Numerical simulation of excavation in elastoplastic soils

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Abstract
A finite element method for simulating excavation in elastoplastic soils which produces a ‘unique’ solution for any number of excavation stages is presented. The proposed method satisfies the uniqueness principle for elastic materials postulated by Ishihara,1 and degenerates to the methods presented in the ADINA code2, 3 and by Brown and Booker4 and Ghaboussi and Pecknold5 for the simple elastic cases. The non‐linear (elastoplastic) finite element equations are derived from a variational formulation which accounts for time‐varying problem domain and boundaries. The roots of these non‐linear equations are solved by Newton's method, using the notion of the consistent tangent operator proposed by Simo and Taylor6 in conjunction with a numerical algorithm based on the ‘radial‐return’ concept for integrating stresses.7–9 Numerical examples demonstrate that in the elastic case the solution to problems involving a ‘shrinking’ (excavation) or ‘expanding’ (fill) domain is superposable and does not depend on the number of construction stages. For a monotonically shrinking elastoplastic domain and the von Mises and Drucker—Prager yield models, it is shown that the proposed method also produces a ‘unique’ solution independent of the number of excavation stages. Finally, the asymptotic quadratic convergence exhibited by the proposed method is demonstrated to show the efficiency engendered by the technique described.

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