Earth Retaining Structures and Slope Stability
What to know
For walls, know lateral earth pressure theory: at-rest K0 = 1 − sin φ' (use for unyielding walls such as basement walls), Rankine active Ka = tan²(45 − φ'/2) for a vertical wall with no wall friction, and passive Kp = 1/Ka. Coulomb adds wall friction and inclined backfill. Add water pressure separately - do not saturate the unit weight and ignore the fluid - and add surcharge pressures (Ka·q for uniform surcharge). For sloping backfill behind a vertical wall, Ka = cos β [cos β − √(cos²β − cos²φ)] / [cos β + √(cos²β − cos²φ)].
Wall stability checks are standard: overturning about the toe (FS ≈ 2), sliding (FS ≈ 1.5, sometimes including passive resistance in front), and bearing capacity/settlement of the base. MSE walls, braced excavations with apparent earth pressure envelopes, and anchored sheet piles each have their own design conventions.
For slopes, know infinite-slope analysis (FS = c'/(γH cos²β sin β) + tan φ'/tan β), the method of slices and Bishop's simplified method, and Taylor's charts. Rapid drawdown, seismic loading with Mononobe–Okabe, and liquefaction susceptibility are frequent topics.
Traps
Neglecting water pressure behind the wall, forgetting that passive resistance is often ignored for sliding, and reversing the FS ratio - resisting moments over driving moments.
Worked example
15-ft wall, level backfill, γ = 120 pcf, φ = 30°, Ka = 1/3. Pa = ½KaγH² = 0.5(0.333)(120)(225) = 4,500 lb/ft acting at H/3 = 5 ft above the base, giving an overturning moment of 22,500 ft-lb/ft.