Question 11.EP.1: Assume a pile having a diameter of 0.3 m and a length of 6 m...
Assume a pile having a diameter of 0.3 m and a length of 6 m will be driven into a nonplastic silty sand deposit having shear strength properties of c = 0 and Φ’ = 30°. Assume that the location of the groundwater table is located 3 m below the ground surface, the total unit weight above the groundwater table is 19 kN/m³, and the buoyant unit weight \gamma_{b} below the groundwater table is 9.9 kN/m³. Using the Terzaghi correlation shown in Fig. 11.13, calculate the allowable end-bearing capacity using a factor of safety of 3.
The vertical effective stress \sigma _{v}^{\prime} at the pile tip equals:
\sigma_{v}^{\prime}=(3 m )\left(19 kN / m ^{3}\right)+(3 m )\left(9.9 kN / m ^{3}\right)=87 kPaFrom Fig. 11.13, using Φ’ = 30° and the Terzaghi relationship, N_{q} = 30
Using Eq. (11.9):
q_{ ult }=\frac{Q_{p}}{\pi r^{2}}=\sigma_{v}^{\prime} N_{q} (11.9)
Ultimate end-bearing capacity q_{\text {ult }} = (87 kPa)(30) = 2600 kPa
Multiplying q_{\text {ult }} by the area of the pile tip (πr²), or:
Using a factor of safety of 3, the allowable pile tip resistance = 60 kN