---
title: "Pile group 4×4, two-layer clay, 2.4 m spacing"
subject: "Foundation Engineering"
chapter: 8
key: "semester_5/foundation_engineering:pile-group-4x4-2-4m-layered"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/pile-group-4x4-2-4m-layered
site: BCT Engineering
---

# Pile group 4×4, two-layer clay, 2.4 m spacing

Foundation Engineering · Chapter 8: Pile Foundations

- Asked in: 2082 Bhadra, 8 marks; 2072 Chaitra, 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-group-4x4-2-4m-layered
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-8

## Question

A 0.8 m dia, 10 m long group of piles (4×4) driven into a clay deposit in a spacing of 2.4 m. The average undrained shear strength along the upper 5 m length of the pile is $40\ \text{kN/m}^2$ and the average undrained shear strength along the lower 5 m length of the pile is $60\ \text{kN/m}^2$. If adhesion factor is 0.6 for both layers, determine the ultimate load capacity of the pile group.

## Short answer

Compute sum of individual pile capacities (shaft friction α c_u perimeter length, end bearing 9 c_u A_p) and block capacity (perimeter friction + 9 c_u B_g L_g). Block capacity 50,560 kN > sum 16,407 kN, so group capacity = 16,407 kN.

## Answer

**Given:** 16 piles (4 × 4), $D = 0.8$ m, $L = 10$ m, spacing $s = 2.4$ m, clay; $c_u = 40$ kN/m² for the top 5 m and $60$ kN/m² for the lower 5 m; adhesion factor $\alpha = 0.6$.

The group capacity is the **smaller** of (1) the sum of the capacities of individual piles and (2) the capacity of the block of soil enclosing the group.

#### 1. Single pile
$$
\begin{aligned} A_p &= \frac{\pi}{4}(0.8)^2 = 0.5027\ \text{m}^2,\quad \text{perimeter } = \pi(0.8) = 2.513\ \text{m} \\ Q_s &= \alpha c_{u1}P L_1 + \alpha c_{u2}PL_2 \\ &= 0.6(40)(2.513)(5) + 0.6(60)(2.513)(5) = 301.6 + 452.4 = 754.0\ \text{kN} \\ Q_p &= 9c_uA_p = 9 \times 60 \times 0.5027 = 271.4\ \text{kN} \\ Q_u &= 754.0 + 271.4 = 1025.4\ \text{kN} \end{aligned}
$$

Sum for 16 piles: $16 \times 1025.4 = 16\,406.7$ kN.

#### 2. Block failure
$$
\begin{aligned} B_g = L_g &= 3(2.4) + 0.8 = 8.0\ \text{m},\quad P_g = 4 \times 8 = 32\ \text{m} \\ Q_{u,block} &= P_g\sum(c_uL) + 9c_uB_gL_g \\ &= 32\,(40 \times 5 + 60 \times 5) + 9 \times 60 \times 8 \times 8 \\ &= 16\,000 + 34\,560 = 50\,560\ \text{kN} \end{aligned}
$$

#### 3. Group capacity
Block capacity (50 560 kN) is greater than the sum of individual piles (16 407 kN), so the piles act individually and the efficiency is 1.

**Answer: ultimate load capacity of the pile group $= 16\,407$ kN (about 16.4 MN).**

## Check yourself

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

1. Group capacity is taken as:
   A. The larger of sum of piles and block
   B. The smaller of sum of individual piles and block capacity
   C. Their average
   D. Block only
   Answer: B. The weaker failure mode governs. (Key point: Governing rule)

2. Single-pile shaft resistance for the two layers is:
   A. 301.6 + 452.4 = 754.0 kN
   B. 754 x 16
   C. 271.4 kN
   D. 1025 kN
   Answer: A. alpha cu P L summed over layers: 0.6 x 40 x 2.513 x 5 + 0.6 x 60 x 2.513 x 5. (Key point: Skin friction)

3. Base resistance uses:
   A. 9 cu Ap with cu at tip layer (60)
   B. cu of the top layer
   C. alpha cu Ap
   D. Nq
   Answer: A. Qp = 9 x 60 x 0.5027 = 271.4 kN. (Key point: Base resistance)

4. Block width for 4x4 piles at 2.4 m spacing, D = 0.8:
   A. 8.0 m
   B. 9.6 m
   C. 7.2 m
   D. 2.4 m
   Answer: A. 3 x 2.4 + 0.8 = 8.0 m. (Key point: Block size)

5. Group capacity is:
   A. 50 560 kN
   B. 16 407 kN
   C. 1025 kN
   D. 34 560 kN
   Answer: B. Block (50 560) exceeds the sum of piles (16 407), so piles act individually. (Key point: Result)

## Related in Foundation Engineering

- [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
- [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×
- [Steel pipe pile group 3×4, layered clay](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Apile-group-steel-pipe-layered-clay) — Foundation Engineering, chapter 8
- [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
- [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
- [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

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