Fragility curves of concrete bridges retrofitted by column jacketing

The Northridge earthquake inflicted various levels of damage upon a large number of Caltrans' bridges not retrofitted by column jacketing.In this respect,this study represents results of fragility curve development for two (2) sample bridges typical in southern California,strengthened for seismic retrofit by means of steel jacketing of bridge columns.Monte Carlo simulation is performed to study nonlinear dynamic responses of the bridges before and after column retrofit.Fragility curves in this study are represented by lognormal distribution functions with two parameters and developed as a function of PGA.The sixty (60) ground acceleration time histories for the Los Angeles area developed for the Federal Emergency Management Agency (FEMA) SAC (SEAOC-ATC CUREe) steel project are used for the dynamic analysis of the bridges. The improvement in the fragility with steel jacketing is quantified by comparing fragility curves of the bridge before and after column retrofit.In this first attempt to formulate the problem of fragility enhancement,the quantification is made by comparing the median values of the fragility curves before and after the retrofit.Under the hypothesis that this quantification also applies to empirical fragility curves developed on the basis of Northridge earthquake damage,the enhanced version of the empirical curves is developed for the ensuing analysis to determine the enhancement of transportation network performance due to the retrofit.

Using experimental data to reduce the single-building sigma of fragility curves:case study of the BRD tower in Bucharest,Romania

The lack of knowledge concerning modelling existing buildings leads to significant variability in fragility curves for single or grouped existing buildings. This study aims to investigate the uncertainties of fragility curves, with special consideration of the single-building sigma. Experimental data and simplified models are applied to the BRD tower in Bucharest, Romania, a RC building with permanent instrumentation. A three-step methodology is applied： （1） adjustment of a linear MDOF model for experimental modal analysis using a Timoshenko beam model and based on Anderson＇s criteria, （2） computation of the structure＇s response to a large set of accelerograms simulated by SIMQKE software, considering twelve ground motion parameters as intensity measurements （IM）, and （3） construction of the fragility curves by comparing numerical interstory drift with the threshold criteria provided by the Hazus methodology for the slight damage state. By introducing experimental data into the model, uncertainty is reduced to 0.02 considering Sd ） as seismic intensity IM and uncertainty related to the model is assessed at 0.03. These values must be compared with the total uncertainty value of around 0.7 provided by the Hazus methodology.

Multiple failure function based fragility curves for structures equipped with TMD

This paper presents a procedure to develop fragility curves of structures equipped with TMD considering multiple failure functions.The failure criteria considered are maximum inter-story drift ratio as a safety criterion,maximum absolute acceleration as a convenience criterion and TMD stroke length.The relationship between intensity measure and responses of the structure was assumed to follow the power-law model,and a regression analysis was used to estimate its properties.A nonlinear eight-story shear building subjected to near-fault earthquakes was used for the numerical studies.Fragility curves using multiple and single failure functions for an uncontrolled structure and a structure equipped with optimal TMDs were developed.Numerical analysis showed that using multiple failure functions led to increasing the fragility when compared with using the single failure function for both the uncontrolled and controlled structures.However,TMDs slightly reduced the seismic fragility and have the capability to improve the reliability of the structure.Also,it was found that the fragility was significantly influenced by the values of the capacity thresholds of both the acceleration of the structure and TMD stroke length,which should be selected by considering the target performance and application of the structure and control device.

Development of seismic fragility curves for precast concrete frames with cast-in-situ concrete shear-walls

Precast reinforced concrete buildings have been well received in some seismic zones worldwide due to advantages such as the ease and the speed of implementation,and the possibility of working in inappropriate atmospheric conditions.In this research,seismic fragility curves were developed for precast concrete frames with a cast-in-situ concrete shear-wall,concerning the important issues of modeling the precast beam-column joints,construction quality,and soil type effects.For this purpose,the incremental dynamic analysis(IDA)was conducted for three-dimensional models of 3-,5-,and 8-story buildings under two record sets corresponding to soil types C and D of the NEHRP code.Beam-column joints were modeled using nonlinear rotational springs with rigid links with respect to the finite size of the joint panel.Results demonstrate that the Weibull distribution can be fitted to the damage state capacities better than the lognormal distribution at the intensities that are more than one standard deviation away from the median damage capacity.The seismic vulnerability of precast structures increases at all damage states as the height of the building increases.It is also observed that soil type has almost no considerable effect on the fragility curve parameters for all damage states considered herein.

Seismic fragility curves for structures using non-parametric representations

Fragility curves are commonly used in civil engineering to assess the vulnerability of structures to earthquakes. The probability of failure associated with a prescribed criterion （e.g., the maximal inter-storey drift of a building exceeding a certain threshold） is represented as a function of the intensity of the earthquake ground motion （e.g., peak ground acceleration or spectral acceleration）. The classical approach relies on assuming a lognormal shape of the fragility curves; it is thus parametric. In this paper, we introduce two non-parametric approaches to establish the fragility curves without employing the above assumption, namely binned Monte Carlo simulation and kernel density estimation. As an illustration, we compute the fragility curves for a three-storey steel frame using a large number of synthetic ground motions. The curves obtained with the non-parametric approaches are compared with respective curves based on the lognormal assumption. A similar comparison is presented for a case when a limited number of recorded ground motions is available. It is found that the accuracy of the lognormal curves depends on the ground motion intensity measure, the failure criterion and most importantly, on the employed method for estimating the parameters of the lognormal shape.

Experimental Study and Fragility Analysis of Effective-Length Factors in Column Buckling

The design of columns relies heavily on the basis of Leonhard Euler’s Theory of Elastic Buckling.However,to increase the accuracy in determining the maximum critical load a column can withstand before buckling,a constant was introduced.This dimensionless coefficient is K,also known as the effective-length factor.This constant is often found in building design codes and varies in value depending on the type of column support that is applied.This paper presents experimental and analytical studies on the determination of the effective-length factor in the buckling stability of columns with partially-fixed support conditions.To this end,the accurate K value of the columns tested by the Instron Testing Machine(ITM)at California State University,Northridge’s(CSUN’s)Mechanics Laboratory is determined.The ITM is used in studying the buckling of columns where the supports are neither pinned nor fixed,and the material cross-section rather rests upon the machine while loading is applied axially.Several column specimens were tested and the experimental data were analyzed in order to estimation of the accurate effective-length factor.The calculations from the tested results as well as the conducted probabilistic analysis shed light on how a fragility curve may aid in predicting the effective-length value of future tests.

A methodology for damage evaluation of underground tunnels subjected to static loading using numerical modeling

We have proposed a methodology to assess the robustness of underground tunnels against potential failure.This involves developing vulnerability functions for various qualities of rock mass and static loading intensities.To account for these variations,we utilized a Monte Carlo Simulation(MCS)technique coupled with the finite difference code FLAC^(3D),to conduct two thousand seven hundred numerical simulations of a horseshoe tunnel located within a rock mass with different geological strength index system(GSIs)and subjected to different states of static loading.To quantify the severity of damage within the rock mass,we selected one stress-based(brittle shear ratio(BSR))and one strain-based failure criterion(plastic damage index(PDI)).Based on these criteria,we then developed fragility curves.Additionally,we used mathematical approximation techniques to produce vulnerability functions that relate the probabilities of various damage states to loading intensities for different quality classes of blocky rock mass.The results indicated that the fragility curves we obtained could accurately depict the evolution of the inner and outer shell damage around the tunnel.Therefore,we have provided engineers with a tool that can predict levels of damages associated with different failure mechanisms based on variations in rock mass quality and in situ stress state.Our method is a numerically developed,multi-variate approach that can aid engineers in making informed decisions about the robustness of underground tunnels.

Seismic fragility analysis of highway bridges considering multi-dimensional performance limit state

Fragility analysis for highway bridges has become increasingly important in the risk assessment of highway transportation networks exposed to seismic hazards. This study introduces a methodology to calculate fragility that considers multi-dimensional performance limit state parameters and makes a first attempt to develop fragility curves for a multi-span continuous (MSC) concrete girder bridge considering two performance limit state parameters: column ductility and transverse deformation in the abutments. The main purpose of this paper is to show that the performance limit states, which are compared with the seismic response parameters in the calculation of fragility, should be properly modeled as randomly interdependent variables instead of deterministic quantities. The sensitivity of fragility curves is also investigated when the dependency between the limit states is different. The results indicate that the proposed method can be used to describe the vulnerable behavior of bridges which are sensitive to multiple response parameters and that the fragility information generated by this method will be more reliable and likely to be implemented into transportation network loss estimation.

Seismic fragility assessment of RC frame structure designed according to modern Chinese code for seismic design of buildings

Following several damaging earthquakes in China, research has been devoted to find the causes of the collapse of reinforced concrete （RC） building sand studying the vulnerability of existing buildings. The Chinese Code for Seismic Design of Buildings （CCSDB） has evolved over time, however, there is still reported earthquake induced damage of newly designed RC buildings. Thus, to investigate modern Chinese seismic design code, three low-, mid- and high-rise RC frames were designed according to the 2010 CCSDB and the corresponding vulnerability curves were derived by computing a probabilistic seismic demand model （PSDM）.The PSDM was computed by carrying out nonlinear time history analysis using thirty ground motions obtained from the Pacific Earthquake Engineering Research Center. Finally, the PSDM was used to generate fragility curves for immediate occupancy, significant damage, and collapse prevention damage levels. Results of the vulnerability assessment indicate that the seismic demands on the three different frames designed according to the 2010 CCSDB meet the seismic requirements and are almost in the same safety level.

Seismic evaluation of rocking structures through performance assessment and fragility analysis

Numerical studies have been conducted for low- and medium-rise rocking structures to investigate their efficiency as earthquake-resisting systems in comparison with conventional structures. Several non-linear time-history analyses have been performed to evaluate seismic performance of selected cases at desired ground shaking levels, based on key parameters such as total and flexural story drifts and residual deformations. The Far-field record set is selected as input ground motions and median peak values of key parameters are taken as best estimates of system response. In addition, in order to evaluate the probability of exceeding relevant damage states, analytical fragility curves have been developed based on the results of the incremental dynamic analysis procedure. Small exceedance probabilities and acceptable margins against collapse, together with minor associated damages in main structural members, can be considered as superior seismic performance for medium-rise rocking systems. Low-rise rocking systems could provide significant performance improvement over their conventional counterparts notwithstanding certain weaknesses in their seismic response.

Seismic fragility analysis of composite frame structure based on performance

Steel-concrete composite structures that share the advantages of both steel structure and concrete structure have been developed rapidly and used widely. It has been a popular structure in high-rise buildings in recent years. Although more and more composite structures have been used in earthquake area, only a few literatures about fragility analysis of this type of structure are available. In this paper, a fragility analysis method based on performance is proposed, in which both the uncertainty due to variability in structures and ground motion are considered. Seismic fragility analysis is performed for a 15-story composite beam-concrete-filled square steel tube column frame by the proposed method. The top-drift-angle and the story-drift-angle are used as quantitative indexes to define the four different performance levels. Then seismic demand probability analysis is carried out and fragility curves are derived to assess the seismic performance of this type of structure.

Evaluation of collapse resistance of RC frame structures for Chinese schools in seismic design categories B and C

According to the Code for Seismic Design of Buildings （GB50011-2001）, ten typical reinforced concrete （RC） frame structures, used as school classroom buildings, are designed with different seismic fortification intensities （SFIs） （SFI=6 to 8.5） and different seismic design categories （SDCs） （SDC=B and C）. The collapse resistance of the frames with SDC=B and C in terms of collapse fragility curves are quantitatively evaluated and compared via incremental dynamic analysis （IDA）. The results show that the collapse resistance of structures should be evaluated based on both the absolute seismic resistance and the corresponding design seismic intensity. For the frames with SFI from 6 to 7.5, because they have relatively low absolute seismic resistance, their collapse resistance is insufficient even when their corresponding SDCs are upgraded from B to C. Thus, further measures are needed to enhance these structures, and some suggestions are proposed.

Effect of seismic retrofit of bridges on transportation networks

The objective of this research is to determine the effect earthquakes have on the performance of transportation network systems.To do this,bridge fragility curves,expressed as a function of peak ground acceleration(PGA)and peak ground velocity(PGV),were developed.Network damage was evaluated under the 1994 Northridge earthquake and scenario earthquakes.A probabilistic model was developed to determine the effect of repair of bridge damage on the improvement of the network performance as days passed after the event.As an example,the system performance degradation measured in terms of an index,'Drivers Delay,'is calculated for the Los Angeles area transportation system,and losses due to Drivers Delay with and without retrofit were estimated.

Vulnerability of ordinary moment resistant concrete frames

The effects of structural modeling （bar slip in lap splice）, ground motion selection process （epsilon effect） and size of a structure （number of bays and stories） on the fragility of reinforced concrete ordinary moment resisting frames are investigated. An analytical model is developed to account for bar slip in lap splice, which exhibits good correlation with existing experimental data. Then, incremental dynamic analysis is used to derive the fragility curves for four model structures. The model structures simulate frames with a different number of bays and stories. Finally, the fragility curves are corrected for the epsilon effect. The results show that slip in the lap splice can significantly increase the failure probability, especially for the collapse prevention limit state. At the same time, it is found that spectral shape has a significant impact on the fragility curves. It is also found that accounting for or ignoring bar slip or epsilon effects increases the probability of failure for larger structures. This indicates an unconservative bias in the safety of larger structures.

The effect of different intensity measures and earthquake directions on the seismic assessment of skewed highway bridges

In this study the probable seismic behavior of skewed bridges with continuous decks under earthquake excitations from different directions is investigated. A 45° skewed bridge is studied. A suite of 20 records is used to perform an Incremental Dynamic Analysis （IDA） for fragility curves. Four different earthquake directions have been considered： -45°, 0°, 22.5, 45°. A sensitivity analysis on different spectral intensity measures is presented; efficiency and practicality of different intensity measures have been studied. The fragility curves obtained indicate that the critical direction for skewed bridges is the skew direction as well as the longitudinal direction. The study shows the importance of finding the most critical earthquake in understanding and predicting the behavior of skewed bridges.

Experimental verification of bridge seismic damage states quantified by calibrating analytical models with empirical field data

Bridges are one of the most vulnerable components of a highway transportation network system subjected to earthquake ground motions. Prediction of resilience and sustainability of bridge performance in a probabilistic manner provides valuable information for pre-event system upgrading and post-event functional recovery of the network. The current study integrates bridge seismic damageability information obtained through empirical, analytical and experimental procedures and quantifies threshold limits of bridge damage states consistent with the physical damage description given in HAZUS. Experimental data from a large-scale shaking table test are utilized for this purpose. This experiment was conducted at the University of Nevada, Reno, where a research team from the University of California, Irvine, participated. Observed experimental damage data are processed to identify and quantify bridge damage states in terms of rotational ductility at bridge column ends. In parallel, a mechanistic model for fragility curves is developed in such a way that the model can be calibrated against empirical fragility curves that have been constructed from damage data obtained during the 1994 Northridge earthquake. This calibration quantifies threshold values of bridge damage states and makes the analytical study consistent with damage data observed in past earthquakes. The mechanistic model is transportable and applicable to most types and sizes of bridges. Finally, calibrated damage state definitions are compared with that obtained using experimental findings. Comparison shows excellent consistency among results from analytical, empirical and experimental observations.

Fragility assessment of tunnels in soft soils using artificial neural networks

Recent earthquakes have shown that tunnels are prone to damage,posing a major threat to safety and having major cascading and socioeconomic impacts.Therefore,reliable models are needed for the seismic fragility assessment of underground structures and the quantitative evaluation of expected losses.Based on previous researches,this paper presented a probabilistic framework based on an artificial neural network(ANN),aiming at the development of fragility curves for circular tunnels in soft soils.Initially,a two-dimensional incremental dynamic analysis of the nonlinear soil-tunnel system was performed to estimate the response of the tunnel under ground shaking.The effects of soil-structure-interaction and the ground motion characteristics on the seismic response and the fragility of tunnels were adequately considered within the proposed framework.An ANN was employed to develop a probabilistic seismic demand model,and its results were compared with the traditional linear regression models.Fragility curves were generated for various damage states,accounting for the associated uncertainties.The results indicate that the proposed ANN-based probabilistic framework can results in reliable fragility models,having similar capabilities as the traditional approaches,and a lower computational cost is required.The proposed fragility models can be adopted for the risk analysis of typical circular tunnel in soft soils subjected to seismic loading,and they are expected to facilitate decision-making and risk management toward more resilient transport infrastructure.

The analysis of the optimal scalar and vector intensity measurements for seismic performance assessment of deep-buried hydraulic arched tunnels

The selection of optimal intensity measures(IMs)has been recommended for generating the seismic demand models with different probabilities by researchers since the seismic IMs are closely associated with earthquake risks and structural safety.However,the seismic design code(mainly for aboveground structures)and dynamic analysis of underground structures conventionally employ the peak ground acceleration(PGA)as an optimal IM.In this paper,the research is to identify the optimal scalar and vector IMs in the fragility investigation of deep-buried hydraulic arched tunnels using the finite element method.A refinement process was performed to determine the optimal scalar IMs by comprehensively comparing their correlation,efficiency,practicality,proficiency,and sufficiency among the examined IMs.Furtherly,the optimum vector IMs were also developed,followed by the three different scalar IMs.Eventually,the dif-ferences between the fragility curves of the tunnel produced using the optimal scalar and vector IM were compared.The generated vector fragility surface can be used to estimate the seismic fragility of identical hydraulic tunnels in an approximative manner.

Centrifuge experiments for shallow tunnels at active reverse fault intersection

Tunnels extend in large stretches with continuous lengths of up to hundreds of kilometers which are vulnerable to faulting in earthquake-prone areas.Assessing the interaction of soil and tunnel at an intersection with an active fault during an earthquake can be a beneficial guideline for tunnel design engineers.Here,a series of 4 centrifuge tests are planned and tested on continuous tunnels.Dip-slip suface faulting in reverse mechanism of 60°is modeled by a fault simulator box in a quasi-static manner.Failure mechanism,progression and locations of damages to the tunnels are assessed through a gradual increase in Permanent Ground Displacement(PGD).The ground surface deformations and strains,fault surface trace,fault scarp and the sinkhole caused by fault movement are observed here.These ground surface deformations are major threats to stability,safety and serviceability of the structures.According to the observations,the modeled tunnels are vulnerable to reverse fault rupture and but the functionality loss is not abrupt,and the tunnel will be able to tolerate some fault displacements.By monitoring the progress of damage states by increasing PGD,the fragility curves corresponding to each damage state were plotted and interpreted in related figures.

Probabilistic collapse analysis of steel frame structures exposed to fire scenarios

In this paper,we propose a probabilistic method for analysing the collapse time of steel frame structures in a fire.The method considers the uncertainty of influencing factors.Tornado diagrams are used for sensitivity analysis of random variables.Structural analysis samples are selected by Monte Carlo method,and the collapse times of different structural samples are calculated by fire time history analysis.A collapse time fragility curve is fitted according to the calculated collapse times of the samples.A reliability index of the collapse time is used as a quantitative standard to evaluate the collapse performance of a steel frame in a fire.Finally,this method is applied to analyse the collapse time fragility of an eight-storey 3 D steel frame structure under different compartment fire scenarios and fire protection levels.According to the collapse time fragility curve,the effects of the different fire scenarios and protection levels on the collapse resistance of the structure under fire are evaluated.