Answer:
a. The active pressure coefficient Ka can be computed using Rankine's theory:
Ka = tan^2(45 + Φ/2) = tan^2(45 + 32/2) = 1.37
The active stress at the base is then Pa = Ka x unit weight x depth
Pa = 1.37 x 18.5 kN/cu.m x 4 m
Pa = 84.84 kPa
b. The passive pressure coefficient Kp can be computed using Rankine's theory:
Kp = tan(45 - Φ/2) = tan(45 - 32/2) = 0.40
The passive stress at the base is then Pp = Kp x unit weight x depth
Pp = 0.40 x 18.5 kN/cu.m x 4 m
Pp = 7.4 kN
c. The active force Fa is computed using the active pressure coefficient Ka and the height of the embankment:
Fa = Ka x unit weight x (height + depth)
Fa = 1.37 x 18.5 kN/cu.m x (12 + 4) m
Fa = 342.4 kN
d. The passive force Fp is computed using the passive pressure coefficient Kp and the height of the embankment:
Fp = Kp x unit weight x (height + depth)
Fp = 0.40 x 18.5 kN/cu.m x (12 + 4) m
Fp = 29.6 kN
e. The factor of safety of the cantilever sheet piling is computed as follows:
F.S. = Fa/Fp = 342.4/29.6 = 11.5
f. No, the structure is not safe if the specification requires F.S. = 1.50.
g. The required depth of embedment ( d+h ) of the sheet pile is computed as follows:
(d+h) = [(F.S. x Fp)/(Ka x unit weight)] - h
(d+h) = [(1.5 x 29.6)/(1.37 x 18.5)] - 12
(d+h) = 9 m