Safety evaluation method of train-bridge system under combined action of wind and wave

Abstract

The application discloses a safety evaluation method for a train-bridge system under the combined action of wind and wave, and relates to the technical field of train-bridge systems. The exceeding probability of each dynamic response of the train-bridge system under each wind speed-wave height combination is obtained; if the exceeding probability of any dynamic response is greater than 0, then the train-bridge system under the wind speed-wave height combination is unsafe. The application has the beneficial effect that whether the train has the objective condition of safely passing through the bridge under the specific wind speed-wave height combination can be determined, the railway staff is helped to make the judgment in advance, the safe driving is guided, and the unnecessary personal and property losses are avoided.

Description

Technical Field

[0001] This invention relates to the field of train-bridge system technology, and in particular to a safety assessment method for train-bridge systems subjected to combined wind and wave effects. Background Technology

[0002] Existing domestic and international regulations and management methods primarily establish speed limits based on wind speed. However, when trains cross sea-crossing railway bridges, the system is subjected to the combined effects of wind and waves. The aforementioned regulations do not consider the impact of waves, nor their combined effect, thus limiting their application.

[0003] In current bridge seismic research, performance-based earthquake engineering and performance-based seismic design have become the main analytical methods and mainstream development trends. These methods are now mature, and seismic vulnerability analysis is widely used in bridge engineering seismic research. Seismic vulnerability analysis measures the probability of a bridge structure experiencing varying degrees of damage under different levels of seismic loading, or the probability of a bridge structure reaching a certain limit state or exceeding a certain performance level. Among these methods, the cloud map method is a type of non-amplitude dynamic analysis method. This method can comprehensively consider the uncertainties of both seismic and bridge parameters. By selecting seismic motions with multiple parameters and performing nonlinear time history analysis on bridges under different parameters, a large number of discrete sample points regarding seismic intensity and structural response can be obtained. Regression analysis of these discrete sample points can reveal the correspondence between the structural seismic demand (D) and seismic intensity. On the other hand, if the structural capacity (C) is known, the failure probability P of the structure can be obtained through the seismic vulnerability function. f The expression is as follows:

[0004] P f =P[D / C≥1] (1)

[0005] The incremental dynamics method selects a certain number of seismic waves that meet the requirements based on the structural and site characteristics, usually at least 20 seismic waves, and then adjusts the selected intensity parameter IM (Intensity Measure) through a series of amplitude modulation coefficients. If the peak ground acceleration (PGA) is used as the intensity parameter and the increment is 0.1g, the peak ground acceleration PGA is 0.1g to 1.0g. Subsequently, the seismic action is applied to the structure for nonlinear time history analysis to obtain the seismic resistance requirements under different IMs. At the same time, different levels of damage index DI (Damage Index) are classified according to the bearing capacity of the structure or component. Finally, based on equation (2), the calculation results are calculated and processed using mathematical statistics methods to obtain the exceedance probability P of various damage states under different IMs. f (like Figure 1 ).

[0006] Pf =P[D / C≥1|IM] (2)

[0007] In seismic vulnerability analysis, earthquake is the sole action. Therefore, peak ground acceleration (PGA), spectral acceleration (SA), or other seismic motion parameters are typically used to apply the seismic action to the structure to obtain structural requirements under different earthquake intensity (IM). As mentioned earlier, commonly used theoretical vulnerability studies include methods such as contour mapping and individual seismic analysis (IDA). However, for wind-wave axle systems, there are both wind and wave actions. The above methods are only applicable to a single action and are therefore not suitable. Summary of the Invention

[0008] The purpose of this invention is to provide a safety assessment method for train-bridge systems subjected to combined wind and wave effects, based on vulnerability analysis methods and considering the specific circumstances of random response in train-bridge systems.

[0009] The technical solution for achieving the objective of this invention is as follows:

[0010] A safety assessment method for train-bridge systems under combined wind and wave effects is used to obtain the exceedance probability of each dynamic response of the train-bridge system under each wind speed-wave height combination. If the exceedance probability of any dynamic response is greater than 0, the train-bridge system under that wind speed-wave height combination is unsafe; the exceedance probability of the dynamic response...

[0011]

[0012] In the formula, U w For wind speed, H s Let μ be the wave height, Φ[·] be the cumulative distribution function of the normal distribution, and μ be the cumulative distribution function of the normal distribution. ln(D) Let μ be the logarithmic mean of D. ln(C) Let σ be the logarithmic mean of C. ln(D) Let σ be the logarithmic standard deviation of D. ln(C) Let ΔU be the logarithmic standard deviation of C. w ×ΔH s Therefore (U) w H s The computational domain is centered at ), D is any dynamic response of the train-bridge system under this wind speed-wave height combination, and C is the response limit of the train or bridge in the train-bridge system corresponding to D; IM1 = U w IM2=H s This indicates that wind speed and wave height are used as intensity parameters.

[0013] The beneficial effect of this invention is that it can determine whether a train has the objective conditions to safely pass over a bridge under a specific wind speed-wave height combination, helping railway staff to make judgments in advance, guiding safe train operation, and avoiding unnecessary personal and property losses. Attached Figure Description

[0014] Figure 1 This is a vulnerability curve based on IDA.

[0015] Figure 2 Therefore (U) w H s A schematic diagram of the computational domain centered on ).

[0016] Figure 3 In a specific embodiment, (U) w =0.1,H s A schematic diagram of the computational domain centered at (=0.1). Detailed Implementation

[0017] This invention provides a safety assessment method for train-bridge systems subjected to the combined effects of wind and waves, aiming to solve the probabilistic safety assessment of train-bridge systems under the combined effects of wind and waves.

[0018] In the technical solution of this invention, wind speed and wave height are used as the strength parameter IM, the vehicle-bridge dynamic response is the demand D, and the capacity C is the limit value of the train or bridge dynamic response determined according to the specifications. Statistical analysis shows that the vehicle-bridge dynamic response follows a log-normal distribution, and the exceedance probability P of the vehicle-bridge dynamic response under any wind speed-wave height combination is... f (U w H s The expression is as follows:

[0019]

[0020] In the formula, U w For wind speed, H s For wave height, μ ln(C) μ ln(D) σ represents the logarithmic mean of C and D, respectively; ln(C) σ ln(D) Then these are the logarithmic standard deviations of C and D, respectively; Φ[·] is the cumulative distribution function of the normal distribution.

[0021] Under seismic action, there are more than 20 structural responses under each IM, so statistical analysis (calculation of mean and variance) can be performed. However, there is only one vehicle-bridge response under any wind speed-wave height combination, which cannot be statistically analyzed, and calculation according to the above formula is meaningless. Therefore, based on the above, this invention proposes the "central domain" method, that is, using the idea of ​​differentiation, all small areas near the specific intensity parameter are regarded as its response, and statistical analysis is performed on the data within the domain, so as to perform probability statistics and exceedance probability calculation. At this time, formula (3) is expressed as:

[0022]

[0023] In the formula, ΔUw ×ΔH s For (U) w H s The computational domain centered on ) such as Figure 2 As shown; the meanings of the other symbols are the same as above.

[0024] In a train-bridge system, the vehicle-bridge performance indicators are the corresponding specification limits for each indicator, and these are all constants. Therefore, we have: Equation (4) then simplifies to:

[0025]

[0026] In seismic vulnerability analysis, demand D is the structural response (i.e., seismic demand) under the action of several seismic waves with a fixed ground motion parameter IM, while capacity C is the structural response limit under different damage states obtained according to structural analysis or code specifications. Thus, the damage exceedance probability of the structure or component is calculated according to equation (2). Corresponding to the "central domain" method proposed based on wind and wave vehicle-bridge systems, demand D is the vehicle-bridge response within the "central domain" with strength parameter IM equal to wind speed and wave height, while capacity C is the bridge or train response limit determined according to code specifications. In summary, both belong to the category of reliability analysis, and the research methods and analysis methods are similar. Therefore, the "central domain" analysis method is effective in the probabilistic safety assessment of wind and wave vehicle-bridge systems. Specific implementation examples:

[0028] Take wind speed (U) w The sequence is (0 m / s, 0.01 m / s, ..., 30.02 m / s), wave height (H) s The sequence is (0m, 0.01m, ..., 3.02m), and a full sequence combination of wind speed and wave height is performed. Based on the wind-wave-vehicle-bridge coupling model, the full sequence combination is used as input to obtain the vehicle-bridge response under the full sequence combination.

[0029] The wind-wave vehicle-bridge coupling model can be obtained from the following scheme:

[0030] 1. Dynamic equations of the train-bridge system

[0031] Under external excitation and track irregularity excitation, the loads on the vehicle and bridge at the wheel-rail contact point in a train-bridge system are a pair of equal and opposite interaction forces. Therefore, the equations of motion for the train-bridge system are as follows:

[0032]

[0033]

[0034] In this system, the vehicle subsystem is identified by the subscript v, and the bridge subsystem by b; M, C, and K represent the mass, damping, and stiffness matrices of the substructure; F vb This represents the force exerted on the train by the bridge at the wheel-rail contact point; F bv This indicates the force exerted on the bridge by the train at the wheel-rail contact point; This represents the displacement, velocity, and acceleration matrix of the substructure; the subscripts wind and wave represent the wind load and wave load on the bridge and train, respectively.

[0035] 2. Coupling of Train-Bridge Systems

[0036] To realize the coupled train-bridge system, after establishing the finite element model of the bridge, the bridge structure is imported as an elastic body into the vehicle model. Basic elements such as constraints and force elements are used to establish the connection between the train and the bridge via the track. Numerical algorithms are used to realize the real-time transmission of discrete information such as force and displacement between the train and the bridge, thereby achieving coupled vibration simulation of the train-bridge system. The track and bridge satisfy the following deformation compatibility conditions and force equilibrium conditions:

[0037] u r (t)=u b (t,s)

[0038]

[0039] In the formula, u r (t) represents the rail displacement; u b (t,s) represents the displacement of the bridge at point s along the longitudinal direction; Y(t) and Q(t) represent the lateral and vertical forces of the wheel and rail; F y (t), F z (t) represents the lateral and vertical forces constrained by the track and bridge.

[0040] 3. Obtaining the vehicle-axle response (obtaining the D value)

[0041] To obtain the vehicle-bridge response under arbitrary wind and wave combinations, firstly, the static and buffeting loads of the vehicle-bridge system are obtained based on the Davenport quasi-steady buffeting force model. Secondly, linear wave theory is used to calculate the wave loads acting on the structure. Finally, the loads are applied to the vehicle-bridge system for numerical calculation, thus obtaining the vehicle-bridge response under arbitrary wind and wave combinations.

[0042] In this embodiment, ΔU is taken. w =0.04m / s, ΔH s =0.04m, taking (0.10m / s, 0.10m) as an example, its central sequence point is as follows Figure 3 As shown, by analyzing Figure 3 P is obtained from the vehicle response statistics of the middle sequence points. f(0.10m / s, 0.10m).

[0043] According to GB / T 5599-2019, Specification for Evaluation and Testing of Dynamic Performance of Locomotives and Rolling Stock, the limit value of lateral force of wheel axle can be given by static axle weight P0: H≤15+P0 / 3=60.75kN, that is, C=60.75.

[0044] Table 1 shows the lateral forces on the wheel axle at a sequence of points centered at (28.25 m / s, 1.50 m). The D values ​​in Table 1 were obtained through numerical simulation.

[0045] Table 1: Lateral forces of the wheel axle sequence centered at (28.25 m / s, 1.50 m)

[0046]

[0047] From Table 1, it can be calculated that when the center point is U... w =28.25m / s, H s =1.50m, the logarithmic mean of the lateral force on the wheel axle of the sequence Log-standard deviation Then we have:

[0048]

[0049] Similarly, the failure exceedance probability of different dynamic indicators of the vehicle-bridge system under any combination of wind speed-wave height sequences can be calculated.

[0050] For specific cross-sea railway bridges, a train-bridge coupling model can be established in advance. By analyzing the wind and wave characteristics of the bridge site area, wind-wave-vehicle coupled vibration calculations can be performed. Since the safety of high-speed trains is extremely important, situations where the failure exceedance probability is objectively unacceptable. After obtaining the failure exceedance probability of different dynamic indicators of the train-bridge system under any combination of wind speed and wave height sequences, it is possible to determine whether the train has the objective conditions to safely cross the bridge under a specific wind speed and wave height combination. This helps railway staff make judgments in advance, guides actual safe train operation, and avoids unnecessary personal injury and property damage.

Claims

1. A safety assessment method for vehicle-bridge systems subjected to combined wind and wave effects, characterized in that, For each wind speed-wave height combination, obtain the exceedance probability of each dynamic response of the train-bridge system; if the exceedance probability of any dynamic response is greater than 0, then the train-bridge system is unsafe for that wind speed-wave height combination; the exceedance probability of the dynamic response... In the formula, U w For wind speed, H s Let μ be the wave height, Φ[·] be the cumulative distribution function of the normal distribution, and μ be the cumulative distribution function of the normal distribution. ln(D) Let μ be the logarithmic mean of D. ln(C) Let σ be the logarithmic mean of C. ln(D) Let σ be the logarithmic standard deviation of D. ln(C) Let ΔU be the logarithmic standard deviation of C. w ×ΔH s Therefore (U) w H s The computational domain is centered at ), D is any dynamic response of the train-bridge system under this wind speed-wave height combination, and C is the response limit of the train or bridge in the train-bridge system corresponding to D; IM1 = U w IM2=H s This indicates that wind speed and wave height are used as intensity parameters.

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