Fig. 12

a A schematic diagram to scale showing the inferred stress changes with seepage. The long axis of a rectangle indicates the major principal stress \(\sigma\), defined positive when the arrow is directed inward. The figure models the situation of run 14 (\(H = 20.0\) cm, \(L = 13.5\) cm, \(h_{\mathrm{w}} = 8\) cm shown in Fig. 6). A red square (circle) indicates the pressure sensor attached to the base (side wall) and measures the \(\sigma _{\mathrm{z}}\) (\(\sigma _{\mathrm{y}}\)). Left: at the beginning of seepage (\(t = 0\) s). Right: at \(t = T_{\mathrm{slide}}\). Near the cliff head, \(\sigma _{\mathrm{z}}\) is the inferred major principal stress, such that active failure (horizontal tension, \(\sigma _{\mathrm{x}} < 0\)) occurs and a tension crack forms. At the cliff toe, the \(\sigma _\mathrm{x}\) is the inferred major principal stress, such that passive failure (horizontal compression, \(\sigma _{\mathrm{x}} > 0\)) occurs. The failure angle is steeper at the head (see text). b Effective Mohr’s circle representation of a passive failure at the cliff toe shown in a right. A black line is the Mohr–Coulomb criterion for saturated (\(S = 1\)) sand (see Additional file 4: Table S1 for \(\mu '\), \(c'\)). \(b \simeq 25^{\circ }\) is the failure angle measured from the horizontal for the experimental case