This research work involves modeling reinforced concrete and steel fibers structural elements, and investigating the safety domain of these structural elements. The main aim is to simulate their behavior until failure, and to estimate their failure probability. Firstly, the Hasofer-Lind model coupled with non-linear computation using the response surface method (RSM) is applied to estimate the reliability index, the scenarios and the failure probability. Furthermore, the direct Monte-Carlo simulation method is applied to assess the failure probability of the systems studied. We validate our formulation and modeling, by comparing the results of our calculations with experimental results and those obtained by other authors. The tests were carried out on RC beam, RC frame and SFRC pile. This comparison shows the efficiency and performance of each model used in this study. Among other things, after studying all possible cases of distribution laws for random load-resistance variables, it was observed that a log-normal law gives a very low failure probability, thus guaranteeing a certain level of safety. A parametric study is carried out for the SFRC pile to determine the influence of variation in modulus of elasticity and concrete strain in compression.
Benyahi et al. (2026) studied this question.