Exceeding probability analysis for rail of high-speed railway under seismic excitations

Purpose–The smoothness of the high-speed railway(HSR)on the bridge may exceed the allowable standard when an earthquake causes vibrations for HSR bridges,which may threaten the safety of running trains.Indeed,few studies have evaluated the exceeding probability of rail displacement exceeding the allowable standard.The purposes of this article are to provide a method for investigating the exceeding probability of the rail displacement of HSRs under seismic excitation and to calculate the exceeding probability.Design/methodology/approach–In order to investigate the exceeding probability of the rail displacement under different seismic excitations,the workflow of analyzing the smoothness of the rail based on incremental dynamic analysis(IDA)is proposed,and the intensity measure and limit state for the exceeding probability analysis of HSRs are defined.Then a finite element model(FEM)of an assumed HSR track-bridge system is constructed,which comprises a five-span simply-supported girder bridge supporting a finite length CRTS II ballastless track.Under different seismic excitations,the seismic displacement response of the rail is calculated;the character of the rail displacement is analyzed;and the exceeding probability of the rail vertical displacement exceeding the allowable standard(2mm)is investigated.Findings–The results show that:(1)The bridge-abutment joint position may form a step-like under seismic excitation,threatening the running safety of high-speed trains under seismic excitations,and the rail displacements at mid-span positions are bigger than that at other positions on the bridge.(2)The exceeding probability of rail displacement is up to about 44%when PGA 50.01g,which is the level-five risk probability and can be described as’very likely to happen’.(3)The exceeding probability of the rail at the mid-span positions is bigger than that above other positions of the bridge,and the mid-span positions of the track-bridge system above the bridge may be the most hazardous area for the running safety of trains under seismic excitation when high-speed trains run on bridges.Originality/value–The work extends the seismic hazardous analysis of HSRs and would lead to a better understanding of the exceeding probability for the rail of HSRs under seismic excitations and better references for the alert of the HSR operation.

Probability Distribution Characteristics of Strong Nonlinear Waves Under Typhoon Conditions in the Northern South China Sea

The generation and propagation mechanism of strong nonlinear waves in the South China Sea is an essential research area. In this study, the third-generation wave model WAVEWATCH Ⅲ is employed to simulate wave fields under extreme sea states. The model, integrating the ST6 source term, is validated against observed data, demonstrating its credibility. The spatial distribution of the occurrence probability of strong nonlinear waves during typhoons is shown, and the waves in the straits and the northeastern part of the South China Sea show strong nonlinear characteristics. The high-order spectral model HOS-ocean is employed to simulate the random wave surface series beneath five different platform areas. The waves during the typhoon exhibit strong nonlinear characteristics, and freak waves exist. The space-varying probability model is established to describe the short-term probability distribution of nonlinear wave series. The exceedance probability distributions of the wave surface beneath different platform areas are compared and analyzed. The results show that with an increase in the platform area, the probability of a strong nonlinear wave beneath the platform increases.

Probability Analysis of the Wave-Slamming Pressure Values of the Horizontal Deck with Elastic Support

This paper presents the probability distribution of the slamming pressure from an experimental study of regular wave slamming on an elastically supported horizontal deck. The time series of the slamming pressure during the wave impact were first obtained through statistical analyses on experimental data. The exceeding probability distribution of the maximum slamming pressure peak and distribution parameters were analyzed, and the results show that the exceeding probability distribution of the maximum slamming pressure peak accords with the three-parameter Weibull distribution. Furthermore, the range and relationships of the distribution parameters were studied. The sum of the location parameter D and the scale parameter L was approximately equal to 1.0, and the exceeding probability was more than 36.79% when the random peak was equal to the sample average during the wave impact. The variation of the distribution parameters and slamming pressure under different model conditions were comprehensively presented, and the parameter values of the Weibull distribution of wave-slamming pressure peaks were different due to different test models. The parameter values were found to decrease due to the increased stiffness of the elastic support. The damage criterion of the structure model caused by the wave impact was initially discussed, and the structure model was destroyed when the average slamming time was greater than a certain value during the duration of the wave impact. The conclusions of the experimental study were then described.

Discussion on the Relationship between “Anti-great Earthquakes” and Ground Motion with a Low Probability of Exceedance

In this paper we discuss the differences and relationship between"great earthquakes",rare ground motion,and very rare ground motion.Taking the Beichuan-Yingxiu potential seismic source zone in Longmenshan seismic belt as an example,we revealed the relationship between the effects of"great earthquakes"and rare ground and very rare ground motion.After pointing out scientific and technical problems in the current seismic fortification system,we suggest that very rare ground motion should be considered if we want to deduce the potential hazard of great earthquakes in the future.

Levels of Probability of Exceedance for Current Code Spectra in China

Long-period acceleration spectra determined by seismic safety evaluation for project sites are generally lower than that given by relative code spectra.In this paper,we discuss the recurrence periods corresponding to the code spectra of different periods,by using ground motion attenuation laws for sites of types Ⅰ and Ⅲ.We show the results that the longer the periods of code spectra are commonly the more conservative the seismic level is.As for the project examples in this paper,when the periods are longer than 3.7 or 5.2 seconds for sites of types Ⅰ or Ⅲ,the recurrence periods corresponding to the code spectra are longer than 5000 years.We suggest that some problems need to be further discussed,including the reliability of the present attenuation laws,the performance of those project structures that suffer long period seismic waves and have been designed according to the conservative codes,and the effects of ground motion parameters such as velocity and displacement on seismic design.

Performance-based passive control analysis of adjacent structures:Optimization of Maxwell dampers

The performance-based passive control analysis of the Maxwell dampers between one 10-story and one 6-story adjacent RC frames is conducted in this work.Not only the optimal parameters but also the optimal arrangements of the Maxwell dampers are proposed based on the optimal target of making the total exceeding probability of the adjacent structures to be minimal.The applicability of the analytical expressions of the Maxwell damper damping parameters under different seismic performance targets are firstly examined and then the preferable damping parameters of the Maxwell dampers are proposed through the extensive parametric studies.Furthermore,the optimal arranging positions and optimal arranging numbers of the Maxwell dampers between the adjacent buildings are derived based on a large number of seismic fragility analyses,as well.The general arranging laws of the Maxwell dampers between the adjacent buildings are generated based on the discussion of the theoretical method through the simplified plane model.The optimal parameters and optimal arrangement of the Maxwell dampers presented make both the adjacent structures have preferable controlled effects under each seismic performance target which can satisfy the requirements of multi-performance seismic resistance of the modern seismic codes.

Study on time-varying seismic vulnerability and analysis of ECC-RC composite piers using high strength reinforcement bars in offshore environment

As the main seismic component of a bridge,seismic damage to the bridge pier has a greater effect on its subsequent service.In the offshore chloride environment,the issues(e.g.,reinforcement bar corrosion and attenuation of concrete strength)of piers caused by chloride ion seriously curtail the normal service life and deteriorate the anti-seismic property of bridge structures.The engineered cementitious composite(ECC)-reinforced concrete(RC)composite pier with high strength reinforcement bars(HSRB)is expected to solve the above problems.This study aims to clarify the time-varying seismic vulnerability(SV)of the HSRBECC-RC composite pier during its full life cycle(FLC).Based on OpenSees,the refined finite element analysis models of RC pier,ECC-RC composite pier,and HSRBECC-RC composite pier have been established.Moreover,using the nonlinear time-path dynamic analysis method,the influence of chloride ion erosion on the time-dependent seismic vulnerability(SV)of these different piers in different service life and different peak ground acceleration(PGA)were analyzed from a dynamic point of view.The research shows that the exceeding probability(EP)of the same damage level increases with the enhancement of service time and PGA and with the increase of destruction,the exceeding probability(EP)of slight damage(DL-1),moderate damage(DL-2),serious damage(DL-3),and complete collapse(DL-4)decreases in turn;the corrosion degree of chloride ion to piers is small during the early service period,the time-varying vulnerability curve of the bridge piers is almost the same as that of a new bridge,and during later service,as the extent of chloride ion corrosion deepens,exceeding probability(EP)under severe damage(DL-3)and complete collapse(DL-4)is increased,and the seismic performance is significantly enhanced.

Discussion on the influence of truncation of ground motion residual distribution on probabilistic seismic hazard assessment

Recent studies on assessment of a very low annual probability of exceeding （APE） ground motions, 10-4 or less, have highlighted the importance of the upper bound of ground motions when very low probability results are acquired. The truncation level adopted in probabilistic seismic hazard analysis （PSHA） should be determined by an aleatory uncertainty model （i.e., distribution model） of ground motions and the possible maximum and minimum ground motion values of a specific earthquake. However, at the present time, it is impossible to establish the upper bound model for ground motions based on the source characteristics and/or ground motion propagation. McGuire suggested a truncation level be fixed at a number of = 6, or the distribution of residuals be truncated in such a manner that site intensity cannot be greater than the epicenter intensity. This study aims to find a reasonable and feasible truncation level to be used in PSHA when the physical mechanism is not available to find the extreme ground motion. A mathematical analysis of the influence of the truncation level on PSHA, case studies of sites in different seismotectonic settings, and a distribution analysis of ground motion residuals are conducted in this study. It is concluded that = 4 is the minimum acceptable value for engineering applications for APEs within 0.002 to 10-4, and for low APEs, such as 10-5 and 10-6, the value of should be no less than 5 in most regions of China.

On the Exceedance Probabilities of Extreme Drift Motions of An Offshore Structure

The response statistics of a compliant offshore structure excited by slowly varying wave drift forces is calculated by use of a numerical path integral solution method. The path integral solution is based on the Ganss-Legendre interpolation scheme, and the values of the response probability density are obtained at the Gauss quadrature points in sub-intervals. It is demonstrated that a distinct advantage of the path integral solution is that the joint probability density of the response displacement and velocity is one of the by products of the calculations. This makes it possible to calculate the mean level up-crossing rates, which provides estimates of the exceedance probabilities of specified response levels for given time periods.

Study on the characteristics of earthquake's impact on cities

Firstly, the impact of historical earthquakes on 34 China province-level capital cities is evaluated by using historical earthquake catalog. The distribution of affected intensity shows, about 53% of cities have even not been affected by earthquake intensity VI, and 44% of cities have been hit by earthquake intensity VII to IX. For most of the cities, occurrence frequency of affected intensity VI is usually higher than that of affected intensity larger than VI, and the value of affected intensity with maximal occurrence frequency may be very different among cities. So both the maximal affected intensity and the affected intensity with maximal occurrence frequency should be taken into account when the prevention seismic intensity needs to be determined. Secondly, considering the incompleteness of records of historical earthquakes, a method of earthquake catalog computer simulation is introduced to study the features of affected intensity of big cities. 69 county-level cities of Fujian Province are selected to be statistical objects. The statistical result shows, for different risk levels the seismic intensity changes greatly among cities, the seismic intensity of 2% probability of exceedance in 50 years can be regarded as the characteristic affected intensity of city, and can be the basis of determining the city special earthquake prevention level and a proper indicator of future earthquakes impact on cities.

Parametric study on collapse margin ratio of structure

The determination of collapse margin ratio(CMR)of structure is influenced by many uncertain factors.Some factors that can affect the calculation of CMR,e.g.,the elongation of the structural fundamental period prior to collapse,the determination of earthquake intensity measure,the seismic hazard probability,and the difference of the spectral shapes between the median spectrum of the ground motions and the design spectrum,were discussed.Considering the elongation of the structural fundamental period,the intensity measure Sa(T1)should be replaced with *aS in the calculation of CMR for short-period and medium-period structures.The reasonable intensity measure should be determined by the correlation analysis between the earthquake intensity measure and the damage index of the structure.Otherwise,CMR should be adjusted according to the seismic hazard probability and the difference in the spectral shapes.For important long-period structures,CMR should be determined by the special site spectrum.The results indicate that both Sa(T1)and spectrum intensity(SI)could be used as intensity measures in the calculation of CMR for medium-period structures,but SI would be a better choice for long-period structures.Moreover,an adjusted CMR that reflects the actual seismic collapse safety of structures is provided.

Discussion on uncertainties，attenuation of ground motion and aseismic design criterion

The usually calculated exceedance probability curves of ground motion are reduced as cumulative probability curves of normal distribution on some assumptions in this paper. These curves clearly displayed the variation of curve shape with the variance of attenuation relation and its physical implication. Similar investigation is also made on uncertainties of hypocenter locations and magnitudes of future earthquakes. The larger the uncertainty,the flatter the exceedance probability curve is. In a broad sense, the less people know future earthquakes, the flatter is the curve. Due to the rich or poor data sets available, the uncertainties of attenuation relation are different from region to region. The acceleration attenuation relations in these regions with no enough strong earthquake records can be obtained by conversion from other region, but with larger uncertainty. The uncertainty contains systematic difference between the two regions in addition to common stochastic error. A method to check and adjust the converted attenuation relation by using the local data is proposed in this paper. If the uncertainty of attenuation relation is too large, the result of seismic hazard assessment may be unaccepted sometimes.In order to realize that the structures do not collapse in large earthquakes, be repairable under moderate ones and without destruction in small earthquakes, this paper suggests that it may be reasonable to get the first and the third levels of aseismic design parameters by some empirical relation on the basis of the second level not by fixing the risk probability levels (63%, 10% and 3%). A particular aseismic design criterion is not only a balance between economic cost and seismic risk but also suited to the human's knowledge of nature.

The Relationship Among Bedrock Seismic Ground Motion Parameters with Different Exceedance Probabilities in the Panxi Area

Based on the calculation of the bedrock effective peak acceleration (EPA) zoning map in the Panxi area, the ratios of EPA with exceedance probabilities of 63%, 5%, 3%, 2% and 1% over 50 years to that of 10% in 50 years are 0.302, 1.30, 1.55, 1.76 and 2.14, respectively. The seismic effect will be conservative and safe if taking this zoning map as the earthquake resistant fortification level and following the relevant rules of the Code for Seismic Design of Buildings (GBJ11 89) to calculate the seismic effect. Furthermore, the main factors that influence the A10/A63 ratios have been found to be the attenuation relationship of seismic ground motion, the division of seismic potential source regions and the seismicity parameters. These achievements are helpful to the spreading and applying of the zoning map.

Long-Term Statistical Characteristics of Air Pollutants in a Traffic-Congested Area of Ranchi, India

In this paper,we present an analysis of the air quality in a traffic-congested area in Ranchi,the proposed smart city as identified by the government of India.The main purpose of this study is to analyze the concentration of pollutants over a long period and to find the best possible way for its prediction.We have selected four air pollutants,particularly RSPM,SPM,SO_(2) and NO_(X),analyzed their distribution and compared with the National Ambient Air Quality standards over the period2005–2015.The obtained data have been processed with two different methods and probability model as well as multiple regression models has been established for the prediction purpose.Since pollutants data are in continuous form,we have employed Easyfit software to find out the distribution pattern.Johnson SB,Error,Burr(4P)and Cauchy distributions were found to be the appropriaterep resentatives of the RSPM,SPM,SO_(2) and NO_(X) concentration patterns,respectively.Inverse cumulative density function has been used to predict the future concentration of particulate matters.With the help of SPSS 17 software,the impacts of the meteorological conditions on the variation of major pollutants have been examined by identifying the correlation between each pollutant and meteorological parameters and among the pollutants themselves.