Train-bridge-soil-shield tunnel system coupled dynamic analysis method

Abstract

The present application belongs to the technical field of shield construction, and aims to solve the problem that the numerical analysis of shield tunnel mode under the high-speed railway bridge is based on local model, and the spatial coupling effect between the two subsystems of ground and underground cannot be considered. A train-bridge-soil-shield tunnel system coupling dynamic analysis method is provided, comprising the following steps: establishing a bridge-track subsystem, and simultaneously establishing a vehicle subsystem; establishing a soil-tunnel subsystem; connecting the bridge-track subsystem and the vehicle subsystem through the wheel-rail contact relationship as a link, and simultaneously connecting the bridge-track subsystem and the soil-tunnel subsystem through the pile-soil interaction relationship as a link, to obtain the coupling model of the train-bridge-soil-shield tunnel system; and performing coupling dynamic analysis on the model based on the asynchronous long method and the time domain integral algorithm. The present application can simultaneously consider the dynamic interaction of train, track, bridge and shield tunnel, and can obtain more accurate structural dynamic response.

Description

Technical Field

[0001] The invention belongs to the technical field of shield construction, and in particular relates to a coupled dynamic analysis method for a train-bridge-soil-shield tunnel system. Background Art

[0002] Currently, due to the widespread distribution of soft soil, the proliferation of high-speed rail networks, and high traffic density in road construction, increasingly large-scale and networked roads, subways, and municipal projects inevitably intersect with existing high-speed rail bridges. Shield tunneling, however, is widely adopted for these crossings due to its minimal environmental impact and rapid construction times. It is foreseeable that the need for shield tunneling under operating high-speed rail bridges will become even more prevalent in the future.

[0003] Shield tunneling can cause changes in ground stress and soil deformation during construction, leading to deformation and displacement of adjacent bridge foundations and additional deformation of the track structure on the bridge, exacerbating track irregularities and impacting train operational safety. Furthermore, the significant dynamic impact of trains passing over railway bridges can also disturb the soil around adjacent piers, creating complex impacts on construction safety.

[0004] However, the vast majority of current research focuses on two separate subsystems: the pile-soil-shield tunnel subsystem, which involves static analysis of soil deformation or deformation of adjacent pier pile foundations caused by shield tunneling; and the train-track-bridge subsystem, which involves dynamic analysis of the coupled effects of the train-track-bridge system. When studying the impact of shield tunneling on train safety, deformation of the bridge rails caused by shield tunneling is considered solely as additional rail irregularities. Current research fails to account for the spatial coupling between the aboveground and underground subsystems, and computational efficiency is a key factor limiting the dynamic analysis of integrated, complex systems. Summary of the Invention

[0005] In order to solve at least one of the above technical problems existing in the prior art, the present invention provides a coupled dynamic analysis method for a train-bridge-soil-shield tunnel system.

[0006] The present invention is implemented by the following technical solution: a coupled dynamic analysis method of a train-bridge-soil-shield tunnel system, comprising the following steps: establishing a bridge-track subsystem, the bridge-track subsystem including finite element models of the track and the bridge;

[0007] Establishing a vehicle subsystem, wherein the vehicle subsystem includes a multi-rigid body model of a train passing through the bridge;

[0008] Establishing a soil-tunnel subsystem, wherein the soil-tunnel subsystem includes a finite element model of soil and shield tunnel construction, and the soil-tunnel subsystem is used to simulate the shield tunnel construction process;

[0009] The bridge-track subsystem and the vehicle subsystem are connected by the wheel-rail contact relationship, and the bridge-track subsystem and the soil-tunnel subsystem are connected by the pile-soil interaction relationship, thus obtaining a coupled model of the train-bridge-soil-shield tunnel system.

[0010] The coupled dynamic analysis of the coupled model was carried out based on the asynchronous length method and time domain integration algorithm, and the dynamic response of the train and structure when the shield tunnel passes under the bridge was obtained.

[0011] Preferably, the method for establishing the finite element model of the bridge is as follows: simulating the bridge based on three-dimensional finite elements, including the main beam, supports, piers, and piles of the bridge, and simulating the vertical, transverse, and longitudinal spring stiffness of the bridge supports according to the vertical and horizontal bearing capacities and allowable displacement ranges of the supports;

[0012] The steps of establishing the track finite element model are as follows: the rails in the track system are simulated based on Timoshenko spatial beam elements, the remaining layers in the track system are simulated using solid elements, and the fasteners between the rails and the track plates are simulated using spring elements.

[0013] Preferably, the method for establishing the multi-rigid body model of the train is as follows:

[0014] The train body, bogie, and wheelset are all considered as rigid bodies, and the elastic deformation of the wheelset is considered when calculating the wheel-rail force in the wheel-rail relationship analysis;

[0015] A multi-rigid body model of a four-axle train with secondary suspension is established: the primary suspension system of the train connects the wheelset and the bogie, and the secondary suspension system connects the bogie and the car body. Spring-damper units are used to simulate the suspension system to establish a multi-rigid body model of the train.

[0016] Preferably, a finite element model of the soil and shield tunnel construction is established, and a method for simulating the shield tunnel construction process is as follows:

[0017] Conduct geotechnical tests on undisturbed soil to determine the physical and mechanical parameters of each soil layer; and use the ideal elastic-plastic constitutive model to simulate the stress-strain relationship of the soil material;

[0018] Taking into account the boundary constraint effect of the stratum, the boundary surface of the finite element model of the soil and shield tunnel construction is taken at 3-5 times the tunnel diameter. 3D solid elements are used to simulate the soil layer, and plate elements are used to simulate the shield shell and segments of the structures involved in shield construction.

[0019] Determine the boundary constraints of the finite element model of soil and shield tunnel construction. The top surface of the finite element model of soil and shield tunnel construction is a free surface, the bottom surface is subject to fixed constraints, and the front, back, left and right boundary surfaces are subject to normal constraints.

[0020] determining a shield tunnel construction load, the shield tunnel construction load including slurry pressure, friction, jack thrust and grouting pressure;

[0021] The shield tunnel construction process is simulated by changing the material properties of the variable unit and the life and death of the control unit, that is, the shield shell unit material properties are assigned ring by ring as the excavation proceeds, the soil unit properties of the current ring are deleted, the friction is applied to the contact surface between the shield shell and the soil, the jack thrust is applied through the segment end face, the slurry pressure is applied to the next ring excavation surface, the grouting pressure is applied to the outer ring surface of the segment, the excavation process is simulated until the excavation is completed.

[0022] Preferably, the wheel-rail contact relationship includes wheel-rail contact geometry and wheel-rail force; wherein the wheel-rail contact geometry includes wheel-rail contact profile, wheel-rail contact point and contact model; the wheel-rail force includes wheel-rail normal force and wheel-rail creep force, the wheel-rail normal force is calculated by using Hertz elastic contact theory, and the wheel-rail creep force is calculated by using FASTSIM algorithm based on Kalker simplified theory.

[0023] Preferably, the expression of the dynamic equation of the coupling model of the train-bridge-soil-shield tunnel system is as follows:

[0024]

[0025]

[0026]

[0027] wherein, , and are mass matrices of vehicle, bridge-rail, and soil-tunnel subsystems, , and are damping matrices of vehicle, bridge-rail, and soil-tunnel subsystems, , and are stiffness matrices of vehicle, bridge-rail, and soil-tunnel subsystems, , and are generalized displacement vectors of vehicle, bridge-rail, and soil-tunnel subsystems, , and are generalized velocity vectors of vehicle, bridge-rail, and soil-tunnel subsystems, , and are the generalized acceleration vectors of the vehicle, bridge-track, and soil-tunnel subsystems, respectively, , and are the generalized load vectors for the vehicle, bridge-track, and soil-tunnel subsystems, respectively.

[0028] Preferably, the dynamic equations of the coupled model of the train-bridge-soil-shield tunnel system are solved based on the asynchronous length method and the time domain integration algorithm:

[0029] The coupled model of the train-bridge-soil-shield tunnel system is decomposed into two subsystems: the train-bridge subsystem and the foundation-soil-shield tunnel subsystem. The two subsystems are connected through a common node on the pile foundation cap.

[0030] The corresponding integration algorithms and time steps are selected for the train-bridge subsystem and the foundation-soil-shield tunnel subsystem respectively;

[0031] In each time step, the dynamic responses of the train-bridge subsystem and the foundation-soil-shield tunnel subsystem are calculated separately. Then, the dynamic response data of the two are interacted to obtain the result of the time step, which is used as the excitation for the next time step.

[0032] In each time step, the calculation of the next time step is performed after the convergence condition is met until the entire calculation is completed.

[0033] Preferably, in the coupled model of the train-bridge-soil-shield tunnel system, the high-frequency part is concentrated in the train-bridge subsystem, and a smaller time step than that of the foundation-soil-shield tunnel subsystem is used in the analysis of the train-bridge subsystem, and the time step selected for the foundation-soil-shield tunnel subsystem is an integer multiple of the train-bridge subsystem.

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] The present invention establishes a coupling model of the train-bridge-soil-shield tunnel system by studying the coupling mechanism of each part of the system and simulating the coupling relationship, as well as determining the shield construction load. It can simultaneously consider the dynamic interaction of complex systems such as high-speed trains, tracks, bridges, soil, shield tunnels, etc., and can obtain more accurate train and structural dynamic responses, better meeting the calculation accuracy requirements when passing under high-speed railway projects; it can calculate the dynamic response of the system under different shield construction stages; at the same time, the asynchronous length method is introduced when solving, and different integral time steps are set according to the frequency distribution characteristics of each part of the system, which significantly improves the solution speed of the complex system. In summary, the present invention can better comprehensively evaluate the impact of shield underpass construction on the operation of high-speed trains on bridges, so as to ensure the safety of high-speed train operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0037] Figure 1 This is a flow chart of the coupled dynamic analysis method for the high-speed train-bridge-soil-shield tunnel system;

[0038] Figure 2 This is a model structure diagram of a single-section train; in the figure: , and They are vehicle length, bogie center distance and wheelbase, , and , are the stiffness and damping of the primary and secondary suspension systems respectively.

[0039] Figure 3(a) is the mid-span cross-section of a simply supported beam (unit: mm);

[0040] Figure 3(b) is a schematic diagram of the support arrangement;

[0041] Figure 4 This is a schematic diagram of shield tunnel construction loads;

[0042] Figure 5(a) shows a sample of track unevenness;

[0043] Figure 5(b) shows a sample with track direction irregularities;

[0044] Figure 5(c) shows a sample of track horizontal irregularity;

[0045] Figure 6 This is a schematic diagram of the train-bridge-soil-shield tunnel coupling system;

[0046] Figure 7(a) shows the time course curve of the train wheel load reduction rate when the train speed is 150km / h and 350km / h respectively;

[0047] Figure 7(b) shows the time history curves of the train axle lateral force when the train speed is 150km / h and 350km / h respectively;

[0048] Figure 8(a) shows the relationship between the maximum value of the vehicle body acceleration and the train speed;

[0049] Figure 8(b) shows the relationship between the maximum acceleration of the second span of the main beam and the train speed. DETAILED DESCRIPTION

[0050] The technical solutions in the embodiments of the present invention are clearly and completely described in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. All other implementations derived by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts are within the scope of protection of the present invention.

[0051] It should be noted that the structures, proportions, sizes, etc. illustrated in the drawings of this specification are only used to match the contents disclosed in the specification for people familiar with this technology to understand and read, and are not used to limit the conditions under which the present invention can be implemented. Therefore, they have no substantive technical significance. Any structural modification, change in proportional relationship or adjustment of size should fall within the scope of the technical content disclosed in the present invention without affecting the efficacy and purpose that can be achieved by the present invention. It should be noted that in this specification, relational terms such as first and second are only used to distinguish one entity from several other entities, and do not necessarily require or imply any actual relationship or order between these entities.

[0052] The present invention provides an embodiment:

[0053] like Figure 1 As shown in FIG8 , a coupled dynamic analysis method for a train-bridge-soil-shield tunnel system includes the following steps:

[0054] A bridge-track subsystem is established, which includes finite element models of the track and bridge; a vehicle subsystem is established, which includes a multi-rigid body model of a train passing through the bridge; a soil-tunnel subsystem is established, which includes finite element models of the soil and shield tunnel construction, and is used to simulate the shield tunnel construction process; the bridge-track subsystem and the vehicle subsystem are connected through the wheel-rail contact relationship, and the bridge-track subsystem and the soil-tunnel subsystem are connected through the pile-soil interaction relationship, to obtain a coupled model of the train-bridge-soil-shield tunnel system; a coupled dynamic analysis of the coupled model is performed based on the asynchronous length method and time domain integration algorithm to obtain the dynamic response of the train and structure when the shield tunnel passes under the bridge.

[0055] In this embodiment, the method for establishing the multi-rigid body model of the train is as follows:

[0056] The train body, bogie, and wheelset are all considered as rigid bodies, and the elastic deformation of the wheelset is considered when calculating the wheel-rail force in the wheel-rail relationship analysis;

[0057] A multi-rigid body model of the train is established using a four-axle train with secondary suspension: each vehicle section consists of a car body, two bogies and four wheelsets, a total of seven rigid bodies. Each rigid body considers six degrees of freedom, namely telescoping, yaw, floating, rolling, nodding and shaking. A single vehicle section contains 6×7 degrees of freedom, a total of 42 degrees of freedom; the primary suspension system of the train connects the wheelset and bogie, and the secondary suspension system connects the bogie and the car body. Spring-damper units are used to simulate the suspension system to establish a multi-rigid body model of the train.

[0058] The method for establishing a finite element model of a bridge is as follows: the bridge is simulated based on a three-dimensional finite element, including the bridge's main beam, supports, piers, and piles. The vertical, transverse, and longitudinal spring stiffnesses of the bridge supports are simulated based on the vertical and horizontal bearing capacities and allowable displacement ranges of the supports;

[0059] The steps to establish the track finite element model are as follows: the rails in the track system are simulated based on the Timoshenko spatial beam element, the remaining layers in the track system are simulated using solid elements, and the fasteners between the rails and the track plate are simulated using spring elements.

[0060] A finite element model of soil and shield tunnel construction was established. The simulation method for the shield tunnel construction process was as follows:

[0061] Geotechnical tests were conducted on the undisturbed soil to determine the physical and mechanical parameters of each soil layer. The soil was simulated using the ideal elastic-plastic constitutive model. The yield criterion was the Drucker-Prager yield criterion, which is expressed as follows:

[0062]

[0063] Where: is the second invariant of the deviatoric stress tensor, is the first invariant of the stress tensor, and are material constants, defined as:

[0064]

[0065]

[0066]

[0067]

[0068] Where: 、 and are the three principal stresses of the soil; and are the cohesion and internal friction angle of the soil, respectively.

[0069] Considering the boundary constraint effect of the stratum, the boundary surface of the finite element model between the soil and the shield tunnel construction is taken at a point 3-5 times the tunnel diameter. 3D solid elements are used to simulate the soil layer. The structures involved in the shield construction include the shield shell, segments, and grouting layer. Plate elements are used to simulate the shield shell and segments in the structures involved in the shield construction.

[0070] Determine the boundary constraints of the finite element model of soil and shield tunnel construction. The top surface of the finite element model of soil and shield tunnel construction is a free surface, the bottom surface is subject to fixed constraints, and the front, back, left and right boundary surfaces are subject to normal constraints.

[0071] Determine the construction load of the shield tunnel. The construction load of the shield tunnel includes mud water pressure, friction, jack thrust and grouting pressure; mud water pressure acts on the excavation surface; friction acts on the contact surface between the shield shell and the soil; jack thrust acts on the segments; and grouting pressure acts on the segments.

[0072] The mud water pressure is determined by the following formula:

[0073]

[0074]

[0075]

[0076] Where: is the mud water pressure; Static earth pressure on the excavation face; is the excavation surface water pressure; To reserve pressure; is the static earth pressure coefficient; is the bulk density of the soil; is the burial depth of the tunnel center; is the Poisson's ratio of soil.

[0077] During shield tunnel construction, the forward movement of the shield machine will cause friction between the shield shell and the soil. The magnitude of the friction is related to the pressure exerted by the soil on the shield shell and is determined by the following formula:

[0078]

[0079]

[0080]

[0081]

[0082] Where: is the burial depth of the shield top; The shield machine's own weight; is the shield diameter; is the shield length.

[0083] The total friction force on the shield can be approximately determined by the following formula:

[0084]

[0085] Where: is the friction between the shield and the soil; is the friction coefficient between the shield and the soil.

[0086] The jack at the tail of the shield acts on the segments, providing sufficient thrust for the shield machine to move forward. The thrust is approximately the sum of the mud water pressure and the friction force, as shown in the following formula:

[0087]

[0088] Where: is the jack thrust;

[0089] The shield tunnel construction process is simulated by transforming the material properties of the cells and controlling the life and death of the cells.

[0090] Summarizing the above subsystem models, the coupled system dynamic equation can be expressed as the following unified form:

[0091] The dynamic equations of the coupled model of the train-bridge-soil-shield tunnel system are expressed as follows:

[0092]

[0093]

[0094]

[0095] in, , and are the mass matrices of the vehicle, bridge-track, and soil-tunnel subsystems, , and are the damping matrices of the vehicle, bridge-track, and soil-tunnel subsystems, , and are the stiffness matrices of the vehicle, bridge-track, and soil-tunnel subsystems, , and are the generalized displacement vectors of the vehicle, bridge-track, and soil-tunnel subsystems, respectively, , and are the generalized velocity vectors of the vehicle, bridge-track and soil-tunnel subsystems, respectively, are the generalized acceleration vectors of the vehicle, bridge-track and soil-tunnel subsystems, respectively, are the generalized load vectors of the vehicle, bridge-track and soil-tunnel subsystems, respectively.

[0096] The wheel-rail contact relationship includes wheel-rail contact geometry and wheel-rail force; wherein the wheel-rail contact geometry contains wheel-rail contact profile, wheel-rail contact point and contact model; the wheel-rail force includes wheel-rail normal force and wheel-rail creep force, the wheel-rail normal force is calculated by using Hertz elastic contact theory, and the wheel-rail creep force is calculated by using FASTSIM algorithm based on Kalker simplified theory.

[0097] The wheel-rail contact relationship is the key of coupling of train and bridge-track system, wherein the wheel-rail normal force refers to the normal force perpendicular to the wheel-rail contact surface in the process of wheel and rail contact, and is calculated according to the following formula:

[0098]

[0099] In the formula, and are the normal penetration and normal penetration velocity between the wheel and rail, respectively; and are the stiffness and damping of the spring, respectively. are the stiffness and damping of the spring, respectively.

[0100] Based on the asynchronous long method and time domain integral algorithm, the dynamic equation of the coupling model of the train-bridge-soil-shield tunnel system is solved:

[0101] The coupling model of the train-bridge-soil-shield tunnel system is divided into two subsystems: train-bridge subsystem and foundation-soil-shield tunnel subsystem, and the two subsystems are combined through the common node on the pile cap;

[0102] The train-bridge subsystem and the foundation-soil-shield tunnel subsystem select corresponding integral algorithm and time step, respectively; in the coupling model of the train-bridge-soil-shield tunnel system, the high frequency part is concentrated in the train-bridge subsystem, a smaller time step is used in the train-bridge subsystem than in the foundation-soil-shield tunnel subsystem, and the time step selected by the foundation-soil-shield tunnel subsystem is an integer multiple of the time step of the train-bridge subsystem;

[0103] ​​​​​This method is essentially different from the method of dividing the whole system into two parts, ground and underground, for separate study. In the substructure method, each subsystem is real-time interactive. In each time step, the dynamic responses of the train-bridge subsystem and the foundation-soil-shield tunnel subsystem are calculated, respectively, and then the dynamic response data of the two subsystems are exchanged to obtain the results of the time step, which are used as the excitation for the next time step.

[0104] In each time step, the calculation of the next time step is performed after the convergence condition is met, and the whole calculation is completed. The convergence criterion is given by the displacement of the subsystem, which is expressed as:

[0105]

[0106] In the formula, E is the allowable relative error, is the foundation displacement, and the superscripts i and i-1 represent the current step and the previous step in the iteration, respectively.

[0107] The specific implementation is as follows:

[0108] Taking a large-diameter shield tunneling under a multi-span simply supported box girder bridge of a high-speed railway as an example, a high-speed train-track-bridge-soil-shield tunnel coupling dynamic analysis is carried out, and the flow chart is shown in Figure 1 .

[0109] The bogies of the currently running high-speed trains are double-axle bogies, and the front and rear two bogies are distributed below the car body. In this embodiment, a four-axle train with secondary suspension is used to establish a multi-body dynamics model of the high-speed train, and the model structure is shown in Figure 2 . A single 8-car (trailer + 6 × motor car + trailer) formation is used.

[0110] In this embodiment, the track system is a CRTS III type standard slab track structure, which is composed of a steel rail, a track slab, a self-compacting concrete layer and a base slab from top to bottom. The steel rail is a 60 kg / m steel rail, which is simulated by a Timoshenko space beam element. The track slab, self-compacting concrete layer and base slab are simulated by solid elements, and the structure parameters are shown in Table 1. For the constraint between the track layers, since the bridge and the base slab are fixed by embedded steel bars, and the track slab and the self-compacting concrete layer are fixed by door-shaped steel bars, the relative displacement between them is not considered. The two protrusions under the self-compacting concrete layer and the corresponding grooves on the base slab are interlocked for limiting, and the self-compacting concrete and the base slab are connected by a nonlinear spring to simulate the "geotextile" isolation layer between the layers, and the friction coefficient is 0.70. The precast unit track slab on the bridge is assembled according to the actual specifications. The fasteners between the steel rail and the track slab are simulated by spring elements.

[0111] Table 1 Track structure parameters

[0112]

[0113] In this example, WJ-8 constant resistance fasteners are used between the rails and the track plates, with a fastener spacing of 0.63 m. Linear spring elements are used to simulate the lateral and vertical stiffness of the fasteners, with stiffness coefficients of 50 kN / mm and 35 kN / mm, respectively. Nonlinear spring elements are used to simulate the longitudinal resistance of the fasteners, and the longitudinal force of the fasteners is:

[0114]

[0115] Where r is the longitudinal resistance of the fastener, unit is kN / (m·rail); x is the longitudinal displacement of the relative component, unit is mm.

[0116] In this example, the bridge is a four-span, 32-meter simply supported box girder bridge. The cross-section of the main girder and the support arrangement are shown in Figure 3. The vertical, transverse, and longitudinal spring stiffnesses were simulated based on the vertical and horizontal bearing capacities and allowable displacement ranges of the supports. The values ​​are shown in Table 2.

[0117] Table 2 Support stiffness parameters

[0118]

[0119] In this example, the net tunnel depth is 10m, and the construction sequence is left-line first, followed by right-line. The tunnel segments are circular, with an outer diameter of 13.25m and an inner diameter of 12.05m. Elevations of the soil and shield tunnel are shown in Figure 3. The soil model dimensions take into account the boundary constraints of the strata, and the model boundary surface is set at five times the tunnel diameter. Because the inclination of the soil layers in this example is relatively small, they can be approximated as horizontal layers. That is, the numerical model uses horizontal layers for simulation, and the soil layers are simulated using solid elements. The soil parameters are shown in Table 3.

[0120] Table 3 Soil material parameters

[0121]

[0122] During the simulated shield construction process, the application position of the construction load is shown in Figure 4 .

[0123] This embodiment uses the German track spectrum to simulate random track irregularities. The spectrum includes three power spectrum density functions: vertical irregularity, directional irregularity, and horizontal irregularity. The expression is as follows:

[0124] Unevenness:

[0125]

[0126] Unsmooth direction:

[0127]

[0128] Horizontal irregularity:

[0129]

[0130] wherein, is the irregularity power spectral density, with unit of ; is the irregularity spatial frequency, , , are the cut-off frequencies, with unit of rad / m, respectively; , is the roughness coefficient, with unit of ; is half of the left and right wheel rolling circle distance, which is taken as 0.75 m in this paper. The empty space irregularity samples are generated by the power spectral density function, as shown in FIG. 5.

[0131] In solving the train-bridge-soil-shield tunnel time-varying coupling system, the entire model is divided into two subsystems: a train-bridge subsystem and a foundation-soil-shield tunnel subsystem, and the two subsystems are combined through the common node on the pile cap, as shown in FIG. 2. Figure 6

[0132] According to the method of the embodiment, the dynamic responses of each part of the system can be obtained, including wheel-rail interaction force, vibration acceleration, displacement and the like of the vehicle, track, bridge and soil. Taking the case that the double-line tunnel is completely excavated as an example, part of the analysis results under different train running speeds are shown in FIGS. 7-8.

[0133] The above merely describes the preferred embodiments of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can easily think of changes or replacements within the technical scope disclosed by the present application, which should be covered in the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.​

Claims

1. A coupled dynamic analysis method for a train-bridge-soil-shield tunnel system, characterized in that: The following steps are involved: Establishing a bridge-track subsystem, wherein the bridge-track subsystem includes finite element models of the track and the bridge; Establishing a vehicle subsystem, wherein the vehicle subsystem includes a multi-rigid body model of a train passing through the bridge; Establishing a soil-tunnel subsystem, wherein the soil-tunnel subsystem includes a finite element model of soil and shield tunnel construction, and the soil-tunnel subsystem is used to simulate the shield tunnel construction process; The bridge-track subsystem and the vehicle subsystem are connected by the wheel-rail contact relationship, and the bridge-track subsystem and the soil-tunnel subsystem are connected by the pile-soil interaction relationship, thus obtaining a coupled model of the train-bridge-soil-shield tunnel system. The coupled dynamic analysis of the coupled model was performed based on the asynchronous length method and time domain integration algorithm to obtain the dynamic response of the train and the structure when the shield tunnel passes under the bridge. The dynamic equations of the coupled model of the train-bridge-soil-shield tunnel system are solved using the asynchronous length method and time-domain integration algorithm. The coupled model is decomposed into two subsystems: the train-bridge subsystem and the foundation-soil-shield tunnel subsystem. These two subsystems are connected via a common node on the pile cap. The corresponding integration algorithm and time step are selected for each subsystem. In each time step, the dynamic responses of the train-bridge subsystem and the foundation-soil-shield tunnel subsystem are calculated separately. Then, the dynamic response data of the two are exchanged to obtain the result of the time step, which is used as the excitation for the next time step. In each time step, the calculation of the next time step is performed after the convergence conditions are met until the entire calculation is completed.

2. The coupled dynamic analysis method for a train-bridge-soil-shield tunnel system according to claim 1 is characterized by: The method for establishing the finite element model of the bridge is as follows: simulating the bridge based on a three-dimensional finite element, including the bridge's main beam, supports, piers, and piles, simulating the vertical, transverse, and longitudinal spring stiffness of the bridge's supports based on the supports' vertical and horizontal bearing capacities and allowable displacement ranges; The steps of establishing the track finite element model are as follows: the rails in the track system are simulated based on Timoshenko spatial beam elements, the remaining layers in the track system are simulated using solid elements, and the fasteners between the rails and the track plates are simulated using spring elements.

3. The coupled dynamic analysis method for a train-bridge-soil-shield tunnel system according to claim 1 is characterized by: The method for establishing the multi-rigid body model of the train is as follows: The train body, bogie, and wheelset are all considered as rigid bodies, and the elastic deformation of the wheelset is considered when calculating the wheel-rail force in the wheel-rail relationship analysis; A multi-rigid body model of a four-axle train with secondary suspension is established: the primary suspension system of the train connects the wheelset and the bogie, and the secondary suspension system connects the bogie and the car body. Spring-damper units are used to simulate the suspension system to establish a multi-rigid body model of the train.

4. The coupled dynamic analysis method for a train-bridge-soil-shield tunnel system according to claim 1 is characterized by: A finite element model of the soil and shield tunnel construction is established, and the method for simulating the shield tunnel construction process is as follows: Conduct geotechnical tests on undisturbed soil to determine the physical and mechanical parameters of each soil layer; and use the ideal elastic-plastic constitutive model to simulate the stress-strain relationship of the soil; Taking into account the boundary constraint effect of the stratum, the boundary surface of the finite element model of the soil and shield tunnel construction is taken at 3-5 times the tunnel diameter. 3D solid elements are used to simulate the soil layer, and plate elements are used to simulate the shield shell and segments of the structures involved in shield construction. Determine the boundary constraints of the finite element model of soil and shield tunnel construction. The top surface of the finite element model of soil and shield tunnel construction is a free surface, the bottom surface is subject to fixed constraints, and the front, back, left and right boundary surfaces are subject to normal constraints. Determining shield tunnel construction loads, wherein the shield tunnel construction loads include mud water pressure, friction, jack thrust, and grouting pressure; The shield tunnel construction process is simulated by transforming the material properties of the cells and controlling the life and death of the cells.

5. The coupled dynamic analysis method for a train-bridge-soil-shield tunnel system according to claim 1 is characterized by: The wheel-rail contact relationship includes the wheel-rail contact geometry and the wheel-rail force; the wheel-rail contact geometry includes the wheel-rail contact profile, the wheel-rail contact point and the contact model; the wheel-rail force includes the wheel-rail normal force and the wheel-rail creep force. The wheel-rail normal force is calculated using the Hertz elastic contact theory, and the wheel-rail creep force is calculated using the FASTSIM algorithm based on the Kalker simplified theory.

6. The train-bridge-soil-shield tunnel system coupled dynamic analysis method according to claim 1, characterized in that: The dynamic equation of the coupled model of the train-bridge-soil-shield tunnel system is expressed as follows: in, , and are the mass matrices of the vehicle, bridge-track, and soil-tunnel subsystems, , and are the damping matrices of the vehicle, bridge-track, and soil-tunnel subsystems, , and are the stiffness matrices of the vehicle, bridge-track, and soil-tunnel subsystems, , and are the generalized displacement vectors of the vehicle, bridge-track, and soil-tunnel subsystems, respectively, , and are the generalized velocity vectors of the vehicle, bridge-track, and soil-tunnel subsystems, respectively, , and are the generalized acceleration vectors of the vehicle, bridge-track, and soil-tunnel subsystems, respectively, , and are the generalized load vectors for the vehicle, bridge-track, and soil-tunnel subsystems, respectively.

7. The coupled dynamic analysis method for a train-bridge-soil-shield tunnel system according to claim 6, characterized in that: In the coupled model of the train-bridge-soil-shield tunnel system, the high-frequency part is concentrated in the train-bridge subsystem. When analyzing the train-bridge subsystem, a smaller time step is used than that of the foundation-soil-shield tunnel subsystem, and the time step selected for the foundation-soil-shield tunnel subsystem is an integer multiple of that of the train-bridge subsystem.

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