---
title: "Spacing of nine piles for efficiency 1"
subject: "Foundation Engineering"
chapter: 8
key: "semester_5/foundation_engineering:pile-group-nine-spacing"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/pile-group-nine-spacing
site: BCT Engineering
---

# Spacing of nine piles for efficiency 1

Foundation Engineering · Chapter 8: Pile Foundations

- Asked in: 2074 Asoj, 7 marks
- Video: [Efficiency of pile group | Pile foundation | Geotechnical | Pile Group Capacity | KTU | GATE | VTU |](https://www.youtube.com/watch?v=5L7Xp9ep3ug) — Dr Rajeev Kumar P
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/pile-group-nine-spacing
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-8

## Question

A group of nine piles, 12 m long and 300 mm in diameter is to be arranged in a square pattern in clay with an average unconfined compressive strength of $75\ \text{kN/m}^2$. Determine the centre to centre spacing of the piles for the efficiency of 1. Neglect the point bearing.

## Short answer

With point bearing neglected and efficiency 1, block skin friction equals 9× single pile skin friction. Equating gives centre-to-centre spacing s=0.91 m (≈3d).

## Answer

**Given:** 9 piles (3 × 3, square pattern), $d = 0.30$ m, $L = 12$ m, $q_u = 75$ kN/m² so $c_u = 37.5$ kN/m². Point bearing is neglected, and the efficiency is to be 1. The adhesion factor is not given, so $\alpha = 1.0$ is assumed.

For efficiency $= 1$, **block capacity = sum of individual pile capacities** (skin friction only).

#### Individual piles
$$
\sum Q_u = 9\,\alpha c_u\pi dL = 9 \times 1.0 \times 37.5 \times \pi \times 0.3 \times 12 = 3817.0\ \text{kN}
$$

#### Block
$$
Q_{block} = 4B_g\,L\,c_u = 4 \times B_g \times 12 \times 37.5 = 1800\,B_g
$$

#### Equate
$$
\begin{aligned} 1800\,B_g &= 3817.0 \Rightarrow B_g = 2.12\ \text{m} \\ B_g &= 2s + d \Rightarrow s = \frac{2.12 - 0.30}{2} = 0.91\ \text{m} \end{aligned}
$$

Thus $s/d = 3.0$. In general $B_g = \dfrac{9\alpha\pi d}{4}$.

**Answer: centre-to-centre spacing $\approx 0.91$ m ($\approx 3d$)** for an efficiency of 1.

## Check yourself

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

1. For efficiency 1 with no point bearing we equate:
   A. Tip bearing only
   B. Weight of soil
   C. Total with FS
   D. Block skin friction 4 B_g L c_u with 9 x pile skin friction
   Answer: D. Block capacity equals sum of individual skin friction capacities. (Key point: Efficiency 1 condition)

2. c_u from q_u = 75 kN/m2 is:
   A. 75
   B. 150
   C. 37.5
   D. 18.75
   Answer: C. c_u = q_u / 2 = 37.5 kPa. (Key point: Cohesion)

3. Equating 1800 B_g = 3817 gives B_g of:
   A. 0.91 m
   B. 2.12 m
   C. 4.24 m
   D. 1.06 m
   Answer: B. B_g = 3817 / 1800 = 2.12 m. (Key point: Block width)

4. For a 3 x 3 group, s is found from:
   A. B_g = 3s, so s = 0.7 m
   B. B_g = s + d
   C. B_g = 2s + d, so s = 0.91 m
   D. B_g = 2s
   Answer: C. Two gaps plus a diameter: s = (2.12 - 0.30)/2 = 0.91 m, about 3d. (Key point: Spacing)

## Related in Foundation Engineering

- [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 spacing for 100% efficiency, 16 piles](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Apile-spacing-100-efficiency-square-30cm) — Foundation Engineering, chapter 8, asked 2×
- [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 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×
- [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
- [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

## Related in other subjects

- [Compressive strength test and classification of bricks](https://www.bctengineer.com/question.md?key=semester_5%2Fdesign_of_timber_and_masonry_structures%3Abrick-compressive-strength-test-classification) — Design of Timber and Masonry Structures, chapter 8