---
title: "Raft 20 m × 30 m, depth of foundation"
subject: "Foundation Engineering"
chapter: 7
key: "semester_5/foundation_engineering:raft-20x30-compensated-depth"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/raft-20x30-compensated-depth
site: BCT Engineering
---

# Raft 20 m × 30 m, depth of foundation

Foundation Engineering · Chapter 7: Mat Foundations

- Asked in: 2075 Chaitra, 3+3 marks
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/raft-20x30-compensated-depth
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-7

## Question

A raft foundation is 20 m × 30 m. The raft is constructed over a soft clay stratum having $C_u = 10\ \text{kN/m}^2$ and $\gamma = 19\ \text{kN/m}^3$. If the live load and dead load on the raft are 100 MN, find the depth of foundation if (a) the foundation is fully compensated, (b) determine the depth of foundation for a factor of safety of 3.

## Short answer

Fully compensated depth Df = total load/(γA) = 100000/(600×19) = 8.77 m. For FS=3, solve Skempton's equation: 10×Nc = 3(166.67−19Df) with Nc=5.68(1+0.01Df) gives Df=7.70 m.

## Answer

**Given:** raft $B = 20$ m, $L = 30$ m, $A = 600$ m², $c_u = 10$ kN/m², $\gamma = 19$ kN/m³, total load $Q = 100$ MN $= 100\,000$ kN.

Gross pressure: $q = \dfrac{100\,000}{600} = 166.67$ kN/m².

#### (a) Fully compensated
Net pressure is zero: $q = \gamma D_f$

$$
D_f = \frac{166.67}{19} = 8.77\ \text{m}
$$

#### (b) Depth for FS = 3
Use Skempton's equation: $q_{nu} = c_uN_c$ and $FS = \dfrac{q_{nu}}{q - \gamma D_f}$. For $D_f/B \le 2.5$:

$$
N_c = \left(0.84 + 0.16\frac{20}{30}\right)\times 6\left(1 + 0.2\frac{D_f}{20}\right) = 5.68\,(1 + 0.01D_f)
$$

$$
\begin{aligned} 10 \times 5.68(1 + 0.01D_f) &= 3\,(166.67 - 19D_f) \\ 56.8 + 0.568D_f &= 500 - 57D_f \\ D_f &= \frac{443.2}{57.568} = 7.70\ \text{m} \end{aligned}
$$

Check: $N_c = 6.12$, $q_{nu} = 61.2$ kN/m², $q_{net} = 166.67 - 19(7.70) = 20.4$ kN/m², $FS = 3.0$ (O.K.; $D_f/B = 0.385$).

**Answer: (a) $D_f = 8.77$ m for a fully compensated raft; (b) $D_f = 7.70$ m for FS = 3.**

## Check yourself

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

1. Gross pressure from 100 MN over 20 x 30 m is:
   A. 100 kN/m^2
   B. 166.67 kN/m^2
   C. 250 kN/m^2
   D. 333 kN/m^2
   Answer: B. 100 000/600 = 166.67 kN/m^2. (Key point: Gross pressure)

2. Depth for full compensation (gamma = 19)?
   A. 7.70 m
   B. 8.77 m
   C. 10 m
   D. 5.2 m
   Answer: B. Df = q/gamma = 166.67/19 = 8.77 m. (Key point: Compensated depth)

3. For part (b), what equation is solved for Df?
   A. cu Nc = 3(q - gamma Df) with Nc depending on Df
   B. cu Nc = q + gamma Df
   C. q = 3 gamma Df
   D. Df = 3B
   Answer: A. FS = q_nu/(q - gamma Df) = 3, with Nc = 5.68(1 + 0.01 Df). (Key point: FS = 3 equation)

4. Why is the depth for FS = 3 (7.70 m) less than for full compensation (8.77 m)?
   A. Some net pressure is allowed since the clay can carry it with FS = 3
   B. The clay is weaker
   C. Load is smaller
   D. Water table is higher
   Answer: A. The raft need not remove all weight; a small net pressure (about 20 kN/m^2) is safely carried by the clay. (Key point: Result comparison)

## Related in Foundation Engineering

- [Fully compensated raft and its depth](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Afully-compensated-raft-depth) — Foundation Engineering, chapter 7
- [Raft 20 m × 10 m, factor of safety](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Araft-20x10-skempton-fos) — Foundation Engineering, chapter 7
- [Raft 14 m × 21 m, depth of foundation](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Araft-14x21-depth-skempton) — Foundation Engineering, chapter 7
- [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
- [Trench bottom heave safety factor](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Atrench-heave-rock) — Foundation Engineering, chapter 4
- [Compensated foundation and types of mat](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Acompensated-foundation-mat-types) — Foundation Engineering, chapter 7, asked 7×

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