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Porous Media pp 251-274 | Cite as

Time adaptive analysis of saturated soil by a discontinuous-Galerkin method

  • Harald Cramer
  • Rudolf Findeiß
  • Walter Wunderlich
Chapter

Abstract

The topic of this presentation is the numerical analysis of saturated soil by the finite element method. As the solution procedure should be extended to describe the flow of the pore fluid through the deforming solid skeleton, a time dependency is introduced into the problem. Therefore, the time coordinate has to be discretized and treated by an appropriate integration scheme. In contrast to adaptive mesh refinement strategies in the spatial domain which are well founded for elasticity and have also been successfully applied to elastic-plastic problems only few papers deal with time adaptive procedures for the quasi-static analysis of consolidation.

Therefore, in this presentation a time discretization dependent on the specific problem is emphasized. For this purpose the time-discontinuous-Galerkin method is applied to the differential equations of first order in time. It is based on a variational form permitting jumps in the temporal evolution of the field variables, where the continuity is satisfied in a weak sense. It can be shown that these jumps may then be used to define a natural error indicator for the temporal discretization error. On the other hand, attention is drawn to another error which arises from the numerical integration of the rate equations of plasticity. In this context, an indicator is derived from the residual of the Kuhn-Tucker conditions within the time interval.

The numerical examples of a one dimensional consolidation problem and a strip footing on a half space demonstrate the applicability of the method to problems in geomechanics. Both indicators are combined to improve the efficiency of the time stepping scheme.

Keywords

Pore Water Pressure Saturated Soil Time Step Size Error Indicator Solid Skeleton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Harald Cramer
    • 1
  • Rudolf Findeiß
    • 2
  • Walter Wunderlich
    • 2
  1. 1.Fachgebiet Baustatik und BaudynamikUniversität RostockRostockGermany
  2. 2.Lehrstuhl für StatikTechnische Universität MünchenMünchenGermany

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