---
title: "Mat 10 m × 15 m with basement, FOS"
subject: "Foundation Engineering"
chapter: 7
key: "semester_5/foundation_engineering:mat-10x15-basement"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/mat-10x15-basement
site: BCT Engineering
---

# Mat 10 m × 15 m with basement, FOS

Foundation Engineering · Chapter 7: Mat Foundations

- Asked in: 2075 Asoj, 6 marks
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/mat-10x15-basement
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-7

## Question

The 10 m × 15 m size mat is constructed at 2.5 m depth having basement for underground parking. The site consists of highly compressible saturated clay having cohesion of $30\ \text{kN/m}^2$. If the mat carries the total load of 4000 kN. Calculate the factor of safety.

## Short answer

For mat 10×15 m, Df=2.5 m, cu=30 kPa, total load 4000 kN. Net ultimate capacity qnu=cu Nc=30×5.96=178.9 kPa. Gross pressure q=26.67 kPa gives FS=6.71; mat is overcompensated if excavation relief considered.

## Answer

**Given:** mat $B = 10$ m, $L = 15$ m, $D_f = 2.5$ m, saturated clay $c_u = 30$ kN/m², total load $Q = 4000$ kN. The unit weight of soil is not given.

**Assumption:** the relief due to excavation is ignored (conservative) because $\gamma$ is not given, so the net applied pressure is taken equal to $Q/A$.

#### Bearing capacity factor (Skempton)
$$
\begin{aligned} N_{c(sq)} &= 6\left(1 + 0.2 \times \frac{2.5}{10}\right) = 6.30 \\ N_{c(rect)} &= \left(0.84 + 0.16\times\frac{10}{15}\right)(6.30) = 5.96 \\ q_{nu} &= c_uN_c = 30 \times 5.964 = 178.9\ \text{kN/m}^2 \end{aligned}
$$

#### Applied pressure and factor of safety
$$
\begin{aligned} q &= \frac{4000}{10 \times 15} = 26.67\ \text{kN/m}^2 \\ FS &= \frac{178.9}{26.67} = 6.71 \end{aligned}
$$

**Answer: factor of safety $\approx 6.7$.** If the weight of the soil excavated for the basement ($\gamma D_f \approx 18 \times 2.5 = 45$ kN/m²) is taken into account, it exceeds the applied pressure of 26.7 kN/m², so the mat is over-compensated and the true factor of safety is even higher.

## Check yourself

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

1. For B = 10, L = 15, Df = 2.5, Nc is about:
   A. 5.96
   B. 9.0
   C. 6.30 with no shape correction
   D. 4.2
   Answer: A. 6.30 x (0.84 + 0.16 x 10/15) = 5.96. (Key point: Skempton Nc)

2. What is assumed since gamma is not given?
   A. Net applied pressure equals Q/A (excavation relief ignored)
   B. gamma = 0 and cu = 0
   C. The mat is floating
   D. FS = 3
   Answer: A. Ignoring the relief is conservative, so applied pressure is Q/A = 26.67 kN/m^2. (Key point: Assumption)

3. FS is about:
   A. 2.1
   B. 4.0
   C. 6.7
   D. 9.0
   Answer: C. 178.9/26.67 = 6.7. (Key point: Factor of safety)

4. If soil weight removed (about 45 kN/m^2) is included, the true FS is:
   A. Lower
   B. Unchanged
   C. Even higher, as the mat is over-compensated
   D. Zero
   Answer: C. Excavated soil weight exceeds the applied 26.7 kN/m^2, so net pressure is nil or negative. (Key point: Effect of excavation relief)

## Related in Foundation Engineering

- [Square footing size in clay, 750 kN](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Asquare-footing-clay-750kn) — Foundation Engineering, chapter 6
- [Mat 8 m × 10 m, Skempton net safe pressure](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Amat-8x10-skempton) — Foundation Engineering, chapter 7
- [Rectangular footing size, 6000 kN](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Afooting-6000kn-rectangular-sand) — Foundation Engineering, chapter 6
- [Strip footing FOS, three water table cases](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Astrip-footing-fos-water-table) — Foundation Engineering, chapter 6
- [Square footing under eccentric load, min depth](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Asquare-footing-eccentric-2000kn) — Foundation Engineering, chapter 6
- [Circular footing depth, 2000 kN](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Acircular-footing-depth-2000kn) — Foundation Engineering, chapter 6

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- [RC wall footing, 1000 kN total load](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Arc-wall-footing-1000-kn-total) — Design of RCC Structure, chapter 11
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- [Saturated clay 20 cc numerical](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Asaturated-clay-void-ratio-gravity) — Soil Mechanics, chapter 2