---
title: "Raft 14 m × 21 m, depth of foundation"
subject: "Foundation Engineering"
chapter: 7
key: "semester_5/foundation_engineering:raft-14x21-depth-skempton"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/raft-14x21-depth-skempton
site: BCT Engineering
---

# Raft 14 m × 21 m, depth of foundation

Foundation Engineering · Chapter 7: Mat Foundations

- Asked in: 2074 Chaitra, 6 marks
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/raft-14x21-depth-skempton
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-7

## Question

A building is to be supported on a reinforced concrete raft covering an area of 14 m × 21 m. The subsoil is clay with an unconfined compressive strength of $14\ \text{kN/m}^2$. The pressure on the soil due to weight of the building and loads it will carry will be $135\ \text{kN/m}^2$, at the base of the raft. If the unit weight of excavated soil is $19\ \text{kN/m}^3$, at what depth should the bottom of the raft be placed to provide a factor of safety of 3? Use Skempton's bearing capacity formula.

## Short answer

Using Skempton: FS = cu Nc/(q−γ Df) with cu=7 kPa, q=135 kPa, γ=19 kN/m³. Nc=5.68(1+0.0143Df). Solving 7Nc = 3(135−19Df) yields required depth Df=6.34 m.

## Answer

**Given:** raft $B = 14$ m, $L = 21$ m, $q_u$ (unconfined) $= 14$ kN/m² so $c_u = 7$ kN/m², gross pressure at base $q = 135$ kN/m², $\gamma = 19$ kN/m³, FS = 3.

**Skempton:** $FS = \dfrac{c_uN_c}{q - \gamma D_f}$ (net ultimate capacity over net pressure). For $D_f/B \le 2.5$:

$$
N_c = \left(0.84 + 0.16\times\frac{14}{21}\right)\times 6\left(1 + 0.2\frac{D_f}{14}\right) = 5.68\,(1 + 0.01429D_f)
$$

$$
\begin{aligned} 7 \times 5.68(1 + 0.01429D_f) &= 3\,(135 - 19D_f) \\ 39.76 + 0.568D_f &= 405 - 57D_f \\ D_f &= \frac{365.24}{57.568} = 6.34\ \text{m} \end{aligned}
$$

Check: $D_f/B = 0.45 < 2.5$; $N_c = 6.19$; $q_{nu} = 43.4$ kN/m²; $q_{net} = 135 - 19(6.34) = 14.5$ kN/m²; $FS = 3.0$.

**Answer: the base of the raft should be placed at a depth of about 6.3 m.**

## Check yourself

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

1. With unconfined strength 14 kN/m^2, cu =
   A. 14
   B. 7
   C. 28
   D. 4.7
   Answer: B. cu = qu/2 = 7 kN/m^2. (Key point: cu from qu)

2. Why must an equation be solved for Df?
   A. Both Nc and net pressure depend on Df
   B. Df is given
   C. Only Nc depends on Df
   D. Df equals B
   Answer: A. Nc = 5.68(1 + 0.01429 Df) and q_net = 135 - 19 Df both contain Df. (Key point: Unknown depth)

3. Which equation is solved?
   A. 7 Nc = 3(135 - 19 Df)
   B. 7 Nc = 135 + 19 Df
   C. 7 Nc = 3 x 135
   D. 7 = 3 Nc
   Answer: A. FS = cu Nc/(q - gamma Df) = 3. (Key point: Equation)

4. The required depth is about:
   A. 2.1 m
   B. 4.5 m
   C. 6.3 m
   D. 9.8 m
   Answer: C. Df = 365.24/57.568 = 6.34 m; check gives FS = 3.0. (Key point: Answer)

## Related in Foundation Engineering

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