A Model for Crack Initiation in Solidifying Lava

We study the thermomechanical evolution of a stationary lava body cooling from the upper surface. The body progressively solidifies and develops a boundary layer made of an upper solid thermoelastic crust and a lower viscoelastic layer. The presented approach to the problem is one-dimensional and quasi-static. Under the assumption that the crust is a brittle solid with a given strength, we study the generation of tensile fractures. We consider a single fracture event and we assume that a fracture is produced when the thermal stress exceeds the strength over a certain depth interval, inferred from the observation of striae. The fracture propagates abruptly across the brittle layer, driven by the difference between the thermal stress and the tensile strength. The model can contribute to explain the formation of striae, surfaces caused by crack advance, in particular, of the first fracture. We find that the Young modulus controls the crack growth. The model provides an explanation for the presence of the rough bands on striae. For its higher values the fracture extends partially into the viscoelastic region; while for lower values the crack is confined to the brittle layer. The maximum opening width is typically in the order of a few thousandths of the vertical length of the crack. The resumption of crack process must await further cooling of the lava body.