Slip surface in sinkholes : an analysis of the slip line of an idealized axisymmetric open karst pipe

A theoretical investigation of an idealized open karst pipe sinkhole in Tennessee is described. The slip surface at failure in an idealized c, φ, γ soil around the open karst pipe sinkhole due to working loads along the surface is evaluated by the theory of plasticity. The mechanical behavior of the soil is approximated by that of an ideal material which obeys the Mohr - Coulomb yield criterion.

The numerical solution by the characteristic method for the axisymmetric case was used to find the stress and velocity fields to the system of partial differential equations of the hyperbolic type.

Average failure stresses along the surface for several overburden thicknesses and diameters of open karst pipes were obtained for the stress fields in the meridianal plane which arise when the Haar von Karman hypothesis was adopted. The pattern of velocity field which gives the real slip surface was obtained from the stress field.

For practical design, a plot of the average failure stress along the surface was also given as a function of the ratio of soil overburden thickness of to diameter of open karst pipe. In addition to the sinkhole problem discussed here, the solution can be applied to the circular excavations.