Method for establishing the internal topological relationship between bridge pier settlement and driving performance index

Abstract

The present invention discloses a method for establishing an intrinsic topological relationship between pier settlement values ​​and driving performance indicators. A train sub-model and a longitudinal slab ballastless track-bridge sub-model are established respectively. The two sub-models are assembled and embedded in a bridge-track deformation general characterization relationship model to form a train-track-bridge system coupling dynamics joint simulation model that considers interlayer connection failure and pier settlement. After verification, the influence of interlayer connection failure and pier settlement on the dynamic characteristics of the train-track-bridge is analyzed, and the intrinsic topological relationship between the pier settlement amplitude and driving dynamic indicators considering interlayer connection failure is explored. Based on the joint simulation model of the present invention, the calculation efficiency and accuracy of the train-track-bridge deformation transmission law and the train dynamic characteristic indicators are significantly improved, providing a new method and further safety guarantee for quickly and accurately evaluating the driving safety on high-speed railway bridges under pier settlement conditions.

Description

Technical Field

[0001] The invention relates to a method for establishing an intrinsic topological relationship between a bridge pier settlement value and a driving performance index. Background Art

[0002] In order to get rid of the limitations of land resources, line environment, geological conditions and track smoothness, and to make trains run smoothly at high speed, bridge structures have been widely used in my country's high-speed rail lines. However, due to the exploitation of underground resources and other factors, bridge pier settlement phenomena are emerging one after another. Many parts of the existing high-speed rail lines have experienced post-construction non-uniform settlement, most of which have exceeded the 5mm limit in the high-speed railway design specifications. The uneven settlement of bridge piers in severe settlement areas is close to the maximum height adjustment of fasteners of 30mm. Once the bridge piers settle, it will inevitably affect the safety and comfort of train operation.

[0003] As the basis for studying the safety of high-speed trains, the characterization model between the deformation of high-speed railway foundations and the deformation of track surfaces has been a hot topic in railway engineering in recent years. For example, Chen et al. derived the mapping relationship between the settlement of bridge piers and the deformation of tracks in slab ballastless track systems. The study showed that the deformation of tracks with multiple pier settlements is the superposition of the deformation of tracks with single pier settlements. Based on the interlayer interaction of ballastless track-bridge systems and the principle of potential energy stationary value, Feng et al. proposed a mapping model between bridge deformation and track surface deformation. It revealed that the deformation of rails has an obvious "follow-up" characteristic with the deformation of bridges. Gou et al. established an analytical model for mapping the deformation of bridge damage such as pier settlement, beam misalignment, and beam end rotation to track surface deformation, and quantitatively studied the influence of bridge deformation amplitude on track surface deformation.

[0004] Existing studies have shown that the additional track irregularity caused by bridge pier settlement is an important factor in the safety of high-speed rail operation. In order to further explore the changing laws of train dynamic characteristics under bridge foundation damage, many scholars have carried out a series of studies. Zhang et al. established a unit plate ballastless track finite element model and a train-track-dynamic interaction model to analyze the impact of bridge pier settlement deformation on high-speed train operation. The results show that the impact of single pier settlement on train operation safety is greater than that of multiple pier settlement. Based on measured data, Hwang et al. studied the correlation between train body acceleration and long-wavelength track irregularity and proposed a control method for long-wavelength track irregularity under seasonal temperature changes.

[0005] However, although there have been many studies on the intrinsic topological relationship between bridge pier settlement and train running performance dynamics indicators based on mapping models, the following problems still exist:

[0006] (1) Existing studies are limited to the fitting regression analysis of single evaluation indicators such as wheel-rail vertical force or vehicle body acceleration, and fail to comprehensively consider driving indicators such as wheel-rail vertical force, wheel load reduction, derailment coefficient and vehicle body vertical acceleration; this will result in the research results being unable to accurately reflect the actual intrinsic topological relationship between bridge pier settlement values ​​and driving performance indicators.

[0007] (2) All existing studies are based on the condition that the bridge-rail interface is in good contact, and do not consider the impact of bridge-rail interface failure caused by bridge settlement on train operation safety. This will cause the calculated driving performance index value to be smaller than the actual situation, thus making the proposed bridge pier settlement limit value too large.

[0008] Therefore, it is necessary to incorporate interlayer connection failure and pier settlement into the track-bridge system, and study the fitting correlation between the changes in train dynamic indicators and the reduced fastener force and settlement value, so as to provide sufficient guarantee for the rapid and accurate evaluation of driving safety on high-speed railway bridges under pier settlement. Summary of the invention

[0009] Based on the limitations and problems of the existing research on the intrinsic topological relationship between the pier settlement value and the driving performance index, the present invention provides a method for analyzing the intrinsic topological relationship between the pier settlement value and the driving performance index, which takes into account the bottom slab void length and the maximum value of the reduced fastener force. The longitudinal slab ballastless track-bridge system is taken as the research object, and a train-track-bridge system coupling dynamics joint simulation model considering interlayer connection failure and pier settlement is established. The fitting correlation between the change in train dynamics index and the reduced fastener force and settlement value is studied, and the quantitative relationship between pier settlement and train mechanical index is derived. The specific technical scheme is as follows:

[0010] A method for establishing an intrinsic topological relationship between a bridge pier settlement value and a driving performance index comprises the following steps:

[0011] 1) Establish a train sub-model;

[0012] 2) Establish a longitudinal slab ballastless track-bridge sub-model;

[0013] 3) Simulation of bridge-track interlayer connection failure and track irregularity caused by pier settlement;

[0014] 4) Assembling the established train sub-model and the longitudinal slab ballastless track-bridge sub-model to obtain a train-track-bridge system coupled dynamics joint simulation model, and embedding the simulated bridge pier settlement-induced bridge-rail interlayer connection failure and track additional irregularity into the train-track-bridge system coupled dynamics joint simulation model to establish a train-track-bridge system coupled dynamics joint simulation model that considers bridge pier settlement and interlayer connection failure;

[0015] 5) Verify the accuracy of the calculation results of the train-track-bridge system coupled dynamics joint simulation model considering interlayer connection failure and pier settlement;

[0016] 6) Analyze the impact of pier settlement and interlayer connection failure on the dynamic characteristics of train-track-bridge, explore the intrinsic topological relationship between the pier settlement amplitude considering interlayer connection failure and the driving dynamic index, and propose a pier settlement threshold based on this.

[0017] In the aforementioned analysis method of the intrinsic topological relationship between the pier settlement value and the driving performance index considering the bottom plate void length and the maximum value of the reduced fastener force, in step 1), the train sub-model is established using dynamics theory; the train sub-model is a four-axle vehicle, which consists of a car body, 2 bogies and 4 wheel sets, with a total of 31 degrees of freedom; the suspension system between the car body, bogies and wheel sets is simulated using a spring-damper unit, the car body and the two bogies consider 5 degrees of freedom: lateral movement, sinking and floating, side rolling, nodding and shaking, each wheelset considers 4 degrees of freedom: lateral movement, sinking and floating, side rolling and shaking, and the car body, frame and wheelset are all rigid bodies.

[0018] The above-mentioned analysis method of the intrinsic topological relationship between the pier settlement value and the driving performance index considering the bottom slab void length and the maximum value of the reduced fastener force, the motion equation of the train sub-model is:

[0019]

[0020] Where: M v , C v , K v and U v are the mass matrix, damping matrix, stiffness matrix and displacement vector of the vehicle, v represents the vehicle; F g and F w are the vehicle’s own weight vector and wheel-rail force vector respectively, g represents the vehicle’s own weight, and w represents the wheel-rail interaction.

[0021] In the aforementioned analysis method of the intrinsic topological relationship between the pier settlement value and the driving performance index considering the bottom slab void length and the maximum value of the reduced fastener force, in step 2), the longitudinal slab ballastless track-bridge sub-model is established using finite element theory, which mainly includes rails, fasteners, track plates, CA mortar layers, base plates, two-cloth-one-membrane sliding layers and simply supported beams; wherein the rails, track plates, base plates and bridges are all simulated using 3D beam units, and the fasteners, CA mortar layers and sliding layers are all simulated using spring-damping units.

[0022] The above-mentioned analysis method of the intrinsic topological relationship between the pier settlement value and the driving performance index considering the bottom slab void length and the maximum value of the reduced fastener force, the motion equation of the longitudinal slab ballastless track-bridge sub-model is:

[0023]

[0024] Where: M tb , C tb , K tb and U tb are the mass matrix, damping matrix, stiffness matrix and displacement vector of the track-bridge subsystem respectively, tb track-bridge subsystem, t represents the track system, and b represents the bridge system.

[0025] In the aforementioned analysis method of the intrinsic topological relationship between the pier settlement value and the driving performance index considering the bottom slab void length and the maximum value of the reduced fastener force, in step 3), the simulation of the bridge-rail interlayer connection failure and the additional track irregularity caused by the pier settlement is carried out in a general standard model of bridge-rail deformation. The bridge-rail interlayer connection failure is the track interlayer connection failure caused by the pier settlement, which is mainly the bottom slab void of the base plate; the pier settlement causes the additional track irregularity is the characterization relationship between the pier settlement and the track deformation, and its general characterization is:

[0026]

[0027] Where: V r represents the rail deformation matrix, V s represents the track plate deformation matrix, V p represents the deformation matrix of the base plate, r represents the rail, s represents the track plate, and p represents the base plate; A, B, C1, C2, D, H1, H2, and I represent the influence matrix of the displacement of each layer of the track structure respectively; Q r , Q s , Q p Represent the self-weight matrix of each layer structure of the track;

[0028] F, P, and N represent the spring force matrix between each layer of the track, expressed as:

[0029]

[0030] Where: k c , k ca , k p Respectively represent the stiffness matrices of fastener spring, mortar spring and contact spring; V b represents the displacement matrix of uneven settlement of roadbed; c represents fastener spring, ca represents mortar spring, p represents contact spring, and b represents roadbed;

[0031] By solving equations (4) to (5) simultaneously, the deformation of each layer of the track structure can be expressed as:

[0032]

[0033] In the formula: In the formula: E represents the unit matrix, kc , k ca , k p They represent the stiffness matrices of the fastener spring, mortar spring and contact spring respectively; c represents the fastener spring, ca represents the mortar spring, p represents the contact spring,

[0034] The Heaviside function is introduced to form a tension-free Winkler beam to describe the unknown stiffness mutations of key track components such as fastener failure, mortar separation, and slab bottom debonding. It is expressed as

[0035]

[0036] Where: y up ,y do They are the deflections of the lower and upper structures of the track system respectively. Up and do are the abbreviations of upward and down, representing the upper and lower structures of the track respectively.

[0037] If there is a discontinuous area of ​​interlayer contact in the representation relationship, the asymptotic approach method is used to solve it.

[0038] In the aforementioned analysis method of the intrinsic topological relationship between the pier settlement value and the driving performance index considering the bottom slab void length and the maximum value of the reduced fastener force, in step 4), the assembly process of the train-track-bridge system coupled dynamics joint simulation model considering interlayer connection failure and pier settlement includes the following sub-steps:

[0039] 4-1) Based on the static sub-model of the track-bridge coupling system and the universal standard model of bridge-track deformation, the additional track irregularity data and interlayer connection failure data caused by pier settlement are obtained through Matlab software programming;

[0040] 4-2) Import the interlayer connection failure data obtained in step 4-1) through Ansys software, establish a longitudinal slab ballastless track-bridge sub-model, and perform modal analysis on the sub-model to obtain a *.full binary file containing the overall mass, stiffness and damping matrix of the sub-model; then, use the HBMAT command to convert the binary file into a Harwell-Boeing file; at the same time, use HBMAT to extract the position information of the mass, stiffness and damping matrix nodes of the sub-model in the binary file, and generate a *.Mapping file;

[0041] 4-3) Convert the Harwell-Boeing file in step 4-2) into a sparse matrix form using Python;

[0042] 4-4) Using the wheel-rail contact relationship, the additional track unevenness data caused by the pier settlement in step 4-1), the .Mapping file of the ballastless track-bridge finite element sub-model in step 4-2), and the sparse matrix in step 4-3) are linked with the train sub-model to establish a coupled dynamics joint simulation model of the train-track-bridge system considering interlayer connection failure and pier settlement; in this joint simulation model, the wheel-rail normal force is simulated by Hertz contact, and the wheel-rail lateral force is the creep force.

[0043] The above-mentioned analysis method of the intrinsic topological relationship between the pier settlement value and the driving performance index considering the bottom slab void length and the maximum value of the reduced fastener force, the dynamic equation group of the train-track-bridge system coupled dynamics joint simulation model considering interlayer connection failure and pier settlement is:

[0044]

[0045] Where M v , C v , K v and U v are the mass matrix, damping matrix, stiffness matrix and displacement vector of the vehicle, M tb , C tb , K tb and U tb are the mass matrix, damping matrix, stiffness matrix and displacement vector of the track-bridge subsystem, respectively. g and F w are the vehicle's own weight vector and wheel-rail force vector, tb track-bridge subsystem, t represents the track system, b represents the bridge system. v represents the vehicle; g represents the vehicle's own weight, and w represents the wheel-rail interaction.

[0046] In the aforementioned analysis method of the intrinsic topological relationship between the pier settlement value and the driving performance index considering the bottom slab void length and the maximum value of the reduced fastener force, in step 6), the analysis of the influence of interlayer connection failure and pier settlement on the dynamic characteristics of the train-track-bridge includes analyzing the vehicle response characteristics under the pier settlement considering the interlayer connection failure and analyzing the influence of different pier settlement values ​​on the vehicle dynamic response;

[0047] The analysis considers the vehicle response characteristics under the pier settlement with interlayer connection failure as follows: when a train passes through a longitudinal slab ballastless track with a single pier settlement of 20 mm at a speed of 350 km·h-1, the dynamic response index of the longitudinal slab ballastless track with and without interlayer connection failure is calculated, and the influence of the existence of slab bottom debonding on the change of train dynamic characteristics is analyzed;

[0048] The analysis of the influence of different pier settlement values ​​on vehicle dynamic response is as follows: piers with settlement values ​​of 10 mm, 20 mm and 30 mm are selected respectively, the bottom slab debonding factor is incorporated, and the wheel-rail vertical force, wheel weight reduction rate, derailment coefficient and vehicle body vertical acceleration are calculated as a function of pier settlement value.

[0049] In the aforementioned analysis method of the intrinsic topological relationship between the pier settlement value and the driving performance index considering the bottom slab void length and the maximum value of the reduced fastener force, in step 6), the pier settlement value is gradually increased from 1mm to 30mm, and the dynamic response index values ​​caused by the change in the bottom slab void length and the maximum value and dynamic mapping value of the dynamic characteristics caused by different pier settlements are calculated respectively. The maximum dynamic characteristic value is analyzed along with the dynamic mapping value, and then the bottom slab void length is fitted with the pier settlement, and then the reduced fastener force is fitted with the pier settlement, and the intrinsic topological relationship between the pier settlement amplitude and the driving dynamic index considering the interlayer connection failure is obtained, and its expression is as follows:

[0050]

[0051] In the formula, F w,max Maximum wheel-rail vertical force, R w,max Maximum wheel load reduction rate, D c,max Maximum derailment coefficient, A c,max Maximum vertical acceleration of the vehicle body;

[0052] The threshold value of uneven settlement of the bridge pier is controlled within 22.47 mm.

[0053] The beneficial effects of the present invention are as follows:

[0054] 1) Based on the established high-speed train-track-bridge integrated model considering interlayer connection failure and pier settlement, the present invention significantly improves the calculation efficiency and accuracy of the train-track-bridge deformation transfer law and the train dynamic characteristic indicators; on this basis, the influence of pier settlement on the vehicle dynamic characteristic indicators is analyzed, and a pier settlement threshold is proposed under comprehensive consideration of multiple dynamic indicators such as wheel-rail vertical force, wheel weight reduction rate, derailment coefficient and vehicle body vertical acceleration.

[0055] 2) The analysis method of the present invention is used to analyze the intrinsic topological relationship between the pier settlement value and the driving performance index considering the bottom slab void length and the maximum value of the reduced fastener force, and the following conclusions are obtained:

[0056] ① The analysis method of the present invention shows that the bottom slab degassing caused by the pier settlement aggravates the change of dynamic characteristic indexes, and is more obvious in the area adjacent to the settlement pier. The maximum values ​​of various indexes when the bottom slab degassing is considered are about twice those when the bottom slab degassing is not considered. This provides a theoretical basis for considering the influence of the bottom slab degassing caused by the pier settlement on the dynamic characteristics of the vehicle in the subsequent high-speed railway route design.

[0057] ② According to the analysis method of the present invention, the linearity (R2) between the dynamic characteristic index and the dynamic mapping value is above 0.996, indicating that the linear relationship is strong. It is proved that the changes in the dynamic characteristics of the vehicle can be quantitatively reflected by the bottom clearance length of the plate, the maximum value of the reduced fastener force and the settlement value of the pier.

[0058] 3) Based on the method of the present invention, the intrinsic topological relationship between the pier settlement value and the driving performance index considering the bottom slab void length and the maximum reduced fastener force is analyzed, and it is obtained that the uneven settlement value of the pier should be controlled within 22.47mm, and the uneven settlement value of the pier calculated by the high-speed train-track-bridge integrated model considering the interlayer connection failure and pier settlement should be controlled within 23.08mm, which provides a new method for quickly and accurately evaluating the driving safety on high-speed railway bridges under the condition of pier settlement. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 Schematic diagram of a train sub-model established in the present invention, wherein (a) is a front view, (b) is a bottom view, and (c) is a side view;

[0060] Figure 2 Schematic diagram of the structure of the train-track-bridge system coupled dynamics joint simulation model considering interlayer connection failure and pier settlement in the present invention

[0061] Figure 3 This is the verification result of the model of the present invention;

[0062] Figure 4 A comparison diagram of dynamic characteristics when considering interlayer damage and not considering interlayer damage for analysis of the present invention;

[0063] Figure 5 The dynamic characteristics analysis results of the system under different pier settlement values ​​in the present invention;

[0064] Figure 6 The analysis results of the maximum value and dynamic mapping value of the dynamic characteristics caused by the settlement of different bridge piers in the present invention;

[0065] Figure 7 The analysis result of the variation law of the maximum dynamic characteristic value with the dynamic mapping value in the present invention;

[0066] Figure 8 This is the fitting result of the relationship between the bottom slab void length and the pier settlement in the present invention;

[0067] Fig. 9 This is the fitting result of the relationship between the reduced fastener force and the pier settlement in the present invention. DETAILED DESCRIPTION

[0068] The following will be combined with the embodiments and drawings to clearly and completely describe the technical solution of the present invention. Obviously, the described embodiments are only preferred embodiments of the present invention, not all embodiments, and are not intended to limit the present invention in other forms. Any technician familiar with the profession may use the disclosed technical content to make changes or modifications. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.

[0069] The specific embodiments are as follows:

[0070] This embodiment is a method for establishing the intrinsic topological relationship between the pier settlement value and the driving performance index. The train sub-model is established by using the dynamics theory, and the longitudinal slab ballastless track-bridge sub-model is established by using the finite element theory; the two sub-models are assembled into a train-track-bridge system coupled dynamics joint simulation model through the wheel-rail contact relationship, such as Figure 2 As shown in the figure, the previously developed universal bridge-track deformation representation relationship model is embedded in the joint simulation model to simulate the failure of the bridge-track interlayer connection and the additional track unevenness, and the joint simulation model is verified; based on the verified model, the influence of interlayer connection failure and pier settlement on the dynamic characteristics of train-track-bridge is analyzed, and the intrinsic topological relationship between the pier settlement amplitude and the driving dynamic index considering the interlayer connection failure is found, and the pier settlement threshold is proposed accordingly. The specific process is as follows:

[0071] 1. Establish a coupled dynamics joint simulation model of the train-track-bridge system considering interlayer connection failure and pier settlement

[0072] 1) Establish the train sub-model

[0073] In this implementation, the train sub-model is established using dynamics theory. The train is a four-axle vehicle with a total of 31 degrees of freedom. Figure 1 As shown in the figure, the train sub-model consists of 1 car body, 2 bogies and 4 wheel sets. The suspension system between the car body, bogie and wheel sets is simulated by spring-damper unit. The car body and two bogies consider 5 degrees of freedom: lateral movement, heave, roll, nod and shake. Each wheel set considers 4 degrees of freedom: lateral movement, heave, roll and shake. It is assumed that the car body, frame and wheel sets are all rigid bodies. The train sub-model motion equation is:

[0074]

[0075] Where: M v , C v , K v and U v are the mass matrix, damping matrix, stiffness matrix and displacement vector of the vehicle, v represents the vehicle; Fg and F w are the vehicle’s own weight vector and wheel-rail force vector respectively, g represents the vehicle’s own weight, and w represents the wheel-rail interaction.

[0076] 2) Establish the longitudinal slab ballastless track-bridge sub-model

[0077] In this implementation, the finite element theory is used to establish a longitudinal slab ballastless track-bridge sub-model, which mainly includes rails, fasteners, track slabs, CA mortar layers, base plates, "two cloths and one membrane" sliding layers and simply supported beams, among which the rails, track slabs, base plates and bridges are simulated by 3D beam units, and the fasteners, CA mortar layers and sliding layers are simulated by spring-damper units.

[0078] The motion equation of the longitudinal slab track-bridge sub-model is:

[0079]

[0080] Where: M tb , C tb , K tb and U tb are the mass matrix, damping matrix, stiffness matrix and displacement vector of the track-bridge subsystem respectively, tb track-bridge subsystem, t represents the track system, and b represents the bridge system.

[0081] 3) Dynamic equations of the train-track-continuous beam bridge coupling system

[0082] According to the dynamic equations of each subsystem, the dynamic equations of the vehicle-track-continuous beam bridge coupled vibration system are established as follows:

[0083]

[0084] Where M v , C v , K v and U v are the mass matrix, damping matrix, stiffness matrix and displacement vector of the vehicle, M tb , C tb , K tb and U tb are the mass matrix, damping matrix, stiffness matrix and displacement vector of the track-bridge subsystem, respectively. g and F w are the vehicle's own weight vector and wheel-rail force vector, tb track-bridge subsystem, t represents the track system, b represents the bridge system. v represents the vehicle; g represents the vehicle's own weight, and w represents the wheel-rail interaction.

[0085] 4) Simulation of additional track irregularities caused by failure of bridge-track connection and pier settlement

[0086] In this embodiment, the data used to simulate the relationship between bridge-rail interlayer connection failure and track additional unevenness is the bridge-rail deformation general representation relationship model developed in the early stage. Its general representation relationship is briefly described as follows:

[0087]

[0088] Where: V r 、V s 、V p They represent the deformation matrices of rail, track plate and base plate respectively, r represents rail, s represents track plate and p represents base plate; A, B, C1, C2, D, H1, H2 and I represent the influence matrices of displacement of each layer of track structure respectively; Q r , Q s , Q p They represent the self-weight matrix of each layer of the track structure; F, P, and N represent the spring force matrix between each layer of the track, expressed as

[0089]

[0090] Where: k c , k ca , k p Respectively represent the stiffness matrices of fastener spring, mortar spring and contact spring; V b represents the displacement matrix of uneven settlement of roadbed; c represents fastener spring, ca represents mortar spring, p represents contact spring, and b represents roadbed;

[0091] By solving equations (4) to (5) simultaneously, the deformation of each layer of the track structure can be expressed as

[0092]

[0093] The Heaviside function is introduced to form a tension-free Winkler beam to describe the unknown stiffness mutations of key track components such as fastener failure, mortar separation, and slab bottom debonding. It is expressed as

[0094]

[0095] Where: y up ,y do They are the deflections of the lower structure of the track system and the upper structure of the roadbed system. Up and do are the abbreviations of upward and down, respectively, representing the upper and lower structures of the track.

[0096] If there are unknown sudden changes in stiffness of key track components such as damage and deformation of the foundation structure between layers, which leads to failure of fasteners, separation of mortar layers, and voiding of the bottom of the slab, there will be discontinuous areas of interlayer contact in the characterization relationship, and the equation will be over-determined and cannot be solved directly. Therefore, the asymptotic approach method is used to solve it.

[0097] 5) Assembly of a coupled dynamics co-simulation model of the train-track-bridge system considering interlayer connection failure and pier settlement

[0098] In this embodiment, the specific steps of assembling the train-track-bridge system coupled dynamics joint simulation model considering interlayer connection failure and pier settlement are as follows:

[0099] (1) Based on the static sub-model of the track-bridge coupling system and the universal standard model of bridge-track deformation, the additional track irregularity data and interlayer connection failure data caused by pier settlement were obtained through Matlab software programming;

[0100] (2) Using Ansys software, import the interlayer failure data in step (1), establish a track-bridge finite element sub-model, perform modal analysis on the model, and obtain a *.full binary file containing the overall mass, stiffness, and damping matrices of the sub-model; then, use the HBMAT command to convert the binary file into a Harwell-Boeing file; at the same time, use HBMAT to extract the locations of the mass, stiffness, and damping matrix nodes in the binary file and generate a *.Mapping file;

[0101] (3) Convert the Harwell-Boeing file in step (2) into a sparse matrix form using Python;

[0102] (4) Using the wheel-rail contact relationship, the track additional unevenness data caused by the pier settlement in step (1), the .Mapping file of the ballastless track-bridge finite element submodel in step (2), and the sparse matrix in step (3) are linked to the train submodel to establish a coupled dynamics joint simulation model of the train-track-bridge system considering interlayer connection failure and pier settlement; in this joint simulation model, the wheel-rail normal force is simulated by Hertz contact, and the wheel-rail lateral force is the creep force.

[0103] 6) Verify the accuracy of the train-track-bridge system coupled dynamics joint simulation model considering interlayer connection failure and pier settlement

[0104] The vehicle-ballastless track-bridge longitudinal and vertical coupled dynamic model established in the literature "Dynamic response analysis of ballastless track on bridge under braking load" is used to verify the accuracy of the calculation results of the train-track-bridge system coupled dynamic joint simulation model considering interlayer connection failure and pier settlement. The comparative verification results are shown in Table 1 and Figure 3 .

[0105] Table 1. Comparative verification of the model of the present invention and the model in the literature

[0106]

[0107] From Table 1 and Figure 3 Compared with the results in the literature, the calculation results of the model of the present invention show that the vertical displacement curves of the rails at the beam end and the mid-span are basically consistent, and the maximum amplitude error does not exceed 5%, which verifies the correctness of the train-track-bridge coupling dynamic model established by the present invention. The main reason for the error is that the train in the model of the present invention runs at a uniform speed of 200km / h, while the speed in the model in the literature is uniformly decelerated from 200km / h to 0, and the braking force of the train is also considered.

[0108] 2. Analyze the impact of interlayer connection failure and pier settlement on the dynamic characteristics of train-track-bridge

[0109] The interlayer connection failure mentioned in this embodiment is caused by the settlement of the bridge pier. Combined with existing research, it can be seen that under the action of the bridge pier settlement, mortar separation is not easy to occur, and the failure of the track interlayer connection is mainly due to the bottom of the base plate being emptied. According to existing relevant reports, the track irregularity value caused by the settlement of the bridge pier is much larger than the initial random irregularity of the line. Therefore, in order to quantitatively reveal the correlation between the settlement of the bridge pier and the train dynamics performance index, this embodiment does not consider the influence of the random irregularity of the line.

[0110] 1) Vehicle response characteristics under pier settlement considering interlayer connection failure

[0111] The established train-track-bridge system coupling dynamic model considering interlayer connection failure and pier settlement was applied, and joint simulation calculations were carried out using MATLAB, ANSYS, and PYTHON software.

[0112] When a high-speed train passes through a longitudinal slab ballastless track with a single pier settlement of 20 mm at a speed of 350 km·h-1, the dynamic response indicators of the longitudinal slab ballastless track with and without interlayer connection failure are calculated as follows: Figure 4 shown.

[0113] Depend on Figure 4 The results show that the settlement of the bridge piers mainly causes the track irregularity in the local area of ​​the settlement piers and their adjacent piers, which makes the dynamic characteristics of the train change significantly when passing through these areas, and the maximum value appears at the settlement piers and their adjacent piers. The existence of the bottom slab debonding intensifies the change of the dynamic characteristics, and it is more obvious in the area adjacent to the settlement piers. The maximum values ​​of each index considering the bottom slab debonding are about twice those not considering it. It can be seen that when studying the dynamic characteristics of high-speed trains, the influence of the bottom slab debonding caused by the settlement of the bridge piers should be taken into consideration.

[0114] 2) Effect of different pier settlement values ​​on vehicle dynamic response

[0115] The pier settlement values ​​of 10 mm, 20 mm and 30 mm were selected, and the bottom slab de-sag factor was taken into account. The wheel-rail vertical force, wheel load reduction rate, derailment coefficient and vehicle vertical acceleration were calculated as the pier settlement values ​​changed. Figure 5 shown.

[0116] Figure 5 The results show that the pier settlement has a significant impact on the wheel-rail vertical force, wheel load reduction rate, derailment coefficient and vehicle vertical acceleration. All indicators gradually increase with the increase of settlement value. The settlement pier and its adjacent piers where the vehicle dynamic response characteristics change significantly are defined as the response area. Figure 5 It can be found that when the vehicle just enters the response area, the response indicators change rapidly, resulting in a series of fluctuations. The pier settlement value and the bottom of the slab have a great influence on the amplitude and range of the fluctuations. When the vehicle leaves the response area, the fluctuations of the indicators gradually stabilize, and the time required for stabilization increases with the participation of the bottom of the slab and the increase of the settlement value. Figure 5 From (a) to (d), the vertical acceleration of the vehicle body is different from other response characteristics. It has two peaks in each response area. This is caused by the time and space differences of the front and rear bogies of the train passing through the bridge pier area. At the same time, it is not difficult to find that both the wheel-rail vertical force and the vehicle body vertical acceleration reach a positive peak when passing through the settlement pier, and reach a negative peak when passing through the adjacent pier of the settlement pier. The two have a relatively consistent change law, while the wheel weight reduction rate and the wheel-rail vertical force have the opposite change law.

[0117] 3. Intrinsic topological relationship between pier settlement amplitude and driving dynamic index considering interlayer connection failure

[0118] The established train-track-bridge system coupled dynamics joint simulation model considering interlayer connection failure and pier settlement is applied to calculate the bottom slab debonding length, reduced fastener force and driving dynamic index caused by each settlement value when the pier settlement value gradually increases from 1mm to 30mm. The bottom slab debonding length and the maximum reduced fastener force in the area where the maximum value of each dynamic response index is located are combined with the pier settlement value to establish the intrinsic topological mapping value formula corresponding to the maximum value of each driving dynamic index; the maximum dynamic characteristic value is analyzed with the dynamic mapping value, and then the bottom slab debonding length is fitted with the pier settlement, and then the reduced fastener force is fitted with the pier settlement, and the intrinsic topological relationship between the pier settlement amplitude and the driving dynamic index considering the interlayer connection failure is obtained, and the pier settlement threshold is proposed accordingly.

[0119] In this embodiment, the change in the length of the bottom of the plate causes the dynamic response index values ​​to be as follows: Figure 6 shown by Figure 6It can be clearly seen that: in the process of the pier settlement value gradually increasing from 1mm to 30mm, the dynamic response indicators show an obvious "step stratification" phenomenon. This phenomenon is closely related to the length of the bottom slab debonding. Changes in the length of the bottom slab debonding cause mutations in the values ​​of the dynamic response indicators. Through research, it was found that the maximum values ​​of the wheel-rail vertical force, wheel weight reduction rate and derailment coefficient after removing the influence of the bottom slab debonding are highly consistent with the maximum value curve of the reduced fastener force at the corresponding position, while the maximum value curve of the vertical acceleration of the vehicle body after removing the influence of the bottom slab debonding is a positive proportional curve to the settlement value curve. Therefore, it is appropriate to evaluate the dynamic response index of the train passing through the pier settlement area by using the bottom slab debonding length, the maximum value of the reduced fastener force and the pier settlement value.

[0120] In this embodiment, the fastener force caused by settlement minus the fastener force when the settlement is 0 can be obtained by the following formula:

[0121] F d =F(d)-F(0) (8)

[0122] Where: Fd represents the reduced fastener force; F(d) represents the fastener force caused by pier settlement, d represents the pier settlement value; F(0) represents the fastener force when the pier settlement is 0.

[0123] Where F(d) and F(0) are calculated using the general bridge-track deformation representation relationship model developed earlier, and the expressions are shown in formula (9):

[0124]

[0125] Combination Figure 2 It can be seen that the maximum values ​​of wheel-rail vertical force, wheel load reduction rate and vehicle vertical acceleration all occur at the settlement pier, while the maximum value of derailment coefficient occurs at the adjacent pier on the left side of the settlement pier. In view of this, the bottom slab clearance length and the maximum reduced fastener force in the area where the maximum value of each dynamic response index is located are combined with the pier settlement value to establish the intrinsic topological mapping value formula corresponding to each dynamic response as shown in formula (10):

[0126]

[0127] Where: F wl_m , R wl_m , D cl_m and A cl_m are the wheel-rail vertical force, wheel load reduction rate, derailment coefficient and vehicle body vertical acceleration intrinsic topological mapping value; F d,2max and F d,3maxare the maximum reduced fastener forces in the left pier area and the settlement pier area of ​​the settlement pier respectively; l2 and l3 are the hollow lengths of the slab bottom in the left pier area and the settlement pier area of ​​the settlement pier respectively; n1, n2, n3 and n4 are the hollow length indices corresponding to each dynamic response index, and their values ​​are 1.505, 1.24, 0.415 and 0.49 respectively.

[0128] In this embodiment, the calculation results of the maximum value of the dynamic characteristics and the dynamic mapping value caused by different pier settlements are as follows: Figure 6 As shown in the figure, the results verify the feasibility of evaluating the impact of pier settlement on the safety of high-speed vehicles passing through the settlement area by reducing the maximum value of the fastener force and the pier settlement value combined with the bottom clearance length of the slab.

[0129] In order to further understand the intrinsic topological relationship between the intrinsic topological mapping value and each response index, the intrinsic topological mapping value is fitted with each response index to obtain the variation law of the maximum value of each dynamic characteristic with the intrinsic topological mapping value, see Figure 7 .

[0130] from Figure 7 It can be seen that there is a strong linear relationship between the dynamic response index and the intrinsic topological mapping value. The linearity (R2) under different dynamic response indicators is above 0.995, which proves that the intrinsic topological mapping value obtained by combining the maximum reduced fastener force value and the pier settlement value with the bottom clearance length of the slab can quantitatively reflect the changes in the vehicle dynamic response.

[0131] The bottom void length of the slab under different settlement values ​​was fitted with the pier settlement. The linearity (R2) was 0.999, and the correlation was strong. The fitting results are shown in Figure 8 As shown, the corresponding fitting formula is shown in formula (11).

[0132]

[0133] F under different sedimentation values 2max and F 3max By solving equation (8), we can get F 2max and F 3max The calculated values ​​were fitted with the pier settlement values, and the linearity was 0.999, with a strong correlation. The final fitting results are as follows: Fig. 9 As shown, the corresponding fitting formula is shown in formula (12)

[0134]

[0135] Combination Figure 8 , Fig. 9 By combining equation (10), we can obtain the intrinsic topological relationship between the pier settlement amplitude and the vehicle dynamics index considering the interlayer connection failure, which is expressed as equation (13):

[0136]

[0137] In the formula, F w,max Maximum wheel-rail vertical force, R w,max Maximum wheel load reduction rate, D c,max Maximum derailment coefficient, A c,max Maximum vertical acceleration of the vehicle body;

[0138] The maximum limits of wheel-rail vertical force, wheel load reduction rate, derailment coefficient and vehicle body vertical acceleration in the specification are 170 kN, 0.6, 0.8 and 0.13 g respectively. Combined with formula (13), the safety threshold of pier settlement is d ≤ 22.47 mm. The uneven settlement value of piers calculated by the high-speed train-track-bridge integrated model considering interlayer connection failure and pier settlement should be controlled within 23.08 mm. The calculation results of the two are quite consistent.

[0139] In summary, the present invention is based on the established train-track-bridge system coupled dynamics joint simulation model that considers interlayer connection failure and pier settlement, which significantly improves the calculation efficiency and accuracy of the train-track-bridge deformation transmission law and train dynamic characteristic indicators. On this basis, the influence of pier settlement on vehicle dynamic characteristic indicators is analyzed, and the pier settlement threshold is proposed under comprehensive consideration of multiple dynamic indicators such as wheel-rail vertical force, wheel weight reduction rate, derailment coefficient and vehicle body vertical acceleration.

[0140] Through the analysis of the method of the present invention, the following conclusions were obtained:

[0141] (1) The bottom slab degassing caused by the pier settlement aggravates the changes in the dynamic characteristics indexes, and is more obvious in the area adjacent to the settled pier. The maximum values ​​of the indexes with the bottom slab degassing considered are about twice those without consideration. Therefore, the influence of the bottom slab degassing caused by the pier settlement on the vehicle dynamic characteristics cannot be ignored.

[0142] (2) The linearity (R2) between the dynamic characteristic index and the dynamic mapping value is above 0.996, indicating that the linear relationship is strong. This proves that the change of vehicle dynamic characteristics can be quantitatively reflected by the bottom clearance length of the slab, the maximum value of the reduced fastener force, and the pier settlement value.

[0143] (3) Based on the intrinsic topological relationship, it was obtained that the uneven settlement value of the bridge pier should be controlled within 22.47 mm. The uneven settlement value of the bridge pier calculated by the high-speed train-track-bridge integrated model considering the interlayer connection failure and bridge pier settlement should be controlled within 23.08 mm. The calculation results of the two are quite consistent, indicating that it is feasible to calculate the bridge pier settlement threshold value through the intrinsic topological relationship. This provides a new method for quickly and accurately evaluating the driving safety on high-speed railway bridges under the condition of bridge pier settlement, and also provides safer theoretical support and guarantee for the design and construction of future high-speed railway bridges.

[0144] It is obvious to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential features of the present invention. Therefore, the embodiments should be regarded as exemplary and non-restrictive from any point of view. In addition, it should be understood that although this specification is described in accordance with the embodiments, it does not contain only one technical solution. This narrative of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in the embodiments can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for establishing an intrinsic topological relationship between a bridge pier settlement value and a driving performance index, characterized in that: The steps include: 1) Establish a train sub-model; 2) Establish a longitudinal slab ballastless track-bridge sub-model; 3) Simulation of bridge-track interlayer connection failure and track irregularity caused by pier settlement; 4) Assembling the established train sub-model and the longitudinal slab ballastless track-bridge sub-model to obtain a train-track-bridge system coupled dynamics joint simulation model, and embedding the simulated bridge pier settlement-induced bridge-rail interlayer connection failure and track additional irregularity into the train-track-bridge system coupled dynamics joint simulation model to establish a train-track-bridge system coupled dynamics joint simulation model that considers bridge pier settlement and interlayer connection failure; 5) Verify the accuracy of the calculation results of the train-track-bridge system coupled dynamics joint simulation model considering bridge pier settlement and interlayer connection failure; 6) Analyze the impact of pier settlement and interlayer connection failure on the dynamic characteristics of train-track-bridge, explore the intrinsic topological relationship between the pier settlement amplitude considering interlayer connection failure and the driving dynamic index, and propose the pier settlement threshold accordingly; in, In step 4), the assembly process of the train-track-bridge system coupled dynamics joint simulation model considering interlayer connection failure and pier settlement includes the following sub-steps: 4-1) Based on the static sub-model of the track-bridge coupling system and the universal standard model of bridge-track deformation, the additional track irregularity data and interlayer connection failure data caused by pier settlement are obtained through Matlab software programming; 4-2) Import the interlayer connection failure data obtained in step 4-1) through Ansys software, establish a longitudinal slab ballastless track-bridge sub-model, and perform modal analysis on the sub-model to obtain a *.full binary file containing the overall mass, stiffness and damping matrix of the sub-model; then, use the HBMAT command to convert the binary file into a Harwell-Boeing file; at the same time, use HBMAT to extract the position information of the mass, stiffness and damping matrix nodes of the sub-model in the binary file, and generate a *.Mapping file; 4-3) Convert the Harwell-Boeing file in step 4-2) into a sparse matrix form using Python; 4-4) Using the wheel-rail contact relationship, the track additional unevenness data caused by the pier settlement in step 4-1), the .Mapping file of the ballastless track-bridge finite element sub-model in step 4-2), and the sparse matrix in step 4-3) are linked with the train sub-model to establish a train-track-bridge system coupled dynamics joint simulation model that considers interlayer connection failure and pier settlement; in this joint simulation model, the wheel-rail normal force is simulated by Hertz contact, and the wheel-rail lateral force is the creep force; The dynamic equations of the train-track-bridge system coupled dynamics joint simulation model considering interlayer connection failure and pier settlement are: Where M v , C v , K v and U v are the mass matrix, damping matrix, stiffness matrix and displacement vector of the vehicle, M tb , C tb , K tb and U tb are the mass matrix, damping matrix, stiffness matrix and displacement vector of the track-bridge subsystem, respectively. g and F w are the vehicle's own weight vector and wheel-rail force vector, tb track-bridge subsystem, t represents the track system, b represents the bridge system, v Indicates a vehicle; g Indicates the vehicle's own weight. w represents the wheel-rail interaction; In step 6), the analysis of the impact of interlayer connection failure and pier settlement on train-track-bridge dynamic characteristics includes: Analyze the vehicle response characteristics under pier settlement considering interlayer connection failure; Analyze the impact of different pier settlement values ​​on vehicle dynamic response; The analysis considers the vehicle response characteristics under pier settlement under interlayer connection failure: train speed 350 km·h -1 When passing through a longitudinal slab ballastless track with a single pier settlement of 20 mm, the dynamic response index of the longitudinal slab ballastless track with and without interlayer connection failure is calculated, and the influence of the existence of slab bottom cavitation on the change of train dynamic characteristics is analyzed; The analysis of the influence of different pier settlement values ​​on vehicle dynamic response is as follows: piers with settlement values ​​of 10 mm, 20 mm and 30 mm are selected respectively, the bottom slab de-slip factor is incorporated, and the wheel-rail vertical force, wheel load reduction rate, derailment coefficient and vehicle body vertical acceleration are calculated along with the pier settlement value. The intrinsic topological relationship between the pier settlement amplitude and the driving dynamic index considering the interlayer connection failure is as follows: the pier settlement value is gradually increased from 1 mm to 30 mm, and the dynamic response index values ​​caused by the change of the bottom slab void length and the maximum value and dynamic mapping value of the dynamic characteristics caused by different pier settlement values ​​are calculated respectively; the change law of the maximum dynamic characteristic value with the dynamic mapping value is analyzed, and then the bottom slab void length is fitted with the pier settlement, and then the reduced fastener force is fitted with the pier settlement, and the intrinsic topological relationship between the pier settlement amplitude and the driving dynamic index considering the interlayer connection failure is obtained, and its expression is as follows: In the formula, F w,max Maximum wheel-rail vertical force, R w,max Maximum wheel load reduction rate, D c,max Maximum derailment coefficient, A c,max Maximum vertical acceleration of the vehicle body; The threshold value of uneven settlement of the bridge pier is controlled within 22.47 mm.

2. The method for establishing the intrinsic topological relationship between the pier settlement value and the driving performance index according to claim 1 is characterized by: In step 1), the train sub-model is established by using dynamics theory; The train sub-model is a four-axle vehicle, consisting of 1 car body, 2 bogies and 4 wheel sets, with a total of 31 degrees of freedom; the suspension system between the car body, bogies and wheelsets is simulated by spring-damper units, and the car body and two bogies consider 5 degrees of freedom: lateral movement, sinking and floating, side rolling, nodding and shaking; each wheelset considers 4 degrees of freedom: lateral movement, sinking and floating, side rolling and shaking; the car body, frame and wheelsets are all rigid bodies.

3. The method for establishing the intrinsic topological relationship between the pier settlement value and the driving performance index according to claim 2 is characterized by: The equation of motion of the train sub-model is: Where: M v , C v , K v and U v are the mass matrix, damping matrix, stiffness matrix and displacement vector of the vehicle respectively, v Indicates vehicle; F g and F w are the vehicle’s own weight vector and wheel-rail force vector, g Indicates the vehicle's own weight. w represents the wheel-rail interaction.

4. The method for establishing the intrinsic topological relationship between the pier settlement value and the driving performance index according to claim 1 is characterized by: In step 2), the longitudinal slab ballastless track-bridge submodel is a static submodel of the track-bridge coupling system established using finite element theory, which mainly includes rails, fasteners, track plates, CA mortar layers, base plates, two-cloth-one-membrane sliding layers and simply supported beams; The rails, track plates, base plates and bridges are all simulated using 3D beam units, and the fasteners, CA mortar layers and sliding layers are all simulated using spring-damping units.

5. The method for establishing the intrinsic topological relationship between the pier settlement value and the driving performance index according to claim 4 is characterized in that: The motion equation of the longitudinal slab ballastless track-bridge sub-model is: Where: M tb , C tb , K tb and U tb are the mass matrix, damping matrix, stiffness matrix and displacement vector of the track-bridge subsystem respectively, tb track-bridge subsystem, t represents the track system, and b represents the bridge system.

6. The method for establishing the intrinsic topological relationship between the pier settlement value and the driving performance index according to claim 1 is characterized by: In step 3), the simulation of the additional track irregularity caused by the failure of the bridge-rail interlayer connection and the pier settlement is carried out in a general standard model of bridge-rail deformation. The failure of the bridge-rail interlayer connection is the failure of the track interlayer connection caused by the pier settlement, which is the bottom of the base plate being emptied; the additional track irregularity caused by the pier settlement is the characterization relationship between the pier settlement and the track deformation, and its general characterization is: Where: V r represents the rail deformation matrix, V s represents the track plate deformation matrix, V p represents the base plate deformation matrix, r Indicates rails, s Indicates the track plate, p represents the base plate; A, B, C1, C2, D, H1, H2, and I represent the influence matrix of the displacement of each layer of the track structure; Q r , Q s , Q p Represent the self-weight matrix of each layer structure of the track; F, P, and N represent the spring force matrices between the track layers, expressed as Where: k c , k ca , k p Respectively represent the stiffness matrices of fastener spring, mortar spring and contact spring; V b Represents the displacement matrix of uneven settlement of roadbed; c Indicates the fastener spring, ca represents the mortar spring, p Indicates contact spring, b Indicates roadbed; By solving equations (4) and (5) simultaneously, the deformation of each layer of the track structure can be expressed as: Where: E represents the unit matrix, k c , k ca , k p represent the fastener spring, mortar spring and contact spring stiffness matrices respectively; c Indicates the fastener spring, ca represents the mortar spring, p Indicates contact spring, The Heaviside function is introduced to form a tension-free Winkler beam to describe the unknown stiffness mutation of key track components caused by fastener failure, mortar separation, and slab bottom debonding. It is expressed as Where: y up is the deflection of the track system superstructure, y do is the deflection of the track system substructure, up , do They are the abbreviations of upward and down, which represent the upper and lower structures of the track respectively; If there are discontinuous areas of interlayer contact in the representation relationship, the asymptotic approach method is used to solve it.

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