Energy-work-based numerical manifold seepage analysis with an efficient scheme to locate the phreatic surface

A major challenge in seepage analysis is to locate the phreatic surface in an unconfined aquifer. The phreatic surface is unknown and assumed as a discontinuity separating the seepage domain into dry and wet parts, thus should be determined iteratively with special schemes. In this study, we systematically developed a new numerical manifold method (NMM) model for unconfined seepage analysis. The NMM is a general numerical method for modeling continuous and discontinuous deformation in a unified mathematical form. The novelty of our NMM model is rooted in the NMM two-cover-mesh system: the mathematical covers are fixed and the physical covers are adjusted with iterations to account for the discontinuity feature of the phreatic surface. We developed an energy-work seepage model, which accommodates flexible approaches for boundary conditions and provides a form consistent with that in mechanical analysis with clarified physical meaning of the potential energy. In the framework of this energy-work seepage model, we proposed a physical concept model (a pipe model) for constructing the penalty function used in the penalty method to uniformly deal with Dirichlet, Neumann, and material boundaries. The new NMM model was applied to study four example problems of unconfined seepage with varying geometric shape, boundary conditions, and material domains. The comparison of our simulation results to those of existing numerical models for these examples indicates that our NMM model can achieve a high accuracy and faster convergence speed with relatively coarse meshes. This NMM seepage model will be a key component of our future coupled hydro-mechanical NMM model. Copyright (c) 2014 John Wiley & Sons, Ltd.