Life-cycle performance of structures: combining expert judgment and results of inspection

Abstract

Current bridge management systems base decisions on the results of visual inspections. These systems consider visual inspection results as accurate and disregard any further information available. In the present study, the result of each inspection is considered as a random variable, dependent of a wide range of factors, that can be integrated with other sources of information, including expert judgment and results of other inspections. The combination of different sources of information results in reliable posterior information and allows more accurate predictions of future deterioration. In the present paper, performance of an existing structure is obtained in terms of the condition index, which describes the effects of deterioration as can be seen by an inspector, and the safety index, which measures the safety margin of the structure. The reduction in uncertainty associated with periodical inspections is considered through updating of performance profiles. The updating of the condition index is direct, as new information on this parameter is collected by the inspector. In terms of safety, however, only indirect information is collected and the uncertainty reduction associated with an inspection is significantly lower. Several realistic examples show the impact of inspections on the predicted life-cycle performance of structures. 2 CONDITION, SAFETY AND COST In the model proposed by Neves and Frangopol (2005) life-cycle performance of an existing structure is characterized by three different timedependent probabilistic indicators: condition index, safety index, and the cumulative maintenance cost. The condition index is an indicator of deterioration as recorded by a bridge inspector. It might be associated with the severity of cracking in reinforced concrete structures, deterioration of painting and rusting in steel structures, or any other visually observable deterioration effect. The safety index is a measure of the reliability or the safety margin of a structure, and can only result from a structural safety evaluation. These two indicators are related, in the sense that both refer to the effects of deterioration on a certain structure. However, full knowledge on one of these factors is not enough to determine the value of the other. In fact, the condition index is only influenced by the observable defects, and only indirectly includes the effects of corrosion, fatigue or cracking. The safety index includes all these aspects directly. In short, the safety index would be a much more interesting measure of performance. However, it is extremely expensive to determine the safety margin of a structure, and the network system reliability analysis of all structures in a large network is close to impossible. In the model proposed by Frangopol (1998) and Neves and Frangopol (2005), the condition and safety indices under no maintenance are defined as bi-linear functions, in terms of 6 random parameters: initial condition, C0, initial safety index, S0, time of initiation of deterioration of condition and safety, tic and ti, respectively, and deterioration rate of condition and safety, αc and α, respectively. The effect of maintenance actions is defined in terms of 8 random parameters, as follows: (a) improvement in condition index and safety index immediately after application, γc and γ, respectively; (b) time during which the deterioration processes of condition index and safety index are suppressed, tdc and td, respectively; (c) time during which the deterioration rate in condition index and safety index are suppressed or reduced, tpdc and tpd, respectively; and (d) deterioration rate reduction of condition index and safety index, δc and δ, respectively. The meaning of each of these random variables is shown in Figure 1. The mean, standard deviation, histograms and percentiles of the life-cycle condition index, safety index, and cumulative cost are computed using Monte-Carlo simulation. A detailed description of the computational platform employed can be found Neves and Frangopol (2005). gc tdc a d c c TIME C O N D IT IO N IN D E X , C tpdc tpi tp tp First application Second application