A note on the instability and pattern formation of shrinkage cracks in viscoplastic soils. (March 2021)

• Record Type: Journal Article
• Authors: Veveakis, Manolis; Poulet, Thomas
• Is Part Of: Geomechanics for energy and the environment. Volume 25(2021)
• Publication Date: 2021-03
• Subjects: Mud-cracks -- Hexagonal patterns -- Bifurcation analysis -- Cnoidal waves; Engineering geology -- Periodicals; Power resources -- Periodicals; Energy development -- Technological innovations -- Periodicals; Engineering geology -- Environmental aspects -- Periodicals; Energy development -- Technological innovations; Engineering geology; Engineering geology -- Environmental aspects; Power resources; Geology -- Periodicals; Energy-Generating Resources -- Periodicals; Periodicals; Electronic journals; 621.042
• DOI: 10.1016/j.gete.2020.100198
• Languages: English
• ISSNs: 2352-3808

Abstract

Abstract: 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. Highlights: We study the creation of pattern formation of cracks in viscoplastic soils like clays. We provide scaling laws for equidistantly placed cracks . We provide optimal self-organization conditions.