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Optimal Bridge Restoration Sequence for Resilient Transportation Networks
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Aman Karamlou1 and Paolo Bocchini2 1
Department of Civil and Environmental Engineering, Advanced Technology for Large Structural Systems (ATLSS) Engineering Research Center, Lehigh University, 117 ATLSS Drive, Bethlehem, PA 18015, USA; PH (610) 758 6108; FAX (610) 738 5553; email:
[email protected] 2 Department of Civil and Environmental Engineering, Advanced Technology for Large Structural Systems (ATLSS) Engineering Research Center, Lehigh University, 117 ATLSS Drive, Bethlehem, PA 18015, USA; PH (610) 758 3066; FAX (610) 738 5553; email:
[email protected] ABSTRACT Transportation networks are necessary infrastructure elements to provide aids to impacted areas after the occurrence of an extreme event. Without functional roads, recovering other damaged facilities and lifelines would be slow and difficult. Therefore, restoring the damages of transportation networks, specifically bridges as their most vulnerable elements, is among the first priorities of disaster management officials. This paper presents a new methodology for scheduling the restoration of damaged bridges. The problem is formulated as a multi-objective combinatorial optimization solved by Genetic Algorithms, which minimizes the time to connect the selected critical locations and maximizes the resilience of the transportation network. The main purpose of developing the algorithm was providing a restoration plan which is practical to be used by decision makers at the time of an event, yet based on solid computations rather than mere engineering judgment. The algorithm is examined with a numerical example. The presented algorithm can be considered as the enhancement of previous work performed at Lehigh University. The results show that the new optimization setup improved the solution quality and efficiency compared to the previous techniques. INTRODUCTION An efficient response to an extreme event is the primary concern of disaster management officials. The key elements of such response consist in reducing the damage caused directly by the extreme event, as well as quickly recovering from the inevitable damages. The concept of disaster resilience, which has received considerable attention from the research community, addresses both of the mentioned key elements of the response. In fact, resilience is defined as the ability to (1) withstand and (2) rapidly recover from a disruptive event.
Structures Congress 2014
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Structures Congress 2014 © ASCE 2014
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Concerning the first phase of resilience, it can be claimed that as a result of performing years of extensive studies on different materials, structures and structural systems, now there is a better understanding of the extent of damage caused by different extreme events and how to reduce losses by using more resistant structures. Today the research community is moving towards the next step, to investigate more about the second part of resilience, which focuses mainly on effective damage restoration and recovery strategies that reduce the amount of indirect losses after an extreme event. Transportation networks are among the most critical infrastructures that require particular attention after extreme events. The quality of emergency response, evacuation process, and restoration of other lifelines are directly affected by the functionality of transportation networks. The damage of transportation networks is predominately concentrated on the bridges, as they are the most vulnerable components of these networks. Several researchers have contributed to exploring resilience of transportation networks and bridge recovery strategies after an extreme event. Cimellaro et al. (2011) and Bocchini and Frangopol (2012a) presented an index for evaluating the performance of road networks after a disruption to measure the resilience index (Bocchini and Frangopol 2011a). Deco et al. (2013) proposed a methodology to assess the seismic resilience of bridges in a probabilistic manner, to help decision makers to budget the rehabilitation program before the occurrence of an earthquake. Chang et al. (2012) developed a framework to find the optimal bridge retrofit strategy that maximizes the post event network evacuation capacity. Bocchini and Frangopol (2012a, 2012b) proposed a technique to optimize the intervention schedule of damaged bridges after an extreme event which maximizes the resilience of the transportation network and minimizes the total intervention cost. Franchin et al. (2006) evaluated the reliability of road networks considering the connectivity of schools, rescue centers and hospitals. Zanini et al. (2013) studied the vulnerability of transportation networks considering the environmental deterioration of bridges. Essahli and Madanat (2012) presented an optimization framework for restoration prioritization of deteriorating bridges of transportation networks to minimize the probability of failure under annual budget constraint. Some techniques proposed for resilience-based optimal restoration scheduling of highway bridges are too complicated or abstract and require highly detailed information about different bridge repair methodologies, post-event behavior of the traffic, and available resources. Sometimes, due to the lack of these types of data, authors have to make unrealistic assumptions. On the other hand, in spite of all of the sophistications in the techniques available in the literature, the current approach used by decision makers is quite simple and mostly based on engineering judgment. Hence, the practical adoption of the techniques currently available in the literature appears unlikely in the near future. For this reason, the current paper presents a new algorithm that provides optimal restoration schedule of bridge networks with a substantially simpler approach. The outcome of the algorithm is easy to interpret and yet relies on scientific computations with a reasonable level of details. The problem is formulated in the form of a bi-objective optimization. The objectives are the maximization of the
Structures Congress 2014
Structures Congress 2014 © ASCE 2014
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resilience of the transportation network (as a long-term goal) and the minimization of the time required to connect the critical locations selected by decision makers (as a short-term goal). Compared to previous work (Bocchini 2013), new design variables have been utilized, which require a completely different set of optimization operations. As a result, the algorithm is more robust and provides higher quality solutions. RESILIECNE OF TRANSPORTATION NETWORKS Several formulations have been proposed to measure resilience. In this paper the following model (Cimellaro 2010, Frangopol and Bocchini 2011) has been used to quantify resilience as one of the objectives of the optimization problem: ( )
=
(1)
is the occurrence time of the extreme event, is the investigated time where horizon, and ( ) is a time-variant measure of the functionality of the network. The functionality of the network at each time step is a function of the condition of the transportation network and the damage level of its bridges. Bocchini and Frangopol (2010) defined ( ) as a function of the performance index Γ(t) as follows: ( )= Γ( ) =
( )
.
(2) ( )
.
(3)
( )
in which Γ and Γ are the performance indices corresponding to the cases where all bridges of the network are out of service and all bridges are in service, respectively. In Equation (3) and are balancing factors for the cost of time and distance covered. TTT and TTD are the total travel time and distance of all of passengers departing in 1 hour, which can be computed by solving the traffic distribution and assignment problem for transportation networks (Bocchini and Frangopol 2011b). The effect of the damaged bridges on the performance of the network is accounted for by the following traffic parameters: =
1+
+∑
∈
,
.
1+
,
.
(4)
where is the time to cover the segment i-j, is the time to cover the segment at free flow, is the traffic flow, and is the practical capacity of the segment. is the minimum detour route time of bridge located in the segment i-j, and is the practical capacity of the detour. , is a parameter that measures the effect of the
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Table 1. Impact of bridge damage and restoration to the traffic. Adapted from Bocchini and Frangopol (2012a) Damage Level Bridge State Restoration in Process , 2≤ 2≤ 1≤ 1≤ 0≤ 0≤
≤4 ≤4
