---
title: "Circular footing on stiff clay, water table"
subject: "Foundation Engineering"
chapter: 6
key: "semester_5/foundation_engineering:circular-footing-stiff-clay"
source: https://www.bctengineer.com/q/semester_5/foundation_engineering/circular-footing-stiff-clay
site: BCT Engineering
---

# Circular footing on stiff clay, water table

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

- Asked in: 2074 Asoj, 8 marks
- Video: [Gross and Net Allowable Load using Terzaghi's Bearing Capacity Equation| Water Table Special Case](https://www.youtube.com/watch?v=J2BFEwo8BNw) — Master Civil Engineering
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/foundation_engineering/circular-footing-stiff-clay
- Whole chapter: https://www.bctengineer.com/md/semester_5/foundation_engineering/chapter-6

## Question

A circular footing is resting on stiff clay with unconfined compression strength of $250\ \text{kN/m}^2$. Determine the diameter of the footing when the depth of foundation is 2 m and the column load is 700 kN assuming a factor of safety as 2.5, the bulk unit weight of soil is $20\ \text{kN/m}^3$. What will be the change in ultimate, net ultimate and safe bearing capacity if the water table is at ground level?

## Short answer

Required diameter is 1.5 m. If water table rises to ground level, ultimate and safe bearing capacities decrease by 19.62 kN/m² each, while net ultimate capacity remains unchanged because φ=0.

## Answer

**Given:** circular footing on stiff clay, $q_{uc} = 250$ kN/m², so $c = q_{uc}/2 = 125$ kN/m² and $\phi = 0$. $D_f = 2$ m, $Q = 700$ kN, FS = 2.5, $\gamma = 20$ kN/m³.

For $\phi = 0$ (Terzaghi): $N_c = 5.7$, $N_q = 1$, $N_\gamma = 0$. Circular footing: $q_u = 1.3cN_c + \gamma D_f N_q$.

#### (a) Diameter (water table deep)
$$
\begin{aligned} q_u &= 1.3 \times 125 \times 5.7 + 20 \times 2 = 926.25 + 40 = 966.25\ \text{kN/m}^2 \\ q_{nu} &= q_u - \gamma D_f = 926.25\ \text{kN/m}^2 \\ q_{ns} &= \frac{926.25}{2.5} = 370.5\ \text{kN/m}^2 \\ q_s &= q_{ns} + \gamma D_f = 370.5 + 40 = 410.5\ \text{kN/m}^2 \end{aligned}
$$

$$
\begin{aligned} A &= \frac{700}{410.5} = 1.705\ \text{m}^2 \\ d &= \sqrt{\frac{4 \times 1.705}{\pi}} = 1.47\ \text{m} \end{aligned}
$$

Provide a diameter of **1.5 m** (capacity $410.5 \times 1.767 = 725$ kN > 700 kN).

#### (b) Water table at ground level
$\gamma' = 20 - 9.81 = 10.19$ kN/m³, so the overburden becomes $q' = 10.19 \times 2 = 20.38$ kN/m². The $N_\gamma$ term is zero, so only the surcharge changes.

$$
\begin{aligned} q_u' &= 926.25 + 20.38 = 946.63\ \text{kN/m}^2 \\ q_{nu}' &= 946.63 - 20.38 = 926.25\ \text{kN/m}^2 \\ q_s' &= \frac{926.25}{2.5} + 20.38 = 390.88\ \text{kN/m}^2 \end{aligned}
$$

| Quantity | WT deep | WT at GL | Change |
|---|---|---|---|
| Ultimate $q_u$ (kN/m²) | 966.25 | 946.63 | $-19.62$ |
| Net ultimate $q_{nu}$ (kN/m²) | 926.25 | 926.25 | 0 |
| Safe $q_s$ (kN/m²) | 410.5 | 390.88 | $-19.62$ |

**Answer: diameter $\approx 1.5$ m. If the water table rises to the ground level, the ultimate and safe bearing capacities fall by 19.62 kN/m² each, while the net ultimate capacity is unchanged** (clay with $\phi = 0$ is affected only through the overburden).

## Check yourself

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

1. c from qu = 250 kN/m2 is
   A. 250
   B. 500
   C. 125 kN/m2
   D. 62.5
   Answer: C. c = qu/2. (Key point: Cohesion)

2. With WT at GL, net ultimate capacity:
   A. Unchanged at 926.25
   B. Falls by 19.62
   C. Rises
   D. Zero
   Answer: A. The overburden is subtracted, Ngamma = 0. (Key point: Net ultimate with WT)

3. Ultimate capacity change with WT at GL:
   A. Rises by 19.62
   B. Falls by 19.62 kN/m2 due to lower overburden
   C. Unchanged
   D. Falls by half
   Answer: B. gamma' Df replaces gamma Df. (Key point: Ultimate with WT)

## 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
- [Circular footing depth, 2000 kN](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Acircular-footing-depth-2000kn) — Foundation Engineering, chapter 6
- [Circular footing 1 m dia, 1000 kN](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Acircular-footing-1m-1000kn) — Foundation Engineering, chapter 6
- [Rectangular footing 3 m × 4 m, water table cases](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Arect-footing-3x4-backfilled) — 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

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