Seismic Resilience of a Health care facility

This paper explains the fundamental concepts of resilience proposing a unified terminology and establishing a common frame of reference for quantitative evaluation of such seismic resilience. The evaluation is based on a non-dimensional analytical function based on loss recovery within a “recovery period”. Distinction is made between direct and indirect losses. The path to recovery is expressed through the use of different recovery functions. The loss functions are weighted through seismic fragilities of systems’ components. The fragilities are determined through the use of a multidimensional performance limit thresholds that allow considering simultaneously different mechanical-physical variables such as forces, velocities, displacements and accelerations along with other functional limits. The above formulation will be exemplified for a hospital system in California considering direct and indirect losses in its physical system and in the population served by the system. The evaluation is using a bi-dimensional fragility formulation with two performance-limitthresholds based on accelerations and displacements. 1 Graduate Research Assistant, Department of Civil, Structural & Environmental Engineering, University at Buffalo (SUNY),Buffalo, NY 14260, USA E-mail: [email protected] 2 Clifford Furnass Professor, Department of Civil, Structural & Environmental Engineering, University at Buffalo (SUNY), Buffalo, NY, 14260, USA. E-mail: [email protected] 3 Professor, Department of Civil, Structural & Environmental Engineering, University at Buffalo (SUNY), Buffalo, NY, 14260, USA. INTRODUCTION Recent events have shown how hospitals are vulnerable to extreme events such as earthquakes. In order to reduce the losses in these essential facilities the emphasis has shifted to mitigations and preventive actions taken before the extreme event happens. Mitigation actions can reduce the vulnerability of a hospital, however also if there is insufficient mitigation, or the event exceeds expectations, damage and recovery are necessary to have a resilient function to the community. Seismic resilience as defined in this paper describes the loss and loss recovery required to maintain the function of the system with minimal disruption. So while mitigation may emphasize use of new technologies and implementation of policies to reduce losses, the resilience considers also the recovery process including behavior of individuals and organizations in the face of a disaster. A wealth of information is available on specific actions, policies or scenarios that can be adopted to reduce the direct and indirect economic losses attributable to earthquakes, but there is little information on procedures on how to quantify these actions and policies. Seismic resilience can compare losses and different pre and post event measures verifying if these strategies and actions can reduce or eliminate disruptions in presence of earthquake events. Bruneau et al (2003) offered a very broad definition of resilience to cover all actions that reduces losses from hazard, including mitigation and more rapid recovery. The above paper defined the community earthquake resilience as “the ability of social units (e.g. organizations, communities) to mitigate hazards, contain the effects of disasters when they occur, and carry out recovery activities in ways to minimize social disruption and mitigate the effectors of further earthquakes”. The authors suggested that resilience can be conceptualized along four interrelated dimensions: technical, organizational, social and economic (TOSE). The first two components are more related to the resilience of critical physical systems such as water systems and hospitals. The last two components are more related to the affected community. The above paper defined a fundamental framework for evaluating community resilience without any actual quantification and implementation. Chang et al. (2004) proposed a series of quantitative measures of resilience and demonstrated them in a case study of an actual community, the seismic mitigation of Memphis water system. This paper attempts to provide a quantitative definition of resilience through the use of an analytical function which allows identification of quantitative measures of resilience. DEFINITIONS AND FORMULATIONS To establish a common frame of reference, the fundamental concepts of resilience are analyzed, a unified terminology is proposed and an application to health care facilities is presented: Definition 1: Resilience is defined as a normalized function indicating capability to sustain a level of functionality or performance for a given building, bridge, lifeline, networks or community over a period of time TLC (life cycle, life span etc. etc) including the recovery period after damage in an extreme event. The time TLC includes the building recovery time TRE and the business interruption time that is usually smaller compared to the other one. Definition 2: The recovery time TRE is the time necessary to restore the functionality of a community or a critical infrastructure system (water supply, electric power, hospital etc.) to a desired level below, same or better than the original, allowing proper operation of the system. The recovery time TRE(I,location) is a random variable with high uncertainties. It typically depends on the earthquake intensities, the type of area considered, the availability of resources such as capital, materials and labor following major seismic event. For these reasons this is the most difficult quantity to predict in the resilience function. Porter et al. (2001) attempted to make distinction between downtime and repair time and he tries to quantify the latter. In his work he combines damage states with repair duration, and probability distributions to estimate assembly repair durations. Another useful concept to define is “a disaster resilient community”. Definition 3: Disaster resilient community is a community that can withstand an extreme event, natural or man made event, with a tolerable level of losses and can take mitigation action consistent with achieving that level of protection. (Mileti, 1999, p5.) This Resilience is defined graphically as the normalized shaded area underneath the function shown in Figure 1 where in the x-axis there is the time range considered to calculate resilience while in the Y-axis there is the functionality Q(t) of the system measured as a non dimensional quantity. Analytically Q(t) is a non stationary stochastic process and each ensemble it is a piecewise continuous function as the one shown in Figure 1. Mathematically the resilience can be expressed by equation (1): Figure 1. Uncoupled Resilience. ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0 0 0E RE 0E 1 1 I E RE R Re 0 t-t 1-L I,T 1 1 1 R= tt 0, N N T α , , E RE I