Probabilistic analysis of foundation settlement

It is at least intuitively evident that variability in soil properties will have a significant effect on total and differential settlement of structural foundations. By modeling soils as spatially random media, whose properties follow certain distributions and spatial correlation structures, estimates of the reliability of foundations against serviceability limit state failure, in the form of excessive differential settlements, can in principle be made. The soil’s property of interest is it’s elastic modulus, , which is represented here using a lognormal marginal distribution and an isotropic correlation structure. Prediction of settlement below a foundation can then be made using the finite element method given a realization of the elastic modulus field underlying the foundation. By generating and analyzing multiple realizations, the statistics and density functions of total and differential settlements can be estimated. This paper estimates 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 a Monte Carlo simulation. For the cases considered, total settlement is found to be well represented by a lognormal distribution and simple relationships are proposed allowing the approximation of the settlement distribution parameters for a footing founded on a spatially random soil of constant depth and fixed Poisson’s ratio. A one-parameter exponential distribution is fitted to differential settlements and found to give reasonable probability estimates, particularly towards the tail of the distribution. A method of predicting the single parameter is given in terms of statistics of the elastic modulus field and local averages over the field. An example is presented to illustrate the proposed methodology for a single footing