The paper examines three-dimensional (3D) analyses of the load bearing capacity of square and strip footings on a spatially variable cohesive–frictional (c–φ) soil. Embedded, rigid and smooth footings are considered. Cohesion and friction angle are modelled using random fields. The vertical scale of fluctuation (SOF) is based on earlier studies of natural soils. For the square footing problem, the horizontal SOF is the subject of a parametric study. For the strip footing, only one value of the horizontal SOF is assumed, and the parametric study concerns the modelled length of the foundation. To generate the fields of strength parameters, the Fourier series method is employed. For both problems analyzed, the influence of the parameters on the probabilistic characteristics of the bearing capacity of the soil is investigated. For the square footing problem, both the mean value of bearing capacity and its coefficient of variation increase with an increasing horizontal fluctuation scale, but they stabilize at higher values of SOF. For the strip footing problem, it appears that 2D modelling is a very conservative approach, and for the precise assessment of the probability of foundation failure, the footing should be modelled in 3D.

The paper deals with application of CPTu test results for the probabilistic modeling of dumping grounds. The statistical measures use results from 42 CPT test points located in the lignite mine dumping ground from the region of Central Europe. Both the tip resistance q_c as well as local friction f_s are tested. Based on the mean values and standard deviations of measured quantities the specific zones in the dumping site profile are distinguished. For three main zones standard deviations of linearly de-trended functions, distributions of normalized de-trended values for q_c and f_s are examined. Also the vertical scales of fluctuation for both measured quantities are estimated. The obtained result shows that lignite mine dumping site can be successfully described with the Random Field Theory. Additional use of f_s values introduces supplementary statistical information.