---
title: "Water tower foundation on weak stratum"
subject: "Soil Mechanics"
chapter: 8
key: "semester_4/soil_mechanics:water-tower-weak-stratum-stress"
source: https://www.bctengineer.com/q/semester_4/soil_mechanics/water-tower-weak-stratum-stress
site: BCT Engineering
---

# Water tower foundation on weak stratum

Soil Mechanics · Chapter 8: Vertical Stresses Below Applied Loads

- Asked in: 2073 Magh; 2076 Baisakh, 6 marks (asked 2 times)
- Video: [Geotechnical Analysis of Foundations](https://www.youtube.com/watch?v=KgKW10iA_4w) — The Engineering Hub
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/water-tower-weak-stratum-stress
- Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-8

## Question

A water tower has a circular foundation of diameter 10 m. The total weight of the tower including the foundation is 1800 tonnes (18000 kN). A very weak stratum having a bearing capacity of 10 t/m² (100 kN/m²) lies 3 m below the foundation level. Calculate the stress due to the foundation load at the top of the weak stratum and ascertain whether it will be safe to construct the water tower at that place with the given foundation size. (The 2076 paper does not print the depth of the weak stratum.)

## Short answer

Using Boussinesq’s equation for a circular area: with q=Q/(πR²)=229.2 kN/m², R/z=5/3, stress Δσz = q[1 − 1/(1+(R/z)²)^(3/2)] = 198 kN/m². This exceeds the weak stratum’s bearing capacity of 100 kN/m², so the tower is unsafe.

## Answer

#### Given

Circular foundation $D = 10$ m ($R = 5$ m). Load $Q = 18000$ kN. Weak stratum at $z = 3$ m below the foundation level (assumed, as the depth is not printed), bearing capacity $q_a = 100$ kN/m².

Contact pressure:

$$
q = \frac{Q}{\pi R^2} = \frac{18000}{\pi \times 5^2} = 229.2\ \text{kN/m}^2
$$

#### Stress at the top of the weak stratum (below the centre)

Boussinesq's equation for a uniformly loaded circular area:

$$
\Delta\sigma_z = q\left[1 - \frac{1}{\left(1 + (R/z)^2\right)^{3/2}}\right]
$$

$$
\frac{R}{z} = \frac{5}{3} = 1.667, \qquad 1 + (R/z)^2 = 3.778, \qquad (3.778)^{3/2} = 7.343
$$

$$
\Delta\sigma_z = 229.2\left[1 - \frac{1}{7.343}\right] = 229.2 \times 0.8638 = 198.0\ \text{kN/m}^2
$$

(A quick check by the 2:1 method: $Q/[\frac{\pi}{4}(10+3)^2] = 135.6$ kN/m², also above 100.)

#### Check

$\Delta\sigma_z = 198\ \text{kN/m}^2 \approx 19.8\ \text{t/m}^2 > 100\ \text{kN/m}^2\ (10\ \text{t/m}^2)$

**Answer: The stress at the top of the weak stratum is about 198 kN/m², which exceeds the bearing capacity of the stratum (100 kN/m²). It is not safe to construct the water tower with this foundation size.**

The foundation must be enlarged (a diameter of about 15 m gives about 97 kN/m²) or the load shifted to a deeper stratum (piles).

## Check yourself

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

1. Contact pressure q for Q = 18000 kN and D = 10 m is about:
   A. 229 kN/m2
   B. 180 kN/m2
   C. 450 kN/m2
   D. 57 kN/m2
   Answer: A. 18000/(pi x 25) = 229.2. (Key point: Contact pressure)

2. Which equation gives stress below the centre of a circular load?
   A. q[1 - 1/(1+(R/z)^2)^1.5]
   B. q (R/z)
   C. q/(1+R/z)
   D. q[1 + (R/z)^2]
   Answer: A. Boussinesq circular area, centre. (Key point: Formula)

3. Stress at z = 3 m is about:
   A. 198 kN/m2
   B. 100 kN/m2
   C. 229 kN/m2
   D. 50 kN/m2
   Answer: A. 229.2 x 0.8638 = 198. (Key point: Stress value)

4. Compared with the stratum capacity of 100 kN/m2, the foundation is:
   A. Safe
   B. Not safe, stress exceeds capacity
   C. Exactly critical
   D. Undetermined
   Answer: B. 198 > 100 so it is unsafe. (Key point: Conclusion)

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