Image based probabilistic slope stability analysis of soil layer interface fluctuations with Brownian bridges

Abstract

Accurate interpretation of stratigraphic profiles, the phreatic surface and the spatial variability of geomaterials are essential to produce representative behaviour of geomechanical systems through numerical simulations. When considering slope stability, variations in soil layer boundaries and the phreatic surface may result in misleading metrics such as the Factor of Safety (FoS) and the Probability of Failure (PoF). This paper presents an image-based technique for generating continuous stratigraphic profiles, including random fluctuations based on Brownian motion. Brownian bridges are used to produce random walks between known points on both soil layer boundaries and the phreatic level that overlap with the slope profile image. Quadtree decomposition is used to discretise the stratigraphy and the phreatic level through an automatic process using generated digital images for mesh generation while also integrating material properties. The Scaled Boundary Finite Element (SBFEM) is used to analyse the slope stability problem. Images based on random walks along an unknown stratigraphic material boundary and the phreatic surface are randomly generated and have many random possibilities, which are used to undertake probabilistic analysis to obtain PoF. This process is complex when using numerical methods, such as the Finite Element Method, as it requires mesh generation from different slope profiles with alternating material interfaces at each probabilistic instance. When the Scaled Boundary Finite Element Method is applied, probabilistic numerical analyses can be fully automated for randomly generated material interfaces. The feasibility of the proposed method is illustrated through several cases of a slope with multiple material layers, in addition to a slope incorporating a Brownian bridge phreatic surface formulation.