Most civil systems are subjected to more than one hazard in its lifetime. When design for more than one hazard, one is frequently confronted with the difficult question of what level of reliability one should aim for each hazard.  The major considerations in a lifecycle cost analysis are proper treatment of uncertainties in the demand and capacity and cost incurred due to unsatisfactory performance. Costs considered include those of construction, maintenance and operation, repair, damage and failure consequence, and discounting of cost over time.  It is reasonable to assume that the number of structural limit states of concern is small and that severe hazards causing the limit states occur infrequently.

Expected lifecycle cost formulation (Wen and Kang, I and II, Journal of Structural Eng, ASCE March 2001)

rumus

LLC method accounts for major factors in rational design decision making. Conventional methods, deterministic, or probabilistic alone, may not be justified from long-term benefit vs cost consideration. The optimal design intensity generally increases with lifetime; however, the increase is small for life > 50yr. The optimal design intensity depends heavily on the consequence of failure; can be the single most important factor overshadowing other factors such as exposure time. Uniform reliability is not required in an optimal design which is generally dominated by hazards that have large uncertainty.

In most current codes, only one of the design wind or earthquake load is considered in the various load combinations but not both because of the small chance of simultaneous occurrence of both design loads. The design is therefore often ‘controlled’ or ‘governed’ by the hazard with higher design load intensity. From the lifecycle cost point of view, however, the lesser hazard may still contribute significantly to the damage and cost over the structure’s life, therefore should not be ignored all together in the design.

The optimal design is highly dependent on failure consequences and often dominated by one hazard, the lesser hazards, however, still contribute. The design in general is not “controlled” or “governed” by one hazard. The reliability of a lifecycle cost-based design is generally higher than that implied in current codes, and different against different hazards. Uniform reliability is not required. The optimal design strength against earthquakes increases with structural life for t < 30 yrs and reaches a saturation point at about 50 yrs, but independent of life against wind. The optimal design is insensitive to capacity uncertainty, moderately dependent on discount rate, and may or may not be sensitive to cost of injury and death depending on location and seismic hazard characteristics. It is more cost-effective and realistic to look at the risks and costs due to all hazards than single out one hazard (such as   earthquakes or blasts) and deal with it separately.

Resume of Prof Y.K. Wen Lecture