Reliability-Based Selection of Retrofit Works for Schools under Seismic Hazard

A reliability-based procedure is proposed to assess and compare the economic effectiveness of three retrofit alternatives for actual schools located in three zones with different seismic hazards. The procedure calculates the school failure probability under the damaged conditions, by considering the damages produced by the 2017 earthquake in Mexico, and the failure probability under each retrofit alternative, from the seismic spectra corresponding to the seismic hazard of each site. The best retrofit alternative is the one with the minimum expected life-cycle cost for each school. The global failure probability is calculated according to the Ditlevsen’s bounds, and the limit states consist of the event in which the maximum moment exceeds the bending capacity for beams, and the combined axial and bending forces exceed the capacity of the columns; the maximum responses are obtained through nonlinear analyses. The proposed retrofit alternatives are column and beam jacketing with steel angles and plates, increment of the concrete cross sections of columns and beams, and the addition of bracing. The effectiveness of each alternative, in terms of failure probability reduction and expected life-cycle cost, was assessed for each school. The procedure may be used to update the current retrofit specifications for schools.

This paper presents a procedure to select the best retrofit strategy among several proposed alternatives to retrofit a school damaged by earthquakes. The proposed alternatives are the jacketing or reinforcement of the concrete sections, the addition of steel cover plates, and the addition of steel bracings, all in the critical sections or zones. For the selection of the best alternative, a cost–benefit analysis is proposed to balance the cost, in terms of the expected life-cycle cost (which includes the cost of failure consequences), with the benefit, which consists of the improvement of structural reliability. These analyses provide information to the owner or designer to make decisions about the desired level of reliability for the corresponding investment to protect schools against future earthquakes at the school location. The methodology was illustrated for three actual schools. The procedure considers the level of risk, according to the number of students exposed to the earthquakes and the level of seismic hazard for each school location. With the proper adaptations to other specific cases, the procedure may complement the engineering judgment, experience, and best practices of designers to guide the search for the optimal retrofit of schools under seismic hazard.