Abstract
One of the great challenges of unconfined seepage through a dam lies in the accurate determination of free surface that depends on the complexity of the seepage model, especially if the model is characterized with complex geometry and sharp variations in permeability distribution. This study presents a practical methodology that combines the adaptive moving-mesh algorithm and the Galerkin finite element method (FEM) to solve an unconfined seepage problem with high efficiency and precision. The methodology employs a set of improvement terms, such as remainder factor, step-size parameter and termination condition, all of which guarantee that the simulation and the refinement fitting can be implemented efficiently until the free surface converges within a given allowable error. In particular, a specialized discussion is presented for the significant relation between the location of the exit point and the corresponding grid fineness. To validate the practicability of the proposed method, a series of examples are performed. Comparing the result with those of other numerical approaches, we conclude that even though the unconfined seepage model may be complicated with arbitrary complex geometry and sharp variations in permeability distribution, the proposed algorithm provides a great improvement in efficiency and accuracy in free-surface searching.
Highlights
Analysis of free-surface seepage problems has been attracting more attention in the past few decades due to its wide variety of scientific and engineering applications, such as geotechnical slopes, earth dams, underground caves, and groundwater movement, and is beneficial for analysing the interaction and coupling between seepage field and stress field[1,2]
We focus solely on economic and accurate solutions to handle complicated model cases, and present a practical and innovative methodology that combines the Galerkin finite element method (FEM) with the adaptive mesh method (AMM), where the main parameters of seepage area can all be calculated at each node
The major conclusions from this study are listed as follows: As the most crucial part of the seepage problem is the precise confirmation of free surface position and the exit point location, the Dupuit assumption is employed to determine the initial free surface, by introducing two www.nature.com/scientificreports novel factors ζ, λ, the mesh can be dynamically reshaped to match the new location of the free surface during the iteration, and subsequently, the accurate location of the exit point can eventually be fitted
Summary
Analysis of free-surface seepage problems has been attracting more attention in the past few decades due to its wide variety of scientific and engineering applications, such as geotechnical slopes, earth dams, underground caves, and groundwater movement, and is beneficial for analysing the interaction and coupling between seepage field and stress field[1,2]. Many previous experimental studies have been conducted to investigate the free surface analysis of unconfined seepage problems with different classical numerical approaches[3,4]. The findings confirmed that, besides the high accordance with the analytic solutions and other numerical solutions, the proposed method possesses the unique advantages of high accuracy and effective convergence These approaches more or less modified the potential of each node by means of calculating the seepage discharge that flowed through the free surface, and executing a sustained calculation process until the discharge was less than a certain given value. The changes in a variable domain can be conveniently confirmed with an adaptive mesh technique by relocating the boundary elements through successive iterations This distinctive characteristic makes it one of the most suitable methods for free surface analysis. Darbandi et al.[19] proposed the moving-mesh finite volume method (FVM) by assuring a mass conservation over modelling cells, it revealed that, regardless of the type of mesh strategies utilized (i.e. fixed-mesh or moving-mesh), the calculation accuracy with FVM is substantially improved
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