(untitled) (Geologica Macedonica, 2013)
Although wedge and plane sliding stability analyses are well established in the geotcchnical literature, certain geologic environments produce blocks which cannot be adequately modelled as either wedges or plane slides. An example is blocks forming in cylindrically folded sedimentary rocks, where the surface of sliding is neither a single plane nor a double plane but is curved. This type of block may be idealized as a prismatic block with multiple sliding planes, all with parallel lines of intersection. If the sliding planes number three or more, the distribution of normal forces and hence the factor of safety is indeterminate. A new analytical model for sliding stability analysis is described in which the distribution of normal forces on the contact planes is chosen to minimize the potential energy of the system. The classic wedge and plane solutions are shown to be special cases of this more general model, which allows determination of the safely factor for any shape of prismatic contact surface. An example from block part of Bregalnica river with a curved sliding surface is described and the factor of safety compared with the standard wedge analysis. It is shown that with three or more contact planes, the safety factor may be significantly lower than that calculated from the wedge model, which provides an upper limit on stability.