Confined seepage analysis of saturated soils using fuzzy fields

Seepage refers to the flow of water through porous materials. This phenomenon has a crucial role in dam, slope, excavation, tunnel, and well design. Performing seepage analysis usually is a challenging task, as one must cope with the uncertainty associated with the parameters such as the hydraulic conductivity in the horizontal and vertical directions that drive this phenomenon. However, at the same time, the data on horizontal and vertical hydraulic conductivities are typically scarce in spatial resolution. In this context, so-called non-traditional approaches for uncertainty quantification (such as intervals and fuzzy variables) offer an interesting alternative to classical probabilistic methods, since they have been shown to be quite effective when limited information on the governing parameters of a phenomenon is available. Therefore, the main contribution of this study is the development of a framework for conducting seepage analysis in saturated soils, where uncertainty associated with hydraulic conductivity is characterized using fuzzy fields. This method to characterize uncertainty extends interval fields towards the domain of fuzzy numbers. In fact, it is illustrated that fuzzy fields are an effective tool for capturing uncertainties with a spatial component, since they allow one to account for available physical measurements. A case study in confined saturated soil shows that with the proposed framework, it is possible to quantify the uncertainty associated with seepage flow, exit gradient, and uplift force effectively.