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Conditions for instabilities in collapsible solids including volume implosion and compaction banding

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Abstract

We review conditions for material instabilities in porous solids induced by a bifurcation of solution into non-unique strain rate fields. Bifurcation modes considered include jumps in the strain rate tensor of ranks one and higher representing deformation band and diffuse instability modes, respectively. Eigenmodes (e-modes) are extracted for each type of instability to fully characterize various frameworks of deformation in collapsible solids. For diffuse instability these e-modes are determined from a homogeneous system of linear equations emanating from the condition of zero jump in the stress rate tensor, which in turn demands that the tangent constitutive tensor be singular for the existence of nontrivial solutions. For isotropic materials we describe two types of singularity of the constitutive tensor: (a) singularity of the constitutive matrix in principal axes, and (b) singularity of spin. Accordingly, we derive the e-modes for each type of singularity. We utilize the singularity of the constitutive matrix in principal axes as a precursor to volume implosion in collapsible solids such as loose sands undergoing liquefaction instability and high-porosity rocks undergoing cataclastic flow. Finally, we compare conditions and e-modes for volume implosion and compaction banding, two similar failure modes ubiquitous in granular soils and rocks.

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Acknowledgments

The author is very grateful to two anonymous reviewers for their expert reviews, and to graduate student Pablo Sanz for rendering the three-dimensional solid figures presented in this paper. This work is supported by National Science Foundation Grant Nos. CMS-0201317 and CMS-0324674, and US Department of Energy Grant No. DE-FG02-03ER15454.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Stanford University, Stanford, CA, 94305, USA

    Ronaldo I. Borja

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Correspondence to Ronaldo I. Borja.

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Supported by U.S. Department of Energy, Grant DE-FG02-03ER15454, and U.S. National Science Foundation, Grants CMS-0201317 and CMS-0324674.

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Borja, R.I. Conditions for instabilities in collapsible solids including volume implosion and compaction banding. Acta Geotech. 1, 107–122 (2006). https://doi.org/10.1007/s11440-006-0012-x

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  • DOI: https://doi.org/10.1007/s11440-006-0012-x

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