Gce Model Questions Vol1 2025 Geography Question 49

A homogeneous earth slope of height 30 m and uniform angle \( \theta = 35^{\circ} \) is potentially susceptible to sliding along a planar surface parallel to the slope face. The soil has cohesion \( c = 15 \ \text{kPa} \) and internal friction angle \( \phi = 20^{\circ} \). Its unit weight is \( \gamma = 18 \ \text{kN m}^{-3} \). The groundwater table lies 10 m below the crest, and the unit weight of water is \( \gamma_w = 9.81 \ \text{kN m}^{-3} \). Assuming pore water pressure acts normal to the slip surface and can be approximated by \( u = \gamma_w \ h_w \cos^{2}\theta \) where \( h_w = 10 \ \text{m} \), calculate:\n\n1. The normal stress \( \sigma_n \) and shear stress \( \tau \) acting on the slip surface per unit area.\n2. The shear strength \( S = c + (\sigma_n - u)\tan\phi \).\n3. The factor of safety \( FS = S / \tau \).\n\nBased on the computed \( FS \), state whether the slope is stable and suggest one engineering measure to improve stability.