Improved ground motion intensity measures for reliability-based demand analysis of structures

In Performance-Based Earthquake Engineering (PBEE), evaluating the seismic performance (or seismic risk) of a structure at a designed site has gained major attention, especially in the past decade. One of the objectives in PBEE is to quantify the seismic reliability of a structure (due to the future random earthquakes) at a site. For that purpose, Probabilistic Seismic Demand Analysis (PSDA) is utilized as a tool to estimate the Mean Annual Frequency (MAF) of exceeding a specified value of a structural Engineering Demand Parameter (EDP). This dissertation focuses mainly on applying an average of a certain number of spectral acceleration ordinates in a certain interval of periods, Sa,avg (T1,…,Tn), as scalar ground motion Intensity Measure (IM) when assessing the seismic performance of inelastic structures. Since the interval of periods where computing Sa,avg is related to the more or less influence of higher vibration modes on the inelastic response, it is appropriate to speak about improved IMs. The results using these improved IMs are compared with a conventional elastic-based scalar IMs (e.g., pseudo spectral acceleration, Sa ( T(¹)), or peak ground acceleration, PGA) and the advanced inelastic-based scalar IM (i.e., inelastic spectral displacement, Sdi). The advantages of applying improved IMs are: (i ) "computability" of the seismic hazard according to traditional Probabilistic Seismic Hazard Analysis (PSHA), because ground motion prediction models are already available for Sa (Ti), and hence it is possibile to employ existing models to assess hazard in terms of Sa,avg, and (ii ) "efficiency" or smaller variability of structural response, which was minimized to assess the optimal range to compute Sa,avg. More work is needed to assess also "sufficiency" and "scaling robustness" desirable properties, which are disregarded in this dissertation. However, for ordinary records (i.e., with no pulse like effects), using the improved IMs is found to be more accurate than using the elastic- and inelastic-based IMs. For structural demands that are dominated by the first mode of vibration, using Sa,avg can be negligible relative to the conventionally-used Sa (T(¹)) and the advanced Sdi. For structural demands with sign.cant higher-mode contribution, an improved scalar IM that incorporates higher modes needs to be utilized. In order to fully understand the influence of the IM on the seismis risk, a simplified closed-form expression for the probability of exceeding a limit state capacity was chosen as a reliability measure under seismic excitations and implemented for Reinforced Concrete (RC) frame structures. This closed-form expression is partuclarly useful for seismic assessment and design of structures, taking into account the uncertainty in the generic variables, structural "demand" and "capacity" as well as the uncertainty in seismic excitations. The assumed framework employs nonlinear Incremental Dynamic Analysis (IDA) procedures in order to estimate variability in the response of the structure (demand) to seismic excitations, conditioned to IM. The estimation of the seismic risk using the simplified closed-form expression is affected by IM, because the final seismic risk is not constant, but with the same order of magnitude. Possible reasons concern the non-linear model assumed, or the insufficiency of the selected IM. Since it is impossibile to state what is the "real" probability of exceeding a limit state looking the total risk, the only way is represented by the optimization of the desirable properties of an IM.

Cost-Effectiveness of Alternative Retrofit Options to Support Decision Making

How to evaluate the cost-effectiveness of repair/retrofit intervention vs. demolition/replacement and what level of shaking intensity can the chosen repairing/retrofit technique sustain are open questions affecting either the pre-earthquake prevention, the post-earthquake emergency and the reconstruction phases. The (mis)conception that the cost of retrofit interventions would increase linearly with the achieved seismic performance (%NBS) often discourages stakeholders to consider repair/retrofit options in a post-earthquake damage situation. Similarly, in a pre-earthquake phase, the minimum (by-law) level of %NBS might be targeted, leading in some cases to no-action. Furthermore, the performance measure enforcing owners to take action, the %NBS, is generally evaluated deterministically. Not directly reflecting epistemic and aleatory uncertainties, the assessment can result in misleading confidence on the expected performance. The present study aims at contributing to the delicate decision-making process of repair/retrofit vs. demolition/replacement, by developing a framework to assist stakeholders with the evaluation of the effects in terms of long-term losses and benefits of an increment in their initial investment (targeted retrofit level) and highlighting the uncertainties hidden behind a deterministic approach. For a pre-1970 case study building, different retrofit solutions are considered, targeting different levels of %NBS, and the actual probability of reaching Collapse when considering a suite of ground-motions is evaluated, providing a correlation between %NBS and Risk. Both a simplified and a probabilistic loss modelling are then undertaken to study the relationship between %NBS and expected direct and indirect losses.

Earthquake forecasting and seismic hazard analysis: some insights on the testing phase and the modeling

This thesis is divided in three chapters. In the first chapter we analyse the results of the world forecasting experiment run by the Collaboratory for the Study of Earthquake Predictability (CSEP). We take the opportunity of this experiment to contribute to the definition of a more robust and reliable statistical procedure to evaluate earthquake forecasting models. We first present the models and the target earthquakes to be forecast. Then we explain the consistency and comparison tests that are used in CSEP experiments to evaluate the performance of the models. Introducing a methodology to create ensemble forecasting models, we show that models, when properly combined, are almost always better performing that any single model. In the second chapter we discuss in depth one of the basic features of PSHA: the declustering of the seismicity rates. We first introduce the Cornell-McGuire method for PSHA and we present the different motivations that stand behind the need of declustering seismic catalogs. Using a theorem of the modern probability (Le Cam's theorem) we show that the declustering is not necessary to obtain a Poissonian behaviour of the exceedances that is usually considered fundamental to transform exceedance rates in exceedance probabilities in the PSHA framework. We present a method to correct PSHA for declustering, building a more realistic PSHA. In the last chapter we explore the methods that are commonly used to take into account the epistemic uncertainty in PSHA. The most widely used method is the logic tree that stands at the basis of the most advanced seismic hazard maps. We illustrate the probabilistic structure of the logic tree, and then we show that this structure is not adequate to describe the epistemic uncertainty. We then propose a new probabilistic framework based on the ensemble modelling that properly accounts for epistemic uncertainties in PSHA.