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

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 desiccation, 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 (Veveakis and Regenauer-Lieb, 2015). 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. (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This study investigates the conditions and formation of cracks in saturated viscoplastic soils under isotropic loading, obtaining a 2D extension of the Cnoidal Waves equations and identifying the characteristic spacing between cracks through numerical solutions. Patterns of triangular, rectangular, and hexagonal cracks can tessellate the domain, with the hexagonal pattern being energetically favored.