PSI - Issue 44

Alessandro Fulco et al. / Procedia Structural Integrity 44 (2023) 195–202 Alessandro Fulco et al. / Structural Integrity Procedia 00 (2022) 000–000

196

2

floor accelerations, etc. The evaluation of the success of a seismic design has to be based, and more and more will have to be based, on the actual performances under a seismic attack, this is especially true when advanced protection systems are applied. This need was felt since the very beginning of the application of new technologies, so procedures for the evaluation of the consequences of a seismic attack on constructions were developed since the '80s and '90s, Thiel, C.C. (1986), Parducci A. et al (1995). Notwithstanding this, the structural design still continues to be based on the control of the EDP's rather than on actual parameters expressing the structure performance, that is the "consequences" of the seismic attack on the structural and non structural elements, on the contents, and, last but not least, on the occupants, for both direct or indirect effects. The consequences depend on the seismic hazard at the site, on the vulnerability of the considered construction, on the exposition of contents and occupants, therefore the rigorous way to account for them is to perform a risk analysis. An analytical evaluation of the seismic risk should account for four main issues. (1) The seismic hazard in terms of intensity of the expected earthquakes: a correlation between the elastic response spectrum parameters, most of all the PGA, and the return period can be used, Cornell C.A. (1968); (2) a correlation between the input seismic demand and the vulnerability of the structure: it can be defined as a function of the required safety level, Crowley H. et al (2004); (3) a correlation between the EDP's characterizing the seismic response and the damage: it can be defined as in Dolce M. et al (2000); (4) a correlation between damage indicators and expected consequences: functions as in Bostrom A. et al (2008) can be adopted. A rigorous methodology of risk assessment is fully probabilistic, since the listed issues are characterized by randomness, and leads to a definition of the expected consequences in terms of probability of occurrence. This approach was originally present in the first guidelines oriented to the PBSD (Performance Base Seismic Design), ATC58 (2007), as well as in successive versions FEMA445 (2006), FEMA P-58-1 (2018). The fully probabilistic procedures are very hard to be carried out so, for the practical use of a PBSD methodology a quick semi-probabilistic procedure, that could be used as a complement of an ordinary tool, as a commercial software for vulnerability assessment and seismic design, is suitable. This paper illustrates an updated version of the procedure f-RACE, Mezzi M. et al (2016) and (2017), that satisfies the requirements of an easy-to-use tool. The updated formulation of the procedure provides for a strong data interchange with a commercial seismic design software and is based on the experience resulted from performed vulnerability assessments, damage analyses, retrofitting projects of buildings damaged by the more recent Italian earthquakes. 2. Outline of the procedure The procedure described in the following concerns the estimation of the economic consequences of an earthquake on a given building. Also the consequences on the occupants can be computed once the exposition is defined for all the sections of the building. The basic procedure develops according to the following steps: • seismic hazard at site in terms of return periods of seismic intensity levels; • numerical model of the structure using a commercial software; o nonlinear static analyses increasing the lateral loads up to achieve the damage state corresponding to the scenario; o consequences (retrofitting cost) of damage on structural / non structural elements and contents (in place of the retrofitting costs, effects on the occupants can be used); o global cost (from direct and indirect costs) of the scenario; • evaluation of the expected consequences in the building lifetime or in a predefined time interval. 3. Damage states and consequences for structural elements Beams, columns and walls are characterized by four damage levels: "light damage" D1 (ST) ; "medium damage" D2 (ST) ; "serious damage" D3 (ST ; "collapse" (conventional) D4 (ST) . The four damage states are identified with reference to the evolution of the moment-curvature correlation characterizing the plastic hinges that develop at the ends of the elements, Botta M. et al. (2008). The damage levels are identified by a status of the material: concrete cracking fixes D1 (ST) ; concrete cover spalling fixes D2 (ST) ; yealding of steel bars fixes D3 (ST) ; confined concrete crashing fixes D4 (ST) corresponds to the of the. A shear failure immediately fixes a damage state D4 (ST) . • assigning damage states to structural / non structural elements and contents ; • definition of a number of global damage conditions (damage scenarios); • steps to be repeated for each of the considered damage scenarios: