Dynamic Programming for Individual Bridge Maintenance Planning

Bridges without maintenance may not reach a targeted service lifetime due to the aging and deterioration. Therefore, bridge maintenance actions must be applied to extend the remaining service lifetime of individual bridges. Individual bridge maintenance planning needs to answer to questions such as what sequence of maintenance actions and when these maintenance actions should take place in order to minimize the life-cycle maintenance cost throughout the entire targeted lifetime period. The life-cycle maintenance cost can be either construction cost that bridge owners have to pay for or user’s cost that includes the time delays and fuel consumption due to detour and/or congestion caused

Figure 1: Effects of “Minor Concrete Repair” on Mean Condition and Safety Indices over Time

Figure 2: Effects of “Silane Treatment” on Mean Condition and Safety Indices over Time

Figure 3: Effects of “Cathodic Protection” on Mean Condition and Safety Indices over Time

(b) Effect on Safety Index

Figure 4: Effects of “Rebuild” on Mean Condition and Safety Indices over Time

by the maintenance actions or combination of both construction and user’s cost. In reality, bridge maintenance planning has to consider the maintenance funding limitation as well.

In this study, the prediction of the remaining service lifetime of individual bridges is based on both bridge condition and safety indices. The bridge condition index increases as the bridge deteriorates with time, while the bridge safety index decreases with time. The maximum condition index is set to be 3.0, and the minimum safety index is assigned to be 0.91 (Denton, 2002). In other words, an individual bridge should always have a condition index less than 3.0 and a safety index greater than 0.91 during the entire service lifetime period. The difference between the predicted remaining service lifetime and the targeted service lifetime of a bridge must be covered by applying maintenance alternatives. Any combination of the above five bridge maintenance alternatives that can extend the
bridge service lifetime to the targeted level may be regarded as a feasible maintenance plan. These feasible maintenance plans may require performing different combinations of the above five maintenance actions at different application times, resulting in different life-cycle maintenance cost. The life-cycle maintenance cost for each feasible maintenance plan are converted to the net present values (NPV), using the discount rates ranging from 2% to 8%. Thus, an optimal bridge maintenance plan is the feasible plan that has a minimum life-cycle maintenance cost in terms of NPV. A dynamic programming (DP) procedure has been developed to identify the optimal bridge maintenance plans for individual bridges (Liu and Frangopol, 2006). Monte Carlo simulations are integrated within the DP procedure for sensitivity studies, considering the probability distributions of all random variables and parameters. As a result, the probabilities that each of the above five maintenance alternatives (including “Do Nothing”) may be conducted at certain time (year) can be obtained for individual bridges. The details of the DP procedure combined with Monte Carlo simulations are presented in Liu and Frangopol (2006).