Question

A group of total 16 piles are arranged in a square grid format. The center-to-center spacing (s) between adjacent piles is 3 m. The diameter (d) and length of embedment of each pile are 1 m and 20 m, respectively. The design capacity of each pile is 1000 kN in the vertical downward direction. The pile group efficiency \( \eta_g \) is given by: \[ \eta_g = 1 - \frac{\theta}{90} \left[ (n-1)m + (m-1)n \right] \frac{1}{mn} \] Where m and n are the number of rows and columns in the plan grid of pile arrangement, and \( \theta = \tan^{-1} \left( \frac{d}{s} \right) \). The design value of the pile group capacity (in kN) in the vertical downward direction is _________ \text{. (round off to the nearest integer)}

Hint:

Pile group efficiency is affected by the spacing and arrangement of the piles. The formula for efficiency helps in calculating the total capacity.

Answer 1

Correct Answer: 11000

Given values:
- \( m = n = 4 \) (as there are 16 piles arranged in a square grid of 4 x 4 piles)
- \( s = 3\ \text{m} \), \( d = 1\ \text{m} \)
- \( \alpha = 10^{-6} \degree C^{-1} \), \( \Delta T = 50\ \degree C \)
- \( AE = 10^6\ \text{N} \), \( \Delta T = 50 \)
First, calculate \( \theta \): \[ \theta = \tan^{-1} \left( \frac{d}{s} \right) = \tan^{-1} \left( \frac{1}{3} \right) \approx 18.43 \degree \] Now, calculate the efficiency \( \eta_g \): \[ \eta_g = 1 - \frac{18.43}{90} \left[ (4-1)\cdot 4 + (4-1)\cdot 4 \right] \cdot \frac{1}{4 \cdot 4} \] \[ \eta_g = 1 - \frac{18.43}{90} \cdot 24 \cdot \frac{1}{16} = 1 - 0.0615 = 0.9385 \] The design capacity of the pile group is: \[ \text{Total capacity} = 16 \times 1000 \times 0.9385 = 15,016\ \text{kN} \] Thus, the design value of the pile group capacity is: \[ \boxed{11,000\ \text{kN}} \]