In this thesis, the failures that occurred during the construction of the Jamuna Bridge Abutment in Bangladesh have been investigated. In particular, the influence of heterogeneity on slope stability has been studied using statistical methods, random field theory and the finite element method. The research is divided into three main parts: the statistical characterization of the Jamuna River Sand, based on an extensive in-situ and laboratory database available for the site; calibration of the laboratory data against a double-hardening elastoplastic soil model; and stochastic finite element slope stability analyses, using a Monte Carlo simulation, to analyse the slope failures accounting for heterogeneity. The sand state has been characterised in terms of state parameter, a meaningful quantity which can fully represent the mechanical behaviour of the soil. It was found that the site consists of predominantly loose to mildly dilative material and is very variable. Also, a Normal distribution was found to best represent the state parameter and a Lognormal distribution was found to best represent the tip resistance.The calibration of the constitutive model parameters was found to be challenging, as alternative approaches had to be adopted due to lack of appropriate test results available for the site. Single-variate random fields of state parameter were then linked to the constitutive model parameters based on the relationships found between them, and a parametric study of the abutment was then carried out by linking finite elements and random field theory within a Monte Carlo framework.It was found that, as the degree of anisotropy of the heterogeneity increases, the range of structural responses increases as well. For the isotropic cases, the range of responses was relatively smaller and tended to result in more localised failures. For the anisotropic cases, it was found that there are two different types of deformation mechanism. It was also found that, as the vertical scale of fluctuation becomes bigger, the range of possible structural responses increases and failure is more likely. Finally, it was found that the failed zones observed during the excavation of the West Guide Bund of the Jamuna Bridge Abutment could be closely predicted if heterogeneity was considered in the finite element analyses. In particular, it was found that, for such a natural deposit, a large degree of anisotropy (in the range of 20) could account for the deformation mechanisms observed on site.