Time-variant reliability using the PH12 method: Principles and validation by Monte Carlo simulation

The study of the reliability of an aging structure requires taking into account the influence of time. The classical approach for performing time-variant reliability analysis relies upon the computation of outcrossing rates (of the limit state surface) by asymptotic formulae. This method requires advanced mathematics and ad-hoc implementation. An alternative approach is possible, which allows to directly compute the outcrossing rate by means of system reliability analysis. This method is called PHI2 in this paper. Thus classical time-invariant reliability tools can be used. Both approaches are compared to closed form solution on simple examples. The quality of the computed upper bound to the probability of failure is assessed by Monte Carlo simulation. A stationary and a non-stationary application examples are proposed. The numerical features and the computational cost of each method are compared; Finally, a more realistic example is solved, namely that of the failure of a concrete beam submitted to creep and a stochastic load.