---
title: "Pile spacing for 100% efficiency, 16 piles"
subject: "Foundation Engineering"
chapter: 8
key: "semester_5/foundation_engineering:pile-spacing-100-efficiency-square-30cm"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/pile-spacing-100-efficiency-square-30cm
site: BCT Engineering
---

# Pile spacing for 100% efficiency, 16 piles

Foundation Engineering · Chapter 8: Pile Foundations

- Asked in: 2074 Chaitra, 7 marks; 2080 Bhadra, 8 marks (asked 2 times)
- Video: [Numerical on Group Capacity of Pile in Clay](https://www.youtube.com/watch?v=UHjqId4wkvc) — Curious Civil Engineer
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/pile-spacing-100-efficiency-square-30cm
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-8

## Question

A group of 16 piles arranged in a square pattern is to be proportioned in a deposit of soft saturated clay. Assuming the piles to be square with side 30 cm and 12 m long, determine the centre to centre spacing of piles for 100% efficiency of the pile group. Take adhesion factor = 0.8 and consider both point bearing and skin friction. (Cu not legible in the 2080 Bhadra scan.)

## Short answer

Equate block and sum of individual capacities (both proportional to c_u). Solve 9B_g^2+48B_g–197.28=0, giving B_g=2.721 m. For a 4×4 square group, centre-to-centre spacing s=(B_g–b)/3=0.807 m≈0.81 m.

## Answer

**Given:** 16 square piles in a 4 × 4 group, side $b = 0.30$ m, $L = 12$ m, soft clay, $\alpha = 0.8$. The value of $c_u$ is not legible, but it cancels out, as both the individual and block capacities are proportional to $c_u$. Point bearing and skin friction are both considered.

For 100% efficiency, **block capacity = sum of individual pile capacities**.

#### Individual pile
$$
\begin{aligned} Q_u &= \alpha c_u(4bL) + 9c_ub^2 \\ &= c_u\left[0.8(4)(0.3)(12) + 9(0.3)^2\right] \\ &= c_u(11.52 + 0.81) = 12.33\,c_u \end{aligned}
$$

Sum for 16 piles $= 16 \times 12.33\,c_u = 197.28\,c_u$.

#### Block of side $B_g$ (square)
$$
Q_{block} = c_u(4B_g)L + 9c_uB_g^2 = c_u\left(48B_g + 9B_g^2\right)
$$

#### Equate
$$
\begin{aligned} 9B_g^2 + 48B_g - 197.28 &= 0 \\ B_g &= \frac{-48 + \sqrt{48^2 + 4(9)(197.28)}}{2(9)} = 2.721\ \text{m} \end{aligned}
$$

For a 4 × 4 group $B_g = 3s + b$:

$$
s = \frac{2.721 - 0.30}{3} = 0.807\ \text{m}
$$

**Answer: centre-to-centre spacing of piles $\approx 0.81$ m ($\approx 2.7b$)** for 100% efficiency. A larger spacing also gives an efficiency of 100%.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. 100% efficiency means:
   A. Block capacity equals sum of individual pile capacities
   B. Spacing equals diameter
   C. Group settles zero
   D. Block capacity is zero
   Answer: A. Efficiency is group/(sum of piles) so equate them. (Key point: Condition)

2. Why is the unreadable cu not needed?
   A. Both capacities are proportional to cu, so it cancels
   B. cu = 0
   C. Adhesion is zero
   D. It is replaced by phi
   Answer: A. Both sides contain cu as a factor. (Key point: Cancelling cu)

3. Single square pile capacity is:
   A. alpha cu (4bL) + 9 cu b^2 = 12.33 cu
   B. cu b L
   C. 9 cu b L
   D. 4 b alpha cu
   Answer: A. 0.8 x 4 x 0.3 x 12 = 11.52 plus 9 x 0.09 = 0.81. (Key point: Single pile)

4. The block capacity (with cu skin and 9 cu base) is:
   A. cu(48Bg + 9Bg^2)
   B. cu(4Bg + 9)
   C. alpha cu 48 Bg
   D. 9 cu Bg
   Answer: A. Perimeter 4Bg x L = 48Bg, base 9Bg^2. (Key point: Block equation)

5. Spacing from Bg = 3s + b with Bg = 2.721 m:
   A. 0.81 m
   B. 0.30 m
   C. 2.4 m
   D. 1.2 m
   Answer: A. s = (2.721 - 0.30)/3 = 0.807 m. (Key point: Spacing)

## Related in Foundation Engineering

- [Pile group 16 piles of 50 cm, efficiency](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Apile-group-16-piles-50cm) — Foundation Engineering, chapter 8
- [Pile group 16 piles, 0.40 m, soft clay](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Apile-group-16-soft-clay-040) — Foundation Engineering, chapter 8
- [12 piles, spacing and diameter, 100% efficiency](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Apile-group-12-circular-spacing-diameter) — Foundation Engineering, chapter 8
- [Pile group 4×4, two-layer clay, 2.4 m spacing](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Apile-group-4x4-2-4m-layered) — Foundation Engineering, chapter 8, asked 2×
- [Spacing of nine piles for efficiency 1](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Apile-group-nine-spacing) — Foundation Engineering, chapter 8
- [Spacing for 4×5 pile group, block failure](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Apile-group-20-piles-block-failure) — Foundation Engineering, chapter 8