Optimal reliability to retrofit structures damaged by earthquakes from the perspective of the life-cycle cost

When an earthquake damages a building, the type and increment on safety level of the retrofit may not be very clear. If that increment is not too large, the next earthquake may produce even more damages to the building; also, the building importance and the seismic hazard levels play a role on that decision. The criterion of minimizing the expected value of the building life-cycle cost brings some guide on that issue. This paper proposes the use of the expected life-cycle cost to identify what is the reliability level which is convenient for the retrofit. The procedure is illustrated by assessing three buildings with different damage level, different level of damage/failure consequences and different seismic hazard. For a school with a damage index of 0.2, a level of damage/failure consequences not so high and a moderate level of seismic hazard, the optimal failure probability for the retrofit is 1.2 * 10(-3). However, for buildings with a damage index of 0.3, and with higher level of damage/failure consequences, and under higher level of seismic hazard, the optimal failure probability for retrofit ranges from 2 to 8 * 10(-4).