Life-cycle Cost Design of Deteriorating Structures

A lifetime optimization methodology for planning the inspection and repair of structures that deteriorate over time is introduced and illustrated through numerical examples. The optimization is based on minimizing the expected total life-cycle cost while maintaining an allowable lifetime reliability for the structure. This method incorporates: (a) the quality of inspection techniques with different detection capabilities; (b) all repair possibilities based on an event tree; (c) the effects of aging, deterior~ti~m: an~ subsequent. r~~air on structural reliability; and (d) the time value of money. The overall cost to be minimized Includes the initial cost and the costs of preventive maintenance, inspection, repair, and failure. The methodology is illustrated using the reinforced concrete T-girders from a highway bridge. An optimum inspection/repair strategy is deve~~ped for these girders that are deteriorating due to corrosion in an aggressive environment. The effect of cntlcal. pa­ rameters such as rate of corrosion, quality of the inspection technique, and the expected cost of structural fallure are all investigated, along with the effects of both uniform and nonuniform inspection time intervals. Ultimately, the reliability-based lifetime approach to developing an optimum inspection/repair strategy demonstrates the potential for cost savings and improved efficiency. INTRODUCTION The management of the nation's infrastructure is a vitally important function of government. The inspection and repair of the transportation network is needed for uninterrupted com­ merce and a functioning economy. With about 600,000 high­ way bridges in the national inventory, the maintenance of these structures alone represents a commitment of billions of dollars annually. In fact, the nation spends at least $5,000,000,000 per year for highway bridge design, construction, replacement, and rehabilitation (Status 1993). Given this huge investment along with an increasing scarcity of resources, it is essential that the funds be used as efficiently as possible. Highway bridges deteriorate over time and need mainte­ nance/inspection programs that detect damage, deterioration, loss of effective strength in members, missing fasteners, frac­ tures, and cracks. Bridge serviceability is highly dependent on the frequency and quality of these maintenance programs. Be­ cause the welfare of many people depends on the health of the highway system, it is important that these bridges be main­ tained and inspected routinely. An efficient bridge maintenance program requires careful planning base~ on potenti~ modes of failure of the structural elements, the history of major struc­ tural repairs done to the bridge, and, of course, the frequency and intensity of the applied loads. Effective maintenal1;ce/in­ spection can extend the life expectancy of a system while re­ ducing the possibility of costly failures in the future. In any bridge, there are many defects that may appear dur­ ing a projected service period, such as potholes in the deck, scour on the piers, or the deterioration of joints or bearings. Corrosion of steel reinforcement, initiated by high chloride concentrations in the concrete, is a serious cause of degrada­ tion in concrete structures (Ting 1989). The corrosion damage is revealed by the initiation and propagation of cracks, which can be detected and repaired by scheduled maintenance and inspection procedures. As a result, the reliability of corrosive 'Prof., Dept. of Civ., Envir., and Arch. Engrg., Univ. of Colorado, Boulder, CO 80309-0428. 'Proj. Mgr., Chung-Shen Inst. of Sci. and Techno\., Taiwan, Republic of China; formerly, Grad. Student, Dept. of Civ., Envir., and Arch. Engrg., Univ. of Colorado, Boulder, CO. 'Grad. Siudent, Dept. of Civ., Envir., and Arch. Engrg., Univ. of Col­ orado. Boulder, CO. critical structures depends not only on the structural design, but also on the inspection and repair procedures. This paper proposes a method to optimize the lifetime inspection/repair strategy of corrosion-critical concrete struc­ tures based on the reliability of the structure and cost-effec­ tiveness. The method is applicable for any type of damage whose evolution can be modeled over time. The reliability­ based analysis of structures, with or without maintenance/in­ spection procedures, is attracting the increased attention of re­ searchers (Thoft-Christensen and Sr6rensen 1987; Mori and Ellingwood 1994a). The optimal lifetime inspection/repair strategy is obtained by minimizing the expected total life-cycle cost while satisfying the constraints on the allowable level of structural lifetime reliability in service. The expected total life­ cycle cost includes the initial cost and the costs of preventive maintenance, inspection, repair, and failure. MAINTENANCEIINSPECTION For many bridges, both preventive and repair maintenance are typically performed. Preventive or routine maintenance in­ cludes replacing small parts, patching concrete, repairing cracks, changing lubricants, and cleaning and painting expo~ed parts. The structure is kept in working condition by delaymg and mitigating the aging effects of wear, fatigue, and related phenomena. In contrast, repair maintenance m~gh~ inclu~e re­ placing a bearing, resurfacing a deck, or modlfymg. a girder. Repair maintenance tends to be less frequent, reqUlres more effort, is usually more costly, and results in a measurable in­ crease in reliability. A sample maintenance strategy is shown in Fig. 1, where T l , T2 , T3 , and T4 represent the times of repair maintenance, and effort is a generic quantity that reflects cost, amount of work performed, and benefit derived from the main­ tenance. While guidance for routine maintenance exists, many repair maintenance strategies are based on experience and local ~rac­ tice rather than on sound theoretical investigations. Mamte-