Variability and uncertainty in empirical ground-motion prediction for probabilistic hazard and risk analyses

© The Author(s) 2015.The terms aleatory variability and epistemic uncertainty mean different things to people who routinely use them within the fields of seismic hazard and risk analysis. This state is not helped by the repetition of loosely framed generic definitions that actually inaccurate. The present paper takes a closer look at the components of total uncertainty that contribute to ground-motion modelling in hazard and risk applications. The sources and nature of uncertainty are discussed and it is shown that the common approach to deciding what should be included within hazard and risk integrals and what should be pushed into logic tree formulations warrants reconsideration. In addition, it is shown that current approaches to the generation of random fields of ground motions for spatial risk analyses are incorrect and a more appropriate framework is presented

Bayesian Network Enhanced with Structural Reliability Methods: Methodology

We combine Bayesian networks (BNs) and structural reliability methods (SRMs) to create a new computational framework, termed enhanced Bayesian network (eBN), for reliability and risk analysis of engineering structures and infrastructure. BNs are efficient in representing and evaluating complex probabilistic dependence structures, as present in infrastructure and structural systems, and they facilitate Bayesian updating of the model when new information becomes available. On the other hand, SRMs enable accurate assessment of probabilities of rare events represented by computationally demanding, physically-based models. By combining the two methods, the eBN framework provides a unified and powerful tool for efficiently computing probabilities of rare events in complex structural and infrastructure systems in which information evolves in time. Strategies for modeling and efficiently analyzing the eBN are described by way of several conceptual examples. The companion paper applies the eBN methodology to example structural and infrastructure systems

Data-driven post-earthquake rapid structural safety assessment

Earthquake prone cities are exposed to important societal and financial losses. An important part of these losses stems from the inability to use structures as shelters or for generating economic activity after the event of an earthquake. The inability to use structures is not only due to collapse or damage; it is also due to the lack of knowledge about their safety state, which prohibits their normal use. Because a diagnosis is required for thousands of structures, city-scale safety assessment requires solutions that are economically sustainable and scalable. Data-driven algorithms supported by sensing technologies have the potential to solve this challenge. Several ambient vibration monitoring studies of buildings, before and after earthquakes, have shown that the extent of damage in a building is correlated with a decrease in the natural frequency. However, the observed worldwide data may not be representative of specific cities due to factors such as construction type, quality, material, age, etc. In this paper we propose a framework that is able to progressively learn the relationship between frequency shift and damage state as a small number of buildings in a city are inspected after an earthquake, and to use that information to predict the safety state of uninspected but monitored buildings. The capacity of the proposed framework to learn and perform prognosis is validated by applying the methodology to a city with 1000 buildings having simulated frequency shifts and damage states

Survival signature-based sensitivity analysis of systems with epistemic uncertainties

The survival signature provides a basis for efficient reliability assessment of systems with more than one component type. Often a perfect probabilistic modelling of the system is not possible due to limited information, vagueness and imprecision. Hence generalized probabilistic methods need to be used. These methods allow to explicitly model the uncertainties without the need of unjustified hypotheses and approximation. In this paper, a novel and efficient sensitivity approach is presented. The proposed approach is based on survival signature, allowing to identify and rank components in a system. A numerical example is used to illustrate the above methods

Risk and sensitivity quantification of fracture failure employing cohesive zone elements

Many structures are subjected to the risk of fatigue failure. For their reliability-based design, it is thus important to calculate the probability of fatigue failure and assess the relative importance of the involved parameters. Although various studies have analyzed the fatigue failure, the stage of fracture failure has been less focused. In particular, the risk analysis of fracture failure needs to be conducted considering its importance in actual structures. This article proposes a new probabilistic framework for the risk and sensitivity analysis of structural fatigue failure employing cohesive zone elements. The proposed framework comprises three steps, namely finite element analysis using cohesive zone elements, response surface construction, and risk and sensitivity analysis of fatigue failure, which require several mathematical techniques and algorithms. The proposed framework is tested by applying it to an illustrative example, and the corresponding analysis results of fracture failure probability with different threshold values of a limit-state function are presented. In addition, the sensitivities of failure risk with respect to the statistical parameters of random variables are presented and their relative importance is discussed

Wavelet-based response spectrum compatible synthesis of accelerograms-Eurocode application (EC8)

An integrated approach for addressing the problem of synthesizing artificial seismic accelerograms compatible with a given displacement design/target spectrum is presented in conjunction with aseismic design applications. Initially, a stochastic dynamics solution is used to obtain a family of simulated non-stationary earthquake records whose response spectrum is on the average in good agreement with the target spectrum. The degree of the agreement depends significantly on the adoption of an appropriate parametric evolutionary power spectral form, which is related to the target spectrum in an approximate manner. The performance of two commonly used spectral forms along with a newly proposed one is assessed with respect to the elastic displacement design spectrum defined by the European code regulations (EC8). Subsequently, the computational versatility of the family of harmonic wavelets is employed to modify iteratively the simulated records to satisfy the compatibility criteria for artificial accelerograms prescribed by EC8. In the process, baseline correction steps, ordinarily taken to ensure that the obtained accelerograms are characterized by physically meaningful velocity and displacement traces, are elucidated. Obviously, the presented approach can be used not only in the case of the EC8, for which extensive numerical results/examples are included, but also for any code provisions mandated by regulatory agencies. In any case, the presented numerical results can be quite useful in any aseismic design process dominated by the EC8 specifications

Flood fragility analysis for bridges with multiple failure modes

Bridges are one of the most important infrastructure systems that provide public and economic bases for humankind. It is also widely known that bridges are exposed to a variety of flood-related risk factors such as bridge scour, structural deterioration, and debris accumulation, which can cause structural damage and even failure of bridges through a variety of failure modes. However, flood fragility has not received as much attention as seismic fragility despite the significant amount of damage and costs resulting from flood hazards. There have been few research efforts to estimate the flood fragility of bridges considering various flood-related factors and the corresponding failure modes. Therefore, this study proposes a new approach for bridge flood fragility analysis. To obtain accurate flood fragility estimates, reliability analysis is performed in conjunction with finite element analysis, which can sophisticatedly simulate the structural response of a bridge under a flood by accounting for flood-related risk factors. The proposed approach is applied to a numerical example of an actual bridge in Korea. Flood fragility curves accounting for multiple failure modes, including lack of pier ductility or pile ductility, pier rebar rupture, pile rupture, and deck loss, are derived and presented in this study.ope

A novel stochastic linearization framework for seismic demand estimation of hysteretic MDOF systems subject to linear response spectra

This paper proposes a novel computationally economical stochastic dynamics framework to estimate the peak inelastic response of yielding structures modelled as nonlinear multi degreeof-freedom (DOF) systems subject to a given linear response spectrum defined for different damping ratios. This is accomplished without undertaking nonlinear response history analyses (RHA) or, to this effect, constructing an ensemble of spectrally matched seismic accelerograms. The proposed approach relies on statistical linearization and enforces pertinent statistical conditions to decompose the inelastic d-DOF system into d linear single DOF oscillators with effective linear properties (ELPs): natural frequency and damping ratio. Each such oscillator is subject to a different stationary random process compatible with the excitation response spectrum with damping ratio equal to the oscillator effective critical damping ratio. This equality is achieved through a small number of iterations to a pre-specified tolerance, while peak inelastic response estimates for all DOFs of interest are obtained by utilization of the excitation response spectrum in conjunction with the ELPs. The applicability of the proposed framework is numerically illustrated using a 3-storey Bouc-Wen hysteretic frame structure exposed to the Eurocode 8 elastic response spectrum. Nonlinear RHA involving a large ensemble of non-stationary Eurocode 8 spectrum compatible accelerograms is conducted to assess the accuracy of the proposed approach in a Monte Carlo-based context. It is found that the novel feature of iterative matching between the excitation response spectrum damping ratio and the ELP damping ratio reduces drastically the error of the estimates (i.e., by an order of magnitude) obtained by non-iterative application of the framework