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The PBEE framework discussed in Section 2.2.1 represents a major step forward toward quantifying and managing earthquake risks of individual buildings. However, a much broader interpretation of performance is needed to understand how communities will be affected, and recover from devastating earthquakes (Krawinkler and Deierlein 2014). More recently, earthquake engineering researchers and practitioners have embraced the concept of seismic resilience as a measure of a community’s ability to contain the effects of an earthquake and achieve a timely recovery (Burton et al. 2015).

Seismic resilience describes the loss and loss recovery required to maintain the function of a system with minimal disruption (Cimellaro et al. 2006). A resilient system is one that illustrates reduced failure probabilities, reduced consequence from failures (loss of life, damage, etc.) and reduced recovery time (restored functionality) (Bruneau and Reinhorn 2006). Bruneau et al. (2003) developed a conceptual framework for quantifying seismic resilience and defined four properties (robustness, redundancy, resourcefulness, and rapidity) and four dimensions of resilience (technical, organizational, social, and economic). Resilience is quantified by using a multidimensional space of performance measures that includes the probability of failure, the consequences of failure, and time to recovery. Studies such as Bruneau et al. (2003), Cimellaro et al. (2006) and Bruneau and Reinhorn (2006) offer a definition of resilience to cover all actions that minimize losses from hazard, considering mitigation and recovery, making it possible to relate probability functions, fragilities, and resilience in a single integrated approach such that resilience can be quantified. Cimellaro et al. (2010) extended these resilience concepts in a unified terminology for a common reference framework for quantification of disaster resilience by means of resilience functions, which provide a comprehensive understanding of damage, response, and recovery as they illustrate the time variation of damage as well as its relationship to response and recovery. Within this framework, a number of studies have explored the seismic resilience of different systems such as healthcare facilities (Bruneau and Reinhorn 2007), water resource systems (Wang and Blackmore 2009) or natural gas distribution networks (Cimellaro et al. 2014).

Seismic resilience is defined as the ability of a system to reduce the chances of a shock, to absorb a shock if it occurs (abrupt reduction of performance) and to recover quickly after a shock (re-establish normal performance), as described in Bruneau et al. (2003). Bruneau and Reinhorn (2004) propose expressing resilience, based on the notion that a measure, Q(t), which varies with time, can be defined to represent the quality of a system or infrastructure. Specifically, performance can range from 0% to 100%, where 100% means no degradation in quality and 0% means total loss as illustrated in Figure 2-4, with restoration expected to occur over time.

Figure 2-4: Conceptual resilience function. Adapted from Bruneau and Reinhorn (2004).

Miles and Chang (2011) developed a model of community recovery (ResilUS) built by characterizing the attributes and behaviours of economic agents within a community, such as households and businesses, and describing relationships between agents themselves and relationships with their environment, such as buildings of residence and transportation networks. Twigg (2009) and Cutter et al. (2010) identify different components of resilience, grouped into thematic areas, which measure the resilience of communities to disasters. Mieler et al. (2015) developed a conceptual framework for connecting specific performance targets for the built environment to community resilience goals. The framework proposes (1) specifying a performance goal at the community level, (2) identifying an undesirable outcome and acceptable level of risk associated with the occurrence of this outcome, (3) identifying vital community functions that must be maintained to prevent the undesirable outcome, and (4) using probabilistic risk assessment to establish a relationship between the probability of losing these vital functions and the occurrence of the undesirable outcome.

As outlined in Burton et al. (2015), most of the previous approaches rely on the generic damage states used in loss estimation (e.g. none, slight, and moderate), which are not related to recovery. A rigorous evaluation of seismic resilience requires methods for incorporating the probabilistic assessment of multiple limit states, which are explicitly linked to recovery of the building inventory. As concluded by Bruneau and Reinhorn (2004), research is most needed to develop tools, such that the resilience objectives defined by a community can be

evaluated by decision makers for compliance. “However, in formulating policies anchored in quantitative resilience targets, one must recognize that resilience targets, while important objectives, are not to be taken as absolutes. This points to the need for a quantitative probabilistic framework and tools anchored in engineering procedures to guide decision makers in consideration of policies, rather than to focus on numerical values in a one-size fits all approach” (Bruneau and Reinhorn 2004).

The seismic resilience of a building may be described as its ability to respond to and recover from a damaging earthquake event. It can be measured as the time needed to restore basic operations. In a building resilience curve, such as the one illustrated in Figure 2-4, the vertical axis represents the loss in functionality due to earthquake damage and the horizontal axis represents the time for recovery. The total impact is a combination of direct repair costs for rebuilding and the cumulative loss in functionality, which can be measured by the integration of loss in function over recovery time. The cumulative loss depends on the combined effects of the amount of damage and the speed of recovery. Thus, resilience can be improved by both reducing the amount of damage incurred and taking measures to accelerate recovery. Existing standards for seismic evaluation do not explicitly address recovery time. Bonowitz (2009) proposes new evaluation criteria to address questions of resilience, with a strong emphasis on recovery time, where more resilience means the ability to recover basic operations faster. The San Francisco Planning and Urban Research Association (SPUR) outlined outline a set of performance objectives for buildings and lifeline infrastructure in San Francisco, under an ‘expected’ earthquake, necessary to increase the seismic resilience of the city (Poland 2009). Seismic performance targets are defined based on their implication to post-earthquake functionality and recovery, considering city wide needs. As illustrated in Figure 2-5, building damage is characterized by the following performance categories: (1) safe and operational, (2) safe and usable during repair, (3) safe and usable after repair. Undesirable outcomes, not considered in Figure 2-5, include (4) safe but not repairable or (5) unsafe. In addition to establishing these specific target goals, Poland (2009) estimates the performance of the current inventory, albeit based largely on “educated guesses about current standards for recovery time” (Burton et al. 2015).

Figure 2-5: Target states of recovery for San Francisco’s building and infrastructure. Source: Adapted from Poland (2009).

Performance Measure: Description: Safe and Operational Safe and usable during repairs Safe and usable after repairs Expected current status

In recognition of the deficiencies associated with existing WSMRF buildings, as discussed in Section 2.1.2, San Francisco’s Earthquake Safety Implementation Program (CAPSS 2011) has plans to develop mandatory evaluation and retrofit requirements for ‘low-performance steel buildings’, as illustrated in task C2.d of their 30 year plan, illustrated in Figure 2-6. According to Bonowitz (2009), San Francisco’s resilience targets for commercial buildings are collapse prevention, to limit response demands, and damage control to limit job loss, and expedite recovery (50% of offices open within 4 months according to the Community Recovery Section in Figure 2-5).

Figure 2-6: CAPSS Earthquake Safety Implementation Program Phase C. Source: Adapted from CAPSS (2011).

Bonowitz (2009) highlights the need for a resilience assessment methodology that enables engineering resilience. In view of this demand, the Structural Engineers Association of Northern California (SEAONC) proposed a rating system for earthquake performance which consists of a scale of 1 through 5 stars, in each of the following three dimensions: safety, repair cost, and time to re-occupy. While the proposed system defines the star rating of each point in the scale, a method by which to derive the rating value from outputs of various accepted standards for evaluation of a building is yet to be proposed (SEAONC 2009). More recently, Almufti and Willford (2013) have proposed a resilience-based earthquake design approach as a holistic process which identifies and mitigates earthquake-induced risks to enable swift recovery in the aftermath of a major earthquake. The approach acknowledges that direct losses, which include the financial costs of post-earthquake repair or reconstruction, make up a significant percentage of earthquake losses, but that the most significant vulnerability may be indirect losses due to downtime. As Almufti and Willford (2013) note: “designing buildings to sustain less damage in earthquakes is a key component of resilience-based design. This significantly decreases the uncertainty in the behaviour of the building and increases the confidence that the building will perform as intended. Resilience-based design explicitly

incorporates the design and performance verification of the structure and all non-structural components […]. However, one of the key differentiators of resilience-based design is preparedness for post-earthquake recovery to ensure continued operation immediately after the earthquake. This process considers the performance of the building (and contents) and the threats posed by the post-earthquake environment which could hinder the primary functions of the organization.” This approach to resilience-based earthquake design is the first to consider indicators of resilience in the form of downtime.

Performance-based methods clearly have an important role in assessing and designing for community resilience. However, to effectively serve this role, PBEE research must expand beyond the current emphasis on calculating direct losses and place greater attention on post- earthquake functionality and repair (Deierlein and Krawinkler 2014). Burton et al. (2015) propose an initial approach to how the current PBEE framework can be adapted and incorporated into a resilience framework to model recovery at the individual building and community scales. It incorporates the assessment of a set of building performance limit states that specifically inform community seismic resilience. However, the proposed method does not directly link to results from the FEMA P58 methodology, such that it can be systematically extended into a method for resilience evaluations. The method does not explicitly account for externalities, such as impeding factors, on recovery, and does not account for the expected variability in the delays associated with different limit states with increasing earthquake ground motion intensities.