A note on the instability and pattern formation of shrinkage cracks in viscoplastic soils

This is a Preprint and has not been peer reviewed. The published version of this Preprint is available: http://doi.org/10.1016/j.gete.2020.100198. This is version 1 of this Preprint.


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Emmanouil Veveakis, Thomas Poulet


In this note we present a theoretical study on the conditions for the onset of cracks, as well as the corresponding pattern formation, in saturated viscoplastic soils under isotropic loading (extension). The type of stress applied is left unspecified, to cover a variety of loadings including shrinkage due to dessication, isotropic thermal expansion, mechanical loading and so forth. By treating the saturated soil as rigid viscoplastic, we obtain a 2D extension of the Cnoidal Waves equations [1]. By numerically solving the corresponding boundary value problem, we retrieve conditions for the onset of cracking instability in 2D loading, and identify the characteristic spacing between cracks to be a length scale combining all the hydro-mechanical parameters of the problem. Finally, we show that in a rectangular slab of clay under isotropic extension, patterns of triangular, rectangular and hexagonal cracks can tessellate the domain, with the hexagonal pattern being the energetically favored, as it minimizes the free energy of the system.




Civil and Environmental Engineering, Engineering, Materials Science and Engineering


bifurcation analysis, cnoidal waves, hexagonal patterns, mud-cracks


Published: 2019-11-07 19:42


GNU Lesser General Public License (LGPL) 2.1

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