---
title: "Assumptions of Boussinesq's equation"
subject: "Soil Mechanics"
chapter: 8
key: "semester_4/soil_mechanics:boussinesq-assumptions"
source: https://www.bctengineer.com/q/semester_4/soil_mechanics/boussinesq-assumptions
site: BCT Engineering
---

# Assumptions of Boussinesq's equation

Soil Mechanics · Chapter 8: Vertical Stresses Below Applied Loads

- Asked in: 2073 Magh
- Video: [Boussinesq' Theory | Assumptions || Vertical stress die to Point Load | Soil Mechanics | Chapter 8](https://www.youtube.com/watch?v=Xi7gq1wYIo8) — Sudip Dhakal
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/boussinesq-assumptions
- Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-8

## Question

State the assumptions of Boussinesq's equation.

## Short answer

The soil is a semi-infinite, homogeneous, isotropic, linearly elastic, weightless half-space. The load is a vertical concentrated point load on the horizontal surface, and vertical stress is independent of elastic constants.

## Answer

Boussinesq's equation for the vertical stress below a point load on the surface is based on these assumptions:

1. The soil mass is a **semi-infinite** half-space bounded by a horizontal surface.
2. The soil is **homogeneous**, with the same properties at all points.
3. The soil is **isotropic**, with the same properties in all directions.
4. The soil is **linearly elastic** (stress proportional to strain, following Hooke's law).
5. The soil is **weightless**; the stresses considered are only those due to the applied load.
6. The load acts as a **concentrated point load** on the surface, vertical, and the soil is initially free of stress.
7. The soil is a continuous medium, and the stress distribution is independent of the elastic constants (the vertical stress does not depend on $E$ or $\nu$).

## Check yourself

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

1. Boussinesq's equation assumes the soil mass is
   A. a layered finite stratum
   B. a semi-infinite half-space bounded by a horizontal surface
   C. a thin clay layer over rock
   D. a saturated plastic material
   Answer: B. The soil is a semi-infinite, homogeneous, isotropic, elastic half-space. (Key point: Soil mass)

2. What stress-strain behaviour is assumed?
   A. Perfectly plastic
   B. Linearly elastic, obeying Hooke's law
   C. Visco-elastic with creep
   D. Non-linear hardening
   Answer: B. Stress is taken as proportional to strain, i.e. linear elastic. (Key point: Stress-strain behaviour)

3. Regarding the weight of the soil, Boussinesq assumes it is
   A. included as overburden stress
   B. equal to the applied load
   C. weightless, so only the applied load causes stress
   D. negligible only below 5 m
   Answer: C. The soil is weightless; stresses considered are only those due to the applied load. (Key point: Weight of soil)

4. How does the vertical stress depend on E and nu?
   A. Proportional to E
   B. Proportional to nu
   C. Depends on both E and nu
   D. Independent of E and nu
   Answer: D. The vertical stress distribution is independent of the elastic constants. (Key point: Elastic constants)

## Related in Soil Mechanics

- [Boussinesq stress below circle center](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aboussinesq-circle-center-stress) — Soil Mechanics, chapter 8

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