Life-cycle management of deteriorating bridge networks with network-level risk bounds and system reliability analysis

Highlights

• A novel method is proposed for life-cycle management of bridge networks.

• The method adopts a non-simulation approach based on network-level risk bounds.

• Probabilities of failure scenarios are obtained in system reliability analysis.

• Optimal maintenance plans are determined by minimizing network-level risk.

• The method can account for the impacts of unlikely, high-impact events.

Abstract

Structural deterioration poses a substantial threat to the safety, serviceability, and functionality of bridges. Since bridges are connected in transportation networks, their failure can dramatically alter traffic flow, causing immense social consequences such as large-scale traffic delay and additional vehicle operating cost. In this paper, a novel method is proposed for life-cycle management of deteriorating bridge networks. The proposed method aims at minimizing network-level risks associated with deterioration-induced bridge failure. To combat the deficiencies of existing Monte Carlo simulation-based risk assessment methods, the proposed method adopts a non-simulation approach that relies on risk bounds of deteriorating bridge networks. In particular, this method uses system reliability analysis to determine the occurrence probabilities of various bridge failure scenarios in a network. For each failure scenario considered, traffic assignment is conducted to predict the traffic flow in the damaged network and the network-level consequences. The upper and lower bounds of the network-level risk are then formulated, allowing for efficient and accurate risk assessment with only a few traffic assignment operations. Estimated by the average value of its upper and lower bounds, the network-level risk is used as the optimization objective in a metaheuristic search procedure to obtain optimal life-cycle maintenance plans including the maintenance schedule and the investment on each maintenance action. The proposed method excels in its ability to account for the impacts of unlikely, yet high-impact events, as well as its ability to obtain optimal or near-optimal life-cycle maintenance plans that can more effectively reduce risks than those obtained using simulation-based methods.

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.