Question

1. Estimate the length of a 600mm diameter bored pile required to support an unfactored load of 1200 kN. The pile is embedded in a cohesive soil with an average undrained shear strength of 150 kPa and bulk unit weight = 20 kN/m³. The adhesion factor, alpha, may be assumed to be 0.4. The required overall factor of safety is to be at least 3.0. (Assume the density of the pile is equal to the density of the soil).

Hint: Express the capacity of the pile in terms of the unknown length, L. Solve for L

2. For the pile in a) estimate the pile head settlement under the unfactored load. The Young’s Modulus of the soil may be assumed to be 230 times the average undrained shear strength. Take the Young’s Modulus of concrete to be 27 GPa.

3. If this pile is part of a group of 8 piles (each with a load of 1200 kN) arranged in a 3 -2 - 3 pattern, estimate the settlement of this pile group at the pile cap level.

Answer 1

Designing the pile for a safety factor = 3

Working Load carried by the pile = Qup = 1200 x 3 = 3600 KN

Capacity of the pile is given by the equation

Qup = Qeb + Qsf.....................eqn(1)

where,

• Qup = Design working load on the pile = 3600 KN
• Qeb = End Bearing Resistance of the Pile, and is give as per Mayerhoff equation as,

(i.e., C = cohesion at the base of the pile = 150 KN/m2 , d = 600 mm = 0.6 m )

Therefore, Qeb = 9 x 150 x (π/4) x 0.6 x 0.6 = 381.703 KN

• Qsf = Skin Friction Resistance, given as per α-method for cohesive soil as,

(i.e., α = Adhesion Factor = 0.4, C = Cohesion over the length of the pile, As = Surface Area = πdL)

Therefore, Qsf = 0.4 x 150 x π x 0.6 x L = 113.097x L

substituting the values of Qeb & Qsf in eqn1

3600 = 381.703 + 113.097*L

L = 28.456 m

Hence provide a pile of length L = 28.5 m

Pile Head settlement is given by the equation

.................................eqn(2)

Where,

• Qup = Load carried at the pile point under working load condition = 3600 KN
• Qsf = Load carried by frictional skin resistance under working load condition = 113.097 x 28.5 = 3223.2645 KN
• Ab = End bearing area / Cross sectional area = 0.2827 m2
• Ep = Modulus of elasticity of pile material = 27 x 109 N/m2
• The magnitude of ℰ depends on the nature of the unit friction resistance distributed along the pile shaft length. If the distribution is uniform ℰ=0.5, for triangular variation ℰ=0.67
• Assuming the unit friction resistance is distributed uniformly along the length of the pile ℰ=0.5
• L = Length of the pile = 28.5 m

Substituting these values in eqn(2) we get

S = 0.01946 m = 19.45 mm

Settlement of pile groups is given by the equatiom

where, Cc = Compression index of the soil = Missing data in the question

Ho = Thickness of clayey Layer

eo = Initial voids ratio of the soil = Missing data in the question

σ1 = Effective overburden pressure till H/2

= Excess pressure over the footing =

Here in this problem we cannot calculate settlement due to group of piles because of missing data