The friction angle φ is the single number Rankine theory needs to turn a soil into wall pressures. It sets both coefficients — active Ka = tan²(45 − φ/2) = (1 − sinφ)/(1 + sinφ) and passive Kp = tan²(45 + φ/2) — and the physical distinction between them: active pressure develops when the wall moves away and the backfill relaxes to its minimum strength, passive when the wall is pushed into the soil and mobilises its maximum resistance. The spread is dramatic: at φ = 30°, Kp is nine times Ka.
On a 5 m wall retaining dry sand at φ = 30° and γ = 18 kN/m³, Ka = 1/3 and the active thrust is Pa = 0.5 × Ka × γ × H² = 75 kN per metre of wall, acting at H/3 above the base as the resultant of a pressure that grows linearly from zero at the top to Ka·γ·H = 30 kPa at the base. The basic Rankine picture assumes a smooth vertical wall and level cohesionless backfill; wall friction calls for Coulomb theory, and sloping ground for the inclined-backfill coefficients.
The same φ resurfaces under the footing: all three bearing-capacity factors are functions of it — Nq = e^(π·tanφ)·tan²(45 + φ/2) and its companions — so a few degrees of friction angle move both how hard soil pushes on a wall and how much load it can carry, with the undrained φ = 0 case as the deliberate limiting analysis for clays.