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.

在本文中，我们对在各向同性载荷（延伸）下的饱和粘塑性土壤中裂纹的发生条件以及相应的花纹形成进行了理论研究。所施加的应力类型未指定，以涵盖各种载荷，包括由于干燥引起的收缩，各向同性热膨胀，机械载荷等。通过将饱和土视为刚性粘塑性，我们获得了Cnoidal Waves方程的二维扩展（Veveakis和Regenauer-Lieb，2015）。通过数值求解相应的边值问题，我们检索了二维加载中裂纹不稳定性发生的条件，并将裂纹之间的特征间距确定为结合该问题的所有水力力学参数的长度尺度。最后，