Simulation analysis method and system for tunnel structure response under multi-source dynamic action

Abstract

The invention provides a simulation analysis method and system for tunnel structure response under the action of multi-source power. The simulation analysis method comprises the following steps: S1, constructing a numerical solution system for coupling load analysis; s2, constructing a track-tunnel-soil body implicit dynamic analysis finite element model based on the numerical solution system, and forming a structure-soil body dynamic coupling system; s3, setting a plurality of types of working conditions according to preset requirements, wherein the working conditions comprise actual measurement and simulation scenes of a vehicle body and an earthquake; s4, analyzing a structure response result to obtain a response rule under the action of multi-source power; a track-tunnel-soil body three-dimensional finite element implicit dynamic analysis model is constructed, key technologies such as static-dynamic ground stress balance conversion, viscoelastic artificial boundaries, seismic oscillation equivalent node force input and train vibration function loading are comprehensively adopted, and a reliable simulation system of tunnel structure response under the multi-source dynamic effect is established.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of tunnel dynamic response simulation, and particularly relates to a simulation analysis method and system for tunnel structure response under multi-source dynamic action. BACKGROUND

[0002] Under the complex background of high-speed metro and earthquake coupling, the nonlinear response characteristics and evolution mechanism of tunnel structure have not been systematically revealed, which limits the engineering applicability and popularization of related research results in the multi-source load coupling environment.

[0003] In the prior art, the tunnel response analysis under the single action of earthquake or high-speed metro vibration is relatively mature, but most of the researches still stay at the stage of treating the two types of loads independently, and lack of in-depth discussion on the synergistic effect under the space-time overlapping situation. At the same time, although the research on train-seismic coupling has developed in recent years, the research focus is mainly concentrated on the superstructure system such as bridge and subgrade, and mainly focuses on the stability and safety of train operation, such as the change of wheel-rail contact force, derailment risk assessment, etc., and less involves the mechanical behavior and failure mechanism of buried tunnel structure under combined load. At the same time, the current research on high-speed metro vibration mainly focuses on the vibration reduction performance optimization of auxiliary components such as fasteners and steel spring floating slab, such as the influence of vibration isolator stiffness, damping parameters and other parameters on the vibration reduction effect, and the overall level research on the propagation path, response amplification and blocking mechanism of train vibration in the track-tunnel-soil system is still relatively insufficient, especially the quantitative response law and transmission mechanism analysis of structure. SUMMARY

[0004] The purpose of the present application is to provide a simulation analysis method for tunnel structure response under multi-source dynamic action, which reveals the amplification trend, nonlinear evolution characteristics and main control failure mechanism of tunnel structure displacement and stress response under the coupling action of high-speed train vibration and ground motion, and clarifies the key sensitive parts of arch waist and its adjacent area for crack initiation, and clarifies the spatial differentiation law of structure response under different excitation intensity.

[0005] In order to achieve the above purpose, one aspect of the present application provides a simulation analysis method for tunnel structure response under multi-source dynamic action, comprising the following steps: S1: constructing a numerical solution system for coupled load analysis; S2: constructing an implicit dynamic analysis finite element model of track-tunnel-soil based on the numerical solution system, forming a structure-soil dynamic coupling system; S3: setting a plurality of types of working conditions according to the preset requirements, the working conditions including measured and simulated scenarios of vehicle body and earthquake; S4: analyzing the structure response results to obtain the response law under multi-source dynamic action.

[0006] Preferably, S1 comprises: The numerical solution system adopts an implicit dynamic algorithm, which is constructed based on dynamic balance differential equations, and the real response is gradually approached by solving the global balance equation of the system at each time step and combining Newton-Raphson iteration to control the convergence of the nonlinear problem.

[0007] Preferably, S2 comprises: the modeling method comprises the following steps: S21: using C3D8R solid elements to model the tunnel lining, track bed, steel rail and soil body; S22: using a double-broken-line elastic-plastic constitutive model to simulate material nonlinear behavior; S23: using Rayleigh damping to simulate the damping effect of each component of the tunnel and the soil body on vibration, and inversely solving the damping parameters α and β based on the frequency matching method; S24: using a multi-directional assignment connection element to simulate the stiffness support and damping vibration attenuation effect of the SFC fastener system.

[0008] Preferably, S2 comprises: in the initial condition construction of the implicit dynamic analysis finite element model, the following steps are included: S25: completing static stress balance by applying a gravity field to the model under fixed boundary conditions; S26: realizing static-dynamic stress conversion by using boundary release and stress field inheritance; S27: introducing viscoelastic boundary conditions to simulate elastic recovery and energy scattering of the semi-infinite foundation; S28: applying a typical track irregularity excitation function to the vehicle body vibration through a pre-set subprogram; S29: after converting to equivalent seismic load through an equivalent section load method, inputting three-directional seismic waves for simulating seismic vibration.

[0009] Preferably, S28 comprises: establishing a programmable train vibration input method for the abaqus platform, comprising the following steps: S281: decomposing the vertical wheel-rail force of the vehicle body into three independent physical excitation sources: vehicle body-suspension system coupling, spring mass rebound, and wheel-rail contact; S282: based on multi-interval distributed excitation modeling of travel speed, excitation frequency, and vehicle grouping parameters; S283: using a time-domain sliding window method to locate the action area, for automatically activating or releasing the moving load in the vehicle body.

[0010] Preferably, the method for simulating the track-tunnel response under continuous excitation of multiple high-speed vehicle bodies comprises the following steps: S284: define constants: a vector height, L typical wavelength, t current time step, v train moving speed, m0 mass of the car body, w circular frequency, and p wheel static load; S285: define the interval of the load region; S286: calculate the trigger time of each region; S287: traverse all the load regions; S288: determine whether the node is in the current load interval; S289: if the node is not in any interval, the load is zero.

[0011] Preferably, S29 comprises a three-dimensional seismic wave input method combining filtering, integration and equivalent node load, comprising the following steps: S291: use a band-pass filter to remove high-frequency noise and low-frequency drift in the seismic record; S292: use time history integration method to convert acceleration to velocity and displacement; S293: use baseline correction to avoid integration drift; S294: apply seismic input to the boundary of the implicit dynamic analysis finite element model through the equivalent node seismic load method.

[0012] Preferably, the working conditions at least include a car body vibration working condition, a seismic working condition, and a car body vibration and seismic load superposition working condition; The car body vibration working condition sets a plurality of car body speeds. The seismic working condition sets a plurality of seismic input intensities.

[0013] Preferably, S4 comprises obtaining the propagation law of the high-speed car body in the structural system, the main stress characteristics of each part of the tunnel, and the influence of seismic load superposition based on the response analysis results under different working conditions.

[0014] Another aspect of the present application provides a simulation analysis system for tunnel structure response under multi-source dynamic action, which uses the simulation analysis method for tunnel structure response under multi-source dynamic action described above, comprising: a modeling module configured to construct an implicit dynamic analysis finite element model of track-tunnel-soil, forming a structure-soil coupling system, the modeling module adopts a solid element modeling method, and includes a connecting element for simulating a fastener system; a solving module configured to perform numerical solving based on an implicit dynamic algorithm to solve the response process of the model under multi-source load action, the solving module adopts an implicit time integration method based on dynamic equilibrium differential equation, and combines Newton-Raphson iteration to control nonlinear convergence; The working condition configuration module is configured to set several types of excitation working conditions, including a vehicle body vibration working condition, an earthquake working condition and a coupling working condition thereof, and support input of measured or simulated train load and earthquake time history data; The load input module is configured to input train vibration load and three-directional earthquake load respectively, the train vibration load is generated by a preset subroutine, and the earthquake load is applied through filtering, integration and equivalent node load mode; And the response analysis module is configured to extract structural response indexes of the model under different working conditions, including acceleration, displacement, principal stress, and identify high stress areas, nonlinear enhancement features and potential crack risks.

[0015] The technical scheme provided by the application can achieve the following beneficial effects: 1. The application constructs a unified three-dimensional track-tunnel-soil coupling model, combines an implicit dynamic analysis framework and a viscoelastic boundary condition, effectively captures the nonlinear dynamic response characteristics of the structure under multiple-source complex excitation, and realizes full-process high-precision simulation of the responses of the rail, track slab, tunnel lining and ground surface.

[0016] 2. Under the action of high-speed train vibration, the dynamic response of the tunnel system shows a significant nonlinear amplification trend, especially when the train running speed is increased to 160km / h, the acceleration and displacement responses of the rail and the ground surface are nonlinearly increased, which reflects the advantages of the method in capturing the nonlinear relationship between speed and response.

[0017] 3. The application can identify high-risk areas such as arch waist and arch foot by extracting principal stress distribution and comparing with material limit parameters, especially under the action of coupled load, it can accurately identify the stress overrun, crack initiation and expansion trend caused by the load enhancement of the stress concentration area, and provide a scientific basis for identifying weak links of the structure.

[0018] 4. The application can simulate the structural response under the independent or superimposed action of train vibration and earthquake motion, especially when the seismic intensity is low (such as 0.05g~0.2g), it can effectively reveal the modulation effect of train vibration on seismic response, such as inhibition of uplift and enhancement of settlement, and has the ability to adapt to complex operating conditions of typical urban track engineering.

[0019] 5. The application can not only be used to analyze the dynamic behavior of the tunnel structure under extreme coupled load, but also can propose key design suggestions for strengthening, crack control and durability improvement of the structure, and is particularly suitable for quantitative guidance of arch waist area reinforcement and seismic optimization in high-speed subway engineering. BRIEF DESCRIPTION OF DRAWINGS

[0020] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the accompanying drawings needed to be used in the embodiments or prior art description will be briefly introduced as follows. Obviously, the accompanying drawings in the following description only only the embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of the provided drawings.

[0021] Figure 1 It is the flow chart of the simulation analysis method of the tunnel structure response under the action of multiple sources provided by the embodiments of the present application. Figure 2 It is the flow chart of the modeling method provided by the embodiments of the present application. Figure 3 It is the meshing diagram of the track-tunnel-soil model provided by the embodiments of the present application. Figure 4 It is the interaction diagram in the finite element model provided by the embodiments of the present application. Figure 5 It is the flow chart of the initial condition construction method of the implicit dynamic analysis finite element model provided by the embodiments of the present application. Figure 6 It is the comparison diagram of the vertical displacement of the rail under the vibration working condition and the coupling working condition of the 160km / h train provided by the embodiments of the present application. Figure 7 It is the ground stress balance diagram under the dynamic boundary condition provided by the embodiments of the present application. Figure 8 It is the viscoelastic boundary diagram in the finite element model provided by the embodiments of the present application. Figure 9 It is the flow chart of the programmable train vibration input method for the abaqus platform provided by the embodiments of the present application. Figure 10 It is the method flow chart of simulating the track-tunnel response under the continuous excitation of multiple high-speed train bodies provided by the embodiments of the present application. Figure 11 It is the three-dimensional seismic wave input method flow chart provided by the embodiments of the present application, which combines filtering, integration and equivalent node load. Figure 12 It is the comparison diagram of the vertical displacement of the rail under the vibration working condition and the coupling working condition of the 160km / h train provided by the embodiments of the present application. Figure 13 It is the tunnel vertical displacement response time history curve diagram under the train, earthquake and coupling three working conditions (0.05g) provided by the embodiments of the present application. Figure 14 It is the tunnel vertical displacement response time history curve diagram under the train, earthquake and coupling three working conditions (0.1g) provided by the embodiments of the present application. Figure 15 is a tunnel vertical displacement response time curve diagram under three working conditions (0.2g) of train, earthquake and coupling provided by the embodiment of the application; Figure 16 is a tunnel vertical displacement response time curve diagram under three working conditions (0.4g) of train, earthquake and coupling provided by the embodiment of the application; Figure 17 is a tunnel maximum principal stress nephogram under a 160km / h train working condition provided by the embodiment of the application; Figure 18 is a tunnel first principal stress nephogram under a 160km / h train and 0.05g earthquake coupling working condition provided by the embodiment of the application; Figure 19 is a tunnel third principal stress nephogram under a 160km / h train and 0.05g earthquake coupling working condition provided by the embodiment of the application; Figure 20 is a simulation analysis system structure schematic diagram of a tunnel structure response under multi-source power provided by the embodiment of the application. DETAILED DESCRIPTION

[0022] Embodiments of the application are described in detail below, examples of which are shown in the drawings, wherein the same or similar reference numbers represent the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the drawings are exemplary and are intended to explain the application, and cannot be understood as a limitation of the application.

[0023] In the description of the present specification, the description of the terms “one embodiment”, “some embodiments”, “an example”, “a specific example”, or “some examples” and the like 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 present application. In the present specification, the illustrative description of the above terms is not necessarily directed to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any appropriate manner in any one or more embodiments or examples. In addition, the person skilled in the art can combine and combine the different embodiments or examples described in the present specification and the features of the different embodiments or examples without contradiction.

[0024] The present application provides a simulation analysis method for tunnel structure response under multi-source power, as shown in Figure 1 , comprising the following steps: S1: Constructing a numerical solution system for coupling load analysis. The numerical solution system adopts an implicit dynamic algorithm, the implicit dynamic algorithm is constructed based on a dynamic balance differential equation, the global balance equation of the system is solved in each time step, and the Newton-Raphson iteration is combined to gradually approach the true response, and the convergence controls the non-linear problem.

[0025] Specifically, the construction of high-precision, strong stability of the numerical solution system is the basis for the development of coupled load analysis. The implicit dynamic algorithm is based on the dynamic equilibrium differential equation of the structural system, and its solution target is the displacement, velocity and acceleration of the structure at each time. The typical implicit integration method uses the time integration scheme based on the Newmark format, and its control equation can be discretized as: ; In the formula, M is the system mass matrix, C is the system damping matrix, K is the system stiffness matrix, is the external load vector of the train excitation force and ground motion at any time.

[0026] The above control equation is a second-order ordinary differential equation. In the implicit integration method, the prediction-correction strategy based on acceleration and velocity is used to convert it into a nonlinear algebraic equation group. Through the incremental form of the update algorithm, the implicit method linearizes the above nonlinear equation group at each time step and iteratively solves it within the specified tolerance range. This strategy is not limited by the conditional stability and can use a larger time step without losing the stability of the solution, which is suitable for low-frequency response problems such as tunnel structure systems. Its control equation can be discretized by the following approximation: ; ; In the formula, , , are the node displacement, velocity and acceleration vectors at the nth time, , , are the node displacement, velocity and acceleration vectors at the n+1 time, Δ t is the time interval between the adjacent two time steps, β is the displacement acceleration weighting coefficient for controlling numerical stability and precision, which is 0.25, is the velocity acceleration weighting coefficient for adjusting the numerical damping characteristics, which is 0.5.

[0027] First, in the initialization stage, the model needs to import the initial stress field obtained by the geostress balance analysis, and introduce the initial displacement and velocity field as the starting conditions of dynamic analysis, to ensure the continuity and physical consistency of static-dynamic analysis.

[0028] Subsequently, time step discretization and load update operations are performed. According to the analysis target, the integral step is set, and the seismic and train vibration loads are interpolated to make the input loads continuously change with time, thereby realizing the loading of the real excitation time history.

[0029] Secondly, in each time step, the implicit integration method is used for nonlinear iterative solution. Through continuous calculation of residual force and tangent stiffness matrix, the Newton-Raphson method is used to gradually correct the node displacement and internal force balance state until the preset convergence criterion is met. The implicit method can capture the subtle response characteristics of the tunnel structure under complex load with high numerical precision in dealing with boundary impedance effect, local nonlinearity, material yield and viscoelasticity, and is suitable for dynamic response simulation of multiple nonlinear mechanisms in the present application.

[0030] Finally, after solving, the time history data of node acceleration, displacement, stress and principal stress are output by the system, and the response of typical cross section and key measuring point is extracted, which provides basic data support for subsequent vibration propagation analysis, coupling effect evaluation and structure safety judgment.

[0031] In one example, a new high-speed subway tunnel system is taken as the research object. Specifically, the train running speed is as high as 160km / h, and the seismic excitation adopts three-direction strong earthquake vertical incidence mode, which constitutes a typical double excitation environment of high-frequency traffic load and sudden earthquake disturbance. The system involves tunnel lining structure, rail system, sleeper foundation and surrounding soil and other subsystems, and shows the characteristics of significant material nonlinearity, complex boundary coupling and fine load time history. In summary, the model analysis mainly has the following three outstanding characteristics: first, the time domain simulation span is large, and the load time-varying is severe, which puts forward higher requirements for the stability and error control ability of numerical algorithm; second, the contact relationship between ground and structure is complex, and the local stiffness changes obviously, so the large deformation, nonlinear constitutive and multi-contact surface effect should be fully considered; finally, the train excitation and seismic vibration exist superposition, interference and even local resonance risk in space and frequency domain, so the continuous and fine capture of the whole process response evolution process is necessary.

[0032] In terms of boundary and load coupling processing, the implicit method can fully support the cooperative action of various complex boundary conditions and load inputs, such as viscoelastic boundary energy absorption, train excitation function loading and three-direction seismic vibration equivalent node force input, and has strong processing ability of mixed input of multiple excitation sources. In addition, in the response output level, the implicit algorithm can continuously track the whole process dynamic response of the structure, accurately capture the maximum stress, maximum displacement, acceleration peak value and evolution path, and provide a solid data foundation for systematic comparative analysis under different load conditions.

[0033] S2: Constructing an implicit dynamic analysis finite element model of the track-tunnel-soil based on the numerical solution system, forming a structure-soil dynamic coupling system.

[0034] Specifically, the present example takes a city rapid rail transit project as the background, focusing on the structural response problem of the high-speed subway tunnel system under the combined action of train vibration and seismic load. The line is a double-track seamless track system, the track type adopts ballastless track, the rail standard is 60 kg / m, and the design running speed reaches 160 km / h. The train type is city D-type vehicle, and the single axle weight is 17 t. The tunnel depth is 19.5 m, and the single-hole single-line arrangement is adopted, and the cross-section size is obviously larger than that of the traditional urban subway tunnel. In terms of track geometric accuracy, the track gauge is controlled within ±2 mm, and the track alignment, height, level and twist indicators are all controlled at the level of 2 mm.

[0035] In the present example, a typical three-dimensional track-tunnel-soil system model is constructed according to the actual engineering parameters, which includes four main components of steel rail, track slab, tunnel lining structure and surrounding rock soil. Among them, the track structure includes steel rail, track slab and fastener system, and the overall arrangement is matched with the vehicle wheelbase.

[0036] As shown in Figure 2 , S2 includes: the modeling method includes the following steps: S21: using C3D8R entity elements to model the tunnel lining, track bed, steel rail and soil.

[0037] Specifically, the tunnel lining, track slab, steel rail and surrounding soil are uniformly discretized by C3D8R entity elements. This element is a three-dimensional eight-node linear reduced integration entity element, which has strong nonlinear solving ability and can effectively deal with complex stress state and multi-source excitation coupling problems under dynamic load. By introducing hourglass control mechanism, the element locking problem caused by reduced integration is overcome, so that the element type can better handle the nonlinear response and multi-field coupling problems in large-scale structure system while maintaining the calculation efficiency, and is suitable for multi-material collaborative modeling of steel-concrete-soil in subway tunnel structure. In order to improve the calculation accuracy and avoid errors caused by element distortion, the grid division of each component is differentiated according to its stiffness, size characteristics and main control response frequency, as shown in the following table 1: Table 1 Grid division of each component of the model S22: using a double-line elastic-plastic constitutive model to handle material nonlinearity.

[0038] Specifically, the steel rail, as the key part to bear high-frequency excitation, is controlled in a grid size of 0.1 m to ensure capturing vibration details; the track slab and the lining part are divided into a medium-density grid with a size of 0.5 m to balance the response capturing ability and computational efficiency; the soil area is divided into a moderately encrypted transition grid, with a higher density near the tunnel area and a proper relaxation in the far field area. The grid division of the track-tunnel-soil model is shown in FIG. 1. Figure 3

[0039] The soil type in the actual engineering area is medium-soft soil, and the soil material parameters are set in combination with the geological conditions of the typical area. The soil around the tunnel is defined as medium-soft soil type, and the specific material parameters are selected according to the typical values of soft soil in coastal areas. In terms of the selection of the lining structure material constitutive, the concrete adopts a simplified softening-type elastic-plastic constitutive model, and the reinforcement part adopts a double-fold line strengthening-type ideal elastic-plastic constitutive; the material parameters are shown in Table 2. Table 2 Grid size and material parameters of each component of the finite element model S23: Rayleigh damping is used, and the damping parameters a and β of the mass and stiffness terms are inversely solved based on the frequency matching method.

[0040] Specifically, in the analysis of the dynamic response of the tunnel, the setting of the damping parameter has a direct impact on the vibration response of the structure and the soil. To effectively simulate the energy dissipation behavior of the material in the actual engineering, Rayleigh damping model is used for processing, and a double-target frequency matching method is introduced to determine the proportional coefficient of the mass term and the stiffness term. The Rayleigh damping model assumes that the total damping matrix of the system is linearly combined by the mass damping term and the stiffness damping term, and its form is expressed as: C = a M + β K； In the formula, C is the system damping matrix, M is the system mass matrix, K is the system stiffness matrix, α is the coefficient related to the mass matrix of the Rayleigh damping, β is the coefficient related to the stiffness matrix of the Rayleigh damping.

[0041] ​To ensure that the damping characteristics can cover the wide frequency excitation range involved in train vibration and ground motion, the target frequency range of this example is set to 0.1 Hz to 500 Hz, corresponding to the lowest and highest dominant frequencies that may occur in engineering, respectively. The Rayleigh damping model of the double-frequency method is used to process the damping, where the lower limit frequency corresponds to the long-period low-frequency response of the structure, and the upper limit target frequency can cover the high-frequency disturbance caused by train load, which is suitable for simulating the energy dissipation behavior of wide-frequency sensitive foundation materials such as soft soil. After the target frequency range is determined, the typical damping ratio is selected, and the mass item coefficient α and the stiffness item coefficient β are inversely solved by the frequency matching method, and the calculation formula is as follows: ; In the formula, ξ is the target damping ratio of the structure, which is 5%, is the lower limit frequency, which is 0.1 (Hz), is the upper limit of the reference frequency, which is 500 (Hz).

[0042] The damping coefficient set by the above method can effectively cover the energy dissipation requirements of the structure in the typical excitation frequency band, and can ensure the calculation stability and physical reasonableness between different frequency responses, avoiding the phenomenon of over-dissipation of low-frequency response or ineffective attenuation of high-frequency vibration. This double-frequency matching method is more suitable for modeling and analysis of tunnel-track-soil system with multiple excitation characteristics, improving the engineering credibility and response fitting degree of dynamic simulation.

[0043] S24: Simulate the SFC fastener system using a multi-directional assignment connection element.

[0044] Specifically, to realize the coordinated deformation and overall response between different structural components, various contact and coupling methods are introduced in the model. In terms of the interaction between the model steel rail and the track slab, the linear elastic fastener connection is distributed and set, and the fastener system is simulated by linear assignment connection with different directions. The stiffness and damping parameters of the fastener system are set according to the SFC fastener of this project, the fastener spacing is 0.6 m, and the vertical, horizontal and longitudinal support stiffness and damping constraints are provided to constrain the relative movement between the rail and the track bed and transfer the dynamic load. The stiffness and damping parameters in each direction are shown in Table 3: Table 3 Fastener Stiffness and Damping Parameters Tie constraint, as a kind of face-to-face rigid connection interaction, is widely used between key components such as track slab and lining, lining and surrounding soil. The basic principle is to divide the two contact surfaces into master and slave surfaces, and force the nodes on the slave surface to have the same displacement as the master surface nodes during the entire dynamic analysis process, so as to realize the effect of node co-moving, avoid the relative slip or disconnection between structures, and the interaction in the finite element model is shown in Figure 4 .

[0045] In the 3D track-tunnel-soil model established in this example, Tie constraints are used between the track slab and the tunnel lining to simulate the close contact between the track slab and the lining foundation. In actual construction, this area is often constructed with ballast mortar or dry hard concrete, which provides high rigidity and strong adhesion, making it difficult to experience significant slippage or delamination under dynamic conditions. Therefore, it can be approximated as a connection with no relative displacement. Similarly, Tie constraints are used to establish the interaction between the tunnel lining and the surrounding soil to maintain deformation consistency between the overall tunnel structure and the surrounding rock system.

[0046] In one example, in the initial condition construction of an implicit dynamic analysis finite element model, such as Figure 5 As shown, the following steps are included: S25: Static geostress equilibrium is achieved by applying a gravity field.

[0047] Specifically, the initial geostress field is established during a static analysis step. This involves applying gravity loads and reasonable boundary constraints to the model, ensuring that the system reaches a stable stress-displacement state under pure gravity. After the calculation is complete, the stress field variables and boundary reactions are extracted and used as initial state inputs in subsequent dynamic analysis steps.

[0048] S26: Use boundary release and field inheritance to achieve static-dynamic ground stress conversion.

[0049] Specifically, after completing the static stress balance, the dynamic analysis needs to continue with the stress field as the initial condition. The control equation in the dynamic solution module must satisfy the system in a static equilibrium state at the initial moment. t =0, The system should meet the following requirements: Ku 0= F 0; Where, u 0 is the node displacement in static equilibrium state, F 0 is gravity and boundary node reaction force.

[0050] S27: Introducing viscoelastic boundary conditions to simulate the elastic recovery and energy scattering of semi-infinite foundations.

[0051] Specifically, in dynamic analysis, if all static loads are not applied correctly at the initial stage or the treatment of boundary constraint reaction is ignored, the model will be in a state of mechanical imbalance, resulting in a false response phenomenon even under zero seismic load conditions, which will seriously interfere with the extraction and analysis of real dynamic response data. Therefore, in the case of changes in boundary conditions, such as the use of traditional fixed boundaries in static analysis and the introduction of viscoelastic boundaries in dynamic analysis, the constraint reaction of the static stage must be converted into equivalent node forces and applied to the model to ensure the consistency of the overall mechanical system and the correctness of the initial dynamic conditions.

[0052] This example introduces a reasonable static-dynamic boundary conversion process in the modeling environment of viscoelastic artificial boundaries, which mainly includes four key steps: First, in the static analysis stage, traditional static boundaries such as roller boundaries or fixed boundaries are applied to complete a series of operations such as self-weight loading and support structure activation, and then the complete static stress field distribution and boundary node constraint reaction are obtained; Subsequently, before entering the dynamic analysis stage, all boundary constraints applied in the static stage should be completely removed to avoid dynamic instability problems caused by inconsistent boundary conditions; Next, viscoelastic dynamic boundaries with energy absorption characteristics are introduced at the model boundary, such as setting spring-damping elements or uniform viscoelastic elements, to realistically simulate the propagation and energy dissipation process of seismic waves; Finally, the self-weight load, support reaction, and boundary reaction extracted in the previous stage need to be converted into equivalent node forces and applied to the model to ensure that the system reaches a strict mechanical equilibrium state at the initial moment of dynamic analysis.

[0053] In subsequent simulations, to achieve a realistic seismic wave propagation path, this example will introduce a viscoelastic boundary and a three-dimensional seismic wave vertical incidence scheme. The viscoelastic boundary absorbs reflected wave energy based on a spring-damping system, and its parameter settings depend on the material parameters and spatial positions of the model boundary nodes. The model is in a strict static equilibrium state at the initial moment, which is a prerequisite for the viscoelastic boundary to normally absorb energy. In addition, the way of applying equivalent node loads to seismic waves is closely related to the setting of boundary conditions.

[0054] The viscoelastic boundary simulates the absorption and dissipation of seismic waves by the soil at infinity by setting a series of spring and damping elements at the truncated boundary of the finite element model. Its basic idea is derived from the elastic half-space wave theory, which equates the elastic recovery capacity of the soil to the action of a spring and the energy dissipation capacity to the action of a damper based on wave propagation characteristics. In actual calculations, the spring stiffness and damping coefficient applied to the boundary nodes are calculated as follows: ; ; where, KT is the tangential direction of the boundary node, KNKs is the normal spring stiffness, CT Kt is the tangential spring stiffness, CN Cn is the normal damping coefficient, cs Vs is the shear wave velocity of soil, cp Vp is the compression wave velocity of soil, aT and αN Cn is the normal damping coefficient, ρ is the density of soil, G G is the shear modulus, R L is the distance from wave source to boundary node, A A is the node control area.

[0055] The implementation of viscoelastic boundary involves a large number of spring stiffness and damping coefficient calculations and settings of nodes. Traditional manual processing is low in efficiency and prone to errors. In order to solve this problem, a secondary development program is written using Python language to automatically calculate and apply spring stiffness and damping coefficient. The key steps of program implementation include: establishment of spring and damping unit, node control area calculation, intermediate transfer of node information in database and automatic assignment of parameters, which significantly improves the calculation efficiency and reliability. In this example, the viscoelastic boundary is introduced as the core boundary control means for the problem of tunnel structure dynamic response under the combined excitation of high-speed subway train vibration and ground motion. By setting spring-damping unit combination in shear and normal direction on the boundary of the model, the energy dissipation process of infinite domain soil to external load fluctuation is simulated. Combined with the boundary node control interface and substructure definition method of the software, a combined input system of train excitation force and equivalent ground motion is constructed, so as to realize synchronous loading and continuous response tracking under double disturbance in a unified calculation framework.

[0056] Comprehensive S25-S27, in the modeling process of track-tunnel-soil model in this example, a logical and orderly modeling path is formed through static geostatic stress balance, static-dynamic geostress balance conversion and viscoelastic boundary application. The boundary condition setting and its role in each step are shown in Table 4: Table 4 Boundary condition setting and its role table Static geostatic stress balance is the basic stage of modeling. As shown in Figure 6 , the stress field and deformation field of the structure and soil system under static load are obtained by solving the fixed boundary condition, so as to establish a reasonable initial stress state.

[0057] After completing the static geostatic stress balance, static-dynamic geostress balance conversion is needed to remove the constraint boundary formed by the original fixed boundary. As shown in Figure 7 , the equivalent boundary node force equivalent to the boundary reaction force in static analysis is applied to maintain the continuous consistency of the mechanical state of the boundary.

[0058] Since the actual soil is a semi-infinite medium, seismic waves will expand to the far field when propagating, and the artificial boundaries in the finite element model will cause wave reflection and interference. Therefore, based on the static-dynamic stress balance conversion, the viscoelastic boundary is introduced to solve the error problem caused by wave reflection in the finite domain modeling. Figure 8 As shown in the figure, by applying viscoelastic boundaries composed of spring-damper units at the bottom and around the model, the impedance characteristics of the infinite medium can be effectively simulated, thereby absorbing the wave energy propagating to the boundary and preventing non-physical reflections from interfering with the internal response calculation.

[0059] The introduction of this boundary condition allows dynamic analysis to achieve greater fidelity in wave propagation while maintaining the rationality of initial stresses. Specifically, the viscoelastic boundary employs a spring-damper parallel unit configuration. By setting stiffness and damping parameters at the boundary nodes to match the soil's impedance characteristics, the energy dissipation of seismic waves as they propagate to the boundary is achieved. This method not only effectively absorbs the incident energy of P and S waves at the boundary but also realistically reproduces the propagation of seismic waves in semi-infinite soil.

[0060] S28: Apply a typical track irregularity excitation function to the vehicle body vibration through a preset subroutine.

[0061] Specifically, the vehicle vibration function in this example study is based on the urban D-type train in actual engineering, and its vehicle parameters are shown in Table 5: Table 5 Vehicle models and parameters S28 includes: establishing a programmable train vibration input method for the abaqus platform, such as Figure 9 As shown, the following steps are included: S281: Decompose the vertical wheel-rail force of the vehicle body into three independent physical excitation sources: vehicle body-suspension system coupling, unsprung mass rebound, and wheel-rail contact.

[0062] Specifically, the vertical wheel-rail force mainly occurs in three frequency ranges: (1) 0.5Hz to 10Hz, caused by the relative motion between the vehicle body and the suspension system; (2) 30Hz to 60Hz, caused by the rebound effect of the unsprung mass and the rail; (3) 100Hz to 400Hz, caused by the resistance of the rail movement to the wheel-rail contact surface. The wheel-rail force is more significant in the range of 0Hz to 60Hz, while the high-frequency range mainly affects the dynamic response of the vehicle body. The vibration load expression reflects the combined influence of the vehicle system characteristics and the track conditions on the vibration load. Its load function expression is: ; ; Where,P 0 is the static load of the wheel, P 1. P 2. P 3 are the vibration load peak values ​​corresponding to the rail vibration circular frequencies, 、 、 are the circular vibration frequencies, t is the train running time, Li is a typical wavelength.

[0063] Among them, let the unsprung mass of the train be M 0, then the corresponding vibration load amplitude is: ; Where, M 0 is the unsprung mass, which is 750 (kg), ai is a typical sag corresponding to the corresponding wavelength, v is the train running speed.

[0064] S282: Multi-interval distributed excitation modeling based on travel speed, excitation frequency, and vehicle formation parameters.

[0065] Specifically, referring to the irregularity excitation model, three representative wavelength and sag parameters were selected: L1 = 10m, a1 = 3.5mm; L2 = 2m, a2 = 0.4mm; and L3 = 0.5m, a3 = 0.08mm. This combination covers typical track excitation types encountered during high-speed train operation, corresponding to vibration inputs in the three frequency ranges of 5-9Hz low-frequency vibration, 25-45Hz medium-frequency vibration, and 100-200Hz high-frequency vibration.

[0066] S283: The time domain sliding window method is used to locate the action area, which is used to automatically activate or release the moving load during the vehicle's movement.

[0067] Specifically, based on the train load function, this example implements real-time dynamic loading of train loads in the finite element model through a subroutine. During the load application process, the movement trajectory of the load along the track is determined according to the train speed. At the same time, the amplitude and frequency parameters of the vibration load function are derived in combination with the train axle weight and track state, thereby establishing a time-varying load that conforms to the actual working conditions. The load function is applied to the rail nodes in the model in a dynamically changing form, simulating the characteristics of the load evolving with time and space during train operation. The use of subroutines for dynamic loading enables the load parameters to be flexibly adjusted to adapt to the influence of different line conditions and speed changes, further improving the model's ability to express the dynamic response characteristics of train loads and the simulation accuracy.

[0068] The S28 input method is more realistic than traditional concentrated loads or periodic sine waves, and provides a key breakthrough in simulating the track-tunnel response under continuous excitation of multiple high-speed vehicles. Figure 10 As shown, the following steps are included: S284: Define constants: a sag, L typical wavelength, t current time step, v train speed, m0 unsprung mass, w circular frequency, and p wheel static load; S285: Define the interval of the load area; S286: Calculate the trigger time of each area; S287: Traverse all load areas; S288: Determine whether the node is within the current load range; S289: If the node is not in any interval, the load is zero.

[0069] S29: After equivalent nodal force conversion, three-way seismic wave input is performed to simulate ground motion.

[0070] S29 includes: a three-way seismic wave input method combining filtering, integration and equivalent nodal loads, such as Figure 11 As shown, the following steps are included: S291: Use a bandpass filter to remove high-frequency noise and low-frequency drift in seismic records; S292: Use the time-history integration method to convert acceleration into velocity and displacement; S293: Use baseline correction to avoid integration drift; S294: Apply seismic input at the boundaries of implicit dynamic analysis finite element models using the equivalent nodal seismic load method.

[0071] Specifically, in the simulation of tunnel dynamic response based on viscoelastic boundary conditions, accurately applying external seismic motion is a key factor in ensuring the physical authenticity and computational accuracy of the numerical results. The seismic motion input method used in this example is the equivalent nodal force input method. The equivalent nodal force input method can convert the incident wave field into an equivalent boundary force, directly apply it to the model boundary nodes, and cooperate with the spring-damper system of the viscoelastic boundary to ensure the boundary energy absorption function while realistically reproducing the incident, reflection, and transmission processes of the seismic wave.

[0072] In terms of implementation, based on the wave field separation theory, the equivalent node force calculation formula under the viscoelastic boundary condition is derived. The core idea is to dynamically calculate the free field stress on the node based on the time history of free field displacement and velocity, combined with the spring stiffness and damping coefficient of the boundary node, and then convert the control area to equivalent concentrated force. Further, based on the ABAQUS platform, a viscoelastic boundary and equivalent node force automatic modeling system is developed, and a Python script driven automatic modeling process is proposed. This process covers the complete steps from extracting node reaction force from ODB database, calculating control area, setting boundary parameters to loading equivalent seismic force, greatly improving the modeling efficiency and accuracy of three-dimensional complex models.

[0073] In the calculation process of equivalent seismic load, the wave field separation theory is used to consider the mutual superposition effect of incident wave and reflected wave. According to the propagation delay relationship of the node from the boundary position, Lagrange interpolation method is used to extract the displacement and velocity response of each node, and then concentrated force is applied. Through this method, without changing the physical model of the boundary, the synchronous expression of excitation input and boundary energy absorption process can be realized, avoiding the common physical incoordination and response distortion problems in displacement input method and acceleration input method.

[0074] In the simulation of tunnel response under the coupling action of high-speed subway vibration and seismic load in this example, the equivalent node force method is used for seismic input, successfully realizing the synchronous loading of train vibration load and seismic load, and ensuring the effective absorption of scattered waves by viscoelastic boundary. The equivalent node force input can accurately reproduce the seismic wave propagation under the viscoelastic boundary, and is highly consistent with the analytical solution.

[0075] The viscoelastic artificial boundary effectively simulates the absorption and energy dissipation mechanism of the semi-infinite soil to the incident wave by introducing spring-damping elements at the model boundary. Its design principle is based on wave theory, which can provide specific elastic recovery and viscous dissipation response for high-frequency components generated by train excitation and low-frequency waves caused by seismic motion, thereby significantly reducing the energy reflection at the structure boundary and ensuring the natural continuity of excitation propagation. Under the condition of train vibration-seismic superposition, the viscoelastic boundary can simultaneously process multi-frequency energy input, avoiding the local amplification and beam aggregation phenomenon caused by single frequency adaptive boundary, and ensuring the physical consistency of boundary conditions and internal propagation field. At the same time, the equivalent node force method is used for seismic input, which shows higher applicability and accuracy under the viscoelastic boundary framework.

[0076] S3: set several types of working conditions according to the preset requirements, including measured and simulated scenarios of vehicle body and earthquake; the working conditions at least include vehicle body vibration working condition, earthquake working condition and vehicle body vibration and earthquake load superposition working condition; wherein the vehicle body vibration working condition sets several vehicle body speeds; the earthquake working condition sets several seismic input intensities.

[0077] Specifically, four groups of coupling working conditions are set to investigate the coupling effect of train vibration and ground motion. The train running speed is uniform at 160 km / h, and three-directional ground motion with peak acceleration of 0.05g, 0.10g, 0.20g and 0.40g is superimposed respectively. The seismic loading time window coincides with the train acceleration peak phase to simulate the most unfavorable load superposition state. All working conditions are consistent in structure configuration, load definition, boundary form and monitoring arrangement to ensure data comparability.

[0078] S4: Analyze the structure response results to obtain the response law under multi-source dynamic action.

[0079] S4 includes: based on the response analysis results under different working conditions, the propagation law of high-speed car body in the structure system, the evolution characteristics of the preset crack position and the influence of seismic load superposition are obtained.

[0080] Specifically, to analyze the vertical displacement response of the rail under the coupling action of train vibration and earthquake, the upward and downward maximum vertical displacement time history curves of the rail nodes under the coupling action of 160 km / h train vibration and 0.05g-0.4g earthquake are extracted and compared with the rail time history curve under the action of 160 km / h train vibration, as shown in Figure 12 .

[0081] Under the action of 160 km / h train vibration alone, the rail nodes produce a maximum downward displacement of 2.46 mm, and the upward response is almost negligible, reflecting that the train excitation is mainly of repeated compression type disturbance. With the introduction of seismic superposition, the rail displacement response is significantly amplified: under the condition of 0.05g seismic motion, the maximum displacement increases to 2.93 mm; under the conditions of 0.1g, 0.2g and 0.4g seismic motion, the displacement peak further grows to 3.61 mm, 4.97 mm and 9.59 mm. The overall trend shows that under multi-source excitation, the dynamic response of the tunnel track system is significantly affected by the intensity of seismic motion, and presents the characteristics of continuous amplification with the peak acceleration of seismic motion.

[0082] It should be noted that this example uses the method of directly applying train load to rail nodes in the form of excitation force function to simulate train vibration. This method effectively simplifies the dynamic interaction problem of train and track system, avoids the modeling and calculation burden brought by complex train entity modeling, and has good numerical stability and certain engineering applicability.

[0083] To further evaluate the vertical deformation characteristics of the tunnel structure under the coupling action of train and earthquake, this paper analyzes the maximum vertical displacement response of the arch top and arch foot under the coupling conditions of 0.05g, 0.1g, 0.2g and 0.4g, and the displacement time history curve is shown in Figure 13 ,14 , 15, 16. From the comparison of the tunnel displacement time-history curves, it can be seen that under the action of 0.05g and 0.4g seismic load, the displacement response amplitude of the structure under the superimposed condition of train vibration and seismic load is obviously offset compared with the single seismic load condition.

[0084] Specifically, under the 0.05g condition, the train vibration has a certain interference effect on the response of the tunnel structure, resulting in a weakening trend of the overall displacement amplitude; while under the 0.4g condition, the displacement amplitude is further amplified after superimposing the train vibration, reflecting that the mutual superposition effect of train vibration and seismic load under high intensity earthquake is more significant. In contrast, under the 0.1g and 0.2g conditions, the coupling response curve basically coincides with the single seismic action response curve, indicating that under the condition of medium intensity seismic load, the influence of train vibration on the overall dynamic response of the tunnel is relatively small, and the multi-source load action presents an approximately linear superposition characteristic. The overall trend shows that the influence of train vibration on the dynamic response of the tunnel structure presents a nonlinear characteristic with the change of seismic intensity, and the train vibration action cannot be ignored under low intensity and high intensity conditions, while the coupling effect has a relatively limited influence in the medium intensity range.

[0085] To further reveal the influence characteristics of the coupling effect of train vibration and seismic load on the local response of the tunnel structure, this example compares and analyzes the vertical maximum displacement peak values of the arch top and arch foot monitoring points under different seismic acceleration peak values, including the upward displacement and downward displacement components, as shown in Table 6.

[0086] From the response characteristics of the arch top, under the single seismic load condition, the displacement response is mainly upward displacement (arch top lifting), and the upward displacement peak value is generally slightly larger than the downward displacement peak value, and it presents an approximately linear growth trend with the increase of the seismic acceleration peak value. For example, under the action of 0.05g seismic load, the upward displacement peak value of the arch top is 1.05mm, and the downward displacement is 0.70mm; when the seismic acceleration peak value increases to 0.4g, the upward displacement of the arch top increases to 8.34mm, and the downward displacement increases to 5.66mm, reflecting the dynamic response characteristics of the arch top area mainly affected by the lifting effect of seismic load.

[0087] Under the coupled conditions of train and ground motion, the dome's displacement response pattern changes significantly. For example, under a 0.05g ground motion superimposed on train vibration, the dome's upward displacement amplitude decreases to 0.75mm, while the downward displacement amplitude increases to 1.02mm. This indicates that the additional downward inertia caused by the train excitation weakens the dome's upward movement and promotes its downward movement. As the ground motion intensity increases, the change in the dome's response becomes more pronounced. Under the condition of a 0.4g peak ground motion superimposed on train vibration, the dome's downward displacement (7.84mm) exceeds its upward displacement (6.32mm), indicating that the dome region shifts from an upward movement to a downward movement under the dual excitation, reflecting a significant nonlinear redistribution of the local dynamic characteristics. The displacement response of the arch foot follows a similar pattern to that of the dome. Under ground motion alone, the upward displacement of the arch foot is always greater than the downward displacement, and this displacement increases gradually with increasing peak ground acceleration.

[0088] Table 6 Maximum vertical displacement peak value of arch crown and arch foot (mm) Taking a 0.05g earthquake as an example, the arch foot's upward displacement is 0.71mm and its downward displacement is 0.51mm. Under a 0.4g earthquake, these increases to 5.65mm and 4.15mm, respectively. After the introduction of train vibration, the upward displacement amplitude of the arch foot decreases, while the downward displacement amplitude generally increases. For example, under a 0.4g earthquake combined with train vibration, the downward displacement of the arch foot reaches 6.23mm, significantly exceeding the upward displacement of 3.70mm, also showing a settlement-dominated response pattern.

[0089] In this example, to identify potential damage areas in concrete structures under subway loads and earthquakes, the principal stress criterion was used to assess the structural stress state. This method is based on the maximum principal stress theory, which analyzes the maximum and minimum principal stresses at a node, corresponding to the potential tensile and crushing states of the concrete, respectively. The design cubic compressive strength of the concrete is 40 MPa. To facilitate comparison with the axial compressive strength in the finite element calculation, the following formula is used to reduce this: ; Where, αc is the cube strength reduction coefficient, which is 0.76. fcu , k is the standard value of concrete cube compressive strength; The axial tensile strength of concrete is estimated by the empirical formula, and its calculation expression is: ; Where, αt is the empirical regression coefficient, taking 0.395, is the axial tensile strength.

[0090] In the post-processing analysis, if the maximum principal stress of a node exceeds the tensile strength of concrete, it can be judged that there is a risk of concrete tensile cracking in this area. If the minimum principal stress exceeds the negative value of the axial compressive strength of concrete, it indicates that the region may appear crushing or plastic yield phenomenon, that is, respectively meet: S 1> ft , S 3<- fc ; In the formula, S 1 is the maximum principal stress, S 3 is the minimum principal stress.

[0091] It can be concluded that the maximum principal stress distribution law of the tunnel structure under the action of 160km / h train vibration: To identify the stress concentration area that may exist in the tunnel lining structure under the action of high-speed train vibration, this paper analyzes the first principal stress nephogram under the 160km / h train load condition based on the maximum principal stress criterion. As shown in Figure 17 , the maximum principal stress value of the tunnel lining structure under the most unfavorable working condition reaches 2.385Mpa, although it has not yet exceeded the axial tensile strength of C40 concrete 2.61MPa, but it has approached its ultimate strength of 91.3%, indicating that there is a high risk of local area tensile cracking.

[0092] Observe along the tunnel axis direction (hereinafter referred to as longitudinal direction), the yellow high stress area in the nephogram presents a clear strip-shaped continuous distribution, extending along the direction of train operation, reflecting that the train excitation force forms a stable and concentrated tensile stress transmission path in the tunnel lining structure. The existence of the longitudinal continuous high stress zone suggests that under the action of long-term periodic load, cracks may be induced along the longitudinal direction of the tunnel, especially in the case of frequent train operation or load superposition effect is significant, the possible evolution of cracks will further increase.

[0093] ​The maximum tensile stress concentration is mainly distributed in the direction of about 45° right bias on the horizontal, i.e. the haunch area. The local high value of tensile stress in this area does not diffuse uniformly along the circular cross-section, indicating that the stress redistribution phenomenon is formed under the combined action of the change of ring stiffness, inertia effect and wave energy propagation path of the structure under the action of train excitation load. The ring stress concentration area has a high risk of crack initiation and propagation under the action of dynamic accumulation, especially in the transition section from the haunch to the vault, which is the key sensitive part of the lining durability deterioration during train excitation process. In addition, the green area shown in the stress cloud map, i.e. near the tunnel arch foot, has a maximum principal stress between 0.5 MPa and 1.5 MPa, which is at a medium to high tensile stress level. Although the arch foot is mainly in compression, the tensile stress level is relatively low compared to the haunch and vault areas, but considering that it still reaches 57% of the material tensile strength, it should be considered as the second priority for potential damage areas. Especially under the action of vibration accumulation or extreme load conditions, the local area of the arch foot may induce stress concentration under complex stress state, increasing the risk of micro-crack initiation. Therefore, the durability and local reinforcement requirements of the structure still need to be reasonably evaluated in practical engineering.

[0094] Based on the above analysis, the maximum principal stress distribution characteristics of the tunnel lining under the action of 160 km / h train vibration can be summarized as follows: the whole tunnel lining has not reached the material ultimate failure condition, but the local area has approached the tensile limit, indicating that the structure has a potential risk of longitudinal and ring crack initiation. A continuous high stress strip is formed along the longitudinal direction of the tunnel, local extremely high tensile stress concentration occurs in the ring haunch area, and medium to high tensile stress level appears in the arch foot area.

[0095] In the future, different protection strategies should be adopted according to the stress level of different areas in tunnel design and maintenance, focusing on improving the tensile toughness of the haunch area, and paying attention to the long-term durability evolution of the arch foot area, in order to improve the performance of the tunnel in the whole life cycle under the action of train vibration load.

[0096] Maximum principal stress distribution law of tunnel structure under 0.05g coupling condition: To evaluate the stress concentration area that may exist in the tunnel lining structure under the coupling action of high-speed subway train vibration and earthquake, the first principal stress cloud map under the coupling action of 160 km / h train vibration and 0.05g three-dimensional earthquake is extracted for analysis, as shown in Figure 18 .

[0097] The results show that the overall stress level is further elevated on the basis of the train load alone, and the maximum principal stress value of the lining reaches 3.210 MPa in the most unfavorable working condition, which is significantly increased by about 34.6% compared with 2.385 MPa under the train vibration load alone. Since this value has exceeded the axial tensile strength of C40 concrete by about 23%, according to the maximum principal stress failure criterion, it is inferred that the local area has the potential risk of concrete cracking.

[0098] From the longitudinal view of the tunnel, the high stress area is still continuously distributed in strips, and after the participation of 0.05g seismic vibration, the longitudinal stress band has a phenomenon of width increase and stress level rise compared with the train load alone, indicating that the periodic disturbance superposition of seismic vibration makes the train excitation force produce a more intense energy accumulation effect in the transmission path of the structure. Especially in the direction of train operation, the longitudinal continuous high stress band is more dense, suggesting that under the condition of long-term coupled disturbance, the possibility of developing longitudinal cracks is further intensified.

[0099] From the circumferential view of the tunnel, compared with the 160km / h train vibration working condition, the maximum tensile stress is still mainly concentrated in the haunch area, but the stress concentration area has a significantly higher amplitude, and there is more obvious circumferential expansion, from local high value concentration to approximately strip-shaped distribution. This feature shows that the three-dimensional disturbance of seismic vibration promotes the further diffusion of vibration energy along the ring path of the tunnel with greater flexibility, intensifying the tensile stress accumulation in the haunch area. This phenomenon suggests that under the combined action of train and seismic load, a more extensive and higher potential circumferential crack initiation zone is formed in the haunch and its vicinity of the tunnel lining. It is worth noting that the stress level of the green area near the springing and the crown also increases to varying degrees, with the maximum principal stress rising to close to +2.0MPa, which is significantly higher than that under the train load alone. Although the overall tensile stress level is still lower than that in the haunch, under the coupling effect, the stress state tends to be complex in the crown and springing areas, with an intensified stress gradient, which may lead to an increased risk of micro-crack accumulation and secondary damage, and needs to be paid attention to in subsequent fatigue assessment.

[0100] Through comprehensive analysis, under the coupling action of 0.05g seismic vibration and 160km / h train load, the maximum principal stress distribution of the tunnel lining structure presents the following characteristics: the longitudinal high stress band is widened and densified, the circumferential stress in the haunch area is significantly enlarged and expanded, and the high stress area in the crown and springing is simultaneously increased. Compared with the train vibration alone, the coupling load not only significantly increases the local tensile stress level, but also intensifies the spatial non-uniformity and concentration of stress distribution, leading to a doubled risk of crack initiation. In future structural design and reinforcement measures, the combined effect of train and seismic superposition on the durability and safety of the tunnel should be fully considered, especially in the haunch and its vicinity, which should be reinforced and fatigue life optimized in accordance with the characteristics of coupled load.

[0101] Distribution law of the third principal stress of tunnel structure under coupling load action Under the coupling condition of 160km / h high-speed train vibration and 0.05g three-dimensional seismic vibration, the minimum principal stress of the tunnel structure reaches 7.74MPa, as shown in FIG. 6. Compared with the axial compressive strength of C40 concrete of 30.4MPa, there is still sufficient safety margin, and the compressive stress level is about 25% of the ultimate strength. This shows that under the current working condition, the tunnel lining structure has not yet entered the crushing or plastic yield stage, and the damage risk induced by compressive stress is relatively low. Figure 19

[0102] Considering that the minimum principal stress level is far below the crushing limit of concrete, and the stress distribution is relatively uniform, the influence of compressive stress on the overall stability and durability of the structure can be considered controllable. In the existing analysis, the minimum principal stress does not show a sharp local peak aggregation phenomenon, and does not show a clear compressive stress instability trend. At the same time, compared with the potential tensile cracking risk corresponding to the maximum principal stress, the structural damage risk caused by compressive stress is significantly lower, so in the durability assessment and reinforcement design in engineering practice, the tensile stress dominated damage possibility should be paid attention to first.

[0103] In summary, through the comprehensive analysis of the maximum principal stress and the minimum principal stress cloud map, it can be concluded that under the action of 160km / h train vibration, the tensile stress concentration phenomenon has been formed in the tunnel haunch area, the maximum principal stress is close to the material limit, which indicates that there is a potential tensile cracking risk along the longitudinal and distributed ring directions of the tunnel. Under the coupling action of train vibration and 0.05g peak acceleration earthquake, the maximum principal stress of the tunnel structure is further amplified, the stress level in the local area exceeds the tensile strength of concrete, the crack initiation risk is significantly intensified, and the stress concentration area expands along the longitudinal and ring directions. At the same time, although a large compressive stress area is formed inside the structure, the minimum principal stress level is far below the compressive limit of concrete, and there is no risk of crushing or plastic yield. Therefore, it can be judged that under the coupling action of train and earthquake, the deterioration mode of the tunnel lining structure is mainly dominated by tensile stress, and the crack development risk is concentrated in the haunch and its adjacent areas, and the compressive stress has little effect on the overall damage. The durability of the tensile stress concentration area should be targeted to be improved in the subsequent design and reinforcement measures, and the overall stress state of the structure should be reasonably controlled to improve the service safety of the tunnel under the action of multiple source loads.

[0104] The application also provides a simulation analysis system for the response of a tunnel structure under the action of multiple source loads, as shown in FIG. 8. Figure 20 ​As shown, the simulation analysis method for tunnel structure response under multi-source power action includes: a modeling module 10 configured to construct an implicit dynamic analysis finite element model of track-tunnel-soil, forming a structure-soil coupling system, the modeling module adopts a solid element modeling method, and includes a connecting element for simulating a fastener system; a solving module 20 configured to perform numerical solving based on an implicit dynamic algorithm to solve the response process of the model under multi-source load action, the solving module adopts an implicit time integration method based on dynamic balance differential equation, and combines Newton-Raphson iteration to control nonlinear convergence; a working condition configuration module 30 configured to set several types of excitation working conditions, including vehicle body vibration working condition, earthquake working condition and coupled working condition, supporting input of measured or simulated train load and earthquake time history data; a load input module 40 configured to input train vibration load and three-direction earthquake load respectively, the train vibration load being generated by a preset subroutine, and the earthquake load being applied by filtering, integration and equivalent node load; and a response analysis module 50 configured to extract structural response indexes of the model under different working conditions, including acceleration, displacement, principal stress, and identify high stress areas, nonlinear enhancement features and potential crack risks.

[0105] Although the embodiments of the present application have been shown and described above, it should be understood by those skilled in the art that the above embodiments are exemplary and cannot be construed as limiting the present application, and those skilled in the art can make changes, modifications, replacements and variations to the above embodiments within the scope of the present application.

Claims

1. A simulation analysis method for tunnel structure response under multi-source dynamics, characterized in that: The following steps are involved: S1: Construct a numerical solution system for coupled load analysis; S2: Based on the numerical solution system, an implicit dynamic analysis finite element model of track-tunnel-soil is constructed to form a structure-soil dynamic coupling system; S3: setting several types of working conditions according to preset requirements, including actual measurement and simulation scenarios of vehicle bodies and earthquakes; S4: Analyze the structural response results and derive the response law under the action of multiple sources of power.

2. The simulation analysis method for tunnel structure response under multi-source dynamics according to claim 1 is characterized in that: S1 includes: The numerical solution system adopts an implicit dynamic algorithm, which is constructed based on the dynamic equilibrium differential equation. By solving the global equilibrium equation of the system in each time step and combining the Newton-Raphson iteration to gradually approximate the true response, the nonlinear problem can be converged and controlled.

3. The simulation analysis method for tunnel structure response under multi-source dynamics according to claim 1 is characterized in that: S2 includes: The modeling approach includes the following steps: S21: Use C3D8R solid elements to perform solid modeling of the tunnel lining, roadbed, rails, and soil; S22: Simulating nonlinear material behavior using a bimodal elastoplastic constitutive model; S23: Use Rayleigh damping to simulate the attenuation effect of tunnel components and soil on vibration, and inversely solve the damping parameters α and β of the mass and stiffness terms based on the frequency matching method; S24: Use multi-directional assigned connection elements to simulate the stiffness support and vibration damping of the SFC fastener system.

4. The simulation analysis method for tunnel structure response under multi-source dynamics according to claim 1 is characterized in that: S2 includes: The initial condition construction of the implicit dynamic analysis finite element model includes the following steps: S25: Static geostress equilibrium is achieved by applying a gravity field to the model under fixed boundary conditions; S26: static-dynamic geostress conversion is achieved by using fixed boundary release and stress field inheritance; S27: Introduction of viscoelastic boundary conditions to simulate elastic recovery and energy scattering of semi-infinite foundations; S28: applying a typical track irregularity excitation function to the vehicle body vibration through a preset subroutine; S29: After converting the equivalent seismic load using the equivalent nodal load method, three-way seismic wave input is performed to simulate ground motion.

5. The simulation analysis method for tunnel structure response under multi-source dynamics according to claim 4 is characterized in that: S28 includes: establishing a programmable train vibration input method for the abaqus platform, including the following steps: S281: Decompose the vertical wheel-rail force of the vehicle body into three independent physical excitation sources: vehicle body-suspension system coupling, unsprung mass rebound, and wheel-rail contact; S282: Multi-interval distributed excitation modeling based on travel speed, excitation frequency, and vehicle formation parameters; S283: The time domain sliding window method is used to locate the action area, which is used to automatically activate or release the moving load during the vehicle's movement.

6. The simulation analysis method for tunnel structure response under multi-source dynamics according to claim 5 is characterized in that: The method for simulating the track-tunnel response under continuous excitation of multiple high-speed vehicles includes the following steps: S284: Define constants: a sag, L typical wavelength, t current time step, v train speed, m0 unsprung mass, w circular frequency, and p wheel static load; S285: Define the interval of the load area; S286: Calculate the trigger time of each area; S287: Traverse all load areas; S288: Determine whether the node is within the current load range; S289: If the node is not in any interval, the load is zero.

7. The simulation analysis method for tunnel structure response under multi-source dynamics according to claim 5 is characterized in that: S29 includes: a three-way seismic wave input method combining filtering, integration and equivalent nodal loads, including the following steps: S291: Use a bandpass filter to remove high-frequency noise and low-frequency drift in seismic records; S292: Use the time integration method to convert acceleration into velocity and displacement; S293: Use baseline correction to avoid integration drift; S294: Apply seismic input at the boundaries of implicit dynamic analysis finite element models using the equivalent nodal seismic load method.

8. The simulation analysis method for tunnel structure response under multi-source dynamics according to claim 1 is characterized in that: The working conditions include at least vehicle body vibration working conditions, earthquake working conditions, and vehicle body vibration and earthquake load superposition working conditions; Wherein, the vehicle body vibration working condition sets several vehicle body speeds; The earthquake working condition sets several earthquake motion input intensities.

9. The simulation analysis method for tunnel structure response under multi-source dynamics according to claim 1 is characterized in that: S4 includes: Based on the response analysis results under different working conditions, the propagation law of the high-speed vehicle body in the structural system, the principal stress characteristics of various parts of the tunnel and the superposition effect of seismic loads were obtained.

10. A simulation analysis system for tunnel structure response under multi-source power, using the simulation analysis method for tunnel structure response under multi-source power according to any one of claims 1 to 9, characterized in that: include: a modeling module configured to construct an implicit dynamic analysis finite element model of a track-tunnel-soil structure to form a structure-soil coupled system, wherein the modeling module adopts a solid element modeling method and includes connection elements for simulating a fastener system; a solution module configured to perform a numerical solution based on an implicit dynamic algorithm to solve the response process of the model under the action of multiple source loads, wherein the solution module adopts an implicit time integration method based on the dynamic equilibrium differential equation and combines Newton-Raphson iteration to control nonlinear convergence; The working condition configuration module is configured to set several types of excitation working conditions, including vehicle body vibration working conditions, earthquake working conditions and their coupled working conditions, and supports the input of measured or simulated train load and earthquake time history data; A load input module is configured to input train vibration loads and three-dimensional earthquake loads respectively, wherein the train vibration loads are generated by a preset subroutine, and the earthquake loads are applied by filtering, integration, and equivalent node loads; and the response analysis module, which is configured to extract the structural response indicators of the model under different working conditions, including acceleration, displacement, and principal stress, and identify high-stress areas, nonlinear enhancement features, and potential crack risks.

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