A parametric study of rock slope stability in three dimensions using a vector-based approach

Abstract

Excavations in rock expose the discontinuum nature of the ground material. While strength criteria, both within the intact material and across discontinuities, are important considerations for engineering interventions involving excavations in rock masses, stability issues are equally serious, possibly leading to sudden failure of the ground material. The factor of safety of potentially unstable wedges of rock thus needs to be established for the excavation to be deemed safe, or for the engineer to appreciate that mitigation efforts are warranted. Considering rock instabilities in three dimensions is challenging, owing to the complexity of the mathematical operations necessary to define the geometry and to solve the trigonometric relationships involved. This dissertation proposes a limit equilibrium method which makes use of vector based algebra, simplifying the mathematical procedures. This allows the excavation faces and kinematically feasible wedges of rock in three dimensions to be defined. The mode of sliding and factor of safety of such wedges are generated via a model of analysis created in Microsoft Excel, with a graphical interface in AutoCad linked to this model to visualise these scenarios. A parametric study is thereafter conducted, which shows that the geometric parameters defining the discontinuity planes of the 3D wedge problem are the parameters to which the safety factor is most sensitive. Other parameters have a less prominent effect on the safety factor when they are varied. Additionally, the presumption that mitigation measures always increase the factor of safety is challenged. In certain cases, increasing the number of prestressed anchors on a wedge does not necessarily increase the safety factor, because the mode of sliding of the wedge is altered in the process. In such cases, anchors may contribute to decrease the factor of safety. Comparisons between 3D wedge sliding scenarios and their 2D simplifications show that the latter mode of analyses always gives a more conservative but less economical result, since the contribution of the two sliding planes is not taken into account in a 2D analysis. Furthermore, the applicability of the model created in this dissertation to practical scenarios depends on the geometry of the wedge problem encountered in practice. Slight modifications to the model are necessary if the wedge geometry does not correspond to the tetrahedron assumed in this analysis.