Improved seismic hazard model with application to probabilistic seismic demand analysis

An improved seismic hazard model for use in performance‐based earthquake engineering is presented. The model is an improved approximation from the so‐called ‘power law’ model, which is linear in log–log space. The mathematics of the model and uncertainty incorporation is briefly discussed. Various means of fitting the approximation to hazard data derived from probabilistic seismic hazard analysis are discussed, including the limitations of the model. Based on these ‘exact’ hazard data for major centres in New Zealand, the parameters for the proposed model are calibrated. To illustrate the significance of the proposed model, a performance‐based assessment is conducted on a typical bridge, via probabilistic seismic demand analysis. The new hazard model is compared to the current power law relationship to illustrate its effects on the risk assessment. The propagation of epistemic uncertainty in the seismic hazard is also considered. To allow further use of the model in conceptual calculations, a semi‐analytical method is proposed to calculate the demand hazard in closed form. For the case study shown, the resulting semi‐analytical closed form solution is shown to be significantly more accurate than the analytical closed‐form solution using the power law hazard model, capturing the ‘exact’ numerical integration solution to within 7% accuracy over the entire range of exceedance rate. Copyright © 2007 John Wiley & Sons, Ltd.     

Self‐centering structural systems with combination of hysteretic and viscous energy dissipations

This paper presents an innovative set of high‐seismic‐resistant structural systems termed Advanced Flag‐Shaped (AFS) systems, where self‐centering elements are used with combinations of various alternative energy dissipation elements (hysteretic, viscous or visco‐elasto‐plastic) in series and/or in parallel. AFS systems is developed using the rationale of combining velocity‐dependent with displacement‐dependent energy dissipation for self‐centering systems, particularly to counteract near‐fault earthquakes. Non‐linear time‐history analyses (NLTHA) on a set of four single‐degree‐of‐freedom (SDOF) systems under a suite of 20 far‐field and 20 near‐fault ground motions are used to compare the seismic performance of AFS systems with the conventional systems. It is shown that AFS systems with a combination in parallel of hysteretic and viscous energy dissipations achieved greater performance in terms of the three performance indices. Furthermore, the use of friction slip in series of viscous energy dissipation is shown to limit the peak response acceleration and induced base‐shear. An extensive parametric analysis is carried out to investigate the influence of two design parameters, λ₁ and λ₂ on the response of SDOF AFS systems with initial periods ranging from 0.2 to 3.0 s and with various strength levels when subjected to far‐field and near‐fault earthquakes. For the design of self‐centering systems with combined hysteretic and viscous energy dissipation (AFS) systems, λ₁ is recommended to be in the range of 0.8–1.6 while λ₂ to be between 0.25 and 0.75 to ensure sufficient self‐centering and energy dissipation capacities, respectively. Copyright © 2010 John Wiley & Sons, Ltd.     

Seismic fragility of traction elevators

Second‐generation performance‐based earthquake engineering (PBEE‐2) requires a library of component fragility functions to estimate probabilistic damage to a wide variety of building components. The present work draws on a large body of (mostly) post‐earthquake reconnaissance and (some) post‐earthquake survey observations of traction elevators to create fragility functions useful in PBEE‐2. Two surveys provide detailed observations of 115 representative elevators at 12 hospitals shaken in the 1989 Loma Prieta and 1994 Northridge earthquakes and selected without regard to or foreknowledge of damage. Of these, 55 failed and 60 did not. Approximately half were installed after an important code change of 1972, so one can distinguish the performance of pre‐1973 and post‐1973 elevator construction. They experienced a range of strong motion: 22 with peak ground acceleration (PGA) < 0.25 g, 93 with 0.25 g < PGA < 0.85 g. The hospitals had elevator failure rates as low as 0% and as high as 100%. A third survey describes damage qualitatively for six sites with PGA ≤ 0.25 and per‐site failure rates of 0% to perhaps 30%. Fragility functions are offered where the damage state is the loss of functionality of the elevator. The elevators in these surveys exhibit a median capacity of PGA ≈ 0.35 g with a logarithmic standard deviation of 0.40. Capacity is modestly sensitive to whether the elevator was installed before or after 1973. Using building‐specific intensity measures such as S_a(T₁) does not improve the fragility functions. Copyright © 2015 John Wiley & Sons, Ltd.     

Identification of critical ground motions for seismic performance assessment of structures

A method is established to identify critical earthquake ground motions that are to be used in physical testing or subsequent advanced computational studies to enable seismic performance to be assessed. The ground motion identification procedure consists of: choosing a suitable suite of ground motions and an appropriate intensity measure; selecting a computational tool and modelling the structure accordingly; performing Incremental Dynamic Analysis on a non‐linear model of the structure; interpreting these results into 50th (median) and 90th percentile performance bounds; and identifying the critical ground motions that are close to these defining probabilistic curves at ground motion intensities corresponding to the design basis earthquake and the maximum considered earthquake. An illustrative example of the procedure is given for a reinforced concrete highway bridge pier designed to New Zealand specifications. Pseudodynamic tests and finite element based time history analyses are performed on the pier using three earthquake ground motions identified as: (i) a Design Basis Earthquake (10% probability in 50 years) with 90 percent confidence of non‐exceedance; (ii) a Maximum Considered Event (2% probability in 50 years) representing a median response; and (iii) a Maximum Considered Event representing 90 percent confidence of non‐exceedance. Copyright © 2006 John Wiley & Sons, Ltd.     

Intensity measures for the seismic response of pile foundations

In this study the efficacy of various ground motion intensity measures for the seismic response of pile foundations embedded in liquefiable and non-liquefiable soils is investigated. A soil-pile-structure model consisting of a two-layer soil deposit with a single pile and a single degree-of-freedom superstructure is used in a parametric study to determine the salient features of the seismic response of the soil-pile-structure system. A suite of ground motion records scaled to various levels of intensity are used to investigate the full range of pile behaviour, from elastic response to failure. Various intensity measures are used to inspect their efficiency in predicting the seismic demand on the pile foundation for a given level of ground motion intensity. It is found that velocity-based intensity measures are the most efficient in predicting the pile response, which is measured in terms of maximum curvature or pile-head displacement. In particular, velocity spectrum intensity (VSI), which represents the integral of the pseudo-velocity spectrum over a wide period range, is found to be the most efficient intensity measure in predicting the seismic demands on the pile foundation. VSI is also found to be a sufficient intensity measure with respect to earthquake magnitude, source-to-site distance, and epsilon, and has a good predictability, thus making it a prime candidate for use in seismic response analysis of pile foundations.     

Error estimation of closed‐form solution for annual rate of structural collapse

With the increasing emphasis of performance‐based earthquake engineering in the engineering community, several investigations have been presented outlining simplified approaches suitable for performance‐based seismic design (PBSD). Central to most of these PBSD approaches is the use of closed‐form analytical solutions to the probabilistic integral equations representing the rate of exceedance of key performance measures. Situations where such closed‐form solutions are not appropriate primarily relate to the problem of extrapolation outside of the region in which parameters of the closed‐form solution are fit. This study presents a critical review of the closed‐form solution for the annual rate of structural collapse. The closed‐form solution requires the assumptions of lognormality of the collapse fragility and power model form of the ground motion hazard, of which the latter is more significant regarding the error of the closed‐form solution. Via a parametric study, the key variables contributing to the error between the closed‐form solution and solution via numerical integration are illustrated. As these key variables cannot be easily measured, it casts doubt on the use of such closed‐form solutions in future PBSD, especially considering the simple and efficient nature of using direct numerical integration to obtain the solution. Copyright © 2008 John Wiley & Sons, Ltd.     

Non‐ergodicity and PEER's framework formula

A framework formula for performance‐based earthquake engineering, advocated and used by researchers at the Pacific Earthquake Engineering Research (PEER) Center, is closely examined. The formula was originally intended for computing the mean annual rate of a performance measure exceeding a specified threshold. However, it has also been used for computing the probability that a performance measure will exceed a specified threshold during a given period of time. It is shown that the use of the formula to compute such probabilities could lead to errors when non‐ergodic variables (aleatory or epistemic) are present. Assuming a Poisson model for the occurrence of earthquakes in time, an exact expression is derived for the probability distribution of the maximum of a performance measure over a given period of time, properly accounting for non‐ergodic uncertainties. This result is used to assess the approximation involved in the PEER formula for computing probabilities. It is found that the PEER approximation of the probability has a negligible error for probabilities less than about 0.01. For larger probabilities, the error depends on the magnitude of non‐ergodic uncertainties and the duration of time considered and can be as much as 20% for probabilities around 0.05 and 30% for probabilities around 0.10. The error is always on the conservative side. Copyright © 2005 John Wiley & Sons, Ltd.     

Alternative closed‐form solutions for the mean rate of exceedance of structural limit states

Two new closed‐form expressions representing the mean rate of exceedance of a given limit state are presented herein. These proposals overcome limitations that were identified with the original formulation of the well‐known SAC/FEMA approach. The new expressions involve new parametric functions for the modeling of the seismic hazard data and for the demand evolution for increasing values of the earthquake intensity measure. Given the carefully selected parametric form of these functions, mathematical tractability is able to be maintained to establish two new closed‐form solutions representing the mean rate of exceedance of a given limit state. The function proposed for the hazard exhibits nonlinear behavior in log‐log space and is able to represent the actual hazard data over a wider range of earthquake intensity levels. The function proposed for the demand evolution addresses issues related to the inadequate performance of the SAC/FEMA approach when force‐based demand parameters such as the shear force are considered. To illustrate the applicability of the new closed‐form solutions, the probability of occurrence of several limit states is determined for a reinforced concrete structure. Copyright © 2013 John Wiley & Sons, Ltd.     

RC框架结构超强系数与地震经济损失风险分析

基于现行的中国抗震设计规范,设计了6个不同参数的钢筋混凝土框架结构模型,利用静力弹塑性(Pushover)分析方法求得各个框架结构的超强系数;同时,利用基于性能的抗震设计(PBSD)的方法,通过增量动力分析(IDA)、易损性分析和地震损失风险分析等,定量的求出各个框架结构的经济损失风险,并比较了不同框架结构超强系数和经...     

Computational and rapid expected annual loss estimation methodologies for structures

Expected annual loss (EAL), which can be expressed in dollars, is an effective way of communicating the seismic vulnerability of constructed facilities to owners and insurers. A simplified method for estimating EAL without conducting time‐consuming non‐linear dynamic analyses is presented. Relationships between intensity measures and engineering demand parameters resulting from a pushover analysis and a modified capacity‐spectrum method are combined with epistemic and aleatory uncertainties to arrive at a probabilistic demand model. Damage measures are established to determine thresholds for damage states from which loss ratios can be defined. Financial implications due to damage can then be quantified in the form of EAL by integrating total losses for all likely earthquake scenarios. This rapid loss estimation method is verified through the computationally intensive incremental dynamic analysis, with the results processed using a distribution‐free methodology. To illustrate the application of the proposed method, the seismic vulnerability of two highway bridge piers is compared; one bridge is traditionally designed for ductility while the other is based on an emerging damage avoidance design (DAD) philosophy. The DAD pier is found to have a clear advantage over the conventional pier; the EAL of the DAD pier is less than 20% of its ductile counterpart. This is shown to be primarily due to its inherent damage‐free behaviour for small to medium earthquake intensities, whose contribution to EAL is significantly more than that of very rare events. Copyright © 2007 John Wiley & Sons, Ltd.