Life-cycle management of deteriorating bridge networks with network-level risk bounds and system reliability analysis
Introduction
Deterioration of surface transportation infrastructure is a major challenge of transportation agencies around the world. Deterioration of bridges is especially detrimental due to their cruciality to network functionality, high maintenance cost, and dire consequences of failure. According to the American Society of Civil Engineers [1], the average age of bridges in the United States is 43 years, already passing the middle age for their design service life. Up to 2016, 9.1% or about 56,000 bridges have been rated structurally deficient, while funding required to clear this backlog by 2030 was estimated at over US$2 trillion. Similar situations are prevalent in many other countries [2], [3]. This deterioration problem is further compounded by the growing traffic load due to socioeconomic development [4], [5], [6] and increasing hazard frequency and intensity due to climate change [7], [8].
The structural performance of a bridge deteriorates gradually as a result of environmental stressors (e.g. corrosion) and long-term effects (e.g. fatigue, shrinkage, and creep). Bridge failure induced by structural deterioration can impose dire consequences upon bridge owners/managers (direct consequences) and society at large (indirect consequences) [9]. Therefore, the risk posed by bridge deterioration should be rigorously controlled through rational life-cycle management [10], [11], [12]. Different from many other assets, bridges are located in transportation networks, in which they are connected by roadway links. Essentially, bridges in a transportation network (herein referred to as a bridge network) form a spatially distributed system, in which spatial correlation exists with respect to bridge conditions and bridge functionality in the network [13]. Yang and Frangopol [14] showed that the maintenance priorities of deteriorating bridges can be drastically different when ranked at network and project levels. Due to this characteristic of spatially distributed systems, risk assessment and management should be conducted at the bridge network level.
Despite the necessity of network-level analysis, risk assessment of bridge networks faces two major challenges: (a) consideration of the correlation of bridge failure events and (b) efficient evaluation of indirect consequences.
As mentioned previously, bridges in a network are spatially distributed. Adjacent bridges may suffer from similar environmental stressors and traffic loads, leading to correlated failure events [14], [15]. Modeling this spatial correlation is conventionally conducted using two approaches: event-based simulation and random field-based approximation. In the first approach, hazards (either deterministic or stochastic) are hypothetically exposed upon a bridge network. Spatial correlation of bridge failure is then obtained by simulating bridge performance under the hazards considering bridge locations, ages, types, and relative distances to one another, among many other factors. This simulation-based technique has been widely used for various types of hazards such as earthquakes [13], [16], [17], floods [18], and overweight trucks [19].
In the second approach, random field theory is used directly to approximate the spatial correlation of bridge failure [20], [21], [22]. Instead of performing Monte Carlo simulation (MCS) for bridges under hazards, this random field-based approximation can directly and efficiently generate failure scenarios of bridges in a network, though this approximation may compromise the actual correlation condition compared to that of event-based simulation. Although the random field models are mainly developed for certain disasters (e.g. due to earthquakes), it is believed that they are also applicable to deteriorating bridge networks under normal traffic conditions [14], [15].
Bridge failure as well as the subsequent reconstruction can severely jeopardize the functionality of bridge networks. Consequences of bridge failure can be categorized as direct consequences, imposed upon transportation agencies, and indirect consequences, imposed upon traffic users. Generally, the latter are usually expressed as the sum of traffic delay and extra vehicle operating costs, which can be several orders higher than the direct consequences [23], [24]. The difficulty in evaluating indirect consequences arises from the need to model variation in traffic flow due to bridge failure [14]. In order to capture this variation, traffic assignment models that can predict traffic flow in a bridge network are needed.
Currently, the few existing studies that do consider traffic flow variation use MCS to generate failure scenarios of bridges and calculate the associated indirect consequences [16], [25], [26], [27], [28]. However, for deteriorating networks where failure probabilities of individual bridges are much lower than those of bridge networks under disasters, MCS with a small number of samples might overlook those failure scenarios that are unlikely to appear in MCS but can trigger enormous consequences (i.e. “black swans”), leading to underestimated risks. If more samples are used to capture these “black swans”, the corresponding computational cost can easily become prohibitive.
To curtail the computational demand, bookkeeping techniques have been employed so that repetitive traffic assignment can be avoided when the same failure scenario of bridges reappears in MCS [14], [29]. Other techniques are also available to reduce computational cost by selecting representative failure scenarios [30] and by using performance proxy [30] or computational surrogates [31] for traffic assignment. Nevertheless, the effects of “black swans” cannot be totally eliminated by using these techniques. To avoid the challenge brought by computationally expensive traffic assignment, many life-cycle risk assessment and management studies chose to use simplistic methods to estimate indirect consequences including using traffic flow data in the intact bridge network [23], [32], [33], [34] and introducing a random variable to represent indirect-to-direct consequence ratio [35], [36]. However, these methods ignore traffic flow variation entirely and, thus, cannot be regarded as network-level risk analysis.
Once network-level risks are determined, life-cycle management of bridge networks becomes a resource-constrained project scheduling (RCPS) problem that has proved to be non-deterministic polynomial-time-hard (NP-hard) [37]. To obtain optimal maintenance plans, most life-cycle management frameworks rely on metaheuristic optimization techniques such as generic algorithm [38], [39], [40], particle swarm optimization [27], [41], harmony search [42], and simulated annealing [43], among others. As a result, the network-level risk needs to be assessed multiple times in the lifespan of bridges as well as for different life-cycle decision alternatives. Hence, the computational challenge previously mentioned become even more amplified.
In this paper, a novel method is proposed for life-cycle management of bridge networks based on network-level risks. The proposed non-simulation method can significantly alleviate the computational demand. The occurrence probabilities of different failure scenarios are determined using the matrix-based system reliability (MSR) method [44], [45], [46]. The MSR method used herein can consider spatial correlation of bridge failure arising from correlated structural capacities and demands. Since the probabilities associated with different network failure scenarios can be directly computed with the MSR method, the expected indirect consequences (i.e. indirect risks) can be calculated analytically by a small number of traffic assignment operations without MCS. Different from existing non-simulation methods for indirect consequence evaluation [47], the proposed method uses risk bounds to (a) reduce the number of failure scenarios needed to be considered and (b) take into account the contribution of unlikely, yet high-impact events. Based on the network-level risk, optimization is then conducted using genetic algorithm to determine optimal life-cycle maintenance plans of deteriorating bridge networks.
Section snippets
Risk bounds of deteriorating bridge networks
The risk of structural failure in a bridge network is related to (a) direct consequences such as debris removal and reconstruction and (b) indirect consequences such as traffic delay and extra vehicle operating costs imposed upon traffic users. As the latter are usually much higher than the former [23], the proposed method considers primarily risks associated with indirect consequences. However, the method can be easily expanded to include direct consequences as exemplified in Yang and
Discussion
The proposed method is first applied to a simple bridge network with 4 nodes, 5 links, and 5 bridges [57]. The bridge network is shown in Fig. 4. The traffic demands consist of 4000 PCUs/hour from Node 1 to Node 2 and 4000 PCUs/hour from Node 3 to Node 2. The practical capacities of Links 1 to 5 are 2000, 4000, 6000, 8000, and 10,000 PCUs/hours, respectively. All links have a length of 50 km, and the free speed on links is 50 km/h. The travel time on a link can be estimated based on the link
Illustrative example
Based on the results from Discussion, the proposed method is employed for life-cycle management of an existing bridge network to demonstrate its application. In this example, the Sioux Falls network is considered. This network, adapted from the transportation network in Sioux Falls, South Dakota, has been widely used to test traffic assignment models [71]. The bridge network consists of 24 nodes, 76 links, and 10 deteriorating bridges located on the links [47]. The spatial distributions of
Conclusions
In this paper, a novel method is proposed for life-cycle management of deteriorating bridge networks. The proposed method uses system reliability analysis to obtain the network-level risk bounds. The risk bounds are then employed to approximate the network-level risk, based on which life-cycle management can be conducted using metaheuristic optimization. Compared to conventional simulation-based methods for network-level risk assessment, the proposed method does not resort to Monte Carlo
Acknowledgements
The authors are grateful for the financial support received from the U.S. National Science Foundation (Grant CMMI 1537926) and the U.S. Department of Transportation Region 3 University Transportation Center (Grant CIAM-UTC-REG6). The opinions and conclusions presented in this paper are those of the authors and do not necessarily reflect the views of the sponsoring organizations.
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