Probabilistic permanent fault displacement hazard via Monte Carlo simulation and its consideration for the probabilistic risk assessment of buried continuous steel pipelines

Permanent fault displacements (PFDs) because of fault ruptures emerging at the surface are critical for seismic design and risk assessment of continuous pipelines. They impose significant compressive and tensile strains to the pipe cross‐section at pipe‐fault crossings. The complexity of fault rupture, inaccurate mapping of fault location and uncertainties in fault‐pipe crossing geometries require probabilistic approaches for assessing the PFD hazard and mitigating pipeline failure risk against PFD. However, the probabilistic approaches are currently waived in seismic design of pipelines. Bearing on these facts, this paper first assesses the probabilistic PFD hazard by using Monte Carlo‐based stochastic simulations whose theory and implementation are given in detail. The computed hazard is then used in the probabilistic risk assessment approach to calculate the failure probability of continuous pipelines under different PFD levels as well as pipe cross‐section properties. Our probabilistic pipeline risk computations consider uncertainties arising from complex fault rupture and geomorphology that result in inaccurate mapping of fault location and fault‐pipe crossings. The results presented in this paper suggest the re‐evaluation of design provisions in current pipeline design guidelines to reduce the seismic risk of these geographically distributed structural systems. Copyright © 2016 John Wiley & Sons, Ltd.     

A simulation‐based framework for risk assessment and probabilistic sensitivity analysis of base‐isolated structures

A versatile, simulation‐based framework for risk assessment and probabilistic sensitivity analysis of base‐isolated structures is discussed in this work. A probabilistic foundation is used to address the various sources of uncertainties, either excitation or structural, and to characterize seismic risk. This risk is given, in this stochastic setting, by some statistics of the system response over the adopted probability models and stochastic simulation is implemented for its evaluation. An efficient, sampling‐based approach is also introduced for establishing a probabilistic sensitivity analysis to identify the importance of each of the uncertain model parameters in affecting the overall risk. This framework facilitates use of complex models for the structural system and the excitation. The adopted structural model explicitly addresses nonlinear characteristics of the isolators and of any supplemental dampers, and the effect of seismic pounding of the base to the surrounding retaining walls. An efficient stochastic ground motion model is also discussed for characterizing future near‐fault ground motions and relating them to the seismic hazard for the structural site. An illustrative example is presented that emphasizes the results from the novel probabilistic sensitivity analysis and their dependence on seismic pounding occurrences and on addition of supplemental dampers. Copyright © 2011 John Wiley & Sons, Ltd.     

Alternative non‐linear demand estimation methods for probability‐based seismic assessments

Alternative non‐linear dynamic analysis procedures, using real ground motion records, can be used to make probability‐based seismic assessments. These procedures can be used both to obtain parameter estimates for specific probabilistic assessment criteria such as demand and capacity factored design and also to make direct probabilistic performance assessments using numerical methods. Multiple‐stripe analysis is a non‐linear dynamic analysis method that can be used for performance‐based assessments for a wide range of ground motion intensities and multiple performance objectives from onset of damage through global collapse. Alternatively, the amount of analysis effort needed in the performance assessments can be reduced by performing the structural analyses and estimating the main parameters in the region of ground motion intensity levels of interest. In particular, single‐stripe and double‐stripe analysis can provide local probabilistic demand assessments using minimal number of structural analyses (around 20 to 40). As a case study, the displacement‐based seismic performance of an older reinforced concrete frame structure, which is known to have suffered shear failure in its columns during the 1994 Northridge Earthquake, is evaluated. Copyright © 2008 John Wiley & Sons, Ltd.     

Probabilistic performance‐based optimum design of seismic isolation for a California high‐speed rail prototype bridge

Previous comparison studies on seismic isolation have demonstrated its beneficial and detrimental effects on the structural performance of high‐speed rail bridges during earthquakes. Striking a balance between these 2 competing effects requires proper tuning of the controlling design parameters in the design of the seismic isolation system. This results in a challenging problem for practical design in performance‐based engineering, particularly when the uncertainty in seismic loading needs to be explicitly accounted for. This problem can be tackled using a novel probabilistic performance‐based optimum seismic design (PPBOSD) framework, which has been previously proposed as an extension of the performance‐based earthquake engineering methodology. For this purpose, a parametric probabilistic demand hazard analysis is performed over a grid in the seismic isolator parameter space, using high‐throughput cloud‐computing resources, for a California high‐speed rail (CHSR) prototype bridge. The derived probabilistic structural demand hazard results conditional on a seismic hazard level and unconditional, i.e., accounting for all seismic hazard levels, are used to define 2 families of risk features, respectively. Various risk features are explored as functions of the key isolator parameters and are used to construct probabilistic objective and constraint functions in defining well‐posed optimization problems. These optimization problems are solved using a grid‐based, brute‐force approach as an application of the PPBOSD framework, seeking optimum seismic isolator parameters for the CHSR prototype bridge. This research shows the promising use of seismic isolation for CHSR bridges, as well as the potential of the versatile PPBOSD framework in solving probabilistic performance‐based real‐world design problems.     

An efficient algorithm for identifying pulse‐like ground motions based on significant velocity half‐cycles

Ground motions with strong velocity pulses are of particular interest to structural earthquake engineers because they have the potential to impose extreme seismic demands on structures. Accurate classification of records is essential in several earthquake engineering fields where pulse‐like ground motions should be distinguished from nonpulse‐like records, such as probabilistic seismic hazard analysis and seismic risk assessment of structures. This study proposes an effective method to identify pulse‐like ground motions having single, multiple, or irregular pulses. To effectively characterize the intrinsic pulse‐like features, the concept of an energy‐based significant velocity half‐cycle, which is visually identifiable, is first presented. Ground motions are classified into 6 categories according to the number of significant half‐cycles in the velocity time series. The pulse energy ratio is used as an indicator for quantitative identification, and then the energy threshold values for each type of ground motions are determined. Comprehensive comparisons of the proposed approach with 4 benchmark identification methods are conducted, and the results indicate that the methodology presented in this study can more accurately and efficiently distinguish pulse‐like and nonpulse‐like ground motions. Also presented are some insights into the reasons why many pulse‐like ground motions are not detected successfully by each of the benchmark methods.     

Effects of two alternative representations of ground‐motion uncertainty on probabilistic seismic demand assessment of structures

A probabilistic representation of the entire ground‐motion time history can be constructed based on a stochastic model that depends on seismic source parameters. An advanced stochastic simulation scheme known as Subset Simulation can then be used to efficiently compute the small failure probabilities corresponding to structural limit states. Alternatively, the uncertainty in the ground motion can be represented by adopting a parameter (or a vector of parameters) known as the intensity measure (IM) that captures the dominant features of the ground shaking. Structural performance assessment based on this representation can be broken down into two parts, namely, the structure‐specific part requiring performance assessment for a given value of the IM, and the site‐specific part requiring estimation of the likelihood that ground shaking with a given value of the IM takes place. The effect of these two alternative representations of ground‐motion uncertainty on probabilistic structural response is investigated for two hazard cases. In the first case, these two approaches are compared for a scenario earthquake event with a given magnitude and distance. In the second case, they are compared using a probabilistic seismic hazard analysis to take into account the potential of the surrounding faults to produce events with a range of possible magnitudes and distances. The two approaches are compared on the basis of the probabilistic response of an existing reinforced‐concrete frame structure, which is known to have suffered shear failure in its columns during the 1994 Northridge Earthquake in Los Angeles, California. Copyright © 2007 John Wiley & Sons, Ltd.     

A practice‐oriented estimation of the failure probability of building structures

In the presented practice‐oriented probabilistic approach for the seismic performance assessment of building structures, the SAC‐FEMA method, which is a part of the broader PEER probabilistic framework and permits probability assessment in closed form, is combined with the pushover‐based N2 method. The most demanding part of the PEER probabilistic framework, that is incremental dynamic analysis, is replaced by the much simpler N2 method, which requires considerably less input data and much less computational time, but which can, nevertheless, often provide: acceptable estimates for the mean values of the structural response. Using some additional simplifying assumptions that are consistent with seismic code procedures, an explicit equation for a quick estimation of the annual probability of “failure” (i.e. the probability of exceeding the near collapse limit state) of a structure can be derived, which is appropriate for practical applications, provided that predetermined default values for the dispersion measures are available. In the paper, this simplified approach is summarized and applied to the estimation of the “failure” probability of reinforced concrete frame buildings representing both old structures, not designed for earthquake resistance, and new structures designed according to Eurocode 8. The results of the analyses indicate a high probability of the “failure” of buildings, which have not been designed for seismic loads. For a building designed according to a modern code, the conservatively determined probability of “failure” is about 30 times less but still significant (about 1% over the lifetime of the structure). Copyright © 2011 John Wiley & Sons, Ltd.     

Approximate seismic risk assessment of building structures with explicit consideration of uncertainties

An approximate seismic risk assessment procedure for building structures, which involves pushover analysis that is performed utilizing a deterministic structural model and uncertainty analysis at the level of the equivalent SDOF model, is introduced. Such an approach is computationally significantly less demanding in comparison with procedures based on uncertainty analysis at the level of the entire structure, but still allows for explicit consideration of the effect of record‐to‐record variability and modelling uncertainties. A new feature of the proposed pushover‐based method is the so‐called probabilistic SDOF model. Herein, the proposed methodology is illustrated only for reinforced concrete (RC) frames, although it could be implemented in the case of any building structure, provided that an appropriate probabilistic SDOF model is available. An extensive parametric analysis has been performed within the scope of this study in order to develop a probabilistic SDOF model, which could be used for the seismic risk assessment of both code‐conforming and old, that is, non code‐conforming RC frames. Based on the results of risk analysis for the four selected examples, it is shown that the proposed procedure can provide conservative estimates of seismic risk with reasonable accuracy, in spite of the employed simplifications and the relatively small number of Monte Carlo simulations with Latin hypercube sampling, which are performed at the level of the SDOF model. An indication of the possible default values of dispersion measures for limit‐state intensities in the case of low to medium‐height RC frames is also presented. Copyright © 2014 John Wiley & Sons, Ltd.     

Intensity measures for probabilistic assessment of non‐structural components acceleration demand

A fundamental issue in the framework of seismic probabilistic risk analysis is the choice of ground motion intensity measures (IMs). Based on the floor response spectrum method, the present contribution focuses on the ability of IMs to predict non‐structural components (NSCs) horizontal acceleration demand. A large panel of IMs is examined and a new IM, namely equipment relative average spectral acceleration (E‐ASA_R), is proposed for the purpose of NSCs acceleration demand prediction. The IMs efficiency and sufficiency comparisons are based on (i) the use of a large dataset of recorded earthquake ground motions; (ii) numerical analyses performed on three‐dimensional numerical models, representing actual structural wall and frame buildings; and (iii) systematic statistical analysis of the results. From the comparative study, the herein introduced E‐ASA_R shows high efficiency with respect to the estimation of maximum floor response spectra ordinates. Such efficiency is particularly remarkable in the case of structural wall buildings. Besides, the sufficiency and the simple formulation allowing the use of existing ground motion prediction models make the E‐ASA_R a promising IMs for seismic probabilistic risk assessment. Copyright © 2015 John Wiley & Sons, Ltd.     

Evaluation of a recently proposed record selection and scaling procedure for low‐rise to mid‐rise reinforced concrete buildings and its use for probabilistic risk assessment studies

This paper evaluates a recent record selection and scaling procedure of the authors that can determine the probabilistic structural response of buildings behaving either in the elastic or post‐elastic range. This feature marks a significant strength on the procedure as the probabilistic structural response distribution conveys important information on probability‐based damage assessment. The paper presents case studies that show the utilization of the proposed record selection and scaling procedure as a tool for the estimation of damage states and derivation of site‐specific and region‐specific fragility functions. The method can be used to describe exceedance probabilities of damage limits under a certain target hazard level with known annual exceedance rate (via probabilistic seismic hazard assessment). Thus, the resulting fragility models can relate the seismicity of the region (or a site) with the resulting building performance in a more accurate manner. Under this context, this simple and computationally efficient record selection and scaling procedure can be benefitted significantly by probability‐based risk assessment methods that have started to be considered as indispensable for developing robust earthquake loss models. Copyright © 2013 John Wiley & Sons, Ltd.     

汶川地区震后钢筋混凝土框架结构的地震易损性研究

以汶川地震为研究背景,针对震后典型钢筋混凝土框架结构进行地震易损性研究。基于Cornell理论框架结合汶川地质资料,拟合出考虑场地特点的地震危险性模型,同时定义损伤水平状态及限值指标,以概率解析易损性研究方法为基础,运用考虑地震动参数的解析易损性评估方法绘制汶川地区钢筋混凝土框架建筑的地震易损性曲线。研究结果表明:考虑地震动参数的概率解析易损性研究方法是一种有效的地震易损性评估方法;以PGA作为地震强度输入指标的结构反应,随自振周期的增大体系最大响应的相关性降低,结构各个损伤状态的失效概率均随之增大。     

Markovian modeling of seismic damage accumulation

Analysis of civil structures at the scale of life‐cycle requires stochastic modeling of degradation. Phenomena causing structures to degrade are typically categorized as aging and point‐in‐time overloads. Earthquake effects are the members of the latter category this study deals with in the framework of performance‐based earthquake engineering (PBEE). The focus is structural seismic reliability, which requires modeling of the stochastic process describing damage progression, because of subsequent events, over time. The presented study explicitly addresses this issue via a Markov‐chain‐based approach, which is able to account for the change in seismic response of damaged structures (i.e. state‐dependent seismic fragility) as well as uncertainty in occurrence and intensity of earthquakes (i.e. seismic hazard). The state‐dependent vulnerability issue arises when the seismic hysteretic response is evolutionary and/or when the damage measure employed is such that the degradation increment probabilistically depends on the conditions of the structure at the time of the shock. The framework set up takes advantage also of the hypotheses of classical probabilistic seismic hazard analysis, allowing to separate the modeling of the process of occurrence of seismic shocks and the effect they produce on the structure. It is also discussed how the reliability assessment, which is in closed‐form, may be virtually extended to describe a generic age‐ and state‐dependent degradation process (e.g. including aging and/or when aftershock risk is of interest). Illustrative applications show the options to calibrate the model and its potential in the context of PBEE. Copyright © 2015 John Wiley & Sons, Ltd.     

A probabilistic framework for correlated seismic downtime and repair cost estimation of geo‐structures

An important component of probabilistic risk assessment methods is the development of models to quantify the direct consequences of damage to geo‐structural components for a given intensity of the hazard. This paper presents a general probabilistic framework for correlated repair cost and downtime estimation of geo‐structures exposed to seismic hazards. The framework uses as input the results of nonlinear time‐history analysis of geo‐structures for the set of earthquake records that are representative of the seismic hazard models for the region of interest. The repair cost and downtime are estimated for individual earthquakes probabilistically considering the uncertainties associated with damage states. In addition, the formulation of the repair cost and downtime accounts for the reduction in the repair requirements as the number of damaged components in the given damage state increases. An analytical linear and two bilinear regression models are proposed for conditional correlated seismic repair cost and downtime estimation of geo‐structures given the intensity measure. The proposed framework is demonstrated by developing seismic repair models of a typical pile‐supported wharf structure on the west coast of the United States. The presented framework is general and can be applied to other types of geo‐structures and hazards and can include other decision variables such as loss of life as well. Copyright © 2013 John Wiley & Sons, Ltd.     

A methodology for the probabilistic assessment of behaviour factors

Given the importance that traditional force-based seismic design still currently exhibits, studies addressing issues related to the definition of the behaviour factor values are considered to be of most interest. A probabilistic methodology is proposed for the calibration of the q-factor relating its value with two fundamental parameters, the displacement ductility capacity measured at a relevant location of the structure and the failure probability P _f . The general foundation of this procedure is based on the probabilistic quantification of the seismic action and, by applying a transformation procedure, of the structural seismic demand in terms of displacement ductility. By recalling well established structural reliability procedures and by making use of nonlinear analysis methods, both static and dynamic, a general probabilistic framework, which is able to relate the ductility capacity, the failure probability P _f and the behaviour factor, is defined. In order to illustrate some of the potentialities of the methodology, an application example is presented, addressing the q-factor assessment for a set of regular and irregular reinforced concrete frame structures, enforcing a given P _f and two different ductility levels.     

Probabilistic seismic demand model for pounding risk assessment

Earthquake‐induced pounding of adjacent structures can cause severe structural damage, and advanced probabilistic approaches are needed to obtain a reliable estimate of the risk of impact. This study aims to develop an efficient and accurate probabilistic seismic demand model (PSDM) for pounding risk assessment between adjacent buildings, which is suitable for use within modern performance‐based engineering frameworks. In developing a PSDM, different choices can be made regarding the intensity measures (IMs) to be used, the record selection, the analysis technique applied for estimating the system response at increasing IM levels, and the model to be employed for describing the response statistics given the IM. In the present paper, some of these choices are analyzed and evaluated first by performing an extensive parametric study for the adjacent buildings modeled as linear single‐degree‐of‐freedom systems, and successively by considering more complex nonlinear multi‐degree‐of‐freedom building models. An efficient and accurate PSDM is defined using advanced intensity measures and a bilinear regression model for the response samples obtained by cloud analysis. The results of the study demonstrate that the proposed PSDM allows accurate estimates of the risk of pounding to be obtained while limiting the number of simulations required. Copyright © 2016 John Wiley & Sons, Ltd.     

Practice‐oriented estimation of the seismic demand hazard using ground motions at few intensity levels

This paper examines the calculation of the seismic demand hazard in a practice‐oriented manner via the use of seismic response analyses at few intensity levels. The seismic demand hazard is a more robust measure for quantifying seismic performance, when seismic hazard is represented in a probabilistic format, than intensity‐based assessments, which remain prevalent in seismic design codes. It is illustrated that, for a relatively complex bridge–foundation–soil system case study, the seismic demand hazard can be estimated with sufficient accuracy using as little as three intensity measure levels that have exceedance probabilities of 50%, 10% and 2% in 50 years which are already of interest in multi‐objective performance‐based design. Compared with the conventional use of the mean demand from an intensity‐based assessment(s), it is illustrated that, for the same number of seismic response analyses, a practice‐oriented ‘approximate’ seismic demand hazard is a more accurate and precise estimate of the ‘exact’ seismic demand hazard. Direct estimation of the seismic demand hazard also provides information of seismic performance at multiple exceedance rates. Thus, it is advocated that if seismic hazard is considered in a probabilistic format, then seismic performance assessment, and acceptance criteria, should be in terms of the seismic demand hazard and not intensity‐based assessments. Copyright © 2013 John Wiley & Sons, Ltd.     

Expected loss‐based alarm threshold set for earthquake early warning systems

Earthquake early warning systems (EEWS) seem to have potential as tools for real‐time seismic risk management and mitigation. In fact, although the evacuation of buildings requires warning time not available in many urbanized areas threatened by seismic hazard, they may still be used for the real‐time protection of critical facilities using automatic systems in order to reduce the losses subsequent to a catastrophic event. This is possible due to the real‐time seismology, which consists of methods and procedures for the rapid estimation of earthquake features, as magnitude and location, based on measurements made on the first seconds of the P‐waves. An earthquake engineering application of earthquake early warning (EEW) may be intended as a system able to issue the alarm, if some recorded parameter exceeds a given threshold, to activate risk mitigation actions before the quake strikes at a site of interest. Feasibility analysis and design of such EEWS require the assessment of the expected loss reduction due to the security action and set of the alarm threshold. In this paper a procedure to carry out these tasks in the performance‐based earthquake engineering probabilistic framework is proposed. A merely illustrative example refers to a simple structure assumed to be a classroom. Structural damage and non‐structural collapses are considered; the security action is to shelter occupants below the desks. The cost due to a false alarm is assumed to be related to the interruption of didactic activities. Results show how the comparison of the expected losses, for the alarm‐issuance and non‐issuance cases, allows setting the alarm threshold on a quantitative and consistent basis, and how it may be a tool for the design of engineering applications of EEW. Copyright © 2007 John Wiley & Sons, Ltd.     

Kriging metamodeling in seismic risk assessment based on stochastic ground motion models

An efficient computational framework is presented for seismic risk assessment within a modeling approach that utilizes stochastic ground motion models to describe the seismic hazard. The framework is based on the use of a kriging surrogate model (metamodel) to provide an approximate relationship between the structural response and the structural and ground motion parameters that are considered as uncertain. The stochastic character of the excitation is addressed by assuming that under the influence of the white noise (used within the ground motion model) the response follows a lognormal distribution. Once the surrogate model is established, a task that involves the formulation of an initial database to inform the metamodel development, it is then directly used for all response evaluations required to estimate seismic risk. The model prediction error stemming from the metamodel is directly incorporated within the seismic risk quantification and assessment, whereas an adaptive approach is developed to refine the database that informs the metamodel development. The ability to efficiently obtain derivative information through the kriging metamodel and its utility for various tasks within the probabilistic seismic risk assessment is also discussed. As an illustrative example, the assessment of seismic risk for a benchmark four‐story concrete office building is presented. The potential that ground motions include near‐fault characteristics is explicitly addressed within the context of this example. The implementation of the framework for the same structure equipped with fluid viscous dampers is also demonstrated. Copyright © 2015 John Wiley & Sons, Ltd.     

Dispersions for the pushover‐based risk assessment of reinforced concrete frames and cantilever walls

The paper presents the results of an investigation into the dispersion values, expressed in terms of limit‐state spectral accelerations, which could be used for the pushover‐based risk assessment of low‐height to mid‐height reinforced concrete frames and cantilever walls. The results of an extensive parametric study of a portfolio of test structures indicated that the dispersion values due to record‐to‐record variability and modelling uncertainty (β_LS,RU) are within the range from 0.3 to 0.55 for the near collapse limit state, and between 0.35 and 0.60 for the collapse limit state. The dispersions β_LS,RU proposed for the code‐conforming and the majority of old (non code‐conforming) frames are in between these values. On the other hand, the dispersions proposed for the old frames with a soft storey and an invariant plastic mechanism, and for the code‐conforming cantilever walls, are at the lower and upper bounds of the presented values, respectively. The structural parameters that influence these dispersions were identified, and the influence of different ground motion sets, and of the models used for the calculation of the rotation capacities of the columns, on the calculated fragility parameters was examined and quantified. The proposed dispersion values were employed in a practice‐oriented pushover‐based method for the estimation of failure probability for eight selected examples. The pushover‐based risk assessment method, although extremely simple and economical when compared with more rigorous probabilistic methods, was able to predict seismic risk with reasonable accuracy, thus showing it to be a practical tool for engineers. Copyright © 2016 John Wiley & Sons, Ltd.     

Application of a Monte‐Carlo simulation approach for the probabilistic assessment of seismic hazard for geographically distributed portfolio

The conventional integral approach is very well established in probabilistic seismic hazard assessment (PSHA). However, Monte‐Carlo (MC) simulations can become an efficient and flexible alternative against conventional PSHA when more complicated factors (e.g. spatial correlation of ground shaking) are involved. This study aims at showing the implementation of MC simulation techniques for computing the annual exceedance rates of dynamic ground‐motion intensity measures (GMIMs) (e.g. peak ground acceleration and spectral acceleration). We use multi‐scale random field technique to incorporate spatial correlation and near‐fault directivity while generating MC simulations to assess the probabilistic seismic hazard of dynamic GMIMs. Our approach is capable of producing conditional hazard curves as well. We show various examples to illustrate the potential use of the proposed procedures in the hazard and risk assessment of geographically distributed structural systems. Copyright © 2015 John Wiley & Sons, Ltd.