Question

A bridge abutment is constructed of cantilever sheet piling, retains a soil height of 12.0 m. and a depth of 4.0m. at the passive side. The soil is sandy clay with a unit weight of 18.5 kN cu.m . and has an angle of internal friction of 32 degrees.

a. Compute the active stress at the base Pa=? (in kPa)
b. Compute the passive stress at the base Pp=? (in kN)
c. Compute the active force Fa=? (in kN)
d. Compute the passive force Fp =? (in kN)
e. What is the factor of safety of the cantilever sheet piling?
f. Is the structure safe if the specification requires F.S. = 1.50?
g. If not, what must be the required depth of embedment ( d+h ) of the sheet pile?

Answer 1

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