---
title: "Circular footing depth, 2000 kN"
subject: "Foundation Engineering"
chapter: 6
key: "semester_5/foundation_engineering:circular-footing-depth-2000kn"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/circular-footing-depth-2000kn
site: BCT Engineering
---

# Circular footing depth, 2000 kN

Foundation Engineering · Chapter 6: Bearing Capacity and Settlement of Shallow Foundations

- Asked in: 2076 Asoj, 7 marks
- Video: [Depth of Circular Footing Numerical](https://www.youtube.com/watch?v=gU0crmgH_BA) — Vikas Vigyan Civil
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/circular-footing-depth-2000kn
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-6

## Question

A circular footing of 2.5 m diameter carries a gross load of 2000 kN. The supporting soil is clayey sand ($\phi = 30^\circ$, $\gamma = 19\ \text{kN/m}^3$). Determine the depth at which the footing should be located to provide the factor of safety 3. Use Terzaghi's theory. $N_c = 37.2$, $N_q = 22.5$, $N_\gamma = 19.7$ for $\phi = 30^\circ$.

## Short answer

Required ultimate pressure is 1222 kN/m². Using Terzaghi's equation for circular footing on sand, depth is found from 0.3γBN_γ + γD_fN_q = 1222, giving D_f = 2.2 m.

## Answer

**Given:** circular footing $B = 2.5$ m, gross load $Q = 2000$ kN, $\phi = 30^\circ$, $c = 0$, $\gamma = 19$ kN/m³, FS = 3, $N_q = 22.5$, $N_\gamma = 19.7$.

Terzaghi's equation for a circular footing: $q_u = 1.3cN_c + \gamma D_f N_q + 0.3\gamma B N_\gamma$. With $c = 0$ the first term is zero.

#### Required ultimate capacity
$$
\begin{aligned} A &= \frac{\pi}{4}(2.5)^2 = 4.909\ \text{m}^2 \\ q_{applied} &= \frac{2000}{4.909} = 407.4\ \text{kN/m}^2 \\ q_u &= FS \times q_{applied} = 3 \times 407.4 = 1222.3\ \text{kN/m}^2 \end{aligned}
$$

#### Solve for depth
$$
\begin{aligned} 0.3\gamma BN_\gamma &= 0.3 \times 19 \times 2.5 \times 19.7 = 280.7\ \text{kN/m}^2 \\ \gamma D_fN_q &= 19 \times 22.5 \times D_f = 427.5\,D_f \\ 1222.3 &= 427.5\,D_f + 280.7 \\ D_f &= \frac{941.6}{427.5} = 2.20\ \text{m} \end{aligned}
$$

**Answer: the footing should be placed at a depth of about 2.2 m** (gross capacity basis; $D_f/B = 0.88 < 1$, so the shallow-footing equation is valid).

## Check yourself

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

1. Gamma-term factor for circular footing:
   A. 0.5
   B. 0.4
   C. 0.3
   D. 1.3
   Answer: C. Circular: 0.3 gamma B Ngamma. (Key point: Circular formula)

2. Required qu =
   A. 407.4
   B. 2000
   C. 611
   D. 3 * 2000 / area = 1222.3 kN/m2
   Answer: D. FS times applied pressure. (Key point: Required qu)

3. Why is the shallow equation valid?
   A. Df/B = 0.88 < 1
   B. Df/B = 3
   C. c is large
   D. Nq is 1
   Answer: A. Terzaghi shallow footings have Df <= B. (Key point: Check)

## Related in Foundation Engineering

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