In this paper, a probabilistic study of a one-dimensional soil consolidation problem has been carried out. The Collocation-based Stochastic Response Surface Method (CSRSM) was employed for the probabilistic analysis. The Young modulus E, the Poisson ratio n, the hydraulic conductivity k h and the uniform surcharge loading q applied at the ground surface were considered as random variables. The probabilistic system responses considered in the analysis were the surface settlement and the consolidation time. Numerical simulations that make use of Biot theory were used for the computation of these system responses. A global sensitivity analysis based on Sobol indices was performed to identify the random variables that have the most contribution in the variability of the system responses. Also, a parametric study was undertaken to investigate the effect of the input geotechnical parameters and the statistical parameters of the random variables on the probability distribution functions of the system responses.

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Soil liquefaction is the source of several major damages during earthquakes on the material and human level. Several authors have studied the probability of liquefaction by in situ and laboratory tests and several models have been proposed to calculate the safety factor. But because of various uncertainties in performance function parameters, we adopted in this paper a reliability analysis that considers uncertainties of parameters and model uncertainties. We used the Monte Carlo simulation (MCS) to calculate the probability of failure to liquefaction based on standard penetration test SPT which soil's parameters are modeled by random variables.The reliability results obtained show that the variability of soil's parameters has an important impact on the probability of liquefaction. A sensitivity analysis based on the coefficient of variation is presented to see the effect of each random variable on the probability of liquefaction.

In this paper, a probabilistic study on durability concrete was carried out. In such a design, initiation time of corrosion must be expressed as a mathematical model using Fick's second law and the statistical distributions properties of theirs parameters was included in this model. The scatter both in the environmental exposure conditions and structural properties was considered as random fields in the mathematical model with a probabilistic design. The main objective of this study is predicted initiation time of corrosion of concrete structures in chloride containing environments. This probabilistic study is developed using Monte Carlo simulation to determine the contribution of each input parameters and the statistical parameters of the random variables on the probability distribution functions of the initiation time of corrosion. Also, a comparison study was carried out to analyze the impact of the probability distribution on the response (the initiation time of corrosion).