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Theory and Numerical Modeling of Geomechanical Multi-material Flow

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Holistic Simulation of Geotechnical Installation Processes

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 80))

Abstract

Multi-material flow describes a situation where several distinct materials separated by sharp material interfaces undergo large deformations. The research presented in this paper addresses a particular class of multi-material flow situations encountered in geomechanics and geotechnical engineering which is characterized by a complex coupled behavior of saturated granular material as well as by a hierarchy of distinct spatial scales. Examples include geotechnical installation processes, liquefaction-induced soil failure, and debris flow. The most attractive numerical approaches to solve such problems use variants of arbitrary Lagrangian–Eulerian descriptions allowing interfaces and free surfaces to flow through the computational mesh. Mesh elements cut by interfaces (multi-material elements) necessarily arise which contain a heterogeneous mixture of two or more materials. The heterogeneous mixture is represented as an effective single-phase material using mixture theory. The paper outlines the specific three-scale mixture theory developed by the authors and the MMALE numerical method to model and simulate geomechanical multi-material flow. In contrast to traditional flow models which consider the motion of multiple single-phase materials or single multi-phase mixture, the present research succeeds in incorporating both the coupled behavior of saturated granular material and its interaction with other (pure) materials.

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Notes

  1. 1.

    We use the term “volume” and “surface area” even though the present section is restricted to two-dimensional problems. In fact, area and length in two dimensions can be regarded as volume and surface area per unit depth in three dimensions.

  2. 2.

    Table V in the original paper [95] has typos in the formulas for the side fractions for case IV, in which C should be in fact \(1-C\), where C is the volume fraction. The correct formulas are in Algorithm 5.

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Acknowledgments

The presented work was carried out under the financial support from the German Research Foundation (DFG; Grant SA 310/26-2) as part of the DFG Research Unit FOR 1136, which is gratefully acknowledged. The authors would like to thank their colleagues in this research unit for collaboration and continuously discussing our work. Special thanks go to Prof. David J. Benson and the Department of Structural Engineering at the University of California, San Diego (UCSD) for the opportunity to undertake collaborative research on MMALE methods.

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Authors and Affiliations

  1. Chair of Soil Mechanics and Geotechnical Engineering, Berlin University of Technology, Secr. TIB1-B7, Gustav-Meyer-Allee 25, 13355, Berlin, Germany

    Daniel Aubram & Stavros A. Savidis

  2. Department of Geotechnical Engineering, Ostbayerische Technische Hochschule Regensburg, Prüfeninger Straße 58, 93049, Regensburg, Germany

    Frank Rackwitz

Authors
  1. Daniel Aubram
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  2. Stavros A. Savidis
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  3. Frank Rackwitz
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Correspondence to Daniel Aubram .

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Editors and Affiliations

  1. KIT Karlsruhe Institute of Technology, Karlsruhe, Baden-Württemberg, Germany

    Theodoros Triantafyllidis

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Aubram, D., Savidis, S.A., Rackwitz, F. (2016). Theory and Numerical Modeling of Geomechanical Multi-material Flow. In: Triantafyllidis, T. (eds) Holistic Simulation of Geotechnical Installation Processes. Lecture Notes in Applied and Computational Mechanics, vol 80. Springer, Cham. https://doi.org/10.1007/978-3-319-23159-4_10

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  • DOI: https://doi.org/10.1007/978-3-319-23159-4_10

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