A methodology for modelling the flow regime in unsaturated infinite slopes

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4. A methodology for modelling the flow regime in unsaturated infinite slopes

The paper presents a novel methodology to calculate the flow regime in unsaturated infinite slopes by means of horizontal ground infiltration models. This is achieved by decomposing the flow regime of the infinite slope into a symmetric part and an antisymmetric part, whose respective solutions are then combined to determine the actual seepage. The solution of the antisymmetric part is trivial and does not even need integration of the continuity equation while the symmetric part reduces to the case of one-dimensional vertical infiltration into a horizontal soil deposit, for which analytical/numerical solutions exist in the literature. The idealised geometry implies that all surface infiltration crosses the slope along the shortest path perpendicular to the ground, while the flux parallel to the slope is fed by an upstream source at infinite distance. The paper also calculates the expression of the piezometric head gradient parallel to the slope, which is the Neumann boundary condition to be imposed on the upstream and downstream sides of any soil slice perpendicular to the inclined ground. This avoids the use of arbitrary boundary conditions in finite element/difference models as done in current practice. The proposed methodology is finally validated against analytical and numerical solutions of transient seepage across an infinite unsaturated slope.

10th European Conference on Numerical Methods in Geotechnical Engineering (NUMGE2023)

2. Finite element, finite difference, discrete element, material point and other methods