---
title: "Raft 20 m × 10 m, factor of safety"
subject: "Foundation Engineering"
chapter: 7
key: "semester_5/foundation_engineering:raft-20x10-skempton-fos"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/raft-20x10-skempton-fos
site: BCT Engineering
---

# Raft 20 m × 10 m, factor of safety

Foundation Engineering · Chapter 7: Mat Foundations

- Asked in: 2076 Chaitra, 6 marks
- Video: [Raft Foundation Numerical || 2023 PU || Factor of Safety calculation](https://www.youtube.com/watch?v=cVC8kuBtxO4) — Sudip Dhakal
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/raft-20x10-skempton-fos
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-7

## Question

A raft foundation is 20 m × 10 m exerts a gross pressure of $200\ \text{kN/m}^2$ at the foundation level. The depth of foundation is 2.5 m. If the soil is clay $C_u = 80\ \text{kN/m}^2$ and $\gamma = 19\ \text{kN/m}^3$. Determine the factor of safety. Use Skempton's equations.

## Short answer

For raft 20×10 m, Df=2.5 m on clay cu=80 kPa, Skempton Nc=5.80, net ultimate 463.7 kPa. Net applied pressure 152.5 kPa gives FS=3.04.

## Answer

**Given:** raft $20\ \text{m} \times 10\ \text{m}$, gross pressure $q = 200$ kN/m², $D_f = 2.5$ m, clay $c_u = 80$ kN/m², $\gamma = 19$ kN/m³.

**Skempton's equation:** $q_{nu} = c_uN_c$, with $B = 10$ m, $L = 20$ m.

$$
\begin{aligned} \frac{D_f}{B} &= \frac{2.5}{10} = 0.25 < 2.5 \\ N_{c(sq)} &= 6\left(1 + 0.2 \times 0.25\right) = 6.30 \\ N_{c(rect)} &= \left(0.84 + 0.16 \times \frac{10}{20}\right)(6.30) = 0.92 \times 6.30 = 5.80 \\ q_{nu} &= 80 \times 5.796 = 463.7\ \text{kN/m}^2 \end{aligned}
$$

Net applied pressure:

$$
q_{net} = q - \gamma D_f = 200 - 19 \times 2.5 = 152.5\ \text{kN/m}^2
$$

$$
FS = \frac{q_{nu}}{q_{net}} = \frac{463.7}{152.5} = 3.04
$$

**Answer: factor of safety $\approx 3.04$.**

## Check yourself

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

1. Which dimension is B in Skempton's Nc for the 20 m x 10 m raft?
   A. 20 m, the longer side
   B. 10 m, the shorter side
   C. Average 15 m
   D. 2.5 m, the depth
   Answer: B. B is the shorter side, so Df/B = 2.5/10 = 0.25 and B/L = 0.5. (Key point: Geometry)

2. What Nc results?
   A. About 5.8
   B. About 9
   C. About 7.5
   D. About 3.1
   Answer: A. Nc(sq) = 6.30 and the shape factor 0.92 gives 5.80. (Key point: Nc value)

3. The net applied pressure used in the FS is:
   A. 200 kN/m^2
   B. 200 - 19 x 2.5 = 152.5 kN/m^2
   C. 200 + 47.5 = 247.5 kN/m^2
   D. 80 kN/m^2
   Answer: B. FS compares net capacity to net pressure, so overburden is subtracted from the gross pressure. (Key point: Net applied pressure)

4. FS = q_nu/q_net equals about:
   A. 1.5
   B. 2.3
   C. 3.04
   D. 4.6
   Answer: C. 463.7/152.5 = 3.04. (Key point: Factor of safety)

## Related in Foundation Engineering

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