Rankine Passive Earth Pressure

K_{p} = \frac{1 + sin ϕ}{1 - sin ϕ} = \frac{1}{K _{a}} P_{p} = \frac{1}{2} K_{p} γ H^{2}

Passive resistance develops when the wall moves into the soil (much larger displacement than active). Kp = tan²(45+φ/2). For φ=30°, Kp=3. Do not count full Pp unless the movement is enough. Surcharge adds Kp q H.

$K_{p}$: Passive coefficient
$P_{p}$ (kN/m): Passive resultant

Step-by-step solved example

φ=30°, H=4.0 m, γ=18 kN/m³, c=0, no surcharge. Pp?

Passive wedge: Kp = 1/Ka, Pp = ½ Kp γ H².

1. Kp
Kp=(1+0.5)/(1−0.5)=3.0.
2. Pp
Pp=0.5×3×18×16=432 kN/m.
$P_{p} = 432 kN/m$

Answer: 432 kN/m

10 practice questions

0/10 correct

1.Kp × Ka equals

2.φ=0 (undrained clay) Rankine Kp=

3.Passive needs

4.Resultant Pp acts at

5.Surcharge q adds

6.If φ increases, Kp

7.Coulomb Kp includes

8.Do not use full Pp for a

9.φ=45°, Kp=

10.Passive pressure at depth z is