---
title: "Fully compensated raft and its depth"
subject: "Foundation Engineering"
chapter: 7
key: "semester_5/foundation_engineering:fully-compensated-raft-depth"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/fully-compensated-raft-depth
site: BCT Engineering
---

# Fully compensated raft and its depth

Foundation Engineering · Chapter 7: Mat Foundations

- Asked in: 2078 Kartik, 1+1 marks
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/fully-compensated-raft-depth
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-7

## Question

Define fully compensated raft foundation. Also derive the relation to calculate its depth.

## Short answer

A fully compensated raft is placed at depth such that excavated soil weight equals total structure weight, net pressure zero, preventing settlement. From equilibrium: Q/A = γ D_f, thus D_f = Q/(γ A).

## Answer

**Fully compensated raft:** a raft placed at such depth that the weight of the soil excavated is equal to the total weight of the structure, including the raft. The net pressure on the soil is then zero, and, in principle, no extra settlement or shear failure occurs.

#### Derivation of depth
Let $Q$ = total load of the structure (including the raft), $A$ = area of the raft, $\gamma$ = unit weight of the excavated soil, $D_f$ = depth of the raft.

Gross pressure at foundation level: $q = \dfrac{Q}{A}$

Weight of soil removed per unit area (overburden pressure): $\gamma D_f$

Net pressure on the soil: $q_{net} = \dfrac{Q}{A} - \gamma D_f$

For a fully compensated raft $q_{net} = 0$:

$$
\frac{Q}{A} = \gamma D_f
$$

$$
D_f = \frac{Q}{\gamma A} = \frac{q}{\gamma}
$$

If the water table is above the raft, the buoyancy reduces the soil weight, so $\gamma D_f$ is replaced by the vertical effective stress at base, or the buoyant uplift is subtracted from $Q$.

## Check yourself

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

1. A fully compensated raft is one in which:
   A. The raft is as thick as it is wide
   B. The excavated soil weight equals the total structure weight, so net pressure is zero
   C. Piles carry all the load
   D. The soil is preloaded
   Answer: B. The weight of soil removed equals the structure weight, so no net pressure is added to the soil. (Key point: Definition)

2. Net pressure at the raft base is:
   A. Q/A + gamma Df
   B. Q/A - gamma Df
   C. gamma Df - Q/A squared
   D. Q/gamma
   Answer: B. Net pressure is the gross pressure Q/A minus the overburden removed, gamma Df. (Key point: Net pressure)

3. Setting net pressure to zero gives the depth:
   A. Df = q gamma
   B. Df = gamma/q
   C. Df = q/gamma
   D. Df = q - gamma
   Answer: C. Q/A = gamma Df gives Df = q/gamma. (Key point: Depth relation)

4. If the water table is above the raft base, the gamma Df term is:
   A. Increased
   B. Replaced by the effective vertical stress at the base (or buoyancy subtracted from Q)
   C. Ignored
   D. Doubled
   Answer: B. Buoyancy reduces the weight of soil removed, so effective stress is used. (Key point: Water table effect)

## Related in Foundation Engineering

- [Raft 20 m × 30 m, depth of foundation](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Araft-20x30-compensated-depth) — 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
- [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×
- [Allowable pressure of raft 3 m × 12 m](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Araft-allowable-pressure-3x12) — 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

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