---
title: "Allowable load of 400 mm pile, layered soil"
subject: "Foundation Engineering"
chapter: 8
key: "semester_5/foundation_engineering:pile-400mm-layered-soil-chart"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/pile-400mm-layered-soil-chart
site: BCT Engineering
---

# Allowable load of 400 mm pile, layered soil

Foundation Engineering · Chapter 8: Pile Foundations

- Asked in: 2078 Bhadra, 10 marks
- Video: [Ultimate and Allowable Capacity of Pile in Three Layered Soil With Water Table|Solved Problem](https://www.youtube.com/watch?v=hfbcwIJfAjw) — Master Civil Engineering
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/pile-400mm-layered-soil-chart
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-8

## Question

Determine the allowable pile load capacity of the 400 mm diameter driven concrete pile shown in the following figure. [Figure: water table at 3 m depth; loose sand 3 m thick, $\gamma = 16\ \text{kN/m}^3$, $\phi = 30^\circ$; soft clay 6 m thick, $\gamma = 16\ \text{kN/m}^3$, $c = 15\ \text{kN/m}^2$; dense sand 5 m thick, $\gamma = 20\ \text{kN/m}^3$, $\phi = 40^\circ$. A chart of bearing capacity factor $N_q$ vs $\phi$ (Meyerhof, Hansen, Berezantzev, Terzaghi) and a table of $\delta$ and $K$: Steel $\delta = 20^\circ$, $K = 0.5$ (loose) / 1 (dense); Concrete $\delta = 0.75\phi$, $K = 1$ / 2; Timber $\delta = 0.67\phi$, $K = 1.5$ / 4 are given.]

## Short answer

Shaft resistance in loose sand (β-method), soft clay (α-method) and dense sand (β-method) summed to 633.6 kN. End bearing uses Berezantsev Nq=130, limited to ql=5454 kN/m², giving 685.4 kN. Ultimate capacity 1319 kN, allowable 440 kN (FS=3).

## Answer

**Given:** driven concrete pile $D = 0.40$ m, length 14 m, water table at 3 m. Layers: loose sand 0–3 m ($\gamma = 16$, $\phi = 30^\circ$); soft clay 3–9 m ($\gamma = 16$, $c = 15$ kN/m²); dense sand 9–14 m ($\gamma = 20$, $\phi = 40^\circ$). For concrete: $\delta = 0.75\phi$, $K = 1$ (loose) and $2$ (dense).

**Assumptions:** $\gamma_w = 9.81$ kN/m³; below the water table the given $\gamma$ values are saturated values; effective stress is limited at the critical depth $L' = 15D = 6$ m (Das/Meyerhof) for both shaft friction and the tip; $N_q$ for $\phi = 40^\circ$ is read from the Berezantsev curve as about 130 (approximate chart reading); $\alpha = 1.0$ for soft clay ($c < 25$ kPa); factor of safety $= 3$ (not given). Pile area $A_p = 0.1257$ m², perimeter $P = 1.257$ m.

#### Effective stress
$$
\sigma'_v(3\ \text{m}) = 16 \times 3 = 48\ \text{kN/m}^2,\qquad \sigma'_v(6\ \text{m}) = 48 + (16 - 9.81)(3) = 66.57\ \text{kN/m}^2 \ (\text{constant below})
$$

#### Shaft resistance
| Layer | Method | Working | $Q_s$ (kN) |
|---|---|---|---|
| Loose sand 0–3 m | $K\sigma'\tan\delta\,P\Delta L$ | $\sigma'_{avg} = 24$; $\delta = 22.5^\circ$; $f_s = 1(24)(0.414) = 9.94$ | 37.5 |
| Soft clay 3–9 m | $\alpha cP\Delta L$ | $1.0 \times 15 \times 1.257 \times 6$ | 113.1 |
| Dense sand 9–14 m | $K\sigma'\tan\delta\,P\Delta L$ | $\sigma' = 66.57$; $\delta = 30^\circ$; $f_s = 2(66.57)(0.577) = 76.9$ | 483.0 |

$Q_s = 37.5 + 113.1 + 483.0 = 633.6$ kN.

#### End bearing
$$
\begin{aligned} q_pN_q &= 66.57 \times 130 = 8654\ \text{kN/m}^2 \\ q_l &= 50N_q\tan\phi = 50(130)\tan 40^\circ = 5454\ \text{kN/m}^2\ (\text{limiting value governs}) \\ Q_p &= 5454 \times 0.1257 = 685.4\ \text{kN} \end{aligned}
$$

#### Capacity
$$
Q_u = 633.6 + 685.4 = 1318.9\ \text{kN},\qquad Q_{all} = \frac{1318.9}{3} = 439.6\ \text{kN}
$$

**Answer: allowable pile load capacity $\approx 440$ kN** (ultimate $\approx 1319$ kN). The result depends on the chart value of $N_q$.

## Check yourself

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

1. Shaft resistance in the soft clay layer is computed with:
   A. K sigma' tan(delta)
   B. alpha c P dL with alpha = 1.0
   C. 9 c A_p
   D. Nq sigma'
   Answer: B. Clay uses adhesion alpha c, with alpha = 1.0 for soft clay: 113.1 kN. (Key point: Shaft resistance by layer)

2. Effective stress is limited at critical depth L' = 15D = 6 m because:
   A. The water table is there
   B. The clay ends there
   C. Stress stops increasing with depth for friction and tip
   D. N_q changes
   Answer: C. Beyond the critical depth effective stress is held constant at 66.57 kPa. (Key point: Critical depth effect)

3. The end bearing used is 5454 kPa because:
   A. It is the larger value
   B. It is the smaller limiting value 50 N_q tan(phi) vs 8654 kPa
   C. N_q is 50
   D. It is the clay value
   Answer: B. q_p cannot exceed 50 N_q tan(phi), which governs over q' N_q. (Key point: Limiting end bearing)

4. Allowable capacity is found by:
   A. Q_u x 3
   B. (Q_s + Q_p)/3 = 1319/3 = 440 kN
   C. Q_s / 3 only
   D. Q_p x 3
   Answer: B. Q_u = 633.6 + 685.4 = 1319 kN, divided by assumed FS 3. (Key point: Allowable load)

## Related in Foundation Engineering

- [Allowable load of 4×4 pile group, layered sand](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Apile-group-4x4-figure-dcr) — Foundation Engineering, chapter 8
- [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, 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 capacity in sand, group effect, load test](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Apile-capacity-sand-group-load-test) — Foundation Engineering, chapter 8
- [Circular footing on stiff clay, water table](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Acircular-footing-stiff-clay) — Foundation Engineering, chapter 6
- [Factors affecting bearing capacity; water table](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Abearing-capacity-factors-water-table) — Foundation Engineering, chapter 6, asked 5×

## Related in other subjects

- [Direct shear on loose and dense sand graphs](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Adirect-shear-sand-graphs) — Soil Mechanics, chapter 10
- [Uniform sand, water table 2 m, capillary](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Auniform-sand-effective-stress-capillary) — Soil Mechanics, chapter 6
- [Clay over sand, effective stress at depths](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aclay-sand-profile-effective-stress-depths) — Soil Mechanics, chapter 6