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A long slope is formed in a soil with shear strength parameters: c' = 0 and φ' = 34°. A firm stratum lies below the slope and it is assumed that the water table is occasionally rise to the surface, with seepage taking place parallel to the slope. Use γsat = 18 kN/m³ and γw = 10 kN/m³. The maximum slope angle (in degrees) to ensure a factor of safety of 1.5, assuming a potential failure surface parallel to the slope, would be

1. 45.3
2. 44.7
3. 12.3
4. 11.3

Correct answer: 11.3

Solution

For an infinite slope with seepage to the surface and c'=0, FS = (gamma'/gamma_sat)*tan(phi')/tan(beta). With gamma'=8, gamma_sat=18, phi'=34deg, FS=1.5: tan(beta)=(8/18)*tan34/1.5=0.200, so beta=11.3deg. The stored 44.7 is wrong; correct is 11.3.

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