Reply on RC1

Probabilistic approaches using fragility functions effectively assess building damage caused by major earthquakes and consequent repair costs. Existing fragility functions, however, are limited to reinforced concrete (RC) frames designed according to U.S. standards, making them unsuitable for frames designed according to other design standards. This study addresses this limitation by developing fragility functions for RC frames with interior beam – column joints classified based on joint strength margins. These margins were calculated using the joint ultimate strength relative to the ultimate strengths of beams and columns, enabling evaluations independent of design standards. Damage states (DSs) from DS1 to DS3 were defined to represent residual cracking, concrete damage, and ultimate state, respectively, with DS3 further subdivided into DS3–1 and DS3–2. Relationships between story drift ratios at damage states and joint strength margins were analyzed using Japanese experimental data. RC frames were ranked by joint strength margins, and a Bayesian approach was applied to evaluate fragility function parameters for each DS across these ranks.

Fragility functions for reinforced concrete columns incorporating recycled aggregates

Fragility functions for fully grouted reinforced masonry (RM) walls under in-plane cyclic loading conditions have been systematically developed in this study. Despite the structural advantages of RM over unreinforced masonry, such as increased strength and ductility, fragility assessments considering various damage states under seismic loads have not been adequately investigated. This study bridges this gap through an integrated approach, by combining experimental and numerical data of these walls to enhance the reliability and applicability of the fragility functions developed. The fragility functions of this research were developed from 152 experimental tests on RM walls, enhanced by robust numerical simulations for varied influencing parameters that were missing from the experimental data. The combined datasets facilitated the definition of three distinct damage states: immediate occupancy, life safety and severe damage, where each of them has been linked to specific levels of in-plane drift of walls, which are critical for predicting potential failure modes under seismic conditions. The determined fragility functions indicate that the shear dominated walls are more vulnerable under in-plane loading than the flexural walls. The fragility functions proposed herein represent, a critical advancement in the domain of performance-based seismic design, offering essential insights for the seismic vulnerability and potential losses assessment of RM walling systems. • A detailed experimental database was developed for close-spaced RM shear walls for drift analysis. • Gaps in the experimental database were analysed through numerical method. • Damage states were defined for close-spaced RM walls for seismic fragility analysis. • Seismic fragility was analysed for RM walls for H/L less than and more than 1.

Empirical hurricane fragility assessment of elevated and slab-on-grade residential houses

A second-generation performance-based earthquake engineering (PBEE-2) procedure has been developed by the Pacific Earthquake Engineering Research (PEER) Center and others that estimates the probabilistic future seismic performance of buildings and bridges in terms of system-level decision variables such as repair cost, casualties, and loss of use (dollars, deaths and downtime). The Applied Technology Council has undertaken to transfer the methodology to professional practice [ATC 2005]. The methodology involves four stages: hazard analysis, structural analysis, damage analysis, and loss analysis. This paper addresses the damage analysis, whose inputs are demand parameters calculated in a suite of multiple-degree-of-freedom nonlinear dynamic analyses, and whose output is the damage state of each damageable structural and nonstructural component in the facility. The analysis uses fragility functions, which in this context give the probability that a component, element or system will be damaged to a given or more severe damage state as a function of a single predictive demand parameter such as story drift or floor acceleration. One such fragility function is required for each component type and damage state. Many building-component fragility functions have been created in the past, but no comprehensive set of procedures exists on how to create them. This paper summarizes such a standard developed for ATC-58. See Porter et al. [2006] for more detail, examples, commentary, and alternative approaches.

This work outlines a methodology developed for considering aftershock-induced damage accumulation in seismic loss assessments. In particular, it adapts this methodology to the case of reinforced concrete (RC) frames in mainland France and incorporates it to an already-developed seismic loss assessment model.The methodology consists in dividing the RC buildings into sub-categories of buildings, depending on parameters influencing the vulnerability of the structures. For each category, a set of discrete damage states is defined. For each state Di, fragility functions are derived, enabling to compute the probability of transitioning to another damage state Di+1, knowing the intensity of the ground motion. Therefore, this methodology allows to estimate the final damage state reached by a structure submitted to a series of ground motions.In order to do so, the pool of French RC buildings is analysed so as to create realistic and general models of RC frames. Ground motions are selected from an open database, following some criteria. Fragility functions are then derived (for each type of building) by applying numerous ground motions to the models and assessing the probabilities of reaching each damage state. The methods for constructing those fragility functions are evaluated from the literature. The choice of relevant parameters measuring damage and measuring ground motion intensity is also scrutinized.

Fragility functions are developed to predict the method of repair required for older reinforced concrete beam‐column joints damaged due to earthquake loading. The results of previous experimental studies are used to develop empirical relationships between damage states and engineering demand parameters, such as interstory drift, joint deformation, and number of load cycles. Damage states are proposed and linked deterministically with commonly employed methods of repair; these damage states are characterized by parameters such as concrete crack width, extent of concrete spalling, and yielding and buckling of reinforcement. Probability distributions are fit to the empirical data and evaluated using standard statistical methods. The results of this effort are families of fragility functions that predict the required method of repair for a damaged joint.

ABSTRACTThe seismic vulnerability modelling of different categories of buildings analytically requires methodologies capable of capturing the wide range of building standards, construction practices, architectural layouts, earthquake design scenarios and available knowledge. Current vulnerability models employ varying assessment approaches, building taxonomies, representations of seismic loading and, in some cases, rely on a limited number of archetype structural models to represent an entire building class. Consequently, these structural models are likely to oversimplify the seismic behaviour of an individual building, fail to adequately capture the reality of building‐to‐building variability and inadequately account for multiple sources of uncertainty, particularly when applied to regional contexts. Addressing these issues requires a probabilistic approach where seismic vulnerability is assessed using models of building portfolios that can reflect features related to engineering design practice, as well as construction variability and quality. To achieve this objective, this article introduces a collaborative framework for the simulated design of buildings, along with the open‐source software package developed for its integration into the Built Environment Data initiative, a planned service within the European Plate Observing System. The simulated design framework accommodates the design of buildings using both historical and modern seismic design procedures and regulations, while capturing building‐to‐building variability. Following the design process, the framework generates OpenSees computational models for nonlinear analysis, facilitating the development of probabilistic seismic demand models, fragility functions and vulnerability models. The framework's capabilities are demonstrated through examples that highlight notable distinctions among the building classes under consideration and emphasise the importance of the attributes involved in the design process. The collaborative nature of the framework presented here enables the earthquake engineering community to contribute to a growing database of seismic design practices, encompassing a wide range of design codes.

Fragility functions have been developed to evaluate the damageability of fully grouted and partially grouted reinforced masonry shear walls subjected to in-plane seismic loading. Six damage states are considered, representing different levels of flexure, diagonal shear, and sliding shear damage. For each damage state, two classes of fragility functions have been developed. One has the story-drift ratio as the demand parameter. The other uses normalized demand parameters that account for the specific loading condition and design details of a wall component. All the fragility functions are derived from experimental data except for those developed for partially grouted walls and the sliding shear damage state. With both classes of fragility functions, the seismic damageability of flexure-dominated cantilever reinforced masonry shear walls in a four-story building has been assessed. It has been shown that the normalized flexural demand parameter provides a better correlation to the degree of damage developed in a wall than the story-drift ratio.

Fragility functions for masonry infill walls in RC frames with the in-plane and out-of-plane loading

SummarySecond‐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 Sa(T1) does not improve the fragility functions. Copyright © 2015 John Wiley & Sons, Ltd.

Indonesia has significant wind energy resources, making it the second-largest renewable energy potential after solar. According to the National Energy Council of Indonesia, Selayar Islands waters is one of the potential areas for developing wind energy. One of the technologies that has been developed for offshore wind power generation is the NREL 5MW. With the higher potential of offshore wind energy, designing longer-lasting structures is essential due to the cyclic environmental load that may reduce their service life. The purpose of this study is to determine the service life based on fatigue analysis using dynamic fatigue and the cumulative damage method in jacket offshore wind turbines.

<p>In scenario-based and probabilistic single-hazard risk and loss estimation over urban building portfolios, it is customary to use specific exposure/vulnerability schemas that entail a set of mutually exclusive, collectively exhaustive (MECE) building classes, each associated with a fragility/vulnerability model focusing on the specific reference hazard., In a multi-risk application, where the same built structure can be subjected to the action of different natural hazards, possibly in close succession, a number of different schemas should be then jointly applied. Another option would be using a single set of building classes with as many fragility / vulnerability models as the considered natural hazards, as in the case for instance of the HAZUS multi-hazard framework. Unfortunately the latter approach requires a multi-hazard calibration that is rarely attainable with consistent results, while the former approach is complicated by the need for harmonizing different types of building classes. Furthermore, although fragility surfaces for independent hazards have been recently reported, they do not consider the nonlinear contribution of the different failure mechanisms (e.g. earthquake and tsunami) to the overall damage of a single asset. A timely update of the exposure model accounting for the progressive damage accumulation, thus describing a dynamic vulnerability framework, is then required.</p> <p>We propose an alternative, innovative approach based on three main components: 1) a comprehensive multi-hazard building taxonomy able to address most of the building attributes driving the vulnerability with respect to different hazards, 2) a generalized description of the damage state of a building based on a set of low-level observable damage types and 3) a methodology to implement probabilistic mapping across different hazard-dependent building schemas and damage states.</p> <p>A matrix describing the degree of compatibility between building types from two different schemas is estimated, partially making use of the fuzzy scores methodology suggested by Pittore et al., 2018. Since two building schemas may have different number of damage states (e.g. four in seismic, and six in tsunami), and are associated to different physical damage descriptions, the probability of the damage states conversion between the different schemas is also required.</p> <p>This transparent and flexible formulation allows the implementation of multi-risk scenario assessment exploiting single-risk fragility/vulnerability models available in literature for a wide range of natural hazards. A preliminary state-dependency of these fragility models is based on expert knowledge. This work has been carried out within the scope of the RIESGOS project and exemplified in a study area in South America and further highlights the importance of defining accurate exposure models and compatible damage states descriptions in a multi- hazard-risk context. </p>

Seismic fragility of Italian RC precast industrial structures

Chapter 20 - Multihazard risk assessments