The Shapes of Collapsed Sinkholes at Limiting Equilibrium

Abstract

Experiments show that the sinkholes’ sizes and shapes are related to their stability. After a sinkhole has been created, its geometry continually evolves towards a more stable form. This process is governed by characteristics of the surrounding geomaterials, and various physical interactions, such as weathering, stress variations caused by cycles of wetting-drying. Buried, dropout and suffosion sinkholes are formed in the soil layer overlying bedrock. Dropout sinkholes (i.e. those with overhanging arches) are more likely to form in cohesive soil; suffosion sinkholes (i.e. those without overhanging arches) are more likely to form in non-cohesive soil. In the literature, most mechanistic analyses focus on dropout sinkhole. Few researchers conduct stability analysis of suffosion sinkhole. The geometry of a sinkhole is an input into most stability analyses, but it is often idealised or back-calculated from post-failure data. There is a need to know the geometry of a sinkhole approaching the point of failure (i.e. the limiting equilibrium). This paper reports on the geometry of collapsed suffosion sinkholes at limiting equilibrium obtained by the slip line theory. Analyses consider nonhomogeneous soils satisfying static equilibrium with soil strength governed by the Mohr-Coulomb failure criterion. The limiting sinkhole geometry is shown to be governed by dimensionless parameters. Exemplary charts are presented for determining this critical geometry given different combinations of soil parameters. Applications are illustrated via an example.