Abstract
The authors present a new method, called the hypercone method, based on the principles of level-2 methods. The main aims of this method are to evaluate the safety index β and to deduce the values of the probability of failure P f by considering the whole geometry of the failure domain. In the first part of this paper, the mathematical principles of the hypercone method are developed. The restrictions and the practical application of the method, in order to assess either P f or its upper and lower bounds are discussed in the second part. The results reported in this paper show that the values of P f deducced from the Hasofer-Lind index β, assuming linearity of the limit state surface, and P f values obtained by Monte Carlo simulations are in accordance with those deduced from the hypercone method. However, the hypothesis stating that the state variable E(E=Resistance-Sollicitation) might follow a Gaussian distribution seems to be slightly inaccurate.
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