AbstractGeological heterogeneity is a result of the natural deposit process of strata with a highly irregular and uncertain distribution of soil mass in the real world. However, compared with the effect of inherent spatial variability of soil properties on geostructures, the effect of geological heterogeneity has received less attention so far. In view of this limitation, this paper adopts a Markov random field model to stochastically simulate the geological heterogeneity for assessing the bearing capacity of a shallow foundation with quantified uncertainty. By mapping the generated stratigraphic realizations in the commercial software FLAC3D version 7.0, an ensemble of numerical models is generated. Computational results show that geological heterogeneity has a significant influence on the estimated capacities. Information entropy is used to characterize the geological uncertainty. It is not surprising that the increase of boreholes could reduce the average information entropy, and thus reduce the standard deviation of bearing capacities. But the effect of increasing the borehole numbers on the uncertainty reduction exhibits a clear nonlinear form with a potential to select an optimal borehole number. Results from the proposed stochastic analysis provide a range of calculated capacities, which can be used to mitigate the risk of insufficient bearing capacity.