Assessment of existing masonry structures using probabilistic methods - state of the art

Nowadays, powerful methods are available for the calculation of structural safety values. These permit to calculate the global probability of failure of complex structures, relying on deterministic techniques able to determine the stability state (limit state) for a prescribed set of parameters. Such techniques are often non linear finite element analyses. The Joint Committee of Structural Safety defines different levels at which the structural safety of existing buildings can be assessed. Level III methods are the most accurate. This paper deals with possible methods to derive a global failure probability according to the level III method. Besides the traditional methods, such as Numerical Integration, (Importance Sampling) Monte Carlo, Directional Sampling and Directional Integration, First Order and Second Order Reliability Methods in combination with a system analysis, recently new methods have been proposed. They intend to limit the number of direct limit state function evaluations. Indeed, in many cases a non-linear finite element analysis will be required, demanding a significant amount of computation time. Therefor the technique of response surfaces has been introduced. However, using the elementary response surface technique, the problem is shifted towards obtaining a good response surface, which again requires numerous limit state function evaluations. Adaptive response surface techniques, such as Directional Adaptive Response Surface Sampling, overcome this disadvantage to a certain extent. These in fact are optimization schemes that minimize the number of direct limit state function evaluations.