Computing the Reliability of Shallow Foundations with Spatially Distributed Measurements

In many geotechnical projects, field data is used to determine the soil parameters. In most instances, however, the statistical analysis is performed ad hoc and the spatial distribution of this data is not (expclitly) accounted for. A more formal statistical approach allows to make better use of the data and combine it in a consistent manner with other information on soil parameters. In particular, Bayesian analysis enables combining information from different sources to learn parameters and models of engineering systems, and facilitates a spatial modeling. In this paper, we apply the Bayesian concept to learn the spatial probability distribution of the friction angle of a silty soil using outcomes of direct shear tests at different locations; we then use the derived distribution to compute the reliability of a shallow foundation. We employ two different approaches for constructing the spatial probabilistic model of the friction angle. Both approaches account for the spatial variability of the soil parameter. In the first approach, we apply a single random variable for modelling the soil property within the area of interest. The inherent spatial variability of the parameter is described by the distribution of the random variable and we use the measurements to update the parameter of this distribution. We adopt the simplifying assumption of a highly fluctuating soil and use the distribution of the mean of the friction angle in conjunction with an analytical model for the bearing capacity to update the reliability of the shallow foundation. The second approach consists of modelling the spatial variability explicitly through a random field model and using the measurements to directly update the random field. Thereby, we employ a finite element model of the soil to assess the reliability of shallow foundation.