Train-bridge-soil body-shield tunnel system coupling dynamic analysis method

Abstract

The invention belongs to the technical field of shield construction, and aims to solve the problem that the spatial coupling effect between an overground subsystem and an underground subsystem cannot be considered because the numerical analysis of a high-speed railway bridge under a shield tunnel mode is based on a local model at present. The train-bridge-soil body-shield tunnel system coupling dynamic analysis method comprises the following steps that a bridge-track subsystem is established, and meanwhile a vehicle subsystem is established; a soil body-tunnel subsystem is established; the bridge-track subsystem and the vehicle subsystem are connected through the wheel-rail contact relation as a link, meanwhile, the bridge-track subsystem and the soil body-tunnel subsystem are connected through the link as a pile-soil interaction relation, and a coupling model of a train-bridge-soil body-shield tunnel system is obtained; and performing coupling dynamic analysis on the model based on an asynchronous length method and a time domain integration algorithm. The dynamic interaction of the train, the track, the bridge and the shield tunnel can be considered at the same time, and more accurate structural dynamic response can be obtained.

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] At present, due to the widespread distribution of soft soil, multiple high-speed rail lines, and high traffic density in road construction, increasingly large-scale and networked roads, subways, and municipal projects inevitably cross existing high-speed rail bridges. The tunnel shield construction method is widely used for crossing lines because of its characteristics of less impact on the surrounding environment and faster construction. It can be foreseen that the demand for shield tunneling under operating high-speed railway bridges will become more common in the future.

[0003] When the shield tunnel is under construction, it will cause changes in stratum stress and soil deformation, causing deformation and displacement of the adjacent bridge foundation, and causing additional deformation of the track structure on the bridge, aggravating the unevenness of the track and affecting the operational safety of the train. On the other hand, when the train passes through the railway bridge, its dynamic load impact is large, which may also cause certain disturbances to the soil around the adjacent piers, forming a complex impact on construction safety.

[0004] However, most of the current research focuses on two subsystems: one is the bridge pile-soil-shield tunnel subsystem, which refers to the static analysis of soil deformation or deformation of adjacent bridge pier pile foundations caused by shield tunneling; the other is the train-track-bridge subsystem, which refers to the dynamic analysis of the coupling effect of the train-track-bridge system. When studying the impact of shield tunneling on train operation safety, only the deformation of the bridge rails caused by shield tunneling construction is considered as additional unevenness of the rails. Current research cannot consider the spatial coupling between the above-ground and underground subsystems, and computational efficiency is also a key factor restricting 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 train-bridge-soil-shield tunnel system coupled dynamic analysis method, comprising the following steps: establishing a bridge-track subsystem, the bridge-track subsystem comprising finite element models of tracks and bridges;

[0007] Establishing a vehicle subsystem, wherein the vehicle subsystem includes a multi-rigid body model of a train passing through a 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, so as to obtain the 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 the structure when the shield machine passed 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, bearings, piers, and piles of the bridge, and simulating the vertical, lateral, and longitudinal spring stiffness of the bearings of the bridge according to the vertical and horizontal bearing capacities and allowable displacement ranges of the bearings;

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

[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 the train is established using a two-stage suspension four-axle train: the primary suspension system of the train connects the wheelset and the bogie, the secondary suspension system connects the bogie and the car body, and a spring-damper unit is 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 soil materials;

[0018] Considering the boundary constraint effect of the stratum, the boundary surface of the finite element model of soil and shield tunnel construction is taken at 3-5 times the tunnel diameter. The soil layer is simulated by three-dimensional solid elements, and the shield shell and pipe segments in the structure involved in the shield construction are simulated by plate elements.

[0019] Determine the boundary constraint conditions of the finite element model of soil and shield tunnel construction, where 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 and rear, left and right boundary surfaces are subject to normal constraints;

[0020] Determine the shield tunnel construction load, wherein the shield tunnel construction load includes mud water pressure, friction force, jack thrust and grouting pressure;

[0021] The shield tunnel construction process is simulated by transforming the material properties of the unit and controlling the life and death of the unit. That is, as the excavation proceeds, the material properties of the shield shell unit are assigned ring by ring, and the soil unit properties of the current ring are deleted. Friction is applied to the contact surface between the shield shell and the soil, and the jack thrust is applied through the end face of the segment. Mud and water pressure is applied to the excavation surface of the next ring, and grouting pressure is applied to the outer ring surface of the segment to simulate the excavation process until the excavation is completed.

[0022] Preferably, the wheel-rail contact relationship includes a wheel-rail contact geometric relationship and a wheel-rail force; wherein the wheel-rail contact geometric relationship includes a wheel-rail contact profile, a wheel-rail contact point and a contact model; the wheel-rail force includes a wheel-rail normal force and a 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.

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

[0024]

[0025]

[0026]

[0027] Among them, M v , M b and M t are the mass matrices of the vehicle, bridge-track, and soil-tunnel subsystems, respectively, and C v , C b and C t are the damping matrices of the vehicle, bridge-track and soil-tunnel subsystems, respectively, and K v , K b and K t are the stiffness matrices of the vehicle, bridge-track and soil-tunnel subsystems, respectively, and u v ,u b and u t 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, R v, R b and R t 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, and the two subsystems are combined through the common node on the pile foundation cap.

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

[0031] 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 are interacted to obtain the result of the time step, which is used as the excitation of the next time step;

[0032] In each time step, once the convergence condition is met, the next time step will be calculated 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 on 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, simulating the coupling relationship, and 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 meet the requirements for calculation accuracy 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 during the solution, 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 safe operation of high-speed trains. 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 drawings required for use in the embodiments will be briefly introduced below. 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 creative work.

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

[0038] Figure 2 This is a model structure diagram of a single train; in the figure: L c , L b and L w are vehicle length, bogie center distance and wheelbase, K ps , C ps and K ss , C ss They are the stiffness and damping of the primary and secondary suspension systems respectively.

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

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

[0041] Figure 4 It is a schematic diagram of the shield tunnel construction load;

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

[0043] Figure 5(b) is a sample with uneven track direction;

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

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

[0046] Figure 7(a) is 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) is the time history curve of the lateral force on the train axle when the train speed is 150km / h and 350km / h respectively;

[0048] FIG8( a ) is a graph showing the relationship between the maximum value of the vehicle body acceleration and the train speed;

[0049] Figure 8(b) is a graph showing the relationship between the maximum value of the acceleration at the mid-span of the second span of the main beam and the train speed. DETAILED DESCRIPTION

[0050] In conjunction with the drawings in the embodiments of the present invention, the technical solutions in the embodiments of the present invention are clearly and completely described. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other implementation methods obtained by ordinary technicians in this field without making creative work 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 so that people familiar with this technology can understand and read them. They are not used to limit the conditions under which the present invention can be implemented, and therefore have no substantive technical significance. Any structural modification, change in proportional relationship or adjustment of size should fall within the scope of the technical contents disclosed in the present invention without affecting the effects and purposes 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 a bridge. A soil-tunnel subsystem is established, which includes finite element models of soil and shield tunnel construction. The soil-tunnel subsystem 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. The coupled model is subjected to coupled dynamic analysis based on the asynchronous length method and the time domain integration algorithm to obtain the dynamic response of the train and the 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 two-stage suspension four-axle train: each vehicle consists of a car body, two bogies and four wheel pairs, a total of 7 rigid bodies. Each rigid body considers 6 degrees of freedom, namely telescopic, yaw, floating, rolling, nodding and shaking. A single vehicle contains 6×7 degrees of freedom, a total of 42 degrees of freedom; 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. The spring-damper unit is used to simulate the suspension system to establish a multi-rigid body model of the train.

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

[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 unit, the remaining layers in the track system are simulated using solid units, and the fasteners between the rails and the track plates are simulated using spring units.

[0060] The finite element model of soil and shield tunnel construction is established, and the simulation method of the shield tunnel construction process is as follows:

[0061] Geotechnical tests were carried out on the original soil to determine the physical and mechanical parameters of each soil layer material; the ideal elastic-plastic constitutive model was used to simulate the soil; the yield criterion was the Drucker-Prager yield criterion, which is expressed as follows:

[0062]

[0063] Where: J2 is the second invariant of the deviatoric stress tensor, I1 is the first invariant of the stress tensor, and α and β are both material constants, defined as:

[0064]

[0065] I1=σ1+σ2+σ3

[0066]

[0067]

[0068] Where: σ1, σ2 and σ3 are the three principal stresses of the soil; c and θ 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 of the soil and shield tunnel construction is taken at 3-5 times the tunnel diameter, and the soil layer is simulated by three-dimensional solid units. The structures involved in the shield construction include the shield shell, segments and grouting layer. Plate units are used to simulate the shield shell and segments in the structures involved in the shield construction.

[0070] Determine the boundary constraint conditions of the finite element model of soil and shield tunnel construction, where 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 and rear, 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] P=P0+P w +P y

[0074] P0=K0γH

[0075]

[0076] Where: P is the mud water pressure; P0 is the static soil pressure on the excavation surface; P w is the water pressure on the excavation surface; P y is the reserved pressure; K0 is the static earth pressure coefficient; γ is the bulk density of the soil; H is the burial depth of the tunnel center; v is the Poisson's ratio of the soil.

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

[0078] P1=γH0

[0079]

[0080] P2=K0γH0

[0081] P3=K0γ(H0+D)

[0082] In the formula: H0 is the buried depth of the shield shell top; G is the shield weight; D is the shield diameter; L is the shield length.

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

[0084] F = μπDL (P1+P1′+P2+P3) / 4

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

[0086] The jack at the tail of the shield acts on the segment to provide 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] T=P+F

[0088] Where: T is the jack thrust;

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

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

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

[0092]

[0093]

[0094]

[0095] Among them, M v , M b and M t are the mass matrices of the vehicle, bridge-track, and soil-tunnel subsystems, respectively, and C v , C b and C t are the damping matrices of the vehicle, bridge-track and soil-tunnel subsystems, respectively, and K v , K b and K t are the stiffness matrices of the vehicle, bridge-track and soil-tunnel subsystems, respectively, and u v ,u b and u t 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, R v , R b and R t are the generalized load vectors for the vehicle, bridge-track, and soil-tunnel subsystems, respectively.

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

[0097] The wheel-rail contact relationship is the key to the coupling between the train and the bridge-track system. The wheel-rail normal force refers to the normal force perpendicular to the wheel-rail contact surface during the contact between the wheel and the rail, which is calculated according to the following formula:

[0098]

[0099] Where: p and are the normal penetration amount and normal penetration velocity between wheel and rail respectively; k and c are the stiffness and damping of the spring respectively.

[0100] Based on the asynchronous length method and time domain integration algorithm, the dynamic equations of the coupled model of the train-bridge-soil-shield tunnel system are solved:

[0101] 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, and the two subsystems are combined through the common node on the pile foundation cap.

[0102] The corresponding integration algorithms and time steps are selected for the train-bridge subsystem and the foundation-soil-shield tunnel subsystem respectively; 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;

[0103] This method is essentially different from the current research status, which divides the entire system into two parts, above ground and underground, and studies them separately. In the substructure method, each subsystem interacts in real time. 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.

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

[0105] ||u i -u i-1 ||≤E·||ui-1 ||

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

[0107] The specific embodiments are as follows:

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

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

[0110] In this embodiment, the track system is a CRTSⅢ standard plate track structure, which consists of rails, track plates, self-compacting concrete and base plates from top to bottom. The rails are 60kg / m rails, which are simulated by Timoshenko space beam units. The track plates, self-compacting concrete layers and base plates are simulated by solid units. The structural parameters are shown in Table 1. For the constraints between the track layers, since the bridge and the base plate are consolidated by embedded steel bars, and the track plates and self-compacting concrete layers are consolidated by gate-shaped bars, the relative displacement between them is not considered. The two bosses under the self-compacting concrete layer and the corresponding grooves on the base plate are interlocked and limited, and the self-compacting concrete and the base plate are connected by nonlinear springs to simulate the "geotextile" isolation layer between the layers, and the friction coefficient is 0.70. The prefabricated unit track plates on the bridge are assembled and combined according to actual specifications. The fasteners between the rails and the track plates are simulated by spring units.

[0111] Table 1 Track structure parameters

[0112]

[0113] In this embodiment, WJ-8 type constant resistance fasteners are used between the rails and the track plates, the fastener spacing is 0.63m, and linear spring units are used to simulate the lateral and vertical stiffness of the fasteners, and their stiffness coefficients are 50kN / mm and 35kN / mm respectively. The longitudinal resistance of the fastener is simulated by nonlinear spring units, and the longitudinal force of the fastener is taken as:

[0114]

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

[0116] In this embodiment, the bridge is a 4-span 32m simply supported box girder bridge, and the cross-sectional form of the main beam and the support arrangement are shown in Figure 3. The vertical, transverse and longitudinal spring stiffnesses are simulated according to the vertical and horizontal bearing capacities and allowable displacement ranges of the supports, and the values ​​are shown in Table 2.

[0117] Table 2 Support stiffness parameters

[0118]

[0119] In this embodiment, the net burial depth of the tunnel is 10m, and the construction order is left line first and then right line. The tunnel segment is circular with an outer diameter of 13.25m and an inner diameter of 12.05m. The elevation view of the soil and the shield tunnel is shown in Figure 3. For the model size of the soil, considering the boundary constraint effect of the stratum, the boundary surface of the model is taken at 5 times the tunnel diameter. Because the inclination of each soil layer in the embodiment is small, it can be approximately considered as a horizontal soil layer, that is, the horizontal soil layer is used for simulation in the numerical model, and the soil layer is simulated by solid units. 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: height irregularities, directional irregularities, and horizontal irregularities. The expression is as follows:

[0124] Uneven height:

[0125]

[0126] Unsmooth direction:

[0127]

[0128] Uneven level:

[0129]

[0130] Where S(Ω) is the power spectral density of the unsmoothness, and the unit is m2 / (rad / m); Ω is the spatial frequency of the unsmoothness, Ω r ,Ω c ,Ω s are the cutoff frequencies, both in rad / m; A v , A a is the roughness coefficient, the unit is m 2rad / m; b is half of the rolling circle distance between the left and right wheels, which is 0.75m in this paper. The power spectrum density function is used to generate the empty space roughness samples, as shown in Figure 5.

[0131] When solving the train-bridge-soil-shield tunnel time-varying coupling system, the entire model is decomposed into two subsystems: the train-bridge subsystem and the foundation-soil-shield tunnel subsystem. The two subsystems are combined through the common node on the pile foundation cap, such as Figure 6 shown.

[0132] According to the method of this embodiment, the dynamic response of each part of the system can be obtained, including wheel-rail force, vibration acceleration and displacement of vehicles, tracks, bridges and soil, etc. Taking the excavation of the double-track tunnel as an example, some analysis results at different train running speeds are shown in Figures 7-8.

[0133] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on 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 a 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, so as to obtain the coupled model of the train-bridge-soil-shield tunnel system. 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 the structure when the shield machine passed under the bridge was obtained.

2. The train-bridge-soil-shield tunnel system coupled dynamic analysis method 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 main beam, bearings, piers, and piles of the bridge, and simulating the vertical, lateral, and longitudinal spring stiffness of the bearings of the bridge according to the vertical and horizontal bearing capacities and allowable displacement ranges of the bearings; The steps of establishing the track finite element model are as follows: the rails in the track system are simulated based on the Timoshenko spatial beam unit, the remaining layers in the track system are simulated using solid units, and the fasteners between the rails and the track plates are simulated using spring units.

3. The train-bridge-soil-shield tunnel system coupled dynamic analysis method according to claim 1 is characterized by: The method of 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 the train is established using a two-stage suspension four-axle train: the primary suspension system of the train connects the wheelset and the bogie, the secondary suspension system connects the bogie and the car body, and a spring-damper unit is used to simulate the suspension system to establish a multi-rigid body model of the train.

4. The train-bridge-soil-shield tunnel system coupled dynamic analysis method according to claim 1 is characterized by: The finite element model of the soil and shield tunnel construction is established, and the simulation method of the shield tunnel construction process is as follows: Conduct geotechnical tests on the original soil to determine the physical and mechanical parameters of each soil layer material; and use the ideal elastic-plastic constitutive model to simulate the stress-strain relationship of the soil; Considering the boundary constraint effect of the stratum, the boundary surface of the finite element model of soil and shield tunnel construction is taken at 3-5 times the tunnel diameter. The soil layer is simulated by three-dimensional solid elements, and the shield shell and pipe segments in the structure involved in the shield construction are simulated by plate elements. Determine the boundary constraint conditions of the finite element model of soil and shield tunnel construction, where 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 and rear, left and right boundary surfaces are subject to normal constraints; Determine the shield tunnel construction load, wherein the shield tunnel construction load includes mud water pressure, friction force, jack thrust and grouting pressure; The shield tunnel construction process is simulated by transforming the material properties of the cells and controlling the birth and death of the cells.

5. The train-bridge-soil-shield tunnel system coupled dynamic analysis method according to claim 1 is characterized by: The wheel-rail contact relationship includes a wheel-rail contact geometric relationship and a wheel-rail force; wherein the wheel-rail contact geometric relationship includes a wheel-rail contact profile, a wheel-rail contact point and a contact model; the wheel-rail force includes a wheel-rail normal force and a 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 is characterized by: The dynamic equation of the coupled model of the train-bridge-soil-shield tunnel system is expressed as follows: Among them, M v , M b and M t are the mass matrices of the vehicle, bridge-track, and soil-tunnel subsystems, respectively, and C v , C b and C t are the damping matrices of the vehicle, bridge-track and soil-tunnel subsystems, respectively, and K v , K b and K t are the stiffness matrices of the vehicle, bridge-track and soil-tunnel subsystems, respectively, and u v ,u b and u t 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 R v , R b and R t are the generalized load vectors for the vehicle, bridge-track, and soil-tunnel subsystems, respectively.

7. The train-bridge-soil-shield tunnel system coupled dynamic analysis method according to claim 6 is characterized by: Based on the asynchronous length method and time domain integration algorithm, the dynamic equations of the coupled model of the train-bridge-soil-shield tunnel system are solved: 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, and the two subsystems are combined through the common node on the pile foundation cap. The train-bridge subsystem and foundation-soil-shield tunnel subsystem select corresponding integration algorithms and time steps respectively; 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 are interacted to obtain the result of the time step, which is used as the excitation of the next time step; In each time step, once the convergence condition is met, the next time step will be calculated until the entire calculation is completed.

8. The train-bridge-soil-shield tunnel system coupled dynamic analysis method according to claim 7 is characterized by: 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 the train-bridge subsystem.

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