Analytical Solutions of Free Surface Evolution Within Originally Dry, Coarse-Grain-Sized Embankment Dam Materials

Tightness of homogeneous embankment dams is often ensured by means of upstream water barriers, such as bituminous concrete facings, concrete slabs, shotcrete membranes, metallic sheets, geomembranes, and cement blankets. The stability analysis of these dams, especially in areas with high seismicity, must include the hydraulic and mechanical effects resulting from an extensive, sudden cracking of the impervious facing. To this purpose, in this paper, simple, original analytical solutions are proposed to estimate the position of the exit point on the downstream slope of the dam, the maximum height of the saturation front at the downstream face, and the time required for the saturation front to reach the downstream face. These variables generally depend on several factors, such as the geometry of the dam, homogeneity or heterogeneity, the permeability coefficient of the dam body materials, and resistance laws to describe the seepage flow. The high number of these factors requires the development of advanced 2D/3D FEM analyses, often computationally heavy and complex to implement. Although approximate, the proposed solutions may however allow us to define the role of the various factors and their interaction, to quickly deduce the main, preliminary design indications.