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Incorporating model uncertainty in collapse reliability assessment of buildings

Structural collapse analysis requires models that capture large deformation response with cyclic strength and stiffness degradation. Although current collapse assessment methods carefully account for the nonlinear response of structures, most of these analyses are conducted with models that reflect the median (or expected) properties of the structural components and do not fully account for model uncertainties associated with variability in the properties and response characteristics of the components. This work discusses several advances in treatment of model uncertainty for collapse safety assessment. A variety of reliability methods are explored and compared to evaluate their ability to characterize accurately the influence of modeling uncertainties and variability in component behavior on overall system response. The examples serve as illustrations of approaches to rigorously assess the influence of model uncertainties and variability in component properties on the collapse behavior of the systems. builds on the findings of Liel et al. (2009). We aim to assess the effects of modeling uncertainties on collapse response with emphasis on quantifying correlation of model parameters. Alternative reliability methods to assess the effects of modeling uncertainty in collapse response assessment are also investigated. 2 COLLAPSE ASSESSMENT PROCEDURE Collapse simulation of structures requires numerical models that can reproduce the nonlinear deformation demands and degradation in stiffness and strength in the elements due to repeated cycles of loading. The component hinge model originally developed by Ibarra et al. (2005) is capable of simulating nonlinear hysteretic behavior of reinforced concrete (RC) beam-column elements. It is based on a tri-linear monotonic backbone curve, relating member moment and rotation, along with nonlinear hysteretic rules to simulate strength and stiffness degradation under cyclic loading. The strength of this model in collapse simulation is due to the post-capping branch that is characterized by a negative slope. This portion of the backbone curve simulates strainsoftening behavior related to concrete crushing, rebar fracture and buckling. The accuracy of the simulation depends on realistic characterization of parameters of the phenomenological model. Therefore, in this study we assume six parameters defining the backbone curve, namely θy, My, θcap,pl, Mc/My, θpc and γ are random variables. An example backbone curve displaying model parameters is provided in Figure 1. Incremental dynamic analysis (IDA) is a fairly established technique used to predict collapse (Vamvatsikos & Cornell 2002). In this technique nonlinear response history analysis is conducted using a ground motion that is scaled to various intensity levels. Collapse intensity is estimated as the intensity level that causes dynamic instability. This procedure is repeated for a number of ground motions. Different ground motions cause collapse at different ground motion intensities, producing recFigure 1. Backbone Curve of the Component Hinge Model. ord-to-record variability in collapse capacities. To account for record-to-record variability, 22 ground motion record pairs from the FEMA-P695 (FEMA 2009) far-field ground motion set are used in this study. The data set is selected such that it consists of extreme motions that may cause structural collapse. In this study, incremental dynamic analysis with a component hinge model is used for collapse assessment with the OpenSees analysis platform. 3 BRIDGE COLUMN MODEL A reinforced concrete bridge column that was tested full-scale in NEES Outdoor Shake Table at UCSD in 2010 (PEER & NEES 2010) is used as a case study structure for the assessment of modeling uncertainties. The bridge column is designed according to Caltrans Seismic Design Criteria and Bridge Design Specifications (Caltrans 2004, 2006) and seismic performance of bridge columns built in compliance with current U.S. standards is aimed to be investigated. The circular column has a diameter of 4 ft (1.2 m) and height of 24 ft (7.2 m). To mobilize the column capacity, a 250 ton (2,245 kN) reinforced concrete block was cast on top of the column (Terzic et al. 2012). The bridge column is modeled as a single degree of freedom structure with a concentrated hinge model defined at the base. The first mode period of the structure (T1) is obtained as 1.11 sec. The backbone curve parameters for the bridge column model have been calibrated using experimental results and the calibrated parameters are assumed to reflect median properties. The bridge column is observed to be highly ductile having a ductility capacity of 6.45. 4 ASSESSMENT OF CORRELATION OF MODEL PARAMETERS BETWEEN AND WITHIN COMPONENTS Haselton et al. (2008) calibrated the concentrated plastic hinge model by Ibarra et al. (2005) to represent nonlinear hysteretic behavior of reinforced concrete (RC) beam-columns. The component calibration database consists of 255 tests of rectangular RC columns that failed either in flexure or in combined flexure-shear mode (Berry et al. 2004, Haselton 2008). The database consists of 42 test groups. A test group refers to a set of tests conducted by one researcher. The number of tests per group range between 1 and 24. Haselton et al. used the database to calibrate empirical predictive equations for the backbone curve parameters. The predictive equations for θpc, θcap,pl, Mc/My and γ are reported in Haselton et al. (2008). Readers are referred to Panagiotakos & Fardis (2001) for equations regarding θy and My. The goodness of fit of the predictive equations is investigated through residuals which are defined using the below equation:

Regional Multi-severity Casualty Estimation Due to Building Damage Following a Mw 8.8 Earthquake Scenario in Lima, Peru

This paper presents the application of a rigorous probabilistic framework that estimates the number, severity, and distribution of casualties over a region. A brief summary of the model is included in this paper. The application is for casualties resulting from a Mw 8.8 earthquake scenario occurring on the sub-duction fault along the coastline of Lima, Peru. The case study demonstrates an application of the casualty model, including the procedures for acquiring the required information, the selection of model parameters, and a step-by-step explanation of the model-solving algorithms. The model provides an estimate of the joint probability distribution of multiseverity casualties, including spatial and across-severity correlations. This paper also shows how the model can be useful for (1) estimating 90th-percentile casualties, (2) identifying unsafe communities and structural typologies, and (3) providing evidence to support hospital collaboration policies across different districts to increase the patient treatment reliability. Additionally, the results demonstrate that empirical fatality prediction methodologies can underestimate fatality rates in countries with scarce and outdated fatality data.