Dynamics of unsaturated soils using various finite element formulations

Abstract

SUMMARYUnsaturated soils are three-phase porous media consisting of a solid skeleton, pore liquid, and pore gas. The coupled mathematical equations representing the dynamics of unsaturated soils can be derived based on the theory of mixtures. Solution of these fully coupled governing equations for unsaturated soils requires tremendous computational resources because three individual phases and interactions between them have to be taken into account. The fully coupled equations governing the dynamics of unsaturated soils are first presented and then two finite element formulations of the governing equations are presented and implemented within a finite element framework. The finite element implementation of all the terms in the governing equations results in the complete formulation and is solved for the first time in this paper. A computationally efficient reduced formulation is obtained by neglecting the relative accelerations and velocities of liquid and gas in the governing equations to investigate the effects of fluid flow in the overall behavior. These two formulations are used to simulate the behavior of an unsaturated silty soil embankment subjected to base shaking and compared with the results from another commonly used partially reduced formulation that neglects the relative accelerations, but takes into account the relative velocities. The stress-strain response of the solid skeleton is modeled as both elastic and elastoplastic in all three analyses. In the elastic analyses no permanent deformations are predicted and the displacements of the partially reduced formulation are in between those of the reduced and complete formulations. The frequency of vibration of the complete formulation in the elastic analysis is closer to the predominant frequency of the base motion and smaller than the frequencies of vibration of the other two analyses. Proper consideration of damping due to fluid flows in the complete formulation is the likely reason for this difference. Permanent deformations are predicted by all three formulations for the elastoplastic analyses. The complete formulation, however, predicts reductions in pore fluid pressures following strong shaking resulting in somewhat smaller displacements than the reduced formulation. The results from complete and reduced formulations are otherwise comparable for elastoplastic analyses. For the elastoplastic analysis, the partially reduced formulation leads to stiffer response than the other two formulations. for this stiffer response in the elastoplastic analysis is the interpolation scheme (linear displacement and linear pore fluid pressures) used in the finite element implementation of the partially reduced formulation.

Numerical Prediction of Seepage and Seismic Behavior of Unsaturated Fill Slope

“…&e (20) where c ep is the elasto-plastic tensor, e e(tr) is the trial elastic strain (given strain). The diŠerentiation of (20) is carried out at each converged stress derived from the local iteration of (19).…”

“…Since the compressibility of pore air plays an important role during liquefaction of unsaturated soil (Kazama et al, 2006), the response of pore air pressure should be taken into consideration when reproducing the liquefaction behavior of unsaturated soil. Recently, pore air pressure has been treated as a primary variable in dynamic analyses (Schre‰er and Scotta, 2001;Ravichandran, 2009;Ravichandran and Muraleetharan, 2009). In addition, constitutive models for the cyclic behavior of unsaturated soil have been proposed using suction as a stress variable (Khalili et al, 2008;Bian and Shahrour, 2009).…”

A Flexible Model for Moisture-Suction Relationship for Unsaturated Soils and Its Application

“…Although complete and partially reduced finite element formulations are available [25], a simplified finite element formulation for unsaturated soil [24] is used in this study. The simplified formulation is free of numerical instabilities arise from other sources for the problems analyzed in this paper [25] and can easily capture if there is any numerical instabilities occur due to proposed SWCC.…”

“…The simplified formulation is free of numerical instabilities arise from other sources for the problems analyzed in this paper [25] and can easily capture if there is any numerical instabilities occur due to proposed SWCC. The complete governing differential equations representing the physics of unsaturated soil derived using mass balance, momentum balance and laws of thermodynamics was simplified by neglecting the relative accelerations and velocities of the pore air and water phases.…”

Effect of hydraulic hysteresis on dynamic response of unsaturated soils

“…net stress and suction, are adopted to cast the constitutive relationships of the soil, e.g. see [8,9]. A major difficulty with the second approach is that it requires determination of two sets of material parameters, one for each of the stress state variables, which in fact may not be independent, and can lead to intractable stress strain relationships.…”