Evaluation method and system for ballastless track-bridge structure system under freeze-thaw cycle action

Abstract

The application provides a kind of frozen-thaw cycle under ballastless track-bridge structure system evaluation method and system, including obtaining the environmental parameter of ballastless track-bridge structure system under the action of frozen-thaw cycle and the soil parameter of frozen ground foundation, frozen-thaw cycle simulation is carried out, and the frozen soil deformation field after frozen-thaw cycle is obtained;The frozen soil deformation field after frozen-thaw cycle is input into the pile soil nonlinear interaction model of ballastless track-bridge structure system, and the bridge pier settlement / embossing deformation data after frozen-thaw cycle is obtained, and then the geometric deformation data of ballastless track after frozen-thaw cycle is obtained;The train-ballastless track-bridge structure dynamic interaction model considering the geometric deformation data of ballastless track after frozen-thaw cycle is constructed and solved, and the corresponding dynamic response is obtained, to evaluate the safety and reliability of ballastless track-bridge structure system.The application can accurately analyze the spatial deformation law and dynamic performance of ballastless track-bridge structure system under frozen-thaw cycle environment.

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:

[0005] On the one hand, the application provides a method for evaluating a ballastless track-bridge structure system under freeze-thaw cycles, comprising:

[0006] (S1) Obtain the environmental parameters of the ballastless track-bridge structure system under freeze-thaw cycles and the soil parameters of the frozen ground corresponding to the ballastless track-bridge structure system, and then simulate the freeze-thaw cycles of the frozen ground corresponding to the ballastless track-bridge structure system to obtain the frozen soil deformation field after freeze-thaw cycles;

[0007] (S2) Input the frozen soil deformation field after freeze-thaw cycles into the pile-soil nonlinear interaction model of the ballastless track-bridge structure system to obtain the settlement / embossing deformation data of the pier after freeze-thaw cycles;

[0008] (S3) Obtain the geometric deformation data of the ballastless track after freeze-thaw cycles based on the settlement / embossing deformation data of the pier after freeze-thaw cycles;

[0009] (S4) Construct a dynamic interaction model of train-ballastless track-bridge structure considering the geometric deformation data of the ballastless track after freeze-thaw cycles and solve it to obtain the dynamic response of the train-ballastless track-bridge structure under freeze-thaw cycles;

[0010] (S5) 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.

[0011] In another aspect, the application provides a system for evaluating a ballastless track-bridge structure system under freeze-thaw cycles, comprising:

[0012] 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 further 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;

[0013] 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;

[0014] a geometric deformation data acquisition module of the ballastless track after freeze-thaw cycles, 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;

[0015] a dynamic response acquisition module, configured to construct a dynamic interaction model of a train-ballastless track-bridge structure considering the geometric deformation data of the ballastless track after freeze-thaw cycles and solve the model to obtain dynamic responses of the train-ballastless track-bridge structure under freeze-thaw cycles;

[0016] an evaluation module, 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 freeze-thaw cycles.

[0017] In another aspect, the 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 method for evaluating a ballastless track-bridge structure system under freeze-thaw cycles when executing the computer program.

[0018] In another aspect, the application provides a computer-readable storage medium having a computer program stored thereon, and the computer program, when executed by a processor, implements the steps of the above-mentioned method for evaluating a ballastless track-bridge structure system under freeze-thaw cycles.

[0019] In another aspect, the 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 method for evaluating a ballastless track-bridge structure system under freeze-thaw cycles.

[0020] Compared with the prior art, the application has the following advantages:

[0021] The application provides a method and system for evaluating a ballastless track-bridge structure system under freeze-thaw cycles, which can accurately analyze the spatial deformation law of the ballastless track-bridge structure system under freeze-thaw cycles and accurately evaluate the dynamic response performance, thereby providing a scientific basis for the maintenance and management of railway infrastructure. BRIEF DESCRIPTION OF DRAWINGS

[0022] 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 needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of the drawings shown.

[0023] Figure 1 A flowchart of the method for evaluating the ballastless track-bridge structure system under freeze-thaw cycles provided in an embodiment. DETAILED DESCRIPTION

[0024] The technical solutions in the embodiments of the present application will be described clearly and completely in the following with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the protection scope of the present application.

[0025] A method for evaluating a ballastless track-bridge structure system under freeze-thaw cycles, comprising:

[0026] (S1) obtaining environmental parameters of the ballastless track-bridge structure system under freeze-thaw cycles and soil parameters of the frozen ground corresponding to the ballastless track-bridge structure system, and then simulating freeze-thaw cycles of the frozen ground corresponding to the ballastless track-bridge structure system to obtain a frozen soil deformation field after freeze-thaw cycles;

[0027] (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;

[0028] (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;

[0029] (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 the model to obtain the dynamic response of the train-ballastless track-bridge structure under freeze-thaw cycles;

[0030] (S5) Based on the dynamic response of the train-ballastless track-bridge structure under the action of freeze-thaw cycles, the safety and reliability of the ballastless track-bridge structure system are evaluated.

[0031] 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, etc. 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, etc., and the soil parameters include initial moisture content, porosity, unfrozen water content curve, latent heat of phase change, thermal conductivity, volumetric heat capacity, etc.

[0032] 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 freeze-thaw cycle is obtained, including the following steps:

[0033] (S1.1) Establish a three-dimensional finite element model of the frozen soil foundation corresponding to the ballastless track-bridge structure system and perform meshing;

[0034] (S1.2) Set the initial temperature field, initial moisture content and environmental thermal boundary of each node of the three-dimensional finite element model, and consider the heat conduction under different working conditions;

[0035] (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, construct the heat conduction differential equation of the frozen region and the heat conduction differential equation of the unfrozen region, perform phase change heat transfer analysis and temperature field solving, and obtain the overall temperature field of the three-dimensional finite element model after freeze-thaw cycle;

[0036] (S1.4) Based on the overall temperature field of the three-dimensional finite element model after freeze-thaw cycle, perform thermal-mechanical coupling analysis to obtain the frozen soil deformation field after freeze-thaw cycle.

[0037] 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 by two-dimensional transient temperature field .

[0038] For the heat conduction differential equation of the frozen region, it can be written as:

[0039] ;

[0040] For the heat conduction differential equation of the unfrozen region, it can be written as:

[0041] ;

[0042] In the formula, thermal conductivity of frozen soil in frozen state; two-dimensional transient temperature field of frozen soil in frozen state; 、 and are volumetric heat capacity of frozen soil in frozen state and thawing state, respectively, subscript , represent frozen and thawing two-phase state of frozen soil.

[0043] Heat transfer finite element implementation of phase change problem: solve the heat conduction differential equation by using the weighted residual method. The typical direction of the weighted residual method can be expressed as:

[0044] ;

[0045] 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.

[0046] According to the Galerkin method and the boundary relationship of the plane field definition domain, the final expression is as follows:

[0047] ;

[0048] 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 volumetric heat capacity, W corresponds trial function, W is the approximate expression of the assumed temperature field which meets the boundary conditions, used in the weighted residual method to "approximate" the real temperature field distribution, s is the boundary (i.e. integral boundary), ds is the microelement (length element or area element, depending on the dimension) on the boundary.

[0049] The final expression of the overall temperature field of the three-dimensional finite element model after the action of freeze-thaw cycle is obtained as follows:

[0050] ;

[0051] In the formula, is the temperature stiffness matrix, is the temperature vector, is the temperature damping matrix, An array of equivalent heat flow boundary conditions for the outside world.

[0052] 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 to obtain the deformation field of frozen soil after freeze-thaw cycle

[0053]

[0054] In the formula, x, y, z direction of the three components of the deformation field of frozen soil after freeze-thaw cycle is the water content of soil, representing the porosity of soil.

[0055] In step (S2), the Desai thin layer contact element is used to simulate the nonlinear contact relationship between the pile and the soil of the ballastless track-bridge structure system, and the normal stiffness model and the tangential stiffness model are simulated by the hyperbolic model, as follows:

[0056]

[0057]

[0058] 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 stress 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.

[0059] In step (S2), based on the nonlinear interaction model of the pile and the soil of the ballastless track-bridge structure system, the settlement / heave deformation data of the pier after freeze-thaw cycle are obtained, including the following steps:

[0060] (S2.1) Based on the deformation field of frozen soil after freeze-thaw cycle, the finite element node force vector in the three-dimensional finite element model is obtained;

[0061]

[0062] wherein is the deformation field of frozen soil after freeze-thaw cycle,​​​​​​ elastic matrix for describing the material constitutive relationship; strain matrix determined by the derivative of the element shape function, reflecting the geometric relationship between displacement and strain, node force vector obtained by integrating the stress-related quantities in the element;

[0063] (S2.2) divide the load into n increments, obtaining n load increments;

[0064] (S2.3) initialize the stiffness matrix of the Desai thin-layer contact element;

[0065] (S2.4) apply the i-th load increment, determine the current step displacement increment and stress increment corresponding to the i-th load increment, ;

[0066] (S2.5) obtain the stiffness of the pile-soil interface in each direction according to the normal stiffness model and the tangential stiffness model, update the stiffness matrix of the Desai thin-layer contact element;

[0067] (S2.6) i = i + 1, return to (S2.4) until the n load increments are applied, and the bridge pier settlement / heave deformation data after freeze-thaw cycles are calculated .

[0068] In step (S3), the geometric deformation data of the ballastless track after freeze-thaw cycles is obtained based on the bridge pier settlement / heave deformation data after freeze-thaw cycles, as follows:

[0069] (S3.1) define the constraint bridge pier degrees of freedom, generate a displacement indicator vector based on the bridge pier settlement / heave deformation data after freeze-thaw cycles, and convert the bridge pier settlement / heave deformation after freeze-thaw cycles into equivalent load.

[0070] wherein is the equivalent load corresponding to the bridge pier settlement / heave deformation after freeze-thaw cycles, is the stiffness matrix, is the displacement indicator vector, is the bridge pier settlement / heave deformation data after freeze-thaw cycles.

[0071] (S3.2) stiffness matrix correction: the u-th row and u-th column of the stiffness matrix correspond to the position of the constraint degree of freedom, the u-th row and u-th column of the stiffness matrix are processed to 0 and 1, the displacement of the constraint degree of freedom is forced to be specified, and the displacement of the constraint degree of freedom is forced to be , while decoupling the relationship between the constraint degree of freedom and the non-constraint degree of freedom, obtaining the modified stiffness matrix ​; wherein the displacement of the unconstrained degree of freedom is unknown and needs to be solved by the balance equation, and therefore the corresponding row and column are not processed by the 0 and 1 processing, and the coupling relationship and the diagonal stiffness in the original stiffness matrix are retained.

[0072] (S3.3) Obtain the modified balance equation based on the modified stiffness matrix, solve the displacement of the unconstrained degree of freedom in the modified balance equation by block, and obtain the geometric deformation data of the ballastless track after the freeze-thaw cycle.

[0073] The modified balance equation is , wherein is the geometric deformation data of the ballastless track after the freeze-thaw cycle to be solved;

[0074] By separating the constrained degree of freedom and the unconstrained degree of freedom by the block matrix, we have

[0075]

[0076] , wherein is the unconstrained degree of freedom stiffness matrix in the modified stiffness matrix, is the constrained degree of freedom stiffness correction matrix in the modified stiffness matrix, in the is the constrained degree of freedom equation, is the known displacement, , is the displacement of the unconstrained degree of freedom, i.e. the unknown displacement to be solved, is the unconstrained degree of freedom equation, which is determined by the external load.

[0077] 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 .

[0078] 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 dynamics response of the train-ballastless track-bridge structure under the action of the freeze-thaw cycle.

[0079] In step (S5), the dynamics 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.

[0080] ​The train-ballastless track-bridge structure dynamic interaction model usually comprises a plurality of 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 deformation data considered by the existing train-ballastless track-bridge structure dynamic interaction model includes track geometry and dynamic deformation, bridge static and dynamic response and wheel-rail contact behavior, etc., and the geometric deformation data of the ballastless track after freeze-thaw cycles is not considered. The present application obtains the environmental parameters of the ballastless track-bridge structure system and the soil parameters of the corresponding frozen soil foundation of the ballastless track-bridge structure system under the action of freeze-thaw cycles, and then simulates the freeze-thaw cycles of the corresponding frozen soil foundation of the ballastless track-bridge structure system, to obtain the frozen soil deformation field after freeze-thaw cycles. The frozen soil deformation field after freeze-thaw cycles is input into the pile-soil nonlinear interaction model of the ballastless track-bridge structure system, to obtain the settlement / upsurge deformation data of the pier after freeze-thaw cycles. The geometric deformation data of the ballastless track after freeze-thaw cycles is obtained based on the settlement / upsurge deformation data of the pier after freeze-thaw cycles. In the solving process of the train-ballastless track-bridge structure dynamic interaction model, in addition to considering the 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 freeze-thaw cycles is also taken into account, to obtain the dynamic response of the train-ballastless track-bridge structure under the action of freeze-thaw cycles, and then to evaluate the safety and reliability of the ballastless track-bridge structure system.

[0081] The construction method of the train-ballastless track-bridge structure dynamic interaction model of the present application is the same as the prior art, and also includes the train model, the ballastless track model, the bridge structure model and the interlayer nonlinear model between the ballastless track and the bridge structure. However, 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.

[0082] Without loss of generality, the train-ballastless track-bridge structure dynamic interaction model is briefly described as follows: the train-ballastless track-bridge structure dynamic interaction model adopts the D'Alembert principle to convert the dynamic problem into a dynamic equilibrium problem, and is established based on the static total potential energy invariable principle, and the total potential energy invariable principle of the elastic system is derived from the virtual work principle.

[0083] For any dynamic equilibrium system, at a certain instantaneous time, the total potential energy of the system is :

[0084] ;

[0085] In the formula, is the strain energy of the system; is the friction potential energy; is the gravity 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.

[0086] 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:

[0087] ;

[0088] We can derive n equilibrium equations corresponding to the total number of displacement parameters. For each displacement parameter, the following equation is satisfied:

[0089] ;

[0090] In the formula Represents the dynamic matrix of the first j OK, Displacement parameters included Represents the dynamic matrix of the first i List.

[0091] 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.

[0092] 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.

[0093] The work done by the inertial force of the train system is negative.

[0094] 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:

[0095] ;

[0096] in Indicates the first The train carriages are numbered to distinguish between different carriages. represents the number of the , the set of rigid body degrees of freedom, which specifically includes 6 degrees of freedom, wherein represents the longitudinal, lateral and vertical components in the linear displacement direction, respectively, represents the yaw, pitch and roll angles in the rotational angle, respectively. represents the number of the represents the generalized acceleration (such as linear acceleration or angular acceleration) of the Gamma represents the generalized displacement (such as linear displacement or angular displacement) of the

[0097] Train system elastic deformation energy: the stiffness matrix of the train system can be derived from the elastic deformation energy of the primary and secondary suspension systems of different vehicles, that is:

[0098] ;

[0099] In the formula, 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.

[0100] Train system damping force negative value. The damping matrix of the train system can be derived from the damping force negative value of the primary and secondary suspension systems of different vehicles, that is:

[0101] ;

[0102] In the formula, and respectively represent the damping force negative value of the primary and secondary suspension damping systems, which is mainly caused by the damper work formed by the relative motion velocity between different rigid bodies.

[0103] Regarding the sub-model of the track model in the dynamic interaction model of the train-ballastless track-bridge structure:​​​​​​​​​​​

[0104] 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.

[0105] Track system mass matrix:

[0106] Track system mass matrix which is derived from the negative value of the work done by the inertial force of the rail beam element and the concrete slab element, and can be expressed as:

[0107]

[0108] wherein: represents the rail element mass matrix, which is composed of the longitudinal mass matrix of the rail element, the transverse mass matrix , the vertical mass matrix , and the torsional mass matrix , and the symbols “ ” and “ ” represent the left and right rails respectively; and represent the transverse and vertical element mass matrices of the track slab respectively. represents the number of track slabs, represents the number of track slab elements, and represents the index of the track slab after being discretized.

[0109] Track system stiffness matrix:

[0110] The track system stiffness matrix 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, that is:

[0111]

[0112] wherein: is the number of rail pads; 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 spring deformation energy of the rail pad caused by the interaction between the rail and the track slab, is the stiffness matrix derived from the spring deformation energy of the mortar layer caused by the interaction between the track slab and the constrained roadbed.

[0113] Track system damping matrix: ​​​​

[0114] Track system damping matrix The negative work done by the damping forces between the rail beam elements and the concrete slab elements and between the concrete slab and the subgrade surface can be expressed as:

[0115] ;

[0116] where is the damping matrix derived from the energy of the rail pad spring deformation caused by the interaction between the rail and the track slab, is the damping matrix derived from the energy of the mortar layer spring deformation caused by the interaction between the track slab and the constrained subgrade.

[0117] Regarding the sub-model, the bridge model, in the dynamic interaction model of the train-ballasted track-bridge structure:

[0118] Bridge stiffness matrix, the stiffness matrix of the bridge element is derived from the axial strain energy of the bridge element, the bending deformation energy around the Y axis and the Z axis, and the free torsional deformation energy, and is expressed as follows:

[0119] ;

[0120] where:

[0121] , ,

[0122] , ,

[0123] ,

[0124] ,

[0125] ,

[0126] ,

[0127] ,

[0128] ,

[0129] ,

[0130] In the formula, is the elastic modulus; is the cross-sectional area of the bridge; and are the moments of inertia of the bridge cross-section around the axis, axis; is the shear modulus of the bridge; is the torsional moment of inertia of the bridge cross section; is the radius of curvature of the bridge; is the length of the bridge element; is the length of the i-th bridge element; n b is the length of the i-th bridge element; is the radius of curvature of the i-th bridge element; n b is the radius of curvature of the i-th bridge element; is the normalized coordinate, taking values in the range [0, 1]; , , , are the axial stiffness matrix, the bending stiffness matrix around the Y axis, the bending stiffness matrix around the X axis, and the torsional stiffness matrix, respectively; Z

[0131] is the bridge mass matrix, which is derived from the negative work of the longitudinal, transverse, vertical, and torsional inertia forces of the bridge element, and is expressed as follows:

[0132] ;

[0133] wherein:

[0134] ,

[0135] ,

[0136] ,

[0137] ,

[0138] wherein: is the mass matrix of the i-th bridge element, n b is the mass matrix of the i-th bridge element, , , , are the longitudinal, transverse, vertical, and torsional mass matrices of the i-th bridge element, n b are the longitudinal, transverse, vertical, and torsional mass matrices of the i-th bridge element, is the length mass of the bridge element; is the polar moment of inertia of the bridge cross section.

[0139] Regarding the sub-model, the interlayer nonlinear model, in the dynamic interaction model of the train-ballastless track-bridge structure, for performing interlayer nonlinear cohesive force simulation.

[0140] ​The bilinear opening-separation function is usually used to represent the damage of the interface in the cohesive zone model (CZM) for the interface constitutive of track structure, as follows:

[0141]

[0142]

[0143] where represents the stress of the interface, where and are the normal and tangential stresses, respectively; and are the cohesive strengths; 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 onset of damage, respectively.

[0144] Based on the nonlinear relationship, the cohesive element representing the interface damage of track structure can be established as follows:

[0145]

[0146] where denotes the local stiffness matrix of the i th cohesive element, denotes the scalar stiffness coefficient of the i th cohesive element, and is the shape function of the cohesive element.

[0147] The Newton-Raphson iteration method is used to solve the nonlinear process, which is assumed to be controlled by the following equation:

[0148]

[0149] where , and denote the nominal nonlinear stiffness matrix function, the force vector, and the displacement vector, respectively; is the total internal force vector of the system; is the unbalanced force vector of each iteration step.

[0150] For the n th iteration step, assuming the displacement solution as , the Taylor expansion of the unbalanced force at is considered, then the n ​​​The nonlinear control equation of the i-th iteration step can be written as

[0151] ;

[0152] wherein, denotes the tangent stiffness matrix; is the unbalance force vector of the i-th iteration step. n

[0153] In another embodiment, a system for evaluating a ballastless track-bridge structure system under freeze-thaw cycles is provided, comprising:

[0154] 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;

[0155] 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;

[0156] a geometric deformation data acquisition module of the ballastless track after freeze-thaw cycles 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;

[0157] a dynamic response acquisition 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;

[0158] 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.

[0159] ​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 the ballastless track-bridge structure system under the action of 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 an external terminal through a network connection.

[0160] In another aspect, the present application provides a computer readable storage medium storing a computer program, and the computer program implements the steps of the method for evaluating the ballastless track-bridge structure system under the action of freeze-thaw cycles according to any one of the above embodiments when executed by a processor.

[0161] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be completed by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer readable storage medium, and when executed, can include the processes of the above-mentioned embodiments. Any reference to memory, storage, database or other medium used in the embodiments provided by 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), Rambus direct RAM (RDRAM), direct RAM bus dynamic RAM (DRDRAM) and memory bus dynamic RAM (RDRAM) and the like.

[0162] The details of the present application are known.

[0163] Any technical features in the above-described embodiments can be combined in any manner, and for the sake of brevity, not all possible combinations are described, however, any combination of the technical features is considered to be within the scope of the present specification.

[0164] The above-described embodiments are merely illustrative for the present application and are not used to limit the present application. It should be pointed out that, for those skilled in the art, some modifications and improvements can be made without departing from the concept of the present application, and these should be included in the protection scope of the present application.

[0165] The above-described embodiments are merely illustrative for the present application and are not used to limit the present application. It should be pointed out that, for those skilled in the art, some modifications and improvements can be made without departing from the concept of the present application, and these should be included in the protection scope of the present application. The above-described embodiments are merely illustrative for the present application and are not used to limit the present application. It should be pointed out that, for those skilled in the art, some modifications and improvements can be made without departing from the concept of the present application, and these should 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, Comprise: (S1) Obtain the environmental parameters of the ballastless track-bridge structure system under the action of freeze-thaw cycle and the soil parameters of the frozen soil foundation corresponding to the ballastless track-bridge structure system, and then simulate the freeze-thaw cycle of the frozen soil foundation corresponding to the ballastless track-bridge structure system, and obtain the frozen soil deformation field after freeze-thaw cycle; (S2) Input the frozen soil deformation field after freeze-thaw cycle into the pile-soil nonlinear interaction model of the ballastless track-bridge structure system, and obtain the bridge pier settlement / upsurge deformation data after freeze-thaw cycle, wherein 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, including: (S2.1) Obtain the finite element node force vector in the three-dimensional finite element model based on the frozen soil deformation field after freeze-thaw cycle; 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 derivative of the element shape function, 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) Initialize the stiffness matrix of the Desai thin layer contact element; (S2.4) Apply the ith load increment, determine the current step displacement increment and stress increment corresponding to the ith load increment, i=1,2,...,n; (S2.5) Obtain the stiffness of the pile-soil interface in each direction according to the normal stiffness model and the tangential stiffness model, and update 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 ; (S3) Obtain the geometric deformation data of the ballastless track after freeze-thaw cycle based on the bridge pier settlement / upsurge deformation data after freeze-thaw cycle; (S4) Construct a train-ballastless track-bridge structure dynamic interaction model considering the geometric deformation data of the ballastless track after freeze-thaw cycle and solve it, and obtain the dynamic response of the train-ballastless track-bridge structure under the action of freeze-thaw cycle; (S5) 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 the action of freeze-thaw cycle.

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, 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 frozen soil deformation field after freeze-thaw cycle is obtained by simulating the freeze-thaw cycle of the frozen soil foundation corresponding to the ballastless track-bridge structure system, including the following steps: (S1.1) Establish a three-dimensional finite element model of the frozen soil foundation corresponding to the ballastless track-bridge structure system and perform meshing; (S1.2) Set the initial temperature field, initial moisture content and environmental thermal boundary of each node of the three-dimensional finite element model, and consider the heat conduction under different working conditions; (S1.3) Consider the environmental parameters of the ballastless track-bridge structure system under the action of freeze-thaw cycle and the soil parameters of the frozen soil foundation corresponding to the ballastless track-bridge structure system, construct the heat conduction differential equation of the frozen region and the heat conduction differential equation of the unfrozen region, and perform phase change heat transfer analysis and temperature field solving to obtain the overall temperature field of the three-dimensional finite element model after freeze-thaw cycle; (S1.4) Perform thermal-mechanical coupling analysis based on the overall temperature field of the three-dimensional finite element model after freeze-thaw cycle to obtain the frozen soil deformation field after freeze-thaw cycle.

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), 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 in 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 (S3), the geometric deformation data of the ballastless track after the freeze-thaw cycle is obtained based on the settlement / heave deformation data of the pier after the freeze-thaw cycle, as follows: (S3.1) Define the constraint pier freedom, generate the displacement indication vector based on the settlement / heave deformation data of the pier after the freeze-thaw cycle, and convert the settlement / heave deformation of the pier after the freeze-thaw cycle into 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) Obtain the modified equilibrium equation based on the modified stiffness matrix, solve the displacement of the non-constrained freedom in the block, and obtain the geometric deformation data of the ballastless track after the freeze-thaw cycle.

6. 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.

7. 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.

8. A system for evaluating a ballastless track-bridge structure system under the action of freeze-thaw cycles, characterized in that, It includes: A freeze-thaw cycle simulation module for obtaining environmental parameters of a ballastless track-bridge structure system under the action of a freeze-thaw cycle and soil parameters of a 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 a pile-soil nonlinear interaction model of the ballastless track-bridge structure system to obtain the settlement / heave deformation data of the pier after the freeze-thaw cycle, wherein 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, including: (S2.1) Obtain 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 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 of displacement to 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) Initialize the stiffness matrix of the Desai thin layer contact element; (S2.4) Apply the ith load increment, determine the current step displacement increment and stress increment corresponding to the ith load increment, i=1,2,...,n; (S2.5) Obtain the stiffness of the pile-soil interface in each direction according to the normal stiffness model and the tangential stiffness model, and update 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 ; A geometric deformation data acquisition module for obtaining the geometric deformation data of the ballastless track after the freeze-thaw cycle based on the settlement / heave deformation data of the pier after the freeze-thaw cycle; The dynamic response acquisition module is configured to construct 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 and to solve the dynamic interaction model to obtain the dynamic response of the train-ballastless track-bridge structure under the freeze-thaw cycle; The evaluation module is 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 the freeze-thaw cycle.

9. The system for evaluating ballastless track-bridge structure system under freeze-thaw cycles according to claim 8, characterized in that, The environmental parameters include solar shortwave radiation, solar longwave radiation, convective heat exchange, evaporative heat exchange 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.

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