Method for predicting vibration response of far-field buildings and structures caused by subway train operation

Abstract

The invention provides a method for predicting the vibration response of a far-field building structure caused by subway train operation, and the method comprises the steps: decomposing a subway train-rail-tunnel-stratum-building structure coupling system into a target subsystem and a remaining system, and obtaining a target interface between the target subsystem and the remaining system; the incomplete stratum in the remaining system is recovered to a free site layer not containing the building structure; performing dynamic calculation on the constructed hypothetical free field system to obtain displacement, speed and stress response caused by the subway train operation induced free wave field on the target interface; introducing a viscoelastic artificial boundary at the target interface, and constructing a three-dimensional finite element model; calculating an equivalent excitation load of vibration response caused by the subway train by using free wave field displacement, speed and stress response in combination with viscoelastic artificial boundary parameters; and applying the equivalent excitation load to a viscoelastic artificial boundary of the three-dimensional dynamic finite element model so as to predict the vibration response of the far-field building structure caused by subway train operation.

Description

Technical Field

[0001] The present application relates to the technical field of subway environmental vibration impact prediction, and in particular to a method for predicting vibration response of far-field buildings induced by subway train operation. Background Art

[0002] During the operation of subway trains, it is inevitable that they will induce vibration responses in the surrounding environment, which will have an adverse impact on the normal life of residents in surrounding sensitive buildings or the normal use of precision instruments. In order to quantify the degree of influence of subway vibration environment, chain empirical formulas or numerical simulations are usually used to predict and evaluate the vibration responses caused by running subway trains, so as to guide the corresponding seismic isolation design.

[0003] The chain empirical formula is an empirical formula based on known physical relationships and a large amount of experimental data, and is usually used to quickly estimate the propagation and attenuation characteristics of subway vibration. Although the chain empirical formula takes into account the influence of factors such as train speed, train type, wheel-rail conditions, tunnel type, distance, building type, and traffic density on subway vibration characteristics, the prediction accuracy of the formula is highly dependent on the rationality of the values ​​of the relevant empirical parameters of each vibration correction term. On the other hand, since the environmental vibration generated by subway operation is a very complex process, it is difficult to select each empirical coefficient in the chain empirical formula to reflect the actual situation well. The prediction accuracy of this method is usually lacking, especially for the prediction of the vibration response of far-field buildings and structures. The disadvantage of the lack of prediction accuracy of this method is likely to be magnified, making it even less suitable for predicting the vibration response of far-field buildings and structures caused by subway operation. More importantly, the chain empirical formula cannot predict the frequency-divided vibration of sensitive buildings and structures, which greatly restricts the use of this formula to carry out detailed vibration reduction and isolation design work for buildings and structures around subway lines.

[0004] Compared with the chain empirical formula, the numerical simulation method shows significant advantages in predicting the vibration impact caused by running subway trains. It can not only give a good frequency-divided vibration response, but also ensure a relatively higher prediction accuracy because it can simulate the actual situation more realistically. At present, the three-dimensional dynamic numerical simulation method based on the finite element method (FEM) has also been widely used in the prediction of the vibration impact caused by running subway trains, and has achieved good results. However, the traditional three-dimensional dynamic numerical simulation method is used to predict the vibration response of far-field structures far away from the subway line induced by running subway trains. It is necessary to include the subway tunnel, the target structure and the vast stratum range between them into the modeling scope. Therefore, it is necessary to build a numerical model with a large number of degrees of freedom, which leads to a large workload of numerical calculation, low calculation efficiency, and even uncalculated situations.

[0005] In summary, the existing methods, including chain empirical formulas and traditional numerical simulations, are still difficult to efficiently, accurately, and comprehensively predict and evaluate the vibration response of far-field structures caused by subway train operation, and have a great adverse impact on the rational implementation of vibration reduction and isolation design of far-field structures along the subway line. Therefore, under this background, it is urgent to develop an effective and accurate prediction method for the vibration response of far-field structures caused by subway train operation. Summary of the invention

[0006] The purpose of the embodiments of the present application is to provide a method for predicting the vibration response of far-field buildings induced by subway train operations, so as to improve the problem of difficulty in balancing prediction accuracy and computability when predicting the vibration impact of far-field buildings induced by subway trains.

[0007] The embodiment of the present application provides a method for predicting the vibration response of far-field structures caused by subway train operation, comprising: decomposing the subway train-track-tunnel-stratum-structure coupling system involved in the problem into a target subsystem and a remaining system according to preset rules, and obtaining multiple interfaces between the target subsystem and the remaining system, recorded as target interfaces, wherein the target subsystem includes structures and the stratum within a certain range around the structures, and the remaining system is composed of all parts of the coupling system except the target subsystem, and the system decomposition should make the interface between the target subsystem and the remaining system consist of four rectangular sides and one rectangular bottom surface with regular shapes and normals along the vertical direction, the longitudinal direction of the line or the horizontal direction perpendicular to the line; in order to promote rapid and accurate analysis of the problem, the incomplete stratum formed by the remaining system of "real coupling system removing the target subsystem" is restored to a free field stratum without structures, and the original target interface is retained to construct a hypothetical free field system corresponding to the remaining system for auxiliary analysis, that is, the free field system will be composed of the same subway train, track, tunnel, ground as the remaining system. The target subsystem is discretized and modeled, and a viscoelastic artificial boundary is introduced at the boundary of the target subsystem, i.e., the target interface, to construct a three-dimensional finite element model for dynamic analysis of the target subsystem. Then, referring to the wave method of seismic wave input in seismic response analysis, the displacement, velocity and stress response of the free wave field on the target interface induced by subway train operation obtained by the 2.5-dimensional dynamic analysis of the hypothetical free field system are used, and the introduced viscoelastic artificial boundary parameters are combined to calculate the equivalent excitation load of the vibration response of the target subsystem induced by subway train operation. The obtained equivalent excitation load is applied to the viscoelastic artificial boundary of the three-dimensional dynamic finite element model of the target subsystem, and the subway vibration wave is input to the target subsystem in the form of a wave source at the artificial boundary, and then a three-dimensional dynamic finite element analysis is carried out, and finally an accurate numerical prediction of the vibration response of far-field structures induced by subway train operation is achieved.

[0008] In an embodiment of the present application, the above-mentioned coupling system may include subway trains, tracks, tunnels, strata, and buildings in some scenarios. For example, the vibration waves generated by the running subway can be transmitted to far-field buildings through tracks, tunnels and strata, thereby triggering vibration responses of the buildings; the above-mentioned buildings are buildings that are far away from the operating subway line (usually greater than 40m), and the buildings can be ground structures, underground structures, or ground structures containing basements; the above-mentioned strata are or can be approximately regarded as single or layered strata with longitudinal consistency before and after the construction of the structures; the above-mentioned tracks and subway tunnels are horizontal or approximately horizontal straight tracks or straight tunnels with or approximately longitudinal consistency.

[0009] In the embodiments of the present application, when using traditional numerical methods to analyze the vibration response of far-field structures caused by subway train operations, it is necessary to construct a three-dimensional dynamic coupling numerical model of the track-tunnel-stratum-structure system on the basis of properly handling the problem of excitation load input generated by the subway train. For the vibration prediction problem of far-field structures, since the structures are far away from the vibration source subway train, the grid and degree of freedom of the corresponding three-dimensional dynamic coupling numerical model will be extremely large, the calculation workload is large, the calculation efficiency is low, and even the situation that the calculation cannot be performed may occur. Therefore, the subway train-track-tunnel-stratum-structure coupling system involved in the problem is decomposed into two subsystems, the target subsystem and the remaining system, according to preset rules, and studied separately, so as to lay the foundation for effectively reducing the calculation and analysis workload of the problem in the later stage and promoting the calculation and analysis of the problem. Among them, the target subsystem formed by decomposition includes buildings and strata within a preset range around the buildings, and the remaining system formed by decomposition is a system composed of all parts of the coupling system except the target subsystem, and the decomposition of the entire coupling system should make the multiple interfaces between the target subsystem and the remaining system include 4 side surfaces and 1 bottom surface, and each interface is a rectangle with a regular shape and a normal along the longitudinal direction of the line or perpendicular to the horizontal direction of the line.

[0010] In the embodiment of the present application, after the subway train-track-tunnel-stratum-building coupling system involved in the problem is decomposed into two subsystems, the target subsystem and the remaining system, according to certain preset rules, it also includes: obtaining multiple interfaces between the target subsystem and the remaining system, recorded as target interfaces, and solving the problem through the following two steps: ① By studying the remaining system, solving the incident wave field of the vibration wave generated by the subway operation transmitted to the target interface according to the remaining system (in this application, "incident wave" or "incident wave field" refers to the system within the encirclement range of the target interface, that is, the incident wave field The first step is to obtain the displacement, velocity and stress response of the target interface caused by the incident wave field (vibration wave or vibration wave field of the system within the range surrounded by the target interface), and apply the incident wave field response (displacement, velocity and stress response) on the target interface obtained in the first step to the target subsystem, and then perform dynamic analysis on the basis of properly handling the reflection problem of the outgoing wave formed by the reflection, refraction and scattering of the stratum interface, ground surface, soil-structure interface, etc. at the target interface in the target subsystem, so as to solve the vibration response of the target structure induced by the running subway train, which is the second step. Since such a step-by-step problem solving strategy does not change the propagation characteristics of the vibration wave induced by the subway train in the target subsystem, it can accurately solve the vibration response of the target structure in the target subsystem caused by the subway train.

[0011] In order to solve the vibration response of the above-mentioned target structures induced by the running subway train, a three-dimensional dynamic finite element model of the target subsystem including a viscoelastic artificial boundary can be constructed, and an equivalent excitation load corresponding to the subway vibration incident wave field obtained by studying the remaining system is applied on the target interface at the artificial boundary of the three-dimensional dynamic finite element model, thereby realizing the three-dimensional dynamic finite element analysis of the target subsystem and the solution of the vibration response of the target structure induced by the running subway train.

[0012] In the implementation process of the above scheme, the viscoelastic artificial boundary is essentially to set up a parallel spring-damper system in three orthogonal directions on the artificial boundary node of the three-dimensional dynamic finite element model. The above spring-damper system includes a spring and a damper, wherein the spring and the damper have parameters such as a spring stiffness coefficient and a damper damping coefficient, respectively. The calculation formulas of these parameters are as follows:

[0013] K bT =α T GA / R,C bT =ρC S A,K bN =α N GA / R,C bN =ρC P A (8)

[0014] Among them, K bT , K bN are the stiffness coefficients of the tangential spring and normal spring at the corresponding boundaries; C bT , C bN are the damping coefficients of the tangential damper and the normal damper at the corresponding boundaries respectively; α T , α N is the correction coefficient of the viscoelastic artificial boundary; R is the vertical distance from the traveling wave source outside the target subsystem (which can be approximately taken as the centroid position of the initial surface before the construction of the target subsystem) to the corresponding viscoelastic artificial boundary; ρ and G are the density and shear modulus of the medium respectively; C S and C P are the shear wave velocity and compression wave velocity of the medium respectively; A is the boundary area represented by the boundary node.

[0015] The equivalent excitation load caused by the real incident wave field at any node on the target subsystem target interface can be calculated as follows:

[0016]

[0017] Wherein, the subscript “b” indicates that the variable is the physical quantity at the target interface (the same below), the superscript “I” indicates the incident wave (the same below), and F b is the corresponding equivalent excitation load, It is the additional node force vector required to make the artificial boundary spring element produce the incident wave field displacement; It is the additional nodal force vector required to make the artificial boundary damper unit generate the incident wave field velocity; is the boundary node force vector induced by the stress tensor in the boundary area represented by the viscoelastic artificial boundary node caused by the incident wave field; are the displacement vector, velocity vector and stress vector of the boundary node of the target subsystem induced by the incident wave in three orthogonal directions; A is the boundary area represented by the boundary node; n is the normal direction vector outside the viscoelastic artificial boundary; K b , C b are the node spring stiffness coefficient matrix and the damper damping coefficient matrix on the viscoelastic artificial boundary, which are the spring and damper parameters K in different directions on the node. bT With K bN and C bT With C bN A diagonal matrix with equal elements arranged in a certain order according to the direction of the outer normal of the boundary surface.

[0018] In the embodiment of the present application, the incident wavefield displacement, velocity and stress response on the target interface in the hypothetical free field system corresponding to the remaining system for auxiliary analysis are used to replace the corresponding incident wavefield response on the target interface of the above-mentioned real target subsystem to solve the equivalent excitation load on the viscoelastic artificial boundary of the three-dimensional dynamic finite element model of the target subsystem. The above-mentioned remaining system is all parts of the coupling system except the target subsystem, so the remaining system will have a rectangular blank part surrounded by 5 regular rectangular target interfaces, which causes the track-tunnel-stratum in the remaining system to no longer be approximately regarded as a longitudinal consistency system. In addition, the range of the soil in the blank part is relatively small, and there is still a large range of strata in the remaining system. Therefore, in order to obtain the incident wavefield response on the target interface through its dynamic analysis, it is still necessary to construct a complex three-dimensional numerical model with a large number of degrees of freedom, and carry out dynamic response analysis to obtain it, which undoubtedly also has the disadvantages of low calculation efficiency, large calculation workload, and even inability to carry out calculation. However, it can be noted that if the remaining part of the above-mentioned remaining system is restored to the situation before the construction of the building, that is, if an imaginary fill with the same stratum as the initial stratum is added to the remaining part, thereby constructing a free field system composed of the same subway train, track, tunnel and stratum as the remaining system and the added imaginary fill, it can be ensured that the subway train induces the incident wave field on the target interface in the imaginary free field system. (The “-” on the variable symbol indicates that the physical quantity is the quantity in the hypothetical free field system, the same below) is equivalent to the incident wave field on the target interface in the corresponding residual system (It should be noted that the wave field is a general term for all dynamic responses of the system such as displacement, velocity, acceleration, strain, stress, etc. during the propagation of vibration waves. In this application, for the sake of simplicity, the wave field is represented by the displacement field symbol, but the wave field should still be understood as a general term for all corresponding dynamic responses). That is, the incident wave field displacement, velocity and stress response induced by the subway train on the target interface in the two systems are the same, satisfying the relationship: This is because before reaching the target interface, the propagation path and medium of the subway vibration wave radiated by the subway tunnel in the hypothetical free field system and the remaining system are exactly the same. Therefore, the incident wave field displacement, velocity and stress response on the target interface in the hypothetical free field system can be used to replace the relevant physical quantities in the remaining system to solve the equivalent excitation load on the viscoelastic artificial boundary of the three-dimensional dynamic finite element model of the target subsystem. Therefore, the equivalent excitation load can be further expressed as:

[0019]

[0020] In the embodiment of the present application, the corresponding response of the incident wave field on the target interface in the hypothetical free field system is replaced by solving the free wave field displacement, velocity and stress response on the target interface in the hypothetical free field system, and then substituting into equation (3) to specifically implement the solution of the equivalent excitation load caused by the subway vibration incident wave field on the artificial boundary of the target subsystem. The vibration wave generated by the subway train radiates from the subway tunnel into the free field layer in the hypothetical free field system and then propagates freely in the layer. When the vibration wave first propagates to the target interface and continues to propagate within the hypothetical fill range, an incident wave field is formed within the hypothetical fill range. (The superscript "I" indicates the incident wave, the same below). Subsequently, the incident wave field is reflected and refracted by the interface between the surface and the stratum within the imaginary fill range, and will again generate an external radiation wave field that propagates from the imaginary fill range to the outside of the target interface. (The superscript "R" indicates the outward radiation wave, the same below). Obviously, the incident wave field Radiation wave field In the hypothetical fill range, a free wave field will be formed by superposition. (The superscript "F" indicates free wave field, the same below), and the dynamic response of any position within the assumed fill range will be determined by the incident wave field Radiation wave field Free wave field Decide that: On the other hand, when numerically solving a hypothetical free-field system, the response at the target interface is usually a free-wave field response. (The subscript "b" indicates that the variable is the wave field at the target interface, the same below), and the incident wave field at the target interface From free wavefield alone (total wavefield) Therefore, it is necessary to further explore the free wave field response at the target interface based on the hypothetical free field system. The method for solving the required equivalent excitation load. It is noted that the viscoelastic artificial boundary has the characteristic of absorbing the outward radiation wave field of the calculation area well. Therefore, it is assumed that at the boundary of the imaginary fill range, that is, at the target interface, the imaginary fill has a viscoelastic artificial boundary that is exactly the same as the three-dimensional dynamic finite element model of the target subsystem. Then the outward radiation wave field in the imaginary fill range propagates toward the outside of the target interface It will also be well absorbed by the viscoelastic artificial boundary, which means that the external radiation wave field at the target interface of the hypothetical free field system Replace the incident wavefield Substituting into equation (3), the equivalent excitation force of the outward radiation wave field at the viscoelastic artificial boundary is approximately equal to 0, as shown in the following equation:

[0021]

[0022] The “≈” in the formula is because the viscoelastic artificial boundaries are usually not completely accurate, and in theory they often cannot completely avoid the reflection of the outgoing wave at the artificial truncation boundary.

[0023] In summary, it is not difficult to find that when solving the equivalent excitation load caused by the real incident wave field on the target interface of the target subsystem, it can be solved by solving the free wave field on the target interface of the hypothetical free field system. The corresponding displacement, velocity and stress response replaces the incident wave field on the target interface in the hypothetical free field system Substitute the corresponding response into equation (3) to solve it. This is because:

[0024]

[0025] Replace them and Substituting into equation (3), and combining equation (4) and equation (5), we have:

[0026]

[0027] That is, the required equivalent excitation force can be calculated as follows:

[0028]

[0029] Among them, the subscript "b" indicates that the variable is a physical quantity at the target interface, the superscript "I" indicates the incident wave, the superscript "R" indicates the outgoing radiated wave, and the superscript "F" indicates the free wave; F b is the equivalent excitation load caused by the corresponding wave field (incident wave field, external radiation wave field or free wave field), It is the additional node force vector required to make the artificial boundary spring unit generate the displacement of the corresponding wave field (incident wave field, outward radiation wave field or free wave field); It is the additional node force vector required to make the artificial boundary damper unit generate the corresponding wave field (incident wave field, outward radiation wave field or free wave field) velocity; u is the boundary node force vector induced by the stress tensor in the boundary area represented by the viscoelastic artificial boundary node caused by the corresponding wave field (incident wave field, external radiation wave field or free wave field); b , σ b are the displacement vector, velocity vector and stress vector of the boundary node of the target subsystem induced by the corresponding wave (incident wave, outward radiation wave or free wave) in three orthogonal directions; A is the boundary area represented by the boundary node; n is the normal direction vector outside the viscoelastic artificial boundary; K b , C b are the node spring stiffness coefficient matrix and the damping coefficient matrix of the damper on the viscoelastic artificial boundary, respectively.b , C b They are the spring and damper parameters K in different directions at the nodes. bT With K bN and C bT With C bN It is a diagonal matrix formed by arranging the elements in a certain order according to the direction of the outer normal of the boundary surface.

[0030] In the embodiment of the present application, a 2.5-dimensional method is applied to calculate the free wave field displacement, velocity and stress response on the target interface caused by the subway train in the hypothetical free field system, so as to realize the efficient and accurate calculation of the free wave field displacement, velocity and stress response on the target interface in the hypothetical free field system. Since the track, subway tunnel and the strata before the construction of the target structure can be regarded as or approximately regarded as having longitudinal consistency, the hypothetical free field system formed by the hypothetical restoration of the fill of the remaining system can also be regarded as or approximately regarded as having longitudinal consistency. Furthermore, on the basis of using multi-rigid body dynamics theory to describe the dynamic behavior of the subway train, a 2.5-dimensional method can be used to model the track, tunnel and strata in the free field system, and a 2.5-dimensional dynamic analysis model of the running subway train-track-tunnel-free field layer can be constructed to greatly reduce the model's degree of freedom while ensuring the calculation accuracy, and improve the analysis and calculation efficiency and calculation feasibility of the problem.

[0031] In the process of implementing the above scheme, the viscoelastic artificial boundary can eliminate the outgoing waves that are reflected, refracted or scattered from the target interface through the stratum interface or the structural surface of the building and then propagate outward through the target interface again. By applying the equivalent excitation load to the above model, we can focus on the response of the target subsystem without the need to perform a full-scale simulation of the entire coupled system, thereby saving computing resources. In addition, the introduction of viscoelastic artificial boundaries in the three-dimensional dynamic finite element model allows the behavior of an infinite domain to be simulated within a limited computational domain, taking into account computational efficiency and resource limitations, thereby improving the problem of traditional methods that are difficult to balance prediction accuracy and computability. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments of the present application will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0033] Figure 1 The decomposition schematic diagram of the coupling system-remaining system+target subsystem provided in the embodiment of the present application is shown;

[0034] Figure 2 A schematic diagram of a three-dimensional finite element dynamic model of a target subsystem provided in an embodiment of the present application is shown;

[0035] Figure 3 The schematic diagram of the steps of applying the equivalent excitation load of the three-dimensional finite element dynamic model of the target subsystem provided by the embodiment of the present application and the vibration response of the building structure is shown;

[0036] Figure 4 A schematic diagram of incident wave field response in a free field system provided in an embodiment of the present application is shown;

[0037] Figure 5 A schematic diagram showing a free wave field response in a free field system provided in an embodiment of the present application is shown;

[0038] Figure 6 A schematic diagram showing that the equivalent excitation loads caused by the incident wavefield response on the target interface in the target subsystem provided by the embodiment of the present application, the incident wavefield response on the target interface in the free field system, and the free wavefield response are equal;

[0039] Figure 7 A schematic diagram of a 2.5-dimensional model of a free-field system provided in an embodiment of the present application is shown;

[0040] Figure 8 The flowchart of the method for predicting the vibration response of far-field structures induced by subway train operation is shown. DETAILED DESCRIPTION

[0041] To make the purpose, technical scheme and advantages of the embodiment of the present application clearer, the technical scheme in the embodiment of the present application will be clearly and completely described below in conjunction with the drawings in the embodiment of the present application. It should be understood that the drawings in the embodiment of the present application only serve the purpose of explanation and description, and are not used to limit the protection scope of the embodiment of the present application. In addition, it should be understood that the schematic drawings are not drawn in real proportion. The flowchart used in the embodiment of the present application shows the operation implemented according to some embodiments of the embodiment of the present application. It should be understood that the operation of the flowchart can be implemented out of order, and the steps without logical context can be reversed in order or implemented simultaneously. In addition, those skilled in the art can add one or more other operations to the flowchart under the guidance of the content of the embodiment of the present application, or remove one or more operations from the flowchart.

[0042] In addition, the described embodiments are only a part of the embodiments of the present application, rather than all embodiments. The components of the embodiments of the present application described and shown in the drawings generally here can be arranged and designed in various configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the embodiments of the present application claimed, but merely represents the selected embodiments of the embodiments of the present application.

[0043] It is understandable that the "first" and "second" in the embodiments of the present application are used to distinguish similar objects. Those skilled in the art will understand that the words "first" and "second" do not limit the quantity and execution order, and the words "first" and "second" do not necessarily limit them to be different. In addition, the term "plurality" refers to more than two (including two), and similarly, "multiple groups" refers to more than two (including two).

[0044] Before introducing the train-induced vibration impact prediction method provided in the embodiment of the present application, some concepts involved in the embodiment of the present application are first introduced:

[0045] Free field layer: Except for vibration source structures such as subway tunnels and their internal structures, there are no other buildings and structures that affect the propagation of subway vibration waves in the strata. In other words, except for vibration source structures such as subway tunnels and their internal structures, subway vibration waves are no longer disturbed by factors outside the strata and can propagate freely.

[0046] Incident wave field: When a vibration wave propagates from a vibration source to a system, the wave field generated by the initial arrival of the vibration wave to induce the vibration of the system medium. In this application, the incident wave field refers to the system within the range of the target interface, that is, specifically refers to the vibration wave or vibration wave field incident on the system within the range of the target interface.

[0047] External radiation wave field: When the incident wave field propagates within a system, it is reflected, refracted and scattered by the surface of the medium, the interface between different media, and the structure or obstacles within the system, and the wave field is regenerated and radiates from the system to the outside of the system.

[0048] Free wave field: The wave field of a system formed by the superposition of the incident wave field and the external radiation wave field.

[0049] Equivalent excitation load: The sum of the excitation load required to generate the corresponding wave field stress at the system's viscoelastic artificial boundary and the two additional excitation loads required to generate the corresponding wave field displacement or velocity at the boundary spring and damper.

[0050] Viscoelastic artificial boundary: It is a spring-damper system with special parameters set at the boundary of the calculation area. Its biggest feature is that it can well absorb the outgoing waves radiating from the calculation area to the outside of the calculation area, and effectively avoid excessive reflection of the outgoing waves at the calculation cutoff boundary, thereby ensuring the accurate solution of the dynamic response in the calculation area.

[0051] The following is an example of an application scenario in which the train-induced vibration impact prediction method is applicable. For example, with the expansion of the subway network and the continuous development of urban construction, the vibration problem caused by subway operation has become increasingly prominent. In this case, this method can be used to predict the impact of subway train operation on the use function, structural safety and durability of far-field buildings and structures, and to assess whether the corresponding buildings and structures are excessively affected by subway vibration, thereby providing a basis for the vibration reduction and isolation design of subways and buildings.

[0052] The use of traditional numerical methods to analyze the vibration response of far-field structures caused by subway train operation requires the construction of a three-dimensional dynamic coupling numerical model of the track-tunnel-stratum-structure system on the basis of properly handling the input of excitation loads generated by subway trains. As for the vibration prediction of far-field structures, since the structures are far away from the vibration source subway tunnel, the mesh and degree of freedom of the corresponding three-dimensional dynamic coupling numerical model will be extremely large, the calculation workload is large, the calculation efficiency is low, and it may even be difficult for ordinary equipment to perform calculations.

[0053] For the above questions, please see Figure 1 The decomposition schematic diagram of the coupling system-remaining system+target subsystem provided in the embodiment of the present application is shown, and the subway train-track-tunnel-stratum-structure coupling system involved in the prediction problem of far-field building vibration response caused by subway train operation is decomposed into two subsystems, namely the target subsystem and the remaining system, according to certain preset rules, and studied separately. The target subsystem includes the building and the stratum within a certain range around the building, and the remaining system is a system composed of all parts of the coupling system except the target subsystem, and the multiple interfaces (4 side surfaces and 1 bottom surface) between the target subsystem and the remaining system should be regular in shape and rectangular with the normal along the longitudinal direction of the line or perpendicular to the horizontal direction of the line.

[0054] In the process of implementing the above scheme, the subway train-track-tunnel-stratum-structure coupling system involved in the problem is decomposed into two subsystems, the target subsystem and the remaining system, according to certain preset rules, and studied separately, so as to lay the foundation for effectively reducing the computational analysis workload of the problem in the later stage. It should be noted that when the vibration waves generated by the subway train operation propagate to each target interface (4 side surfaces + 1 bottom surface), incident waves or outgoing waves will be generated. The incident waves or outgoing waves are for the system within the encirclement of the target interface, that is, the vibration waves of the system incident into the encirclement of the target interface or the vibration waves of the incident waves passing through the target interface again after reflection, refraction and scattering. The corresponding incident wave field or outgoing wave field refers to the vibration wave field of the system incident into the encirclement of the target interface or the vibration wave field of the incident wave passing through the target interface again after reflection, refraction and scattering. For ease of understanding, Figure 1 provided in the example of this application only illustrates the vibration wave propagation process of the system cross-section to represent the vibration wave propagation process of the entire system, and uses one incident wave or outward-traveling wave to represent all incident waves or all outward-traveling waves that may be generated by the vibration wave on all target interfaces, and the same applies below.

[0055] After decomposing the subway train-track-tunnel-stratum-structure coupling system involved in the problem into two subsystems, the target subsystem and the remaining system, according to certain preset rules, multiple interfaces between the target subsystem and the remaining system are obtained, recorded as target interfaces, and the problem is solved in the following two steps: ① By studying the remaining system, the incident wave field generated by the subway operation and transmitted to the target interface is solved, and the displacement, velocity and stress response of the target interface caused by the incident wave field are obtained. This is the first step, where "incident wave" or "incident wave field" refers to For the system within the range of the target interface, it refers to the vibration wave or vibration wave field incident on the system within the range of the target interface; ② The incident wave field response (displacement, velocity and stress response) on the target interface obtained in the first step is applied to the target subsystem, and then after properly handling the reflection problem of the outgoing wave at the target interface formed by the reflection, refraction and scattering of the stratum interface, ground surface, soil-structure interface, etc. in the target subsystem, a dynamic analysis is performed to solve the vibration response of the target structure induced by the running subway train. This is the second step. Since such a step-by-step problem solving strategy does not change the propagation characteristics of the vibration wave induced by the subway train in the target subsystem, it can accurately solve the vibration response of the target structure in the target subsystem induced by the subway train.

[0056] In order to solve the vibration response of the target structure induced by the running subway train in the second step, a three-dimensional dynamic finite element model of the target subsystem containing a viscoelastic artificial boundary can be constructed, and at the artificial boundary of the three-dimensional dynamic finite element model, that is, the target interface, an equivalent excitation load corresponding to the subway vibration incident wave field obtained by studying the remaining system is applied on the target interface, so as to realize the three-dimensional dynamic finite element analysis of the target subsystem and the solution of the vibration response of the target structure induced by the running subway train. See Figure 2 The schematic diagram of the three-dimensional finite element dynamic model of the target subsystem provided in the embodiment of the present application is shown. The target subsystem is discretized and modeled, and a viscoelastic artificial boundary is introduced at the boundary of the target subsystem, i.e., the target interface, to construct a three-dimensional finite element model for dynamic analysis of the target subsystem. Then, the real incident subway vibration wave is input into the target subsystem through an equivalent excitation load in the form of a wave source at the artificial boundary, and finally an accurate numerical prediction of the vibration response of far-field structures caused by subway train operation is achieved (for ease of understanding, Figure 3 provided in the example of the present application uses a cross-section of the target subsystem instead of the entire three-dimensional system to illustrate the steps of applying the equivalent excitation load and the vibration response of the structure).

[0057] In the implementation process of the above scheme, the viscoelastic artificial boundary is essentially to set up a parallel spring-damper system in three orthogonal directions on the artificial boundary node of the three-dimensional dynamic finite element model. The above spring-damper system includes a spring and a damper, wherein the spring and the damper have parameters such as a spring stiffness coefficient and a damper damping coefficient, respectively. The calculation formulas of these parameters are as follows:

[0058] K bT =α T GA / R,C bT =ρC S A,K bN =α N GA / R,C bN =ρC P A (15)

[0059] Among them, K bT , K bN are the stiffness coefficients of the tangential spring and normal spring at the corresponding boundaries; C bT , C bN are the damping coefficients of the tangential damper and the normal damper at the corresponding boundaries respectively; α T , α N is the correction coefficient of the viscoelastic artificial boundary; R is the vertical distance from the traveling wave source outside the target subsystem (which can be approximately taken as the centroid position of the initial surface before the construction of the target subsystem) to the corresponding viscoelastic artificial boundary; ρ and G are the density and shear modulus of the medium respectively; C S and C Pare the shear wave velocity and compression wave velocity of the medium respectively; A is the boundary area represented by the boundary node.

[0060] The equivalent excitation load caused by the real incident wave field at any node on the target subsystem target interface can be calculated as follows:

[0061]

[0062] Wherein, the subscript “b” indicates that the variable is the physical quantity at the target interface (the same below), the superscript “I” indicates the incident wave (the same below), and F b is the corresponding equivalent excitation load, It is the additional node force vector required to make the artificial boundary spring element produce the incident wave field displacement; It is the additional nodal force vector required to make the artificial boundary damper unit generate the incident wave field velocity; is the boundary node force vector induced by the stress tensor in the boundary area represented by the viscoelastic artificial boundary node caused by the incident wave field; are the displacement vector, velocity vector and stress vector of the boundary node of the target subsystem induced by the incident wave in three orthogonal directions; A is the boundary area represented by the boundary node; n is the normal direction vector outside the viscoelastic artificial boundary; K b , C b are the node spring stiffness coefficient matrix and the damper damping coefficient matrix on the viscoelastic artificial boundary, which are the spring and damper parameters K in different directions on the node. bT With K bN and C bT With C bN A diagonal matrix with equal elements arranged in a certain order according to the direction of the outer normal of the boundary surface.

[0063] In the first step above, the remaining system is all parts of the coupled system except the target subsystem. Therefore, there will be a cuboid empty part surrounded by five regular rectangular target interfaces in the remaining system. This empty part causes the track-tunnel-stratum in the remaining system to no longer be approximately regarded as a longitudinal consistency system. In addition, the range of the soil in the empty part is relatively small, and there is still a large range of strata in the remaining system. Therefore, in order to obtain the incident wave field response on the target interface through its dynamic analysis, it is still necessary to construct a complex three-dimensional numerical model with a large number of degrees of freedom and carry out dynamic response analysis to obtain it. This undoubtedly also has the disadvantages of low computational efficiency, large computational workload, and even inability to carry out calculations.

[0064] In view of the above problem, if the remaining part of the remaining system is restored to the situation before the construction of the structure, that is, an imaginary fill with the same ground layer as the initial ground layer is added to the remaining part, so as to construct a free field system composed of the same subway train, track, tunnel and ground layer as the remaining system and the added imaginary fill, it can be ensured that the subway train induces the incident wave field on the target interface in the imaginary free field system. (The “-” on the variable symbol indicates that the physical quantity is the quantity in the hypothetical free field system, the same below) is equivalent to the incident wave field on the target interface in the corresponding residual system That is, the displacement, velocity and stress responses of the incident wave field induced by the subway train on the target interface in the two systems are the same, satisfying the relationship: This is because before reaching the target interface, the propagation path of the subway vibration wave radiated by the subway tunnel in the hypothetical free field system and the remaining system is exactly the same as the medium.

[0065] Therefore, see Figure 4 The schematic diagram of the incident wave field response in the free field system provided by the embodiment of the present application is shown. The incident wave field displacement, velocity and stress response on the target interface in the imaginary free field system corresponding to the remaining system and used for auxiliary analysis can be used to replace the corresponding incident wave field response on the target interface of the real target subsystem to solve the equivalent excitation load on the viscoelastic artificial boundary of the three-dimensional dynamic finite element model of the target subsystem. Therefore, the equivalent excitation load can be further expressed as:

[0066]

[0067] It should be noted that the wave field is a general term for all dynamic responses of the system such as displacement, velocity, acceleration, strain, stress, etc. during the propagation of vibration waves. In this application, for the sake of simplicity, the wave field is represented by the displacement field symbol, but the wave field should still be understood as a general term for all corresponding dynamic responses.

[0068] Since the vibration waves generated by the subway train radiate from the subway tunnel into the free field layer in the hypothetical free field system and propagate freely in the stratum, when the vibration waves first propagate to the target interface and continue to propagate within the hypothetical fill range, an incident wave field is formed within the hypothetical fill range. (The superscript "I" indicates the incident wave, the same below). Subsequently, the incident wave field is reflected and refracted by the interface between the surface and the stratum within the imaginary fill range, and will again generate an external radiation wave field that propagates from the imaginary fill range to the outside of the target interface. (The superscript "R" indicates the outward radiation wave, the same below). Obviously, the incident wave field Radiation wave field In the hypothetical fill range, a free wave field will be formed by superposition. (The superscript "F" indicates free wave field, the same below), and the dynamic response of any position within the assumed fill range will be determined by the incident wave field Radiation wave field Free wave field Decide that: On the other hand, when numerically solving a hypothetical free-field system, the response at the target interface is usually a free-wave field response. (The subscript "b" indicates that the variable is the wave field at the target interface, the same below), and the incident wave field at the target interface From free wavefield alone (total wavefield) It is very difficult and not easy to implement to pick it up and solve it.

[0069] In view of the above problems, it is necessary to further explore the free wave field response at the target interface based on the hypothetical free field system. Methods for solving for the required equivalent excitation loads. See Figure 5 The schematic diagram of the free wave field response in the free field system provided by the embodiment of the present application is shown. It is noted that the viscoelastic artificial boundary has the characteristic of absorbing the outward radiation wave field of the calculation area well. Therefore, it is assumed that at the boundary of the imaginary fill range, that is, at the target interface, the imaginary fill has a viscoelastic artificial boundary that is exactly the same as the three-dimensional dynamic finite element model of the target subsystem, then the outward radiation wave field in the imaginary fill range propagates toward the outside of the target interface It will also be well absorbed by the viscoelastic artificial boundary, which means that the external radiation wave field at the target interface of the hypothetical free field system Replace the incident wavefield Substituting into equation (3), the equivalent excitation force of the outward radiation wave field at the viscoelastic artificial boundary is approximately equal to 0, as shown in the following equation:

[0070]

[0071] The “≈” in the formula is because the viscoelastic artificial boundaries are usually not completely accurate, and in theory they often cannot completely avoid the reflection of the outgoing wave at the artificial truncation boundary.

[0072] Therefore, when solving the equivalent excitation load caused by the real incident wave field on the target interface of the target subsystem, the free wave field on the target interface of the hypothetical free field system can be solved. The corresponding displacement, velocity and stress response replaces the incident wave field on the target interface in the hypothetical free field system Substitute the corresponding response into equation (3) to solve it. This is because:

[0073]

[0074] Replace them and Substituting into equation (3), and combining equation (4) and equation (5), we have:

[0075]

[0076] That is, the required equivalent excitation force can be calculated as follows:

[0077]

[0078] Among them, the subscript "b" indicates that the variable is a physical quantity at the target interface, the superscript "I" indicates the incident wave, the superscript "R" indicates the outgoing radiated wave, and the superscript "F" indicates the free wave; F b is the equivalent excitation load caused by the corresponding wave field (incident wave field, external radiation wave field or free wave field), It is the additional node force vector required to make the artificial boundary spring unit generate the displacement of the corresponding wave field (incident wave field, outward radiation wave field or free wave field); It is the additional node force vector required to make the artificial boundary damper unit generate the corresponding wave field (incident wave field, outward radiation wave field or free wave field) velocity; u is the boundary node force vector induced by the stress tensor in the boundary area represented by the viscoelastic artificial boundary node caused by the corresponding wave field (incident wave field, external radiation wave field or free wave field); b , σ b are the displacement vector, velocity vector and stress vector of the boundary node of the target subsystem induced by the corresponding wave (incident wave, outward radiation wave or free wave) in three orthogonal directions; A is the boundary area represented by the boundary node; n is the normal direction vector outside the viscoelastic artificial boundary; K b , C b are the node spring stiffness coefficient matrix and the damping coefficient matrix of the damper on the viscoelastic artificial boundary, respectively. b , C b They are the spring and damper parameters K in different directions at the nodes. bT With K bN and C bT With C bN It is a diagonal matrix formed by arranging the elements in a certain order according to the direction of the outer normal of the boundary surface.

[0079] In summary, it is assumed that at the boundary of the imaginary fill range in the free field system, that is, at the target interface, a viscoelastic artificial boundary that is exactly the same as the three-dimensional dynamic finite element model of the target subsystem is introduced, and the equivalent excitation load caused by the real incident wave field and the equivalent excitation load caused by the free wave field on the target interface of the target subsystem are equal. (For ease of understanding, the present application example provides Figure 6 to illustrate that the incident wave field response on the target interface in the target subsystem, the incident wave field response on the target interface in the free field system, and the equivalent excitation load caused by the free wave field response are equal.) Therefore, the corresponding response of the incident wave field on the target interface in the imaginary free field system can be replaced by solving the free wave field displacement, velocity and stress response on the target interface in the imaginary free field system, and then substituted into formula (3) to specifically realize the solution of the equivalent excitation load caused by the subway vibration incident wave field on the artificial boundary of the target subsystem.

[0080] See also Figure 7 The schematic diagram of the 2.5-dimensional model of the free field system provided by the embodiment of the present application is shown. Since the track, subway tunnel and the strata before the construction of the target building can be regarded as or approximately regarded as having longitudinal consistency, the hypothetical free field system formed by the hypothetical restoration of the remaining system can also be regarded as or approximately regarded as having longitudinal consistency. Furthermore, on the basis of using the multi-rigid body dynamics theory to describe the dynamic behavior of the subway train, a 2.5-dimensional method can be used to model the track, tunnel and strata in the free field system, and a 2.5-dimensional dynamic analysis model of the running subway train-track-tunnel-free field layer can be constructed. The model is used to calculate the free wave field displacement, velocity and stress response on the target interface caused by the subway train in the hypothetical free field system, so as to realize the efficient and accurate calculation of the free wave field displacement, velocity and stress response on the target interface in the hypothetical free field system, so as to greatly reduce the model degree of freedom under the premise of ensuring the calculation accuracy, and improve the analysis and calculation efficiency and calculation feasibility of the problem.

[0081] In summary, a method for predicting the vibration response of far-field buildings and structures caused by subway train operation can be obtained. Figure 8 The flowchart of the method for predicting the vibration response of far-field buildings and structures induced by subway train operation is shown. The embodiment of the present application provides a method for predicting the vibration response of far-field buildings and structures induced by subway train operation, comprising:

[0082] Step 110: Decompose the subway train-track-tunnel-stratum-building structure coupling system into a target subsystem and a remaining system, and obtain a target interface between the target subsystem and the remaining system.

[0083] Among them, multiple interfaces between the target subsystem and the remaining system can be recorded as the above-mentioned target interfaces, the target subsystem includes buildings and structures and strata within a certain range around the buildings, the remaining system is composed of all parts of the coupled system except the target subsystem, and the system decomposition should make the interface between the target subsystem and the remaining system consist of four rectangular sides and one rectangular bottom with regular shapes and normals along the vertical direction, the longitudinal direction of the line or the horizontal direction perpendicular to the line.

[0084] Since the use of traditional numerical methods to analyze the vibration response of far-field structures caused by subway train operation requires the construction of a three-dimensional dynamic coupling numerical model of the track-tunnel-stratum-structure system on the basis of properly handling the input problem of the excitation load generated by the subway train. As for the vibration prediction problem of far-field structures, since the structures are far away from the vibration source subway tunnel, the mesh and degree of freedom of the corresponding three-dimensional dynamic coupling numerical model will be extremely large, the calculation workload is large, the calculation efficiency is low, and even the calculation may not be possible. Therefore, the subway train-track-tunnel-stratum-structure coupling system involved in the problem is decomposed into two subsystems, the target subsystem and the remaining system, according to the preset rules, and studied separately, so as to lay the foundation for effectively reducing the calculation and analysis workload of the problem in the later stage and promoting the calculation and analysis of the problem.

[0085] Step 120: restore the incomplete strata in the remaining system to a free field layer without buildings and structures, and construct a hypothetical free field system corresponding to the remaining system on the basis of retaining the original target interface.

[0086] Among them, the above-mentioned incomplete stratum is formed by "removing the target subsystem from the real coupled system". The hypothetical free-field system is composed of the same subway trains, tracks, tunnels, strata and hypothetical fill as the remaining systems. It can be understood that the hypothetical free-field system is a system used to assist analysis, rather than a real system.

[0087] Step 130: Apply the 2.5-dimensional method to perform dynamic calculations on the hypothetical free field system to obtain the displacement, velocity and stress response caused by the free wave field induced by the subway train operation on the target interface.

[0088] Step 140: Discretize and model the target subsystem, introduce a viscoelastic artificial boundary at the target interface, and construct a three-dimensional finite element model for dynamic analysis of the target subsystem.

[0089] Step 150: Using the displacement, velocity and stress response of the free wave field induced by subway train operation on the target interface, combined with the introduced viscoelastic artificial boundary parameters, the equivalent excitation load of the vibration response of the target subsystem induced by subway train operation is calculated.

[0090] Step 160: Apply an equivalent excitation load to the viscoelastic artificial boundary of the three-dimensional dynamic finite element model, input the subway vibration wave to the target subsystem in the form of a wave source at the artificial boundary, and perform three-dimensional dynamic finite element processing to numerically predict the vibration response of far-field structures caused by subway train operation.

[0091] It should be noted that the subway train refers to the target train whose vibration impact on buildings and structures needs to be evaluated, and the subway train usually refers to the subway train; the building is a building outside the preset length (usually greater than 40m) of the operating subway line, and the building can be either a ground building or an underground building; the stratum is a single or layered stratum with longitudinal consistency before and after the construction of the building; the track and the subway tunnel are horizontal or approximately horizontal straight tracks or straight tunnels with or approximately longitudinal consistency; the above-mentioned coupling system may include subway trains, tracks, strata, and buildings in some scenarios; for example, the vibration waves of a running subway can be transmitted to the building through the track and the stratum, and the subway can induce the vibration response of the far-field building.

[0092] It should be noted that the various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0093] In several embodiments provided by the embodiments of the present application, it should be understood that the disclosed method can also be implemented in other ways. The method embodiments described above are only schematic, for example, the flow chart and block diagram in the accompanying drawings show the possible implementation architecture, function and operation of the method and computer program product according to the multiple embodiments of the embodiments of the present application. In this regard, each box in the flow chart or block diagram can represent a part of a program segment or code, and a part of a program segment or code includes one or more executable instructions for realizing the specified logical function.

[0094] In addition, in the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", "some examples", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the embodiments of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine different embodiments or examples described in this specification and the features of different embodiments or examples, unless they are contradictory.

[0095] The above description is only an optional implementation manner of the embodiments of the present application, but the protection scope of the embodiments of the present application is not limited thereto. Any technician familiar with the technical field can easily think of changes or replacements within the technical scope disclosed in the embodiments of the present application, which should be covered within the protection scope of the embodiments of the present application.

Claims

1. A method for predicting the vibration response of far-field buildings and structures caused by subway train operation, characterized in that: include: Decompose the subway train-track-tunnel-stratum-building coupling system into the target subsystem and the remaining system, and obtain the target interface between the target subsystem and the remaining system; The incomplete strata in the remaining system are restored to free-field strata without buildings and structures, and a hypothetical free-field system corresponding to the remaining system is constructed on the basis of retaining the original target interface, wherein the hypothetical free-field system is composed of the same subway trains, tracks, tunnels, strata and hypothetical fill as the remaining system; The 2.5-dimensional method is used to perform dynamic calculations on the hypothetical free field system to obtain the displacement, velocity and stress response of the free wave field induced by subway train operation on the target interface. Discretize the target subsystem and introduce a viscoelastic artificial boundary at the target interface to construct a three-dimensional dynamic finite element model for dynamic analysis of the target subsystem. Using the displacement, velocity and stress response of the free wave field induced by the subway train operation on the target interface, combined with the introduced viscoelastic artificial boundary parameters, the equivalent excitation load of the vibration response of the target subsystem induced by the subway train operation is calculated; An equivalent excitation load is applied to the viscoelastic artificial boundary of the three-dimensional dynamic finite element model, the subway vibration wave is input into the target subsystem in the form of a wave source at the artificial boundary, and three-dimensional dynamic finite element processing is carried out to numerically predict the vibration response of far-field structures caused by subway train operation.

2. The method according to claim 1, characterized in that The structure is a structure that is more than 40m away from the operating line of the subway train. The structure includes: ground structure, underground structure or ground structure with a basement. The stratum is a single or layered stratum with longitudinal consistency, and the track and tunnel both have longitudinal consistency.

3. The method according to claim 1, characterized in that The subway train-track-tunnel-stratum-building structure coupling system is decomposed into target subsystems and remaining systems according to preset rules, including: The subway train-track-tunnel-stratum-structure coupling system involved in the problem of predicting the vibration response of far-field structures caused by subway train operation is decomposed into target subsystems and residual systems according to preset rules; The target subsystem includes buildings and strata within a preset range around the buildings, the remaining system is a system composed of all parts of the coupling system except the target subsystem, and the interface between the target subsystem and the remaining system is composed of four rectangular side surfaces and one rectangular bottom surface with regular shapes and normals along the vertical direction, the longitudinal direction of the line or the horizontal direction perpendicular to the line.

4. The method according to claim 1, characterized in that: After decomposing the subway train-track-tunnel-ground-structure coupling system into the target subsystem and the remaining system, it also includes: Solve the incident wave field of the vibration wave generated by subway operation and transmitted to the target interface according to the remaining system, and obtain the displacement, velocity and stress response of the target interface caused by the incident wave field; The displacement, velocity and stress response of the target interface induced by the incident wave field are applied to the target subsystem, and then a dynamic analysis is performed based on the reflection problem of the outward traveling wave at the target interface formed after reflection, refraction and scattering at the stratum interface, ground surface and soil-structure interface in the target subsystem.

5. The method according to claim 4, characterized in that The applying the equivalent excitation load to the viscoelastic artificial boundary of the three-dimensional dynamic finite element model comprises: A three-dimensional dynamic finite element model of a target subsystem including the viscoelastic artificial boundary is constructed through the viscoelastic artificial boundary; At the target interface of the three-dimensional dynamic finite element model including the viscoelastic artificial boundary, an equivalent excitation load corresponding to the subway vibration incident wave field obtained for the remaining system is applied on the target interface.

6. The method according to claim 5, characterized in that The viscoelastic artificial boundary is a parallel spring-damper system in three orthogonal directions set at the artificial boundary node of the three-dimensional dynamic finite element model. The spring-damper system includes a spring and a damper, wherein the spring and the damper have a stiffness coefficient and a damping coefficient respectively, and the calculation formula is as follows: K bT =a T GA / R,C bT =ρC S A,K bN =a N GA / R,C bN =ρC P A (1) Among them, K bT , K bN are the stiffness coefficients of the tangential spring and normal spring at the corresponding boundaries; C bT , C bN are the damping coefficients of the tangential damper and the normal damper at the corresponding boundaries respectively; α T , α N is the correction coefficient of the viscoelastic artificial boundary; R is the vertical distance from the traveling wave source outside the target subsystem (taken as the centroid position of the initial surface in front of the building constructed for the target subsystem) to the corresponding viscoelastic artificial boundary; ρ and G are the density and shear modulus of the medium respectively; C S and C P are the shear wave velocity and compression wave velocity of the medium respectively; A is the boundary area represented by the boundary node.

7. The method according to claim 5, characterized in that The equivalent excitation load of the target subsystem caused by the vibration response of the subway train operation includes: The equivalent excitation load caused by the real incident wave field at any node on the target interface is calculated as follows: Wherein, the subscript "b" indicates that the variable is the physical quantity at the target interface (the same below), the superscript "I" indicates the incident wave (the same below), and F b is the corresponding equivalent excitation load, It is the additional node force vector required to make the artificial boundary spring element produce the incident wave field displacement; It is the additional nodal force vector required to make the artificial boundary damper unit generate the incident wave field velocity; is the boundary node force vector induced by the stress tensor in the boundary area represented by the viscoelastic artificial boundary node caused by the incident wave field; are the displacement vector, velocity vector and stress vector of the boundary node of the target subsystem induced by the incident wave in three orthogonal directions; A is the boundary area represented by the boundary node; n is the normal direction vector outside the viscoelastic artificial boundary; K b , C b are the node spring stiffness coefficient matrix and the damping coefficient matrix of the damper on the viscoelastic artificial boundary, respectively. b , C b They are the spring and damper parameters K in different directions at the nodes. bT With K bN and C bT With C bN It is a diagonal matrix formed by arranging the elements in a certain order according to the direction of the outer normal of the boundary surface.

8. The method according to claim 7, characterized in that Also includes: The incident wavefield displacement, velocity and stress response on the target interface in the imaginary free field system corresponding to the remaining system are used to replace the corresponding incident wavefield response on the target interface of the real target subsystem to solve the equivalent excitation load on the viscoelastic artificial boundary of the three-dimensional dynamic finite element model of the target subsystem. The calculation formula is as follows: Among them, the remaining system is all the parts of the coupled system except the target subsystem. The remaining system has a rectangular empty part surrounded by 5 regular rectangular target interfaces. The empty part causes the track-tunnel-stratum in the remaining system to no longer be approximately regarded as a longitudinal consistency system. In addition, the soil range of the empty part is relatively small, and there is a large range of strata in the remaining system. The incident wave field response on the target interface is obtained through dynamic analysis, a three-dimensional numerical model with a large number of degrees of freedom is constructed, and dynamic response analysis is carried out to obtain that if the remaining part of the remaining system is restored to the situation before the construction of the structure, that is, an imaginary fill identical to the initial stratum is added to the empty part, thereby constructing a free field system composed of the same subway train, track, tunnel and stratum as the remaining system and the added imaginary fill, it is ensured that the subway train induces the incident wave field on the target interface in the imaginary free field system (The "-" on the variable symbol indicates that the physical quantity is a quantity in an imaginary free field system, the same below) is equivalent to the incident wave field on the target interface in the corresponding residual system That is, the displacement, velocity and stress responses of the incident wave field induced by the subway train on the target interface in the two systems are the same, satisfying the relationship:

9. The method according to claim 8, characterized in that Also includes: The free wave field displacement, velocity and stress response on the target interface in the hypothetical free field system are solved to replace the corresponding response of the incident wave field on the target interface in the hypothetical free field system, and then substituted into formula (3) to solve the equivalent excitation load caused by the subway vibration incident wave field on the artificial boundary of the target subsystem. The vibration waves generated by the subway train radiate from the subway tunnel into the free field layer in the hypothetical free field system and propagate freely in the layer; When the vibration wave propagates to the target interface for the first time and continues to propagate within the imaginary fill range, an incident wave field is formed within the imaginary fill range. (The superscript "I" indicates the incident wave, the same below). The incident wave field is reflected and refracted by the interface between the surface and the stratum within the imaginary fill range, and will again generate an external radiation wave field that propagates from the imaginary fill range to the outside of the target interface. (The superscript "R" indicates the outward radiation wave, the same below); Incident wave field Radiation wave field In the hypothetical fill range, a free wave field will be formed by superposition. (The superscript "F" indicates free wave field, the same below), and the dynamic response of any position within the assumed fill range will be determined by the incident wave field Radiation wave field Free wave field Decide that: When numerically solving the hypothetical free field system, the response at the target interface is the free wave field response. (The subscript "b" indicates that the variable is the wave field at the target interface, the same below). Therefore, the free wave field (total wave field) at the target interface in the hypothetical free field system is Substituting the incident wave field on the target interface in a hypothetical free field system Based on the free wave field response at the target interface of the hypothetical free field system Solve for the required equivalent excitation loads.

10. The method according to claim 9, characterized in that Also includes: The imaginary fill at the target interface has the same viscoelastic artificial boundary as the three-dimensional dynamic finite element model of the target subsystem. Then the outward radiation wave field propagating toward the target interface within the imaginary fill range is It will also be well absorbed by the viscoelastic artificial boundary, assuming that the outward radiation wave field at the target interface of the free field system Replace the incident wavefield Substituting into equation (3), the equivalent excitation force of the outward radiation wave field at the viscoelastic artificial boundary is approximately equal to 0, as shown in the following equation: Among them, when solving the equivalent excitation load caused by the real incident wave field on the target interface of the target subsystem, the free wave field on the target interface of the hypothetical free field system is solved. The corresponding displacement, velocity and stress response replaces the incident wave field on the target interface in the hypothetical free field system Substitute the corresponding response into equation (3) to solve; Will and replace and Substituting into equation (3), and combining equation (4) and equation (5), we have: The above equivalent excitation force is calculated as follows: Among them, the subscript "b" indicates that the variable is a physical quantity at the target interface, the superscript "I" indicates the incident wave, the superscript "R" indicates the outgoing radiated wave, and the superscript "F" indicates the free wave; F b is the equivalent excitation load caused by the corresponding wave field (incident wave field, external radiation wave field or free wave field), It is the additional node force vector required to make the artificial boundary spring unit generate the displacement of the corresponding wave field (incident wave field, outward radiation wave field or free wave field); It is the additional node force vector required to make the artificial boundary damper unit generate the corresponding wave field (incident wave field, outward radiation wave field or free wave field) velocity; u is the boundary node force vector induced by the stress tensor in the boundary area represented by the viscoelastic artificial boundary node caused by the corresponding wave field (incident wave field, outward radiation wave field or free wave field); b , σ b are the displacement vector, velocity vector and stress vector of the boundary node of the target subsystem induced by the corresponding wave (incident wave, outward radiation wave or free wave) in three orthogonal directions; A is the boundary area represented by the boundary node; n is the normal direction vector outside the viscoelastic artificial boundary; K b , C b are the node spring stiffness coefficient matrix and the damping coefficient matrix of the damper on the viscoelastic artificial boundary, respectively. b , C b They are the spring and damper parameters K in different directions at the nodes. bT With K bN and C bT With C bN It is a diagonal matrix formed by arranging the elements in a certain order according to the direction of the outer normal of the boundary surface.

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