Design Charts for Jointed Rock Slopes Susceptible to Slide-Head Toppling Failure

Design charts provide one of the preliminary ways used to determine slope stability by aiding the complex limit equilibrium analysis through provision of supporting data towards achieving a solution. The previously developed charts for slide-head toppling were mostly developed based on the toppling rather than the sliding of the blocks on the slope. Furthermore, the previously developed charts were based on the assumption that the base and inter-block friction are equal (ϕp=ϕd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\phi }_{p}={\phi }_{d}$$\end{document}). However, this may not usually be the case since there exists a possibility for the failure plane to counter-tilt within the slope owing to geological disparities (discontinuity characteristics). It is therefore possible for the frictional resistances to vary within the rockmass. This paper presents 2D and 3D charts based on the sliding equation to aid in the limit equilibrium analysis for slide-head toppling based on the variation of friction concerning the basal plane and the inter-block resistance (ϕp≠ϕd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\phi }_{p}\ne {\phi }_{d}$$\end{document}). A case study in Zambia has been presented for the prescribed situation to illustrate application of the developed charts. The results of the case study indicate that the charts can be applied on both the initial and counter-tilted weak planes. Furthermore, positive values for zeta (ζ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\zeta$$\end{document}) have been observed for weak plane (ψp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\uppsi }}_{\text{p}}$$\end{document}) angles that are less than the base friction and vice-versa for values of ψp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\uppsi }}_{\text{p}}$$\end{document} greater than base friction. Apart from aiding in the determination of slide-head toppling, the developed charts also illustrate the relationship that exists between base friction and inter-block friction.