Probabilistic foundation settlement on spatially random soil

By modeling soils as spatially random media, estimates of the reliability of foundations against serviceability limit state failure, in the form of excessive differential settlements, can be made. The soil's property of primary interest is its elastic modulus, E, which is represented here using a lognormal distribution and an isotropic correlation structure. Prediction of settlement below a foundation is then obtained using the finite element method. By generating and analyzing multiple realizations, the statistics and density functions of total and differential settlements are estimated. In this paper probabilistic measures of total settlement under a single spread footing and of differential settlement under a pair of spread footings using a two-dimensional model combined with Monte Carlo simulations are presented. For the cases considered, total settlement is found to be represented well by a lognormal distribution. Probabilities associated with differential settlement are conservatively estimated through the use of a normal distribution with parameters derived from the statistics of local averages of the elastic modulus field under each footing.