Reliability with respect to settlement limit-states of shallow foundations on linearly-deformable subsoil

A step by step procedure for applying the response surface and SORM methods in estimating the reliability index associated with exceeding a certain allowable settlement level by a shallow foundation is presented in this paper. Two random variables, the Young modulus and Poisson's ratio, of lognormal and beta distribution respectively, in a single soil layer are taken into account. A linearly-deformable model of soil is assumed which is most frequently used in engineering practice when the serviceability limit state is considered. The main problem encountered in using the response surface methodology was the existence of false design points that prevented coordinate calculations of the real ones. Two procedures were employed. The first one consisted of widening the area covered by the response surface (polynomial of the second degree) with an additional “oedometric” term. Inserting the oedometric term improves the quality of the fitting and enables one to extend the range of approximation. The latter added a barrier to prevent the procedure from moving into the false design point region. Moreover, the paper presents the effect of random variation of the Young modulus E and Poisson's ratio ν as well as their mutual correlation, on the reliability index associated with exceeding the assumed level of a shallow foundation settlement.