International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP) (12th : 2015)

A probabilistic approach in estimating optimal evacuation scenarios for seismic emergency management Zanini, Mariano A.; Pellegrino, Carlo; Rossi, Riccardo; Gastaldi, Massimiliano; Modena, Claudio Jul 31, 2015

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12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  1 A Probabilistic Approach In Estimating Optimal Evacuation Scenarios For Seismic Emergency Management Mariano A. Zanini Ph.D. Student, Dept. of Civil, Environmental and Architecture Engineering, University of Padova, Padova, Italy Carlo Pellegrino Full Professor, Dept. of Civil, Environmental and Architecture Engineering, University of Padova, Padova, Italy Riccardo Rossi Assistant Professor, Dept. of Civil, Environmental and Architecture Engineering, University of Padova, Padova, Italy Massimiliano Gastaldi Assistant Professor, Dept. of Civil, Environmental and Architecture Engineering, University of Padova, Padova, Italy Claudio Modena Full Professor, Dept. of Civil, Environmental and Architecture Engineering, University of Padova, Padova, Italy ABSTRACT: In recent earthquake experiences proper evacuation planning and potential emergency actions to be conducted to help the citizens of the quake municipalities were significant issues. In this work the effects of earthquake scenarios were shown in terms of seismic damages to residential and industrial buildings and also to infrastructural networks through the use of probabilistic approaches. The analyses were conducted on the building and infrastructural assets of the municipality of Conegliano, a town of 40000 inhabitants located in the northern part of the province of Treviso, North-Eastern Italy. A preliminary study on historical seismicity and geological substructures of the surrounding areas was performed, followed by the evaluation of the potential seismic damages to the built heritage. On the basis of these results, the issues of the post-quake accessibility and the management of the inhabitants optimal evacuation using the procedure described in Hadas et al. 2013 were performed. Information about building and infrastructural damages, spatial distribution and capacity of harvesting areas, boundary conditions in terms of predetermined maximum timing for carrying out the evacuation and needed costs for the seismic retrofit of bridges belonging to network links involved in the evacuation were the main input data for the simulations. Road network infrastructure is vulnerable for extreme events, and as a result its ability to supply the required capacity, when needed most, can be seriously hampered. Hence, it is crucial to identify those critical segments which prohibit safe evacuation, and find an optimal retrofit scheme at the network level in order to minimize evacuation time. In this work an emergency evacuation model able to consider infrastructures vulnerability caused by bridges and building damages, event location and magnitude, road network, transportation demand and evacuation areas is developed in order to identify the critical infrastructures and recommend budget allocation for increasing network capacity and minimizing evacuation time, given budget alternatives. 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  2 Evacuation analysis requires a multidisciplinary approach integrating transportation, structural engineering, operations research, and social sciences. With reference to the structural aspects, in emergency situations the first requirement is to investigate the effects induced on infrastructures by hazardous events, and to identify possible relations between these physical and mechanical impacts and the functional characteristics both of single components and of the road network as a whole. It is important that the transportation system remain operative or that its function be repaired or restored as soon as possible (Nicholson and Du 1997). In particular, past experience has shown too often that earthquake damage to road network components can severely interrupt traffic flow, thus negatively impacting on the economic activity of a region as well as on post-earthquake emergency response, evacuation and recovery activities (Franchin et al. 2006). Past works have focused on seismic performance assessment of individual components of road network, whereas few pay attention to system performance assessment and therefore to the optimal economic allocation in the network before the earthquake in order to improve/retrofit the components (Gastaldi et al. 2013; Modena et al. 2014), which is crucial for fast evacuation of the population, if needed. Bridges’ seismic vulnerability assessment is necessary for a proper planning of the emergency response and to define priority on retrofit interventions. Fragility curves allow assessing bridge seismic vulnerabilities (Lupoi and Franchin 2006; Carturan et al. 2014; Zanini et al. 2013; Padgett and DesRoches 2008; Shinozuka et al. 2003; Borzi et al. 2014), taking into account uncertainties of the variables and using probabilistic distributions to describe the properties of the materials composing the structure. These curves can be developed empirically as well as analytically.  Regarding the issues concerning network design, evacuation planning can be related to the facility location problem, and network design and flow models. In particular: - facility location problems (Nagy and Salhi 2007) aim at locating a set of facilities, both serving and being served, in a network, in order to achieve an objective function with a set of constraints (Avella and Boccia 2009); - the network design problem (Magnanti and Wong 1984) is a set of issues designed to construct networks with different objective functions in mind, given the flow which can be served by a network constrained by capacity; - network flow models (Ahuja et al. 1993) determine the flow in various network structures, objective functions, and constraints. Network flow models, such as the maximum-flow and minimum-cost problems (Hillier and Lieberman 2005) are well known problems that find the total flow from origin to destination (the former), or the minimal cost for flow from origin to destination, given costs associated with arcs and nodes (the later). These models assume costs per unit, rather than construction costs associated with network design problems and facility location problems.  In this context, Hadas and Laor 2013 were the first to present a model for the design of an optimal network in terms of minimizing both evacuation time and network constructions costs.  In this paper a revised optimization model that consider retrofit alternatives, in order to minimize evacuation time and budget allocation is presented. The revised procedure takes also into account the capacity reductions induced to each network link in relation to the potential interaction between damaged jutting buildings and the roadways as well as considering potential damages to bridges. 1. INTEGRATED PROCEDURE Figure 1 shows the framework of the integrated procedure; it is composed by four basic components: Bridges Information System (BrIS), 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  3 Seismic Information System (SIS), Buildings Information System (BuIS) and Transportation and Land-use Information System (TLIS). A description of the procedure components is addressed in the following.   Figure 1: General evacuation analysis framework.  1.1. Bridges Information System System components potentially directly subjected to risk in road network risk assessment are usually bridges, tunnels, slopes, retaining walls and roads (Morbin et al. 2014). Each exposed bridge structure is surveyed, its fragility parameters are evaluated, and stored into a specific Bridges Information System (BrIS). For a proper analysis of the potential bridges’ criticalities due to an earthquake occurrence it is necessary to know bridge physical and geometrical characteristics (Pellegrino et al. 2014), which are essential input data for the fragility characterization in probabilistic terms. Another significant element in the BrIS is the collection of the possible retrofit intervention costs (Padgett et al. 2010). They are suitable indexes for assigning the most effective retrofit intervention among possible alternatives. 1.2. Seismic Information System The Seismic Information System (SIS) contains data regarding seismogenetic sources and their parameters to build seismic hazard maps; examples of this information are geo-localized seismogenetic source area, focal mechanism, seismic source depth, annual occurrence ratio. 1.3. Buildings Information System Previous literature studies have underlined the need of deal with the evaluation of the short and long term interaction between road network and damaged buildings (Goretti and Sarli 2006) without deepen this issue at structural level. The Building Information System (BuIS) is organized similarly to the bridges’ one, requiring the knowledge of the physical and geometrical description of the main buildings’ features subsequently functional to their seismic fragility characterization through the use of specific fragility curves sets (Rota et al. 2008). 1.4. Stochastic damage state assessment The level of vulnerability of an infrastructure reflects its attitude in the face of physical damage (physical vulnerability) and/or loss of functionality (functional vulnerability). Structural damage states are defined according to bridge fragility curves for each specific structure with a Montecarlo random number generation.  1.5. Transportation and land-use system analysis With regard to post-earthquake the evaluation of the variation in production and attraction indexes of Origin and Destination zones is of primary interest. The functionality of an element is likely to change as the consequence of a certain event and this represents the functional vulnerability of that element. In this situation, therefore, the physical response of the infrastructure assumes the role of input, as the functional conditions of the single element are evaluated according to a suitably defined capacity function. 1.6. Retrofit strategy A retrofit strategy is a set of possible retrofits coupled with estimated cost and estimated capacity. For each bridge belonging to the analysed transportation network, an evaluation of retrofit intervention types has to be identified. Each retrofit intervention is characterized by a set of corrective coefficients to be applied for deriving retrofitted bridge fragility curves and again to evaluate the new Bridge Damage Indexes (BrDIs) in the case of a quake 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  4 occurrence on the same retrofitted bridge. BrDIs are then related to Link Damage Indexes (LDIs) by joining a set of possible reduced link capacity values to the BrDI outcomes of the Montecarlo method. In addition, also link reductions induced by jutting building collapses are considered through the evaluation of the BuDIs and the subsequent related LDIs. The whole LDIs derived from the seismic assessment of both BrIS and BuIS contribute to the definition of the damaged network characterized by links with reduced capacities, on which performing the following evacuation optimization procedure. 1.7. Evacuation analysis The evacuation analysis procedure (Hadas et al. 2013) applied in this study is based on the assumption that a simplified ideal network is considered with a set of origin nodes designed to serve as populated districts each with capacity; a set of destination nodes designed to serve as evacuation areas such as assembly areas, shelters, safe zones, each with capacity as well; a set of given transportation infrastructure, each with capacity and a set of links representing critical infrastructures such as bridges and tunnels which can be damaged, each with a set of retrofit alternatives (retrofit intervention costs and resulted capacities). For a public authority the main objective is planning a series of retrofit interventions aimed at strengthening and the elimination of possible network criticalities induced by a quake occurrence, hence we are looking for a recommendation for a set of retrofits that will minimize costs, given a set of evacuation time alternatives. The algorithm described by Hadas et al. 2013 provides the distribution of the assigned flow over links; the retrofit budget required to attain the desired evacuation time; the selected bridge retrofit scheme and the related global retrofit costs; the non-evacuees units for each origin zone and the description of the used attraction capacity of each selected evacuation area. 2. METHODOLOGY APPLICATION  The Municipality of Conegliano, a town of 40,000 inhabitants located in the northern part of the province of Treviso (North-Eastern Italy), chosen for its significant seismic hazard, has been identified as a test area in order to verify the effectiveness of the proposed procedure.  2.1. Bridge Information System characteristics In this test area there are 51 bridges of various typologies: single span, multi span, concrete, steel, and masonry bridges, straight or skewed. Data used to build the BrIS were retrieved from a preliminary in situ survey, performed to evaluate and collect the main physical and geometrical characteristics of each bridge. Fragility curves were built using the procedure described in Risk-UE Project (Risk-UE 2004) for estimating damages on bridges. Finally, BrDIs have been evaluated through the use of the MonteCarlo Method for each SE. 2.2. Seismic Information System characteristics The SIS has been constructed based on the historical seismicity and geological substructures of the area surrounding the Conegliano municipality (Meroni et al. 2008; Poli et al. 2008). On the basis of the historical seismicity, a finite number of scenario earthquakes has been considered for the execution of the simulations, each one characterized by a specific magnitude level, related to the seismogenic zones characteristics, and a geographical definition of possible epicenters. For sake of synthesis, only one of them is described in this work, characterized by a Mw 6.6 and an epicentral distance of 10 Km (Lat. 45.8443°, Lon. 12.1786°) from the Municipality center. Soil characterization has been carried out by the use of the Vs,30 map of the Treviso Province (USGS Seismic Hazard Analysis Tools 2010) and finally, the most recent GMPE formulation (Bindi et al. 2011) has been considered for the detection of the seismic action spatial distribution. 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  5 2.3. Buildings Information System  A preliminary in situ survey has been performed to evaluate and collect the main physical and geometrical characteristics of bridges and residential/industrial buildings. Residential buildings were grouped in sub-areas characterized by a predominance of a structural typology between residential RC buildings, residential masonry buildings and productive and commercial RC structures (Figure 2). For each building structural typology, fragility curves for the estimation of damages have been built according to Rota et al. 2008 and sub-areas BuDIs have been evaluated through the use of the MonteCarlo Method.  2.4. Land-use and Transportation Information System characteristics A Land Use and Transportation Information System was developed for the Municipality (Rossi et al. 2008), characterized by the supply subsystem (road network) with links' capacities, the demand subsystem represented by 59 origin zones and 12 destination zones (evacuation areas). In Figure 2 evacuation areas are represented with dots of different dimensions in relation to their specific capacities. Figure 3 shows a part of the road network model developed for the evacuation analysis.  2.5. Stochastic damage state assessment and transportation land-use system analysis The fragility assessment was performed, first deriving seismic actions for each bridge and buildings subarea, and subsequently using Montecarlo method (10,000 iterations) for the definition of the respective BrDIs and BuDIs. Figure 4 represents the BrDIs and BuDIs for the considered SE. Results obtained from BrDIs and BuDIs were coupled with the TLIS to derive the respective Link Damage Indexes (LDIs) useful for the characterization of the damaged network due to the potential failures of bridges and jutting buildings. A correlation has been made to relate the BrDI to the LDI according to Shinozuka et al. 2006, using the following relation:      (1)  Link Damage Indexes were subsequently used to determine the functionality reduction, caused by bridge damages, to be applied to damaged network links: in particular 100% functionality was considered in case of none or slight damages, 50% for moderate damage condition, 25% for extensive damage state and 0% in case of structural collapse damage state. With reference to damaged buildings, a correlation has been made between also for BuDIs derived for each building sub-area and the related LDIs. In particular, jutting buildings belonging to collapsed buildings sub-areas have been considered interfering with road functionality, implying an obstructed road width equal to 70% of their building height. This criterion, coupled with the choice of considering a 0% functionality for links with residual road widths lower than 2.5 m, has led to take also into account the issue related to urban roads obstructions caused by jutting building collapses, thus obtaining a more refined and realistic overview of the LDIs belonging to each SE damaged network.    Figure 2: Conegliano’s residential, commercial and evacuation areas.  2bridge linkLDI BDI= ∑12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  6  Figure 3: A part of the network model developed for the evacuation analysis optimization.  2.6. Retrofit strategy Costs for seismic retrofit of bridges and the relative updated fragility curves were estimated with the procedure proposed by Padgett et al. 2010 for 8 of the 51 bridges belonging to the analysed network; they are the most important ones (all multi-span bridges) and also actually needs for retrofitting.     Figure 4: BrDIs and BuDIs for the considered SE.   This decision was taken since the majority of the other bridges are single-span structures, in many case buried shallow ones, characterized by lower values of seismic vulnerability and therefore able to ensure an adequate residual functionality. For each bridge the updated BrDIs and subsequently relative LDIs have been calculated. 3. RESULTS AND DISCUSSION The evacuation optimization model was then applied for each SE, considering a range of different evacuation time and the evacuation of citizens belonging to building sub-areas characterized by a damage level at least exstensive. Traffic simulations were performed considering two different traffic demand conditions, respectively in the morning and at night. Each execution provided a series of results related to the flow distribution among the whole network links; the retrofit budget required to attain the desired evacuation time; the selected bridge retrofit scheme; the related global retrofit interventions costs; the non-evacuees units for each origin zone and the description of the used attraction capacity of each selected evacuation area. For sake of synthesis, Figure 5 gives a GIS representation only of the evacuation analysis results obtained for a fixed evacuation time of 30 minutes for the considered morning SE.    Figure 5: Representation of the evacuation analysis traffic flows distributions for the considered SE.  12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015  7 The outcomes of the whole analyses performed have shown how it is necessary to retrofit bridges for ensuring a complete evacuation of citizens for time values lower than 90 minutes, whereas in the case of evacuation time values higher than 90 minutes no retrofits are needed to complete evacuation operations. In both cases costs for setting up the evacuation areas have to be taken into account. Cost objective functions (i.e. the sum of bridges’ retrofit costs and evacuation areas setting up costs) are represented in Figure 6 for the considered SE: they are decreasing for growing evacuation time values, asymptotically stabilizing around the evacuation areas setting up total costs value.  Non-evacuees number asymptotically decreases for higher evacuation times stabilizing around a fixed value representative of the number of citizens trapped due to the presence of link closed for collapsed buildings, i.e. in the case of network links full loss of accessibility (Figure 7). The procedure can also be applied by setting evacuation time values significantly lower than 10 minutes, clearly providing at the same time growing non-evacuees percentage values.   Figure 6: Representation of the evacuation analysis cost objective functions for the considered SE.    Figure 7: Representation of the number of not evacuated units for the considered SE.  4. CONCLUSIONS In this paper an integrated procedure for infrastructures retrofitting based on a network level multi-disciplinary approach was proposed. The procedure allows assessing consequences of a given earthquake in terms of bridges and buildings structural damages and related link functionality reductions, subsequently using these outcomes to identify a bridges’ retrofit scheme able to strengthen the network functionality in order to ensure the evacuation of citizens in a defined evacuation time value. The proposed procedure was applied to a urban network case study subjected to a set of earthquake scenarios, providing for each of them the flow distribution among the whole network links, the retrofit budget required to attain different evacuation times, the selected bridge retrofit schemes, the related global retrofit interventions costs, the non-evacuees units for each origin zone and, at last, the description of the used attraction capacity of each selected evacuation area.  5. REFERENCES  Ahuja, R. K., T. L. Magnanti, and J. B. Orlin. Network flows  : theory, algorithms, and applications. 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