The sparse polynomial chaos expansion (SPCE) methodology is an efficient approach that deals with uncertainties propagation in case of high-dimensional problems (i.e., when a large number of random variables is involved). This methodology significantly reduces the computational cost with respect to the classical full PCE methodology. Notice however that when dealing with computationally-expensive deterministic models, the time cost remains important even with the use of the SPCE. In this paper, an efficient combined use of the SPCE methodology and the Global Sensitivity Analysis is proposed to solve such problem. The proposed methodology is firstly validated using a relatively non-expensive deterministic model that involves the computation of the PDF of the ultimate bearing capacity of a strip footing resting on a weightless spatially varying soil where the soil cohesion and angle of internal friction are modeled by two anisotropic non-Gaussian cross-correlated random fields. This methodology is then applied to an expensive model that considers the case of a ponderable soil. A brief parametric study is presented in this case to show the efficiency of the proposed methodology. Copyright © 2014 John Wiley & Sons, Ltd.