---
title: "Allowable pressure of raft 3 m × 12 m"
subject: "Foundation Engineering"
chapter: 7
key: "semester_5/foundation_engineering:raft-allowable-pressure-3x12"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/raft-allowable-pressure-3x12
site: BCT Engineering
---

# Allowable pressure of raft 3 m × 12 m

Foundation Engineering · Chapter 7: Mat Foundations

- Asked in: 2078 Kartik, 4 marks
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/raft-allowable-pressure-3x12
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-7

## Question

Determine the allowable bearing pressure of a raft foundation 3 m × 12 m in plan, resting at depth of 2 m on cohesionless soil. The corrected N value over a depth of 12 m was 22. It is specified that the differential settlement is not to exceed 20 mm. Water table is at depth of 4 m below the ground level.

## Short answer

Use Meyerhof SPT method: depth factor Fd=1.22, net allowable qna=19.16×22×1.22×(20/25.4)=404.9 kN/m². Water table correction Cw=0.90 yields net allowable pressure ≈365 kN/m².

## Answer

**Given:** raft $B = 3$ m, $L = 12$ m, $D_f = 2$ m, corrected $N = 22$, cohesionless soil, water table 4 m below GL.

**Method (Meyerhof/Bowles, SPT-based, for raft):** for a raft the settlement is nearly independent of width, so the net allowable pressure for a settlement $S_a$ is

$$
q_{na} = 19.16\,N\,F_d\,\frac{S_a}{25.4}\ \ \text{(kN/m}^2\text{, } S_a \text{ in mm)},\qquad F_d = 1 + 0.33\frac{D_f}{B} \le 1.33
$$

**Allowable settlement:** the differential settlement is limited to 20 mm. As the total settlement is at least equal to the differential settlement, the conservative value $S_a = 20$ mm is used.

#### Calculation
$$
\begin{aligned} F_d &= 1 + 0.33\times\frac{2}{3} = 1.22 \\ q_{na} &= 19.16 \times 22 \times 1.22 \times \frac{20}{25.4} = 404.9\ \text{kN/m}^2 \end{aligned}
$$

#### Water table correction
The water table lies at 4 m, which is within a depth $B$ below the base ($D_f + B = 5$ m), so

$$
C_w = 0.5 + 0.5\frac{D_w}{D_f + B} = 0.5 + 0.5\times\frac{4}{5} = 0.90
$$

$$
q_{na}' = 404.9 \times 0.90 = 364.4\ \text{kN/m}^2
$$

**Answer: net allowable bearing pressure of the raft $\approx 365$ kN/m²** (settlement criterion governs; the shear failure check will have a large margin in sand).

## Check yourself

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

1. Which criterion fixes the allowable pressure in this problem?
   A. Shear failure with Nq
   B. Allowable settlement (20 mm) using the SPT formula
   C. Frost action
   D. Water content
   Answer: B. The settlement limit governs in sand, using q_na = 19.16 N Fd Sa/25.4. (Key point: Governing criterion)

2. Fd = 1 + 0.33 Df/B for Df = 2 m and B = 3 m equals:
   A. 1.00
   B. 1.22
   C. 1.33
   D. 1.50
   Answer: B. 1 + 0.33 x 2/3 = 1.22, which is below the limit of 1.33. (Key point: Depth factor)

3. Why is Sa = 20 mm used?
   A. Total settlement is at least the differential settlement, so 20 mm is conservative
   B. 20 mm is the code limit for total settlement
   C. It is the settlement of a plate test
   D. It equals B/150
   Answer: A. Total settlement is not less than differential settlement, so using 20 mm is conservative. (Key point: Settlement value)

4. Water table at 4 m with Df + B = 5 m gives Cw =
   A. 1.0
   B. 0.90
   C. 0.50
   D. 0.80
   Answer: B. Cw = 0.5 + 0.5 x 4/5 = 0.90, reducing q_na from 404.9 to about 364 kN/m^2. (Key point: Water table correction)

## 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
- [Allowable load of 400 mm pile, layered soil](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Apile-400mm-layered-soil-chart) — Foundation Engineering, chapter 8
- [SPT corrected N-value, dense sand](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Aspt-dilatancy-20m) — Foundation Engineering, chapter 2
- [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
- [Mat bearing capacity: cohesive vs cohesionless](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Amat-bc-cohesive-vs-cohesionless) — Foundation Engineering, chapter 7, asked 2×

## Related in other subjects

- [Foundation settlement, effects, black cotton soil](https://www.bctengineer.com/question.md?key=semester_6%2Fbuilding_technology%3Asettlement-black-cotton-062ba) — Building Technology, chapter 2
- [Stable depth: Q 20, d 40 mm](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Astable-depth-q20-d40mm) — Irrigation and Drainage Engineering, chapter 4, asked 2×
- [Water tower foundation on weak stratum](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Awater-tower-weak-stratum-stress) — Soil Mechanics, chapter 8, asked 2×
- [Water hammer: rectangular grid and specified intervals](https://www.bctengineer.com/question.md?key=semester_8%2Fcomputational_techniques_in_civil_engineering%3Awater-hammer-numerical-solution) — Computational Techniques in Civil Engineering, chapter 6