---
title: "Mat 18 m × 22 m, safe building weight"
subject: "Foundation Engineering"
chapter: 7
key: "semester_5/foundation_engineering:mat-18x22-clay-ucs75"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/mat-18x22-clay-ucs75
site: BCT Engineering
---

# Mat 18 m × 22 m, safe building weight

Foundation Engineering · Chapter 7: Mat Foundations

- Asked in: 2081 Baisakh, 6 marks; 2073 Shrawan, 4 marks (asked 2 times)
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/mat-18x22-clay-ucs75
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-7

## Question

A mat 18 m × 22 m in plan has its base 3 m below the surface of the deposit of clay with unit weight of $20\ \text{kN/m}^3$. The unconfined compressive strength of clay is $75\ \text{kN/m}^2$. The factor of safety against bearing capacity failure must be 3. Determine total weight of building plus the foundation the raft can safely support.

## Short answer

Use Skempton: c_u=37.5 kN/m², Df/B=0.167, N_c(sq)=6.20, N_c(rect)=6.02, q_nu=225.7 kN/m², q_ns=75.2, gross safe pressure=135.2 kN/m². Safe total weight = 135.2 × 396 = 53 557 kN (≈53.6 MN).

## Answer

**Given:** mat $B = 18$ m, $L = 22$ m, $D_f = 3$ m, $\gamma = 20$ kN/m³, $q_u$ (unconfined) $= 75$ kN/m², so $c_u = 37.5$ kN/m², FS = 3.

Use **Skempton's** equation for clay ($\phi = 0$).

#### Bearing capacity factor
$$
\begin{aligned} \frac{D_f}{B} &= \frac{3}{18} = 0.167 < 2.5 \\ N_{c(sq)} &= 6\left(1 + 0.2 \times 0.167\right) = 6.20 \\ N_{c(rect)} &= \left(0.84 + 0.16\frac{B}{L}\right)N_{c(sq)} = (0.84 + 0.1309)(6.20) = 6.02 \end{aligned}
$$

#### Safe pressure
$$
\begin{aligned} q_{nu} &= c_uN_c = 37.5 \times 6.02 = 225.7\ \text{kN/m}^2 \\ q_{ns} &= \frac{225.7}{3} = 75.2\ \text{kN/m}^2 \\ q_s &= q_{ns} + \gamma D_f = 75.2 + 20 \times 3 = 135.2\ \text{kN/m}^2 \end{aligned}
$$

#### Safe total weight
$$
Q_{safe} = q_s \times A = 135.2 \times (18 \times 22) = 135.2 \times 396 = 53\,557\ \text{kN}
$$

**Answer: the raft can safely support a total weight (building plus foundation) of about 53 600 kN (53.6 MN).**

## Check yourself

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

1. How is the undrained cohesion obtained from qu = 75 kN/m^2?
   A. cu = qu = 75 kN/m^2
   B. cu = qu/2 = 37.5 kN/m^2
   C. cu = qu/3 = 25 kN/m^2
   D. cu = 2qu = 150 kN/m^2
   Answer: B. For phi = 0 clay, cu = qu/2. (Key point: cu from unconfined test)

2. What is the Nc for the rectangular mat (B = 18, L = 22, Df = 3) in the answer?
   A. 6.20 for the square, 6.02 after the rectangle shape factor
   B. 9.0
   C. 5.14
   D. 7.5
   Answer: A. Nc(sq) = 6(1 + 0.2 x 0.167) = 6.20 and the shape factor (0.84 + 0.16 B/L) gives about 6.02. (Key point: Rectangular Nc)

3. After finding net safe pressure q_ns = 75.2 kN/m^2, how is the gross safe pressure found?
   A. Multiply by FS = 3
   B. Add gamma Df = 60 kN/m^2
   C. Subtract gamma Df = 60 kN/m^2
   D. Add cu = 37.5 kN/m^2
   Answer: B. The net value excludes the overburden, so q_s = q_ns + gamma Df = 135.2 kN/m^2. (Key point: Gross safe pressure)

4. What total weight can the raft safely carry?
   A. About 29 800 kN
   B. About 53 600 kN
   C. About 89 400 kN
   D. About 135 kN
   Answer: B. Q = q_s x A = 135.2 x 396, about 53 600 kN. (Key point: Safe total weight)

## Related in Foundation Engineering

- [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
- [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×
- [Skempton's findings on clay bearing capacity](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Askempton-net-safe-bc) — Foundation Engineering, chapter 6
- [Circular footing on stiff clay, water table](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Acircular-footing-stiff-clay) — Foundation Engineering, chapter 6
- [Trench bottom heave safety factor](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Atrench-heave-rock) — Foundation Engineering, chapter 4
- [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

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