Method and system for evaluating ballastless track-bridge structure system under action of freeze-thaw cycle

Abstract

The invention provides a method and system for evaluating a ballastless track-bridge structure system under the action of freeze-thaw cycle, and the method comprises the steps: obtaining environment parameters of the ballastless track-bridge structure system under the action of freeze-thaw cycle and soil parameters of a frozen soil foundation, carrying out the simulation of the freeze-thaw cycle, and obtaining a frozen soil deformation field after the freeze-thaw cycle; inputting the frozen soil deformation field after the freeze-thaw cycle into a pile-soil nonlinear interaction model of the ballastless track-bridge structure system to obtain pier settlement / upheaval deformation data after the freeze-thaw cycle, and further obtaining geometric deformation data of the ballastless track after the freeze-thaw cycle; and constructing a dynamic interaction model of the train-ballastless track-bridge structure considering the geometric deformation data of the ballastless track after the freeze-thaw cycle, solving the model to obtain a corresponding dynamic response, and evaluating the safety and reliability of the ballastless track-bridge structure system. According to the method, the space deformation rule and the dynamic performance of the ballastless track-beam structure system in the freezing and thawing cycle environment can be accurately analyzed.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of civil engineering and transportation engineering, and in particular to a method and system for evaluating a ballastless track-bridge structure system under freeze-thaw cycles. BACKGROUND

[0002] In cold regions, railway infrastructure faces severe challenges from freeze-thaw cycles. As a key component of the railway, the performance of the ballastless track-bridge structure system under freeze-thaw cycles directly affects the safe operation of the railway. Freeze-thaw cycles can cause damage to the ballastless track structure, such as cracking of the track bed slab and loosening of the fasteners, and also have adverse effects on the durability of the bridge structure. Existing research and technology have deficiencies in accurately evaluating the spatial deformation mapping relationship and dynamic performance of the ballastless track-bridge structure system under freeze-thaw cycles, making it difficult to meet the high-precision requirements of structural safety monitoring and evaluation in actual engineering. SUMMARY

[0003] To solve the above problems in the prior art, the application provides a method and system for evaluating a ballastless track-bridge structure system under freeze-thaw cycles.

[0004] To achieve the above-mentioned purposes, the technical solutions adopted by the application are as follows: On the one hand, the application provides a method for evaluating a ballastless track-bridge structure system under freeze-thaw cycles, comprising: (S1) obtaining environmental parameters of the ballastless track-bridge structure system under freeze-thaw cycles and soil parameters of the frozen ground foundation corresponding to the ballastless track-bridge structure system, and then simulating freeze-thaw cycles of the frozen ground foundation corresponding to the ballastless track-bridge structure system to obtain a frozen soil deformation field after freeze-thaw cycles; (S2) inputting the frozen soil deformation field after freeze-thaw cycles into a pile-soil nonlinear interaction model of the ballastless track-bridge structure system to obtain bridge pier settlement / embossment deformation data after freeze-thaw cycles; (S3) obtaining geometric deformation data of the ballastless track after freeze-thaw cycles based on the bridge pier settlement / embossment deformation data after freeze-thaw cycles; (S4) constructing a train-ballastless track-bridge structure dynamic interaction model considering the geometric deformation data of the ballastless track after freeze-thaw cycles and solving it to obtain the dynamic response of the train-ballastless track-bridge structure under freeze-thaw cycles; (S5) evaluating the safety and reliability of the ballastless track-bridge structure system based on the dynamic response of the train-ballastless track-bridge structure under freeze-thaw cycles.

[0005] On the other hand, a system for evaluating a ballastless track-bridge structure system under freeze-thaw cycles is provided, comprising: The freeze-thaw cycle simulation module is configured to obtain environmental parameters of the ballastless track-bridge structure system and soil parameters of a frozen soil foundation corresponding to the ballastless track-bridge structure system under the action of freeze-thaw cycles, and then simulate the freeze-thaw cycles of the frozen soil foundation corresponding to the ballastless track-bridge structure system to obtain a frozen soil deformation field after the freeze-thaw cycles; The pile-soil nonlinear interaction module is configured to input the frozen soil deformation field after the freeze-thaw cycles into a pile-soil nonlinear interaction model of the ballastless track-bridge structure system to obtain bridge pier settlement / embossment deformation data after the freeze-thaw cycles. The geometric deformation data obtaining module of the ballastless track after the freeze-thaw cycles is configured to obtain geometric deformation data of the ballastless track after the freeze-thaw cycles based on the bridge pier settlement / embossment deformation data after the freeze-thaw cycles. The dynamic response obtaining module is configured to construct a dynamic interaction model of a train-ballastless track-bridge structure considering the geometric deformation data of the ballastless track after the freeze-thaw cycles and solve the dynamic interaction model to obtain dynamic responses of the train-ballastless track-bridge structure under the action of the freeze-thaw cycles. The evaluation module is configured to evaluate the safety and reliability of the ballastless track-bridge structure system based on the dynamic responses of the train-ballastless track-bridge structure under the action of the freeze-thaw cycles.

[0006] In another aspect, the present application provides a computer device comprising a memory and a processor, the memory storing a computer program, and the processor implementing the steps of the above-mentioned ballastless track-bridge structure system evaluation method under the action of freeze-thaw cycles when executing the computer program.

[0007] In another aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, and the computer program is executed by a processor to implement the steps of the above-mentioned ballastless track-bridge structure system evaluation method under the action of freeze-thaw cycles.

[0008] In another aspect, the present application provides a computer program product stored on a computer-readable storage medium and comprising computer instructions, which, when executed by a processor, cause a computer device to implement the steps of the above-mentioned ballastless track-bridge structure system evaluation method under the action of freeze-thaw cycles.

[0009] Compared with the prior art, the present application has the following advantages: The present application provides a ballastless track-bridge structure system evaluation method and system under the action of freeze-thaw cycles to accurately analyze the spatial deformation law of the ballastless track-bridge structure system under the freeze-thaw cycle environment and accurately evaluate the dynamic response performance, thereby providing a scientific basis for the maintenance and management of railway infrastructure. BRIEF DESCRIPTION OF DRAWINGS

[0010] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required by the embodiments or prior art description. Obviously, the drawings in the following description only show some of the embodiments of the present application, and for those skilled in the art, other drawings can also be obtained from the structures shown in the drawings without creative labor.

[0011] Figure 1 A flow chart of the method for evaluating the ballastless track-bridge structure system under the action of freeze-thaw cycles is provided in an embodiment. DETAILED DESCRIPTION

[0012] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0013] A method for evaluating a ballastless track-bridge structure system under the action of freeze-thaw cycles, comprising: (S1) obtaining the environmental parameters of the ballastless track-bridge structure system under the action of freeze-thaw cycles and the soil parameters of the frozen ground foundation corresponding to the ballastless track-bridge structure system, and then simulating the freeze-thaw cycles of the frozen ground foundation corresponding to the ballastless track-bridge structure system to obtain the frozen soil deformation field after freeze-thaw cycles; (S2) inputting the frozen soil deformation field after freeze-thaw cycles into a pile-soil nonlinear interaction model of the ballastless track-bridge structure system to obtain the bridge pier settlement / embossing deformation data after freeze-thaw cycles; (S3) obtaining the geometric deformation data of the ballastless track after freeze-thaw cycles based on the bridge pier settlement / embossing deformation data after freeze-thaw cycles; (S4) constructing a train-ballastless track-bridge structure dynamic interaction model considering the geometric deformation data of the ballastless track after freeze-thaw cycles and solving it to obtain the dynamic response of the train-ballastless track-bridge structure under the action of freeze-thaw cycles; (S5) evaluating the safety and reliability of the ballastless track-bridge structure system based on the dynamic response of the train-ballastless track-bridge structure under the action of freeze-thaw cycles.

[0014] The main factors affecting the thermal conditions of frozen soil and the surface of the engineering structure are: solar shortwave radiation, longwave radiation, convective heat transfer, evaporative heat transfer, surface heat flow, and the like. The present application considers these factors for subsequent engineering thermal numerical simulation. In step (S1), the environmental parameters considered include solar shortwave radiation, solar longwave radiation, convective heat transfer, evaporative heat transfer, surface heat flow, and the like, and the soil parameters include initial moisture content, porosity, unfrozen water content curve, latent heat of phase change, thermal conductivity, volumetric heat capacity, and the like.

[0015] In step (S1), the finite element model is used to simulate the freeze-thaw cycle of the frozen soil foundation corresponding to the ballastless track-bridge structure system, and the frozen soil deformation field after the freeze-thaw cycle is obtained, including the following steps: (S1.1) Establishing a three-dimensional finite element model of the frozen soil foundation corresponding to the ballastless track-bridge structure system and performing mesh division; (S1.2) Setting the initial temperature field, initial moisture content and environmental thermal boundary of each node of the three-dimensional finite element model, and considering the heat conduction under different working conditions; (S1.3) Considering the environmental parameters of the ballastless track-bridge structure system and the soil parameters of the frozen soil foundation corresponding to the ballastless track-bridge structure system under the action of freeze-thaw cycle, constructing the heat conduction differential equation of the frozen region and the heat conduction differential equation of the unfrozen region, and performing phase change heat transfer analysis and temperature field solving to obtain the overall temperature field of the three-dimensional finite element model after the freeze-thaw cycle; (S1.4) Based on the overall temperature field of the three-dimensional finite element model after the freeze-thaw cycle, performing thermal-mechanical coupling analysis to obtain the frozen soil deformation field after the freeze-thaw cycle.

[0016] The heat transfer finite element processing of the phase change problem is established, and most of the engineering heat transfer problems in the frozen soil area can be solved through the two-dimensional transient temperature field of the phase change problem .

[0017] For the heat conduction differential equation of the frozen region, it can be written as: . For the heat conduction differential equation of the unfrozen region, it can be written as: . In the formula, is the thermal conductivity of the frozen soil in the frozen state; is the two-dimensional transient temperature field of the frozen soil in the frozen state; , are the volumetric heat capacity of the frozen soil in the frozen state and the thawing state, respectively, and the subscript , respectively represent the frozen and thawing two-phase states of the frozen soil.

[0018] The heat transfer finite element implementation of phase change problem: the heat conduction differential equation is solved by using the weighted residual method. The typical direction of the weighted residual method can be expressed as: ; In the formula, is the weighted function, which makes the "residual" (the deviation between the theoretical solution and the trial solution) of the heat conduction differential equation zero in the integral sense, so as to realize the approximate solution of the heat conduction equation, is the residual, is the integral area, is the trial function.

[0019] According to the Galerkin method and the boundary relationship of the plane field domain, the final expression is as follows: ; In the formula, T is the temperature vector, which is a vector composed of the temperatures of each node in the finite element model, is the temperature of the th node in the finite element model; is the density, is the input heat flow intensity, is the thermal conductivity, is the volume heat capacity, W corresponds trial function, W is the approximate expression of the assumed temperature field that satisfies the boundary conditions, which is used to "approximate" the real temperature field distribution in the weighted residual method, s is the boundary (i.e. the integral boundary), ds is the microelement (length element or area element, depending on the dimension) on the boundary.

[0020] The final expression of the overall temperature field of the three-dimensional finite element model after freeze-thaw cycle is obtained as follows: ; In the formula, is the temperature stiffness matrix, is the temperature vector, is the temperature damping matrix, is the equivalent heat flow boundary condition array of the outside world.

[0021] Based on the overall temperature field of the three-dimensional finite element model after freeze-thaw cycle, the thermal-mechanical coupling analysis is carried out, and the deformation field of frozen soil after freeze-thaw cycle is obtained as follows: ; In the formula, is the x, y, z direction of the three components of the deformation field of frozen soil after freeze-thaw cycle ; is the water content of the soil, represents the porosity of the soil.

[0022] In step (S2), in the pile-soil nonlinear interaction model of the ballastless track-bridge structure system, the Desai thin-layer contact element is used to simulate the nonlinear contact relationship between the pile and the ballastless track-bridge structure system, wherein the normal stiffness model and the tangential stiffness model are simulated by a hyperbolic model, and the formula is as follows: ; ; wherein, and are the normal stiffness and the tangential stiffness, and are the initial normal stiffness and the initial tangential stiffness, is the cohesive force, is the friction coefficient, is the friction shear slip angle, is the damage ratio, , are the tangential shear stresses of the xy plane and the yz plane, i.e. the actual shear stress on the contact surface; is the normal stress acting on the contact surface.

[0023] In step (S2), based on the pile-soil nonlinear interaction model of the ballastless track-bridge structure system, the bridge pier settlement / ups and down deformation data after the freeze-thaw cycle are obtained, including the following steps: (S2.1) obtaining the finite element node force vector in the three-dimensional finite element model based on the frozen soil deformation field after the freeze-thaw cycle; ; wherein is the frozen soil deformation field after the freeze-thaw cycle, is the elastic matrix for describing the material constitutive relationship; is the strain matrix determined by the derivative of the element shape function, reflecting the geometric relationship between the displacement and the strain, is the node force vector obtained by integrating the stress-related quantities in the element; (S2.2) dividing into n parts to obtain n load increments; (S2.3) initializing the stiffness matrix of the Desai thin-layer contact element; (S2.4) applying the i-th load increment, determining the current step displacement increment and stress increment corresponding to the i-th load increment, ; (S2.5) obtaining the stiffness of the pile-soil interface in each direction according to the normal stiffness model and the tangential stiffness model, updating the stiffness matrix of the Desai thin-layer contact element; (S2.6) i = i + 1, return (S2.4) until n load increments are applied, and the pier settlement / heave deformation data after freeze-thaw cycles are calculated .

[0024] In step (S3), the geometric deformation data of the ballastless track after freeze-thaw cycles are obtained based on the pier settlement / heave deformation data after freeze-thaw cycles, as follows: (S3.1) define the constraint pier freedom, generate the displacement indicator vector based on the pier settlement / heave deformation data after freeze-thaw cycles, and convert the pier settlement / heave deformation after freeze-thaw cycles into equivalent load.

[0025] wherein is the equivalent load corresponding to the pier settlement / heave deformation after freeze-thaw cycles, is the stiffness matrix, is the displacement indicator vector, is the pier settlement / heave deformation data after freeze-thaw cycles.

[0026] (S3.2) stiffness matrix correction: the stiffness matrix The u-th row and u-th column of the stiffness matrix correspond to the position of the constraint freedom, and the u-th row and u-th column of the stiffness matrix are processed by 0 to 1, and the displacement of the constraint freedom is forcibly specified. The displacement of the constraint freedom is forced to be , while decoupling the relationship between the constraint freedom and the non-constraint freedom, to obtain the modified stiffness matrix ; wherein the displacement of the non-constraint freedom is unknown and needs to be solved by the balance equation, so the corresponding row and column are not processed by 0 to 1, and the coupling relationship and diagonal stiffness in the original stiffness matrix are retained.

[0027] (S3.3) obtain the modified balance equation based on the modified stiffness matrix, solve the displacement of the non-constraint freedom therein by block, and obtain the geometric deformation data of the ballastless track after freeze-thaw cycles.

[0028] The modified balance equation is wherein is the geometric deformation data of the ballastless track after freeze-thaw cycles to be solved; By separating the constraint freedom and the non-constraint freedom by block matrix, we have: ; wherein is the non-constraint freedom stiffness matrix in the modified stiffness matrix, is the constraint freedom stiffness correction matrix in the modified stiffness matrix, in the is the constraint freedom equation, is the displacement of the known displacement, , is the displacement of the non-constrained degree of freedom, i.e., the unknown displacement to be solved, is the equation of the non-constrained degree of freedom, which is determined by the external load.

[0029] Through the above matrix operation, the pier settlement boundary condition can be efficiently introduced in the finite element model, and finally the geometric deformation data of the ballastless track after the freeze-thaw cycle is obtained by solving .

[0030] In step (S4), a train-ballastless track-bridge structure dynamic interaction model considering the geometric deformation data of the ballastless track after the freeze-thaw cycle is constructed, wherein the train-ballastless track-bridge structure dynamic interaction model includes a train model, a ballastless track model, a bridge structure model, and an interlayer nonlinear model between the ballastless track and the bridge structure. The constructed model is solved to obtain the dynamic response of the train-ballastless track-bridge structure under the action of the freeze-thaw cycle.

[0031] In step (S5), the dynamic response of the train-ballastless track-bridge structure under the action of the freeze-thaw cycle is compared with the set safety threshold, and then the safety and reliability of the ballastless track-bridge structure system are evaluated.

[0032] The train-ballastless track-bridge structure dynamic interaction model generally includes multiple sub-models, mainly including the following sub-models: a train model, a ballastless track model, a bridge structure model, and an interlayer nonlinear model between the ballastless track and the bridge structure. The existing train-ballastless track-bridge structure dynamic interaction model considers deformation data including track geometry and dynamic deformation, bridge static and dynamic response, and wheel-rail contact behavior, etc., and does not consider the geometric deformation data of the ballastless track after the freeze-thaw cycle. The present application obtains the environmental parameters of the ballastless track-bridge structure system and the soil parameters of the corresponding frozen ground of the ballastless track-bridge structure system under the action of the freeze-thaw cycle, and then simulates the freeze-thaw cycle of the corresponding frozen ground of the ballastless track-bridge structure system to obtain the frozen soil deformation field after the freeze-thaw cycle; the frozen soil deformation field after the freeze-thaw cycle is input into the pile-soil nonlinear interaction model of the ballastless track-bridge structure system to obtain the pier settlement / embossing deformation data after the freeze-thaw cycle; and the geometric deformation data of the ballastless track after the freeze-thaw cycle is obtained based on the pier settlement / embossing deformation data after the freeze-thaw cycle. In the solving process of the train-ballastless track-bridge structure dynamic interaction model, in addition to considering track geometry and dynamic deformation, bridge static and dynamic response, and wheel-rail contact behavior, etc., the geometric deformation data of the ballastless track after the freeze-thaw cycle is also taken into account to obtain the dynamic response of the train-ballastless track-bridge structure under the action of the freeze-thaw cycle, and then the safety and reliability of the ballastless track-bridge structure system are evaluated.

[0033] The method for constructing the dynamic interaction model of the train-ballastless track-bridge structure in this invention is the same as that in the prior art, including the train model, the ballastless track model, the bridge structure model, and the interlayer nonlinear model between the ballastless track and the bridge structure. The only difference is that when considering the displacement parameters in the train-ballastless track-bridge structure system, the geometric deformation data of the ballastless track after freeze-thaw cycles is added.

[0034] Without loss of generality, a brief explanation of the dynamic interaction model of the train-ballastless track-bridge structure is provided: The dynamic interaction model of the train-ballastless track-bridge structure adopts d'Alembert's principle, transforming the dynamic problem into a dynamic equilibrium problem. Based on the idea of ​​establishing the principle of constant total potential energy in statics, the principle of constant total potential energy in the dynamics of the elastic system is derived from the principle of virtual work.

[0035] For any dynamically balanced system, at a certain instant, the total potential energy of the system is... for: ; In the formula, For system strain energy; It is the potential energy of friction; It is gravitational potential energy; The work done by inertial force is negative; The work done by the damping force is negative; The negative value represents the work done by the interference force.

[0036] Based on the principle of stationary potential energy, assuming a dynamic interaction model of the train-ballastless track-bridge structure, considering the train-ballastless track-bridge structure system... n Displacement parameters Let the total potential energy of the elastic dynamic interaction system be... displacement parameters If the function is: ; We can derive n equilibrium equations corresponding to the total number of displacement parameters. For each displacement parameter, the following equation is satisfied: ; In the formula Represents the dynamic matrix of the first j OK, Displacement parameters included Represents the dynamic matrix of the first i List.

[0037] The above is applied to elastic dynamic interaction systems, and a dynamic interaction model of the train-ballastless track-bridge structure can be constructed accordingly. The displacement parameters considered in the dynamic interaction model of the train-ballastless track-bridge structure in this invention include the geometric deformation data of the ballastless track after freeze-thaw cycles, i.e., the above-mentioned... n Each displacement parameter includes the geometric deformation data of the ballastless track after freeze-thaw cycles.

[0038] Regarding the sub-model of the dynamic interaction model of train-ballastless track-bridge structure—the train model—in the train-structure dynamic analysis model, the train is regarded as a multi-rigid-body model connected by primary and secondary suspensions. The following introduces the train vibration energy calculation formula when the mass, stiffness and damping matrix of the train system are formed.

[0039] The work done by the inertial force of the train system is negative.

[0040] Quality matrix of train system It is mainly derived from the negative work done by the inertial forces of the various rigid bodies of the train, that is: ; in Indicates the first The train carriages are numbered to distinguish between different carriages. Indicates the first The first carriage of the train The numbering of rigid components is used to distinguish different components within the car body (such as bogies, car bodies, etc.). The set of degrees of freedom of a rigid body specifically includes 6 degrees of freedom, among which These represent the longitudinal, transverse, and vertical components of the linear displacement direction, respectively. These represent the yaw angle, pitch angle, and roll angle in the rotation angle, respectively. Indicates the first The first carriage of the train The rigid component in the first Generalized mass in a degree of freedom is represented by mass for linear displacement of a rigid body and by moment of inertia for angular displacement. Indicates the first The first carriage of the train The rigid component in the first Gamma Generalized acceleration (such as linear acceleration or angular acceleration) in a degree of freedom. Indicates the first The first carriage of the train The rigid component in the first Generalized displacements (such as linear or angular displacements) in a degree of freedom.

[0041] Elastic deformation energy of train system: stiffness matrix of train system The elastic deformation energy of the primary and secondary suspension systems of different vehicles can be derived, i.e.: ; wherein, and respectively represent the elastic deformation energy of the primary and secondary suspension spring systems, which is mainly caused by the spring compression (stretching) formed by the relative motion displacement between different rigid bodies.

[0042] The negative value of the damping force work done of the train system. The damping matrix of the train system The negative value of the damping force work done of the primary and secondary suspension systems of different vehicles can be derived, i.e.: ; wherein, and respectively represent the negative value of the damping force work done of the primary and secondary suspension damping systems, which is mainly caused by the damper work done caused by the relative motion velocity between different rigid bodies.

[0043] Regarding the sub-model, track model, in the dynamic interaction model of the train-ballastless track-bridge structure: The track system in the train-ballastless track-bridge structure is a typical long and large longitudinal multilayer structure, which supports and guides the normal operation of the train system.

[0044] Track system mass matrix: Track system mass matrix The negative value of the inertia force work done of the rail beam element and the concrete slab element is derived, which can be expressed as: ; wherein: , , represent the mass matrix of the rail element, which is composed of the longitudinal mass matrix , the transverse mass matrix , the vertical mass matrix and the torsional mass matrix of the rail element, and the symbols “ ” and “ ” respectively represent the left and right rails; and respectively represent the transverse and vertical element mass matrices of the track slab. represents the number of track slabs, represents the number of track slab elements, and represents the index of the track slab after being discretized. represents the number of rail elements, and represents the index of the rail after being discretized into multiple finite elements.

[0045] Track system stiffness matrix: The stiffness matrix of the track system is derived from the displacement (strain) variation of the bending deformation energy, strain energy and elastic deformation energy of the rail beam element, concrete slab element and system spring element, i.e. ; In the formula, is the number of rubber pads under the track; is the stiffness matrix derived from the strain energy of the rail beam element, is the stiffness matrix derived from the bending deformation energy of the track slab element, is the stiffness matrix derived from the deformation energy of the rubber pad spring under the track caused by the interaction between the rail and the track slab, is the stiffness matrix derived from the deformation energy of the mortar layer spring caused by the interaction between the track slab and the constrained subgrade.

[0046] The damping matrix of the track system is: The damping matrix of the track system is derived from the negative value of the damping force work between the rail beam element and the concrete slab element and between the concrete slab and the surface layer of the subgrade, and can be expressed as: ; In the formula, is the damping matrix derived from the deformation energy of the rubber pad spring under the track caused by the interaction between the rail and the track slab, is the damping matrix derived from the deformation energy of the mortar layer spring caused by the interaction between the track slab and the constrained subgrade.

[0047] Regarding the sub-model of the bridge model in the dynamic interaction model of the train-ballastless track-bridge structure: The stiffness matrix of the bridge is the stiffness matrix of the bridge element derived from the axial strain energy, bending deformation energy around the Y axis and Z axis, and free torsional deformation energy of the bridge element, and is expressed as: ; In the formula, , , , , , , , , , , , In the formula, is the elastic modulus; is the cross-sectional area of the bridge; and are the moments of inertia of the cross-section of the bridge about the X-axis, the Y-axis; is the shear modulus of the bridge; is the polar moment of inertia of the cross-section of the bridge; is the radius of curvature of the bridge; is the length of the bridge element; is the length of the n b th bridge element; is the radius of curvature of the n b th bridge element; is the normalized coordinate, taking values in the range [0, 1]; , , , are the axial stiffness matrix, the bending stiffness matrix about the Y-axis, the bending stiffness matrix about the Z X-axis, the torsional stiffness matrix, respectively; is the bridge mass matrix, which is derived from the negative work done by the longitudinal, transverse, vertical and torsional inertia forces of the bridge element, and is expressed as follows: ; wherein: , , , , In the formula, is the mass matrix of the n b th bridge element, , , , are the mass matrices of the longitudinal, transverse, vertical and torsional of the n b th bridge element, is the length mass of the bridge element; is the polar moment of inertia of the cross-section of the bridge.

[0048] Regarding the sub-model, the interlayer nonlinear model in the dynamic interaction model of the train-ballastless track-bridge structure, which is used for interlayer nonlinear cohesive force simulation.

[0049] For the interface damage constitutive of track structure, the bilinear opening-separation function is usually used to represent the damage of interface in the cohesive zone model (CZM), as follows: ; ; where represents the stress of interface, in which and are the normal and tangential stresses, respectively; and are the cohesive strengths, respectively; denotes the relative (opening) displacement; and denote the normal and tangential opening displacements at full damage, respectively; and denote the normal and tangential opening displacements at the beginning of damage, respectively.

[0050] Based on the nonlinear relationship, the cohesive element representing the interface damage of track structure can be established, as follows: ; where denotes the local stiffness matrix of the i th cohesive element, denotes the scalar stiffness coefficient of the i th cohesive element, and are the shape functions of the cohesive element.

[0051] The Newton-Raphson iteration method is used to solve the nonlinear process, which is assumed to be controlled by the following equation: ; where , and denote the nominal nonlinear stiffness matrix function, force vector and displacement vector, respectively; is the total internal force vector of the system; is the unbalanced force vector of each iteration step.

[0052] n For the th iteration step, assuming the displacement solution is , the Taylor expansion of the unbalanced force at n can be written as ; where denotes the tangent stiffness matrix; is then unbalanced force vector of the iteration step.

[0053] In another embodiment, a system for evaluating a ballastless track-bridge structure system under freeze-thaw cycles is provided, comprising: a freeze-thaw cycle simulation module configured to obtain environmental parameters of the ballastless track-bridge structure system under freeze-thaw cycles and soil parameters of a frozen soil foundation corresponding to the ballastless track-bridge structure system, and to simulate freeze-thaw cycles of the frozen soil foundation corresponding to the ballastless track-bridge structure system to obtain a frozen soil deformation field after freeze-thaw cycles; a pile-soil nonlinear interaction module configured to input the frozen soil deformation field after freeze-thaw cycles into a pile-soil nonlinear interaction model of the ballastless track-bridge structure system to obtain bridge pier settlement / embossment deformation data after freeze-thaw cycles; a geometric deformation data obtaining module configured to obtain geometric deformation data of the ballastless track after freeze-thaw cycles based on the bridge pier settlement / embossment deformation data after freeze-thaw cycles; a dynamic response obtaining module configured to construct a train-ballastless track-bridge structure dynamic interaction model considering the geometric deformation data of the ballastless track after freeze-thaw cycles and to solve the model to obtain a dynamic response of the train-ballastless track-bridge structure under freeze-thaw cycles; an evaluation module configured to evaluate the safety and reliability of the ballastless track-bridge structure system based on the dynamic response of the train-ballastless track-bridge structure under freeze-thaw cycles.

[0054] In another aspect, the present application provides a computer device comprising a memory and a processor, the memory storing a computer program, and the processor implementing the steps of the method for evaluating a ballastless track-bridge structure system under freeze-thaw cycles according to any one of the above embodiments when executing the computer program. The computer device can be a server. The computer device comprises a processor, a memory, a network interface and a database connected by a system bus. The processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device comprises a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operating system and the computer program in the non-volatile storage medium to run. The database of the computer device is configured to store sample data. The network interface of the computer device is configured to communicate with external terminals through network connection.

[0055] In another aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, the computer program being executed by a processor to implement the steps of the method for evaluating a ballastless track-bridge structure system under freeze-thaw cycles according to any one of the above embodiments.

[0056] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer readable storage medium, and when the computer program is executed, the processes of the above-mentioned embodiments of the methods can be included. Any reference to memory, storage, database or other medium used in the embodiments provided in the present application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. As an illustration but not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0057] The details of the present application are as follows.

[0058] The technical features of the above embodiments can be combined in any way. In order to make the description simple, all possible combinations of the technical features in the above embodiments are not described, but as long as the combination of the technical features does not exist, it should be considered as the scope of the present application.

[0059] The above embodiments only express several embodiments of the present application, and the description is more specific and detailed, but it should not be understood as a limitation on the scope of the application. It should be pointed out that for ordinary skilled in the art, without departing from the concept of the present application, a number of modifications and improvements can be made, which are within the scope of the present application.

[0060] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A method for evaluating a ballastless track-bridge structure system under the action of freeze-thaw cycles, characterized in that, The method comprises the following steps: (S1) obtaining environmental parameters of the ballastless track-bridge structure system under the action of freeze-thaw cycles and soil parameters of the frozen soil foundation corresponding to the ballastless track-bridge structure system, and then simulating the freeze-thaw cycles of the frozen soil foundation corresponding to the ballastless track-bridge structure system to obtain a frozen soil deformation field after the freeze-thaw cycles; (S2) inputting the frozen soil deformation field after the freeze-thaw cycles into a pile-soil nonlinear interaction model of the ballastless track-bridge structure system to obtain bridge pier settlement / upsurge deformation data after the freeze-thaw cycles; (S3) obtaining geometric deformation data of the ballastless track after the freeze-thaw cycles based on the bridge pier settlement / upsurge deformation data after the freeze-thaw cycles; (S4) constructing a train-ballastless track-bridge structure dynamic interaction model considering the geometric deformation data of the ballastless track after the freeze-thaw cycles and solving the model to obtain the dynamic response of the train-ballastless track-bridge structure under the action of the freeze-thaw cycles; (S5) evaluating the safety and reliability of the ballastless track-bridge structure system based on the dynamic response of the train-ballastless track-bridge structure under the action of the freeze-thaw cycles.

2. The method for evaluating the ballastless track-bridge structure system under freeze-thaw cycles according to claim 1, characterized in that, In step (S1), the environmental parameters include solar shortwave radiation, solar longwave radiation, convective heat transfer, evaporative heat transfer and surface heat flow, and the soil parameters include initial moisture content, porosity, unfrozen water content curve, phase change latent heat, thermal conductivity and volume heat capacity.

3. The method for evaluating ballastless track-bridge structure system under freeze-thaw cycles according to claim 2, characterized in that, In step (S1), the freeze-thaw cycles of the frozen soil foundation corresponding to the ballastless track-bridge structure system are simulated to obtain the frozen soil deformation field after the freeze-thaw cycles, which comprises the following steps: (S1.1) establishing a three-dimensional finite element model of the frozen soil foundation corresponding to the ballastless track-bridge structure system and performing mesh division; (S1.2) setting initial temperature fields, initial moisture contents and environmental thermal boundaries of each node of the three-dimensional finite element model, and considering the thermal conduction under different working conditions; (S1.3) considering the environmental parameters of the ballastless track-bridge structure system under the action of the freeze-thaw cycles and the soil parameters of the frozen soil foundation corresponding to the ballastless track-bridge structure system, constructing a frozen region heat conduction differential equation and an unfrozen region heat conduction differential equation, performing phase change heat transfer analysis and temperature field solving to obtain an overall temperature field of the three-dimensional finite element model after the freeze-thaw cycles; (S1.4) performing thermal-mechanical coupling analysis based on the overall temperature field of the three-dimensional finite element model after the freeze-thaw cycles to obtain the frozen soil deformation field after the freeze-thaw cycles.

4. The method for evaluating ballastless track-bridge structure system under freeze-thaw cycles according to any one of claims 1 to 3, characterized in that, In step (S2), in the pile-soil nonlinear interaction model of the ballastless track-bridge structure system, the Desai thin layer contact element is used to simulate the pile-soil nonlinear contact relationship of the pile-ballastless track-bridge structure system, wherein the normal stiffness model and the tangential stiffness model are simulated by a hyperbolic model, and the formula is as follows: ； ； wherein, and are the normal stiffness, the tangential stiffness, respectively, and are the initial normal stiffness, the initial tangential stiffness, respectively, is the cohesion, is the friction coefficient, is the frictional shear slip angle, is the failure ratio, , are the tangential shear stresses of the xy-plane, the yz-plane, respectively, i.e. the shear stresses actually taken up on the contact surface; is the normal stress acting on the contact surface.

5. The method for evaluating ballastless track-bridge structure system under freeze-thaw cycles according to claim 4, characterized in that, In step (S2), based on the pile-soil nonlinear interaction model of the ballastless track-bridge structure system, the bridge pier settlement / upsurge deformation data after the freeze-thaw cycles are obtained, which comprises the following steps: (S2.1) obtaining the finite element node force vector in the three-dimensional finite element model based on the frozen soil deformation field after the freeze-thaw cycles; ； wherein is the frozen soil deformation field after freeze-thaw cycles, is the elastic matrix describing the material constitutive relation; is the strain matrix determined by the shape function derivative of the element, reflecting the geometric relationship between displacement and strain, is the node force vector obtained by integrating the stress-related quantities within the element. (S2.2) dividing into n parts, resulting in n load increments; (S2.3) initializing the stiffness matrix of the Desai thin layer contact element; (S2.4) applying an i-th load increment, determining a current step displacement increment and a stress increment corresponding to the i-th load increment, ; (S2.5) obtaining the stiffness of the pile-soil interface in each direction according to the normal stiffness model and the tangential stiffness model, and updating the stiffness matrix of the Desai thin-layer contact element; (S2.6) i = i + 1, return to (S2.4) until n load increments are applied, and the pier settlement / heave deformation data after freeze-thaw cycles are calculated .

6. The method for evaluating ballastless track-bridge structure system under freeze-thaw cycles according to claim 5, characterized in that, In step (S3), the geometric deformation data of the ballastless track after the freeze-thaw cycle is obtained based on the pier settlement / heave deformation data after the freeze-thaw cycle, as follows: (S3.1) defining the constraint pier degrees of freedom, generating a displacement indicator vector based on the pier settlement / heave deformation data after the freeze-thaw cycle, and converting the pier settlement / heave deformation after the freeze-thaw cycle into an equivalent load; (S3.2) Stiffness matrix modification: the u-th row and u-th column of the stiffness matrix correspond to the position of the constrained degree of freedom, and the u-th row and u-th column of the stiffness matrix are processed to be 1, the displacement of the constrained degree of freedom is forced to be specified, and the displacement of the forced constrained degree of freedom is the settlement / heave deformation data of the pier after the freeze-thaw cycle , while decoupling the relationship between the constrained degree of freedom and the unconstrained degree of freedom, to obtain the modified stiffness matrix ; (S3.3) obtaining the modified equilibrium equation based on the modified stiffness matrix, solving the displacement of the non-constrained degrees of freedom in the block, and obtaining the geometric deformation data of the ballastless track after the freeze-thaw cycle.

7. The method for evaluating ballastless track-bridge structure system under freeze-thaw cycles according to claim 1, characterized in that, In step (S4), a train-ballastless track-bridge structure dynamic interaction model considering the geometric deformation data of the ballastless track after the freeze-thaw cycle is constructed, wherein the train-ballastless track-bridge structure dynamic interaction model includes a train model, a ballastless track model, a bridge structure model, and an interlayer nonlinear model between the ballastless track and the bridge structure. The model is solved to obtain the dynamic response of the train-ballastless track-bridge structure under the action of the freeze-thaw cycle.

8. The method for evaluating ballastless track-bridge structure system under freeze-thaw cycles according to claim 1, characterized in that, In step (S5), the dynamic response of the train-ballastless track-bridge structure under the action of the freeze-thaw cycle is compared with the set safety threshold, and then the safety and reliability of the ballastless track-bridge structure system are evaluated.

9. A system for evaluating a ballastless track-bridge structure system under the action of freeze-thaw cycles, characterized in that, It comprises: a freeze-thaw cycle simulation module for obtaining environmental parameters of the ballastless track-bridge structure system under the action of the freeze-thaw cycle and soil parameters of the frozen soil foundation corresponding to the ballastless track-bridge structure system, and then simulating the freeze-thaw cycle of the frozen soil foundation corresponding to the ballastless track-bridge structure system to obtain the frozen soil deformation field after the freeze-thaw cycle; a pile-soil nonlinear interaction module for inputting the frozen soil deformation field after the freeze-thaw cycle into the pile-soil nonlinear interaction model of the ballastless track-bridge structure system to obtain the pier settlement / heave deformation data after the freeze-thaw cycle; a geometric deformation data acquisition module for obtaining the geometric deformation data of the ballastless track after the freeze-thaw cycle based on the pier settlement / heave deformation data after the freeze-thaw cycle; a dynamic response acquisition module for constructing a train-ballastless track-bridge structure dynamic interaction model considering the geometric deformation data of the ballastless track after the freeze-thaw cycle and solving the model to obtain the dynamic response of the train-ballastless track-bridge structure under the action of the freeze-thaw cycle; an evaluation module for evaluating the safety and reliability of the ballastless track-bridge structure system based on the dynamic response of the train-ballastless track-bridge structure under the action of the freeze-thaw cycle.

10. The system for evaluating ballastless track-bridge structure system under freeze-thaw cycles according to claim 9, characterized in that, The environmental parameters include solar shortwave radiation, solar longwave radiation, convective heat transfer, evaporative heat transfer, and surface heat flow. The soil parameters include initial moisture content, porosity, unfrozen water content curve, phase change latent heat, thermal conductivity, and volumetric heat capacity.

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