Reliability analysis of seepage using an applicable procedure based on stochastic scaled boundary finite element method

This paper presents a practical approach for reliability analysis of steady-state seepage by modeling spatial variability of the soil permeability. The traditional semi-analytical method; named Scaled Boundary Finite-Element Method (SBFEM) is extended by a coded program to develop a stochastic SBFEM coupled with random field theory. The domain is discretized into several non-uniform SBFEM sub-domains. The flow quantities such as exit gradient, flow rate, and the reliability index of piping safety factor are estimated. The precision of the outputs and the accuracy of the method are verified with the Finite-Element Method (FEM). A set of stochastic analysis is performed in three illustrative examples to illuminate the applicability of the proposed method. In these examples, the effect of the variations in the position of the sub-domain discretization center, the cutoff location, and the cutoff length are investigated stochastically. Further, the influence of the permeability's Coefficient of Variation (COVk) and the correlation length is evaluated. The results are shown acceptable agreement with those obtained by the conventional Stochastic Finite-Element Method (SFEM). The proposed approach has potential to model the complex geometries and cutoffs in different locations without additional efforts to deal with the spatial variability of the permeability.