Generalized unconfined seepage flow model using displacement based formulation

• A generalized numerical FE, model to predict seepage through porous media, is shown.
• The iterative procedure to obtain free surfaces is implemented in this model.
• Several relevant aspects of fast emptying of a reservoir are explored.
• Hints on the more significant aspects in the earth dams design are justified.

Modeling seepage along with the mechanical response of deformable Earth dams under transient conditions is a very complicated task, since it involves coupling between different phases, computation of free surface variables in time, and thus it requires algorithms for integration in time. These aspects represent a combination of several problems, which are usually undertaken in a separate way, uncoupling mechanical response and flow through the porous media. When such computations are carried out, most of the times rigid solid skeleton is considered without a comprehensive analysis of the degree of accuracy achieved with such assumptions. Moreover, it is rather difficult to find in the literature coupled formulations under transient conditions. In this paper, a numerical finite element, coupled, transient model for analyzing unconfined seepage through Earth dams is presented. This model is based on Biot's equations, in terms of displacements (so called u–w formulation). The iterative procedure to obtain free surfaces by changing impermeability boundary conditions is implemented in this model. This generalized model is validated against several cases found in the literature. After that, several relevant aspects of the particular problem of fast emptying of a reservoir, and the calculation of the limiting drawdown speed for not compromising the Earth dam safety, are explored. Thus, the influences of different drawdown speeds, soil permeability values, stiffness and geometries in a theoretical rectangular Earth dam have been analyzed in terms of effective vertical stress changes at relevant points inside the dam. In summary, all these studied cases show the suitability of the presented methodology for evaluating such situations in real Earth dams, and give hints on the more significant aspects to be considered in the Earth dam design.