A simplified mechanics-based procedure for the seismic risk assessment of unreinforced masonry buildings

Student: Luis Fernando Restrepo Velez
Supervisor: Dr. G. Magenes

Abstract

A simplified mechanics-based procedure for the seismic risk assessment of unreinforced masonry buildings is developed, based on some of the ideas presented in the original procedure proposed by Calvi [1999]. This new procedure is based on the application of a displacement-based approach for vulnerability evaluation of classes of buildings, but relevant changes have been carried out, in order to correct the main drawbacks identified. One drawback is related to the out-of-plane behaviour that has not been originally included. Another drawback is related to the definition of the joint probability density function JPDF of displacement D and period T; the real JPDF must consider the fact that D and T are not two independent variables.

For the in-plane mechanisms the demand is represented by the displacement response spectrum which is obtained from the regional probabilistic seismic hazard study, and must be defined by the median or mean value for each spectral period and also by the standard deviation. For the out-of-plane mechanisms the demand is represented according with the formulation presented in Eurocode 8 to compute the acceleration for non-structural components.

Appropriate definition of the JPDF would be necessary to be included in the methodology; however, two main problems arise: the first is the definition of the JPDF, which should include the effect of all the related sources of uncertainty and that cannot be estimated from the sample with enough accuracy, but rather have to be possibly chosen by means of a heuristic approaching. The second problem is related with the integration of the JPDF over the failure domain, in order to compute the probability of failure. An alternative path has been chosen to overcome these problems, by estimating the CDF of D and T using first order reliability methods (FORM).

Considering all the sources of uncertainty, the strategy used in the procedure can treat the uncertainty coming from the material properties and structural response, and the uncertainty coming from the statistics of the population of buildings. The former is directly included in the computation of the probability of failure for a single building or class of building, whilst the latter is considered in a second stage.

As a complement of the proposed methodology a survey data form has been designed to gather the data field required for the application of the methodology in real cases.

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