An operator‐split ALE model for large deformation analysis of geomaterials

Abstract

SUMMARYAnalysis of large deformation of geomaterials subjected to time-varying load poses a very difficult problem for the geotechnical profession. Conventional finite element schemes using the updated Lagrangian formulation may suffer from serious numerical difficulties when the deformation of geomaterials is significantly large such that the discretized elements are severely distorted. In this paper, an operator-split arbitrary Lagrangian-Eulerian (ALE) finite element model is proposed for large deformation analysis of a soil mass subjected to either static or dynamic loading, where the soil is modelled as a saturated porous material with solid-fluid coupling and strong material non-linearity. Each time step of the operator-split ALE algorithm consists of a Lagrangian step and an Eulerian step. In the Lagrangian step, the equilibrium equation and continuity equation of the saturated soil are solved by the updated Lagrangian method. In the Eulerian step, mesh smoothing is performed for the deformed body and the state variables obtained in the updated Lagrangian step are then transferred to the new mesh system. The accuracy and efficiency of the proposed ALE method are verified by comparison of its results with the results produced by an analytical solution for one-dimensional finite elastic consolidation of a soil column and with the results from the small strain finite element analysis and the updated Lagrangian analysis. Its performance is further illustrated by simulation of a complex problem involving the transient response of an embankment subjected to earthquake loading.

An ALE method for penetration into sand utilizing optimization-based mesh motion

“…The majority of ALE methods on unstructured meshes employs smoothing algorithms which are not governed by quality evolution, including heuristic procedures [27,12,31] and physically-based smoothing [32,9]. Even though these methods are computationally attractive, they cannot ensure that any mesh processed is not worse than before.…”

“…Finite volume methods have traditionally been pursued by the CFD community [38,39] and have earned broad recognition in the history of development of ALE and related methods [2,5,6,40,12,41]. They are conservative because they solve the integral form of the conservation law (4) 2 ,…”

“…The current method approximates this term by a weighted donor-cell (Godunov-type) flux function. Donor-cell advection is used in many ALE codes [2,6,40,12,41] because it has some highly desirable features [38,39].…”

“…Examples include [7,8,9,10,11,12], but the employed methods reveal two limitations when applied to penetration into sand. First, common algorithms for node relocation are not qualified to smooth the non-convex mesh regions that inevitably occur during penetration of blunt bodies.…”

Discussion: On seismic landslide hazard assessment

“…When there is a need to go beyond this simplified approach, comprehensive numerical procedures such as fully coupled, elastic-plastic finite element analyses in the time domain should be sought. One of the recent advances worth mentioning is that the strong material non-linearity and geometry nonlinearity as well as the pore water pressure response involved in the large deformation of liquefying soil masses during earthquakes can now be successfully allowed for (Di et al, 2007). …”