Fig. 13

A schematic diagram showing the geometry of the method of slices used to evaluate cliff stability. The slip plane is circular (center C, radius R), passing through the origin (O). The landslide head length \(L_{\mathrm{head}}\) is measured from the intercept of the slip circle at the top or rear plane of the cliff. The phreatic surface h(x) is parabolic, such that \(h(0) = 0\) and \(h(L) = h_{\mathrm{w}}\). Wet sand is saturated (unsaturated) below (above) the h(x), and corresponding values of \(\rho\), \(\mu '\), \(c'\) are used. \(\Delta x\) (\(= 1.35\) mm) is the slice width. \(z_{\mathrm{i}}\), \(l_\mathrm{i}\), and \(\delta _{\mathrm{i}}\) are the height, length, and slope angle of the slip plane, respectively, at the slice number i. \(s_{\mathrm{i}}\) and \(\tau _{\mathrm{i}}\) are the resisting and disturbing tangential stress, respectively, at the slip plane