d 线桩距 + d 桩建距 ; r p (Unit: m) is the diameter of a single pile in the pile group structure;A 1. A 2. A 3. A 4 is the coefficient to be determined in the formula.

[0015] S6: Within the value range of each parameter determined in step S3, refine the design of each parameter, and randomly combine each parameter to form a variety of design working conditions to be selected; specifically: according to actual engineering requirements, within the value range of each parameter determined in step S3, refine the design of pile length increment parameters, pile group layout position parameters and pile diameter parameters that meet the layout requirements, select at least 4 working conditions for each parameter, and then randomly combine different working conditions of the three parameters to form at least 64 design working conditions.

[0016] S7: Calculate the effective value of the vibration acceleration response of the sensitive building under all working conditions in step S6 using the variable length pile group structure parameter selection formula obtained in step S5; Specifically: Substitute the three determined parameters corresponding to each design working condition obtained in step S6 into the fitting formula obtained in step S5 to solve the effective value of the vibration acceleration response of the vibration sensitive building under each working condition a rms,B .

[0017] S8: Select the parameters corresponding to the minimum effective value of the vibration acceleration response calculated in step S7 as the parameters of the variable length pile group structure actually set in the project; specifically: compare the effective values of the vibration acceleration response under all working conditions calculated in step S7 a rms,B And the effective value of vibration acceleration response under all working conditions in step S4 a rms,B , the minimum effective value of vibration acceleration response in all working conditions a rms,B The corresponding parameters can be determined as the parameters of the variable-length pile group structure actually set in the project.

[0018] Combining all the above technical solutions, the advantages and positive effects of the present invention are as follows:

[0019] 1. This invention proposes a design concept, method, and specific process for a variable-length pile group structure. By rationally comparing and selecting parameters, the variable-length pile group structure can control vibrations at sensitive points along the railway caused by railway operations while avoiding municipal pipelines. This significantly improves the design efficiency and control capability of the variable-length pile group structure for vibrations at sensitive points, greatly enhancing its market application potential.

[0020] 2. This paper proposes a parameter selection formula for variable-length pile group structures and establishes the relationship between the effective value of the vibration acceleration response, the pile length increment parameters, the pile group layout location parameters, and the pile diameter parameters of the variable-length pile group structure. This allows the variable-length pile group structure to effectively reduce the impact of railway train-induced vibration on vibration-sensitive buildings along the line by rationally designing the pile length increment parameters, the pile group layout location parameters, and the pile diameter parameters within the permitted range of the project.

[0021] 3. Under the conditions of meeting engineering construction requirements and avoiding underground pipelines, the closer the variable-length pile group structure is to vibration-sensitive buildings, the longer the pile diameter is, and the positive pile length increment parameter is, the more effective it is in controlling the vibration generated by train operation.

[0022] 4. The variable-length pile group design method for railway vibration control in this invention can significantly improve the efficiency of parameter selection for variable-length pile group structure design, providing a new approach and effective means for vibration control in vibration-sensitive areas along railway lines.

[0023] In addition, the following important aspects serve as auxiliary evidence for the inventiveness of the present invention:

[0024] 1. The technical solution of this invention, once implemented, can significantly reduce the design and construction costs and time associated with line rerouting due to excessive vibration from vibration-sensitive buildings. It can also reduce secondary investment in protecting existing vibration-sensitive buildings, resulting in significant economic benefits. Furthermore, the variable-length pile group structural parameter selection formula proposed in this invention provides a scientific approach for variable-length pile group design, saving time and material costs while ensuring effective vibration control.

[0025] 2. This invention fills the research gap in the engineering field regarding the design method of variable-length pile groups for vibration control along railway lines. It studies the length increment, layout position, and pile diameter parameters of the pile group structure, and proposes a calculation formula for the parameter selection of the variable-length pile group structure to ensure vibration reduction effects.

[0026] 3. The technical solution of the present invention solves the problem of difficulty in controlling vibration of vibration-sensitive buildings by setting up pile groups when there are unavoidable underground pipelines. The variable-length pile groups can avoid underground pipelines while also reducing the impact of vibration caused by train operation on the surrounding environment, thus solving a technical problem that people have long been eager to solve but have never been able to successfully solve. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present disclosure and, together with the description, serve to explain the principles of the present disclosure;

[0028] Figure 1 It is a diagram of the three-dimensional vehicle-track coupling analytical model in the present invention;

[0029] Figure 2 It is a schematic diagram of various parameters required for designing the variable length pile group involved in the present invention;

[0030] Figure 3 This is a time history curve of a standard vibration source intensity load calculated using a three-dimensional vehicle-track coupling analytical model, provided by an embodiment of the present invention;

[0031] Figure 4 This is a schematic diagram of a three-dimensional finite element analysis model of roadbed-soil-variable-length pile group structure-stratum-building provided by an embodiment of the present invention;

[0032] Figure 5 The present invention is a flow chart of a variable-length pile group design method for vibration control along railway lines. DETAILED DESCRIPTION

[0033] To make the above-mentioned objects, features, and advantages of the present invention more readily apparent, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings. The following description sets forth numerous specific details to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways than those described herein, and those skilled in the art may make similar modifications without departing from the scope of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0034] One of the key points of the present invention is to set reasonable value ranges for parameters such as pile length increment, pile diameter, and layout position of the variable-length pile group structure based on the actual conditions at the engineering site, and to determine no less than 10 calculation conditions using the orthogonal analysis method; a second key point is to use finite element analysis software to establish a calculation model to solve the effective value of vibration acceleration at the vibration-sensitive building under each working condition, and to use the calculation results to obtain the values of each coefficient in the variable-length pile group structure parameter comparison formula in step S5 through a fitting method; a third key point is to design as many variable-length pile group structure working conditions as possible within the range of satisfying engineering layout conditions, use the obtained variable-length pile group structure parameter comparison formula to calculate the actual effects of various working conditions, and compare and select the optimal layout scheme of the variable-length pile group structure. Example 1

[0035] The specific implementation of the variable-length pile group design method for vibration control along railway lines is as follows:

[0036] 1. A historical site (an ancient pagoda) is located 42 meters from a new high-speed rail line. The geological parameters are shown in Table 1. Multiple municipal pipelines and optical cables lie within the stratum between the railway line and the pagoda, making it difficult to deploy a pile group with uniform lengths.

[0037] Table 1 Formation parameters

[0038] Serial number Soil type Ground floor elevation / m Thickness / m <![CDATA[Shear wave velocity / (m·s -1 )]]> <![CDATA[Density / (kg·m -3 )]]> Poisson's ratio Dynamic elastic modulus / MPa 1 Backfill 5.0 5.0 140 1650 0.32 114.0 2 silt 39.7 34.7 320 2130 0.38 325.0

[0039] 2. Utilize Figure 1 The three-dimensional vehicle-track coupling analytical model shown calculates the standard vibration source strength load of a railway train running. The train has 8 carriages, an axle load of 14 tons, and an operating speed of 120 km / h. Figure 1 In the vehicle part of the three-dimensional vehicle-track coupling analytical model, the multi-rigid body theory is used to simplify the single-section vehicle into a model with one body, two bogies and four wheel sets. The different components are connected with spring damping units. In the track part, the rail is simplified into an Euler beam model. The sleepers and roadbed are simulated with mass blocks. The various parts are connected with spring damping units. The calculated standard vibration source strength load is as follows: Figure 3 shown.

[0040] 3. Based on the locations of railway lines, ancient towers, underground pipelines, etc. determined in step 1, determine the length of a single pile according to the actual conditions on site. L max Cannot exceed 20m, the pile group structure meets the construction conditions of 3 rows, the pile length increment parameter of underground pipeline The pile group layout parameters must be within the range of -3m~-6m and +3m~+6m. The values can be 0.1, 0.25, 0.5 and 0.75, and the pile diameter parameter The value range is 1m~2m.

[0041] 4. Within the range of the variable length pile group structure parameters determined in step 3, the orthogonal analysis method was used to design 10 calculation and analysis conditions as shown in Table 2. Subsequently, a three-dimensional finite element analysis model of the roadbed-soil-variable length pile group structure-stratum-building was established in the Midas GTS-NX software for these ten analysis conditions. The standard vibration source load obtained in step 2 was applied to the roadbed part of the finite element analysis model, and the effective value of the vibration acceleration at the vibration-sensitive building under each condition was calculated. It should be noted that when the length of a single pile is L max After determination, if the pile length increment parameter Δ is a negative number, the length of a single pile in the row of piles closest to the railway line is the longest; if the pile length increment parameter Δ is a positive number, the length of a single pile in the row of piles closest to the vibration-sensitive building is the longest. Figure 4 A schematic diagram of a three-dimensional finite element analysis model of roadbed-soil-variable length pile group structure-stratum-building is given with the incremental parameter Δ being a negative number.

[0042] Table 2 Working condition design table

[0043]

[0044] 5. Use the 10 working conditions calculated in step 4 and the a rms,B According to the following formula for selecting the parameters of variable length pile group structures, the coefficients in the formula A 1. A 2. A 3. A 4 Perform fitting calculations to obtain the definite values of each coefficient.

[0045] Formula (1)

[0046] Where, a rms,B (Unit: m / s 2 ) represents the effective value of the vibration acceleration response at the vibration-sensitive building; Δ (unit: m) is the increment of pile length between each row of piles in the pile group structure; is the pile group layout parameter, where d 线桩距 (Unit: m) is the distance from the railway line to the center point of the pile group structure, d 线建距 (Unit: m) is the distance from the railway line to the vibration-sensitive building, d 桩建距 (Unit: m) is the distance from the center of the pile group structure to the vibration-sensitive building. d 线建距 = d 线桩距 + d 桩建距 ; r p (Unit: m) is the diameter of a single pile in the pile group structure; A 1. A 2. A 3. A 4 is the coefficient to be determined in the formula.

[0047] Finally obtained A 1=2.93, A 2=-0.021, A 3=-0.34, A 4=-0.49.

[0048] In this project, the formula for selecting the structural parameters of variable-length pile groups is:

[0049] Formula (2)

[0050] 6. Within the parameter ranges determined in Step 3, refine the design of the pile length increment parameters, pile group location parameters, and pile diameter parameters. Take the pile length increment parameters as -4m, -6m, 4m, and 6m, the pile group location parameters as 0.1, 0.25, 0.5, and 0.75, and the pile diameter parameters as 1m, 1.2m, 1.6m, and 2m. Randomly combine these three parameters to form the 64 calculation conditions shown in Table 3.

[0051] Table 3 Random combination working conditions

[0052]

[0053] 7. Substitute the parameters corresponding to all calculation conditions in step 6 into the variable length pile group structure parameter selection formula in step 5 to calculate the effective value of the vibration acceleration response for each condition. a rms,B , the calculation results are shown in Table 4.

[0054] Table 4 Random combination operating conditions

[0055]

[0056] 8. The effective value of the vibration acceleration response at the vibration-sensitive building under all working conditions in steps 4 and 7 a rms,B Compare and determine the working condition 48 in step 7 a rms,B =0.2547mm / s 2 is the minimum value of all effective values of vibration acceleration responses, and the corresponding parameters in working condition 48 are determined to be the final parameters of the variable-length pile group structure actually designed in this project.

[0057] Application Example 1:

[0058] The method for identifying the excitation force of an active device under a railway vehicle provided in the above embodiment can also be run on a computer device, which includes: at least one processor, a memory, and a computer program stored in the memory and runnable on the at least one processor. When the processor executes the computer program, the method in the above embodiment is implemented.

[0059] Application Example 2:

[0060] The method for identifying the excitation force of an active device under a railway vehicle provided in the above embodiment can also be run on a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the method in the above embodiment can be implemented.

[0061] Application Example 3:

[0062] The method for identifying the excitation force of active equipment under a railway vehicle provided in the above embodiment can also be run on an information data processing terminal. When the information data processing terminal is implemented on an electronic device, it provides a user input interface to implement the method in the above embodiment. The information data processing terminal is not limited to mobile phones, computers, and switches.

[0063] Application Example 4:

[0064] The method for identifying the excitation force of an active device under a railway vehicle provided in the above embodiment can also be run on a server. When the server is implemented on an electronic device, it provides a user input interface to implement the method in the above embodiment.

[0065] Application Example 5:

[0066] The method for identifying the excitation force of an active device under a railway vehicle provided in the above embodiment can also be run on a computer program product. When the computer program product runs on an electronic device, the method in the above embodiment can be implemented when the electronic device executes it.

[0067] The present invention can implement all or part of the steps in the above-described method embodiments by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium. When executed by a processor, the computer program can implement the steps of each of the above-described method embodiments. The computer program includes computer program code, which can be in source code form, object code form, an executable file, or some intermediate form. The computer-readable medium can include at least any entity or device capable of carrying the computer program code to a camera / terminal device, a recording medium, computer memory, read-only memory (ROM), random access memory (RAM), an electrical carrier signal, a telecommunications signal, and a software distribution medium. Examples include a USB flash drive, a removable hard drive, a magnetic disk, or an optical disk.

[0068] The above description is only a preferred embodiment of the present invention. It should be understood that the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative work are within the scope of protection of the present invention. The present invention is not limited to the form disclosed herein and should not be regarded as excluding other embodiments, but can be used in various other combinations, modifications and environments. Changes and modifications made by those skilled in the art do not depart from the spirit and scope of the present invention and should be within the scope of protection of the claims appended to the present invention.

Claims

1. A variable-length pile group design method for vibration control along railway lines, characterized by: The following steps are involved: S1: Define the ground parameters of the vibration control area and determine the geometric locations of railway lines, vibration-sensitive buildings, and underground pipelines; S2: Establish a three-dimensional vehicle-track coupling analytical model to calculate the standard vibration source load; S3: Determine the value ranges of pile length increment parameters, pile group layout position parameters, and pile diameter parameters that meet the requirements of avoiding underground pipelines; S4: Use the orthogonal design method to design the calculation conditions within the range of the parameters in step S3, establish a three-dimensional roadbed-stratum-variable length pile group structure-sensitive building finite element simulation calculation model, and calculate the effective value of the vibration acceleration response at the vibration-sensitive building under the load obtained in step S2 ； S5: Using the calculation results of step S4, the coefficient values in the variable length pile group structure parameter selection formula are fitted. The variable length pile group structure parameter selection formula is as follows: Formula (1) Where, a rms,B Indicates the effective value of the vibration acceleration response at a vibration-sensitive building, unit: mm / s 2 ; Δ is the pile length increment between each row of piles in the pile group structure, unit: m; Set location parameters for pile groups; r p is the diameter of a single pile in the pile group structure, unit: m; A 1. A 2. A 3. A 4 is the coefficient to be determined in the formula; S6: Within the value range of each parameter determined in step S3, refine the design parameters and randomly combine different parameters to form multiple candidate design conditions; S7: Calculate the effective value of the vibration acceleration response at the sensitive building under all working conditions in step S6 using the variable-length pile group structural parameter selection formula obtained in step S5; S8: Select the parameters corresponding to the minimum vibration acceleration response effective value working condition calculated in step S7 as the parameters of the variable-length pile group structure actually designed in the project.

2. The variable-length pile group design method for vibration control along railway lines according to claim 1 is characterized by: In step S3, the maximum length of the pile group structure is set according to the geometric positions of the railway line, vibration-sensitive buildings and underground pipelines determined in step S1. L max Then determine the pile length increment parameter Δ and pile group layout position parameter to avoid underground pipelines. , pile diameter parameters The value range of .

3. The variable-length pile group design method for vibration control along railway lines according to claim 2 is characterized by: The pile group structure is arranged in three rows, and the pile spacing is consistent with the pile diameter parameters.

4. The variable-length pile group design method for vibration control along railway lines according to claim 1 is characterized by: In step S4, at least 10 working conditions are designed using the orthogonal design method within the range of pile group structure parameters determined in step S3, and a three-dimensional roadbed-stratum-variable length pile group structure-sensitive building finite element simulation calculation model is established. The effective value of the vibration acceleration response at the vibration-sensitive building under the strong load of the standard vibration source calculated in step S2 is calculated for each working condition. a rms,B .

5. The variable-length pile group design method for vibration control along railway lines according to claim 1 is characterized by: In the variable length pile group structure parameter selection formula, is the pile group layout parameter, where d 线桩距 is the distance from the railway line to the center point of the pile group structure, unit: m; d 线建距 is the distance from the railway line to the vibration-sensitive building, unit: m; d 桩建距 is the distance from the center point of the pile group structure to the vibration-sensitive building, unit: m; d 线建距 = d 线桩距 + d 桩建距 。 6. The variable-length pile group design method for vibration control along railway lines according to claim 5 is characterized by: In step S5, the working conditions and the effective value of the vibration acceleration response under each working condition calculated in step S4 are used. a rms,B , according to the formula for selecting the parameters of variable length pile group structure, the coefficients in the formula A 1. A 2. A 3. A 4 Perform fitting calculations to obtain the definite values of each coefficient.

7. The variable-length pile group design method for vibration control along railway lines according to claim 1 is characterized by: In step S6, based on the actual engineering requirements, within the value range of each parameter determined in step S3, the pile length increment parameters, pile group layout position parameters, and pile diameter parameters that meet the layout requirements are refined and designed. At least four working conditions are selected for each parameter, and then the different working conditions of the three parameters are randomly combined to form at least 64 design working conditions.

8. The variable-length pile group design method for vibration control along railway lines according to claim 1 is characterized by: In step S7, the three corresponding parameters obtained in step S6 for each design condition are substituted into the fitting formula obtained in step S5 to solve the effective value of the vibration acceleration response of the vibration sensitive building under each condition. a rms,B .

9. The variable-length pile group design method for vibration control along railway lines according to claim 1 is characterized by: In step S8, the effective values of the vibration acceleration responses under all working conditions calculated in step S7 are compared and selected. a rms,B And the effective value of vibration acceleration response under all working conditions in step S4 a rms,B , the minimum effective value of vibration acceleration response in all working conditions a rms,B The corresponding parameters can be determined as the parameters of the variable-length pile group structure actually set in the project.

10. A computer device, characterized in that: The computer device includes a memory and a processor, the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the variable-length pile group design method for vibration control along railway traffic as described in any one of claims 1 to 9.

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