Method for predicting seismic-induced geometric irregularities in high-speed railway targets under longitudinal earthquakes

Abstract

This invention relates to the field of bridge engineering technology, specifically disclosing a method for predicting the seismically induced geometric irregularities of a high-speed railway under longitudinal earthquakes. The method includes the following steps: establishing a random sample library of seismically induced geometric irregularities on the high-speed railway bridge; considering the seismically induced geometric irregularities as a product of shape and amplitude variables; establishing a shape function expression for the target seismically induced geometric irregularities; fitting the upper bound spectrum of the peak displacement at the top of the high-speed railway piers using uncertainty analysis; solving for the amplitude variable using the structural period and the upper bound spectrum of the peak displacement at the top of the piers; and constructing time-domain samples of the target seismically induced geometric irregularities based on the shape function and amplitude variables. This invention can rapidly predict the geometric irregularities under longitudinal earthquake action, quickly assess the post-earthquake traffic capacity of high-speed railway bridges, and provide a basis for optimizing post-earthquake speed limits and emergency response plans for high-speed railways.

Description

Technical Field

[0001] This invention relates to the field of bridge engineering technology, specifically to a method for predicting seismic-induced geometric irregularities in high-speed railway targets under longitudinal earthquakes. Background Technology

[0002] High-speed railways are characterized by dense networks, high traffic volume, and high train density. They traverse large areas of seismic zones with high earthquake frequency, making it impossible for them to completely avoid potential earthquake threats both spatially and temporally. Seismic-induced residual deformation of components is mapped to the rail surface through the interlayer interaction of the track-bridge system, leading to deterioration of rail surface smoothness—that is, seismic-induced track geometric irregularities on high-speed railway bridges. Research on seismic-induced track geometric irregularities primarily focuses on lateral earthquakes. However, high-speed railway bridges also experience significant seismic-induced component damage and shape / position changes under longitudinal earthquakes. Ignoring seismic-induced track geometric irregularities on high-speed railway bridges under longitudinal earthquakes can underestimate the extreme state of post-earthquake wheel-rail contact, affecting the accuracy of traffic safety assessments for bridge engineering. Therefore, there is an urgent need to develop a method for predicting target seismic-induced high and low geometric irregularities in high-speed railways under longitudinal earthquakes to address the problems in existing technologies. Summary of the Invention

[0003] The purpose of this invention is to provide a method for predicting seismic-induced geometric irregularities in the elevation of high-speed railway targets under longitudinal earthquakes. The specific technical solution is as follows:

[0004] A method for predicting seismic-induced geometric irregularities in the elevation of high-speed railway targets under longitudinal earthquakes includes the following steps:

[0005] Step S1: Establish a random sample library of seismically induced geometric irregularities on high-speed railway bridges;

[0006] Step S2: Decouple the seismic-induced elevation and elevation geometric irregularities into shape functions and amplitude variables;

[0007] Step S3: Establish the expression for the shape function of the target seismically induced elevation and elevation geometric irregularities;

[0008] Step S4: Fit the upper bound spectrum of the peak displacement at the top of the high-speed railway piers using uncertainty analysis;

[0009] Step S5: Solve for the amplitude variable by using the structural period and the upper limit spectrum of the peak displacement at the pier top;

[0010] Step S6: Construct the target seismic-induced elevation and elevation geometric irregularities based on the shape function and amplitude variable.

[0011] Optionally, in step S1, the process of establishing a sample library of seismically induced elevation and elevation geometric irregularities includes:

[0012] A numerical simulation model of the high-speed railway track-bridge system was established. A random set of ground motions was selected and nonlinear time history analysis was carried out. The displacement sets of the left and right rails were extracted from the time history analysis results. Based on the correspondence between rail displacement and track irregularities, a sample library of seismically induced high and low geometric irregularities was established.

[0013] Optionally, in step S2, the decoupling process of the vibration-induced elevation geometric irregularities includes:

[0014] The seismic-induced elevation and elevation geometric irregularities are decoupled into the product of a dimensionless shape function and a dimensional amplitude variable, where the amplitude variable reflects the overall intensity of the track irregularity and the shape function reflects the spatial distribution characteristics of the track irregularity.

[0015] Optionally, in step S3, the process of establishing the shape function expression includes:

[0016] Based on the obvious periodicity of seismic-induced elevation and depression geometric irregularities, the irregularities are divided into multiple sub-blocks after being divided by their amplitude. The function expression of the first sub-block is fitted. Based on the antisymmetric nature of each sub-block, the first sub-block is translated and flipped to establish the function expressions of all sub-blocks, thus completing the establishment of the shape function expression.

[0017] Optionally, in step S4, the fitting steps for the upper bound spectrum of the peak displacement at the pier top are as follows:

[0018] In the numerical simulation model, the height of each pier is set to a random integer within a certain range. Modal analysis is carried out and the first-order longitudinal natural vibration period is recorded. Nonlinear time history analysis is carried out and the upper limit of the peak displacement of the pier top is constructed. The above process is repeated 100 times to establish the first-order longitudinal natural vibration period matrix and the upper limit matrix of the peak displacement of the pier top. The natural vibration period matrix and the upper limit matrix of the peak displacement of the pier top are used as independent and dependent variables, respectively, to fit the upper limit spectrum of the peak displacement of the high-speed railway pier top under longitudinal earthquake.

[0019] Optionally, in step S5, the process of calculating the amplitude variable includes:

[0020] For random structures with arbitrary pier height and span, modal analysis is performed to record their first-order longitudinal natural vibration period. The upper limit of the longitudinal displacement at the pier top is calculated by combining the upper limit spectrum of the peak displacement at the pier top. Based on the correspondence between the longitudinal displacement at the pier top and the amplitude of the seismically induced vertical geometric irregularity, the amplitude variable of the target seismically induced vertical geometric irregularity is calculated.

[0021] Optionally, in step S5, the process of calculating the correspondence between the longitudinal displacement of the pier top and the amplitude of the seismically induced geometric irregularities includes:

[0022] Using real earthquake data as the excitation of the numerical simulation model, nonlinear time history analysis was carried out. The time histories of vertical displacement of rail nodes on both sides of the pier and longitudinal displacement of the pier top under different pier height conditions were extracted from the time history analysis results. The slope of the fitting function between the vertical displacement of the rail nodes and the longitudinal displacement of the pier top was fitted. The fitting function is the correspondence between the longitudinal displacement of the pier top and the amplitude of the seismically induced geometric irregularity.

[0023] Optionally, in step S6, the process of constructing the target seismically induced elevation geometric irregularities includes:

[0024] The shape function of the target earthquake-induced elevation and depression geometric irregularities is multiplied by the amplitude variable and then superimposed to form the final time-domain sample of the target earthquake-induced elevation and depression geometric irregularities.

[0025] The application of the technical solution of the present invention has the following beneficial effects:

[0026] This invention proposes a method for predicting the geometries of high-speed railways under longitudinal earthquakes. It can fully consider the randomness of ground motion and the randomness of bridge structure, quantify the track deterioration level of high-speed railway bridges under longitudinal earthquake action, and realize the rapid assessment of the risk of train operation on bridges after an earthquake.

[0027] In addition to the objectives, features, and advantages described above, the present invention has other objectives, features, and advantages. The invention will now be described in further detail with reference to the figures. Attached Figure Description

[0028] To more clearly illustrate the technical solutions of the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0029] Figure 1 This is a flowchart of the steps in the method for predicting the seismic-induced geometric irregularities of a high-speed railway target under longitudinal earthquakes in a preferred embodiment of the present invention.

[0030] Figure 2 This is a schematic diagram of a sample set of geometric irregularities in elevation caused by a longitudinal earthquake.

[0031] Figure 3 It is a schematic diagram of a mathematical model of the geometric irregularities in elevation caused by a longitudinal earthquake.

[0032] Figure 4 This is a schematic diagram of the upper limit spectrum of the peak displacement at the top of the piers of a high-speed railway under longitudinal earthquakes.

[0033] Figure 5This is a schematic diagram showing the slope of the fitting function for the vertical displacement of the rail node and the longitudinal displacement of the pier top under different pier height conditions;

[0034] Figure 6 This is a schematic diagram of the train dynamic response indicators under different track irregularities. Detailed Implementation

[0035] To enable those skilled in the art to better understand the present invention, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are merely some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0036] Example:

[0037] like Figure 1 As shown, this embodiment provides a method for predicting seismically induced geometric irregularities in the elevation of a high-speed railway target under longitudinal earthquakes, including the following steps (S1 to S6):

[0038] Step S1: Establish a random sample library of seismically induced geometric irregularities on high-speed railway bridges.

[0039] In this embodiment, the process of establishing a sample library of seismically induced elevation and elevation geometric irregularities includes:

[0040] A numerical simulation model of the high-speed railway track-bridge system was established. A random set of ground motions was selected and nonlinear time history analysis was performed. Left and right rail displacement sets were extracted from the time history analysis results. Based on the correspondence between rail displacement and track irregularities, a sample library of seismically induced high-low geometric irregularities was established. Figure 2 As shown.

[0041] Step S2: Decouple the seismic-induced geometric irregularities into shape functions and amplitude variables.

[0042] In this embodiment, the decoupling process of earthquake-induced elevation geometric irregularities includes:

[0043] The seismic-induced elevation and elevation geometric irregularities are decoupled into the product of a dimensionless shape function and a dimensional amplitude variable. The amplitude variable reflects the overall intensity of the track irregularity, while the shape function reflects its spatial distribution characteristics. Figure 3 As shown. In Figure 3 middle arrive Represents a dimensionless shape function. arrive This represents the intersection of the shape function and the zero-scale axis. A 1 to A4 represents a dimensional amplitude variable. Specifically, the dividing point can be represented as follows:

[0044] ;

[0045] Step S3: Establish the expression for the shape function of the geometric irregularities caused by the earthquake in the target.

[0046] The process of establishing a shape function expression includes:

[0047] Based on the obvious periodicity of earthquake-induced elevation irregularities, the irregularities are divided into multiple sub-blocks after being divided by their amplitude. The function expressions for the first two sub-blocks are fitted. Based on the antisymmetric nature of each sub-block, the first sub-block is translated and flipped to establish the function expressions for all sub-blocks, thus completing the establishment of the shape function expression. Specifically, the shape function... and It can be represented as follows:

[0048] ;

[0049] ;

[0050] ;

[0051] ;

[0052] ;

[0053] because and They are opposite symmetries. arrive They are mutually opposing symmetric, for and After performing translation and flipping, all shape functions can be constructed:

[0054] ;

[0055] ;

[0056] Step S4: Fit the upper limit spectrum of the peak displacement of the high-speed railway pier top by combining uncertainty analysis.

[0057] In this embodiment, the fitting steps for the upper bound spectrum of the peak displacement at the pier top are as follows:

[0058] In the numerical simulation model, the heights of each pier are set to random integers within a certain range. Modal analysis is performed and the first-order longitudinal natural period is recorded. T 1. Conduct nonlinear time history analysis and construct the upper bound of the peak displacement at the pier top. Repeat the above process 100 times to establish a first-order longitudinal natural period matrix and an upper bound matrix for the peak displacement at the pier top. Using the natural period matrix and the upper bound matrix for the peak displacement at the pier top as independent and dependent variables, respectively, fit the upper bound spectrum of the peak displacement at the pier top of the high-speed railway under longitudinal earthquakes. Specifically, in this embodiment, a first-order longitudinal natural period matrix ( T 1, T 2, , T 100 ) and the upper bound matrix of peak displacement at the pier top And by using the two as independent and dependent variables respectively, the following fit was obtained: Figure 4 The upper limit spectrum of the peak displacement at the pier top is shown. This upper limit spectrum is used to quickly predict the upper limit of the longitudinal displacement at the pier top under earthquakes, and its expression is as follows:

[0059] ;

[0060] in, This indicates the upper limit of the longitudinal displacement of the pier top. T This represents the first-order natural period of the structure.

[0061] Step S5: Solve for the amplitude variable by using the structural period and the upper limit spectrum of the peak displacement at the pier top.

[0062] In this embodiment, the calculation process of the amplitude variable includes:

[0063] For a random structure with arbitrary pier height and number of spans, modal analysis is performed to record its first-order longitudinal natural period. The upper limit of the longitudinal displacement at the pier top is calculated by combining the upper limit spectrum of the peak displacement at the pier top. The amplitude variable of the target seismically induced geometric irregularity is calculated based on the correspondence between the longitudinal displacement of the pier top and the amplitude of the seismically induced elevation-reduction geometric irregularity. .

[0064] Furthermore, the calculation steps for the correspondence between the longitudinal displacement of the pier top and the amplitude of the seismically induced geometric irregularities include:

[0065] Nonlinear time history analysis was conducted on numerical simulation models under different pier heights. The time histories of vertical displacement at the rail joints on both sides of the pier and longitudinal displacement at the pier top under different pier heights were extracted from the time history analysis results. The slope of the fitting function between the vertical displacement of the rail joints and the longitudinal displacement at the pier top was then fitted. Figure 5 As shown, where Indicates the height of the bridge pier.

[0066] Step S6: Construct the target seismic-induced elevation and elevation geometric irregularities based on the shape function and amplitude variable.

[0067] In this embodiment, the process of constructing a target-induced elevation geometric irregularity includes:

[0068] The amplitude variable that causes the target to vibrate with geometrically uneven elevations. A 1 to A 4 are all taken as shape function arrive With amplitude variable A 1 to A The four products are multiplied and superimposed to form the final target seismic-induced geometric irregularities in the time domain.

[0069] The method described in this embodiment can provide more comprehensive excitation input conditions for vehicle-bridge coupled vibration analysis of trains running on bridges after an earthquake in high-speed railways. It can achieve accurate assessment of the wheel-rail contact state of trains running on bridges after an earthquake, provide decision support for post-earthquake train speed limits based on probabilistic reliability, improve the efficiency and safety of post-earthquake operation recovery, maximize the safety and economic benefits of bridges throughout their entire life cycle, and enhance the overall service resilience of bridges in earthquake zones.

[0070] This embodiment verifies the effectiveness of the method through simulation experiments, the process of which is as follows:

[0071] The actual set of seismically induced geometric irregularities and the target seismically induced geometric irregularities obtained by the method in this embodiment are used as track irregularity excitations in the coupled numerical simulation model of the high-speed train-track-bridge system, respectively. The train speed is set to 300 km / h, and the peak value of the train dynamic response index is calculated. Figure 6 The diagrams show the vertical wheel-rail force response index and wheel load reduction rate response index under different track irregularity excitations. The red legend represents the excitation using the actual seismically induced high and low geometric irregularity set, while the gray legend represents the excitation using the target seismically induced high and low geometric irregularity obtained by the method of this embodiment. The circular characters 1 to 50 represent the track irregularity numbers, respectively. Under the excitation of the target seismically induced high and low geometric irregularity, the peak value of the train response index has good envelope to the seismically induced high and low track irregularity set, which verifies the rationality of the method of this embodiment.

[0072] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for predicting target seismic-induced high-low geometric irregularities of high-speed railways under longitudinal earthquakes, characterized in that, The method comprises the following steps: Step S1: establishing a random sample library of seismic-induced high-low geometric irregularities on a high-speed railway bridge; Step S2: decoupling the seismic-induced high-low geometric irregularities into a shape function and an amplitude variable; Step S3: establishing an expression of the shape function of the target seismic-induced high-low geometric irregularity; Step S4: fitting an upper bound spectrum of a peak value of a displacement at a pier top in combination with uncertainty analysis; Step S5: solving the amplitude variable through a structural period and the upper bound spectrum of the peak value of the displacement at the pier top; Step S6: constructing the target seismic-induced high-low geometric irregularity based on the shape function and the amplitude variable; In step S2, the decoupling process of the seismic-induced high-low geometric irregularity comprises: decoupling the seismic-induced high-low geometric irregularity into a dimensionless shape function and a dimensioned amplitude variable, wherein the amplitude variable reflects the overall strength of the track irregularity, and the shape function reflects the spatial distribution characteristics of the track irregularity; In step S5, the process of calculating the amplitude variable comprises: for a random structure with an arbitrary pier height and span number, carrying out modal analysis to record a first-order longitudinal self-vibration period, combining the upper bound spectrum of the peak value of the displacement at the pier top to calculate an upper bound of the longitudinal displacement at the pier top, and based on the corresponding relationship between the longitudinal displacement at the pier top and the amplitude of the seismic-induced high-low geometric irregularity, calculating the amplitude variable of the target seismic-induced high-low geometric irregularity; the process of calculating the corresponding relationship between the longitudinal displacement at the pier top and the amplitude of the seismic-induced high-low geometric irregularity comprises: taking real earthquake data as a numerical simulation model excitation and carrying out nonlinear time-history analysis, extracting the vertical displacement time-history of the rail node on both sides of the bridge pier and the longitudinal displacement time-history at the pier top under different pier heights from the time-history analysis results, fitting the slope of the fitting function between the vertical displacement of the rail node and the longitudinal displacement at the pier top, and the fitting function is the corresponding relationship between the longitudinal displacement at the pier top and the amplitude of the seismic-induced high-low geometric irregularity; In step S6, the process of constructing the target seismic-induced high-low geometric irregularity comprises: multiplying the shape function of the target seismic-induced high-low geometric irregularity and the amplitude variable and then superimposing to form the final target seismic-induced high-low geometric irregularity time-domain sample.

2. The method for predicting target seismic induced high-low geometric irregularities of high-speed railway under longitudinal earthquake according to claim 1, characterized in that, In step S1, the process of establishing the sample library of the seismic-induced high-low geometric irregularity comprises: establishing a numerical simulation model of a high-speed railway track-bridge system, selecting a random set of ground motions and carrying out nonlinear time-history analysis, extracting a set of left and right rail displacements from the time-history analysis results, and based on the corresponding relationship between the rail displacement and the track irregularity, establishing a sample library of the seismic-induced high-low geometric irregularity.

3. The method for predicting target seismic induced high-low geometric irregularities of high-speed railway under longitudinal earthquake according to claim 1, characterized in that, In step S3, the process of establishing the expression of the shape function comprises: based on the characteristic that the seismic-induced high-low geometric irregularity has obvious periodicity, dividing the seismic-induced high-low geometric irregularity by its amplitude to split into multiple sub-blocks, fitting the function expression of the first sub-block, based on the characteristic that each sub-block is anti-symmetric to each other, carrying out translation and flipping on the first sub-block, establishing the function expression of all sub-blocks, and completing the establishment of the shape function expression.

4. The method for predicting target seismic induced high-low geometric irregularities of high-speed railway under longitudinal earthquake according to claim 3, characterized in that, In step S4, the fitting steps of the upper bound spectrum of the peak value of the displacement at the pier top are as follows: The height of each pier in the numerical simulation model is set as a random integer in a certain range. The modal analysis is carried out, and the first-order longitudinal natural vibration period is recorded. The nonlinear time-history analysis is carried out, and the upper bound of the pier top displacement peak value is constructed. The above process is repeated 100 times, and the first-order longitudinal natural vibration period matrix and the upper bound of the pier top displacement peak value matrix are established. The natural vibration period matrix and the upper bound of the pier top displacement peak value matrix are taken as independent variables and dependent variables respectively, and the upper bound spectrum of the pier top displacement peak value of the high-speed railway under the longitudinal earthquake is fitted.

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