Viscoelastic damage modeling of sinkhole formation

The sinkholes along the Dead Sea coast are observed in two main sedimentary environments: alluvial fan sinkholes, which usually form abruptly as deep (∼20 m) and narrow (∼3 m) sinkholes, and mud-flat sinkholes, which usually form as shallow (a few centimeters) and wide (>5 m) sinkholes and deepen later. The mechanical collapse of all sinkholes is triggered by cavities created by the dissolution of an underlying salt layer by relatively fresh groundwater. The processes attributed to the mechanical formation of the sinkholes are viscous flow and brittle fracture failure. We use a two-dimensional viscoelastic damage rheology numerical model to quantitatively explain the brittle and ductile aspects of collapsed sinkholes. Three cases of the rheology of the collapsed sediments are simulated, 1) damage controlled failure, 2) viscoelastic controlled failure, and 3) an intermediate damage-viscoelastic case. Results show that viscoelasticity cannot be the sole process acting on the deformed layer because all sinkholes are characterized by sharp boundaries. The damage accumulation progresses until arched cavities are created in the soil layer. Because of the geometric heterogeneity of the layer (represented by the heterogeneity of the mesh) smaller blocks continue to fall after the first breakup into the cavity, advancing the arched cavity upwards. This propagation finally stops when the cavity is shallow enough to hold the irregular arch. The combination of these two processes creates competition within the stress reduction mechanism that may lead to either magnified or reduced deformation. The deformation is magnified in high shear stress locations, where the dispersion of the viscous flow spreads damage failure, and it is reduced in low shear stress locations where viscous flow disperses shear stress before the onset of damage.