Stresses In Soil – Boussinesq And Westergaard’s Theory

In this article, we will study “stresses in soil”. It is very important for engineers to study the behavior of soil before starting any construction. Stresses in the soil can determine which type of foundation will be provided.

Usually, there is two popular theory to calculate stresses in soil.

1. Boussinesq Theory
2. Westergaard Theory

First, we will learn some terms related to stress.

What is Effective Stress in Soil?

When the stress is transferred from grain to grain at the point of contact via a soil mass is called effective stress. It is also known as intergranular stress. It is denoted by σ’.

The effective stress in soil is the difference between the total stress and the pore water pressure. Mathematically, it can be represented by the following formula:

σ′ = σ_t – U_w

where: σ′ = effective stress σ_t = total stress U_w = pore water pressure

This formula is widely used in geotechnical engineering and soil mechanics to analyze the behavior of soils under different loading conditions.

What is Pore Water Stress?

When the pores of soil are filled with water and the pressure-induced tries to detach the grain then it is known as pore water stress or neutral stress. It is denoted by Uw.

U_w = σ_t – σ′

What is Total Stress in Soil?

It is the summation of effective stress and pore water pressure. It is denoted by σt.

σ_t = U_w+ σ′

Calculation of Stress Distribution in Soil Due to the load Acting on the Surface?

Following are the formulas used to calculate stress distribution in soil:

1. Boussinesq’s Formula:

It was used to find the stress at point P at a depth z due to the load acting on the surface. It was developed in 1885.

The assumption made for this formula is:

1. The soil is elastic, isotropic, semi-infinite, and homogenous.
2. The soil is weightless.
3. The load acting is a point load.

2. Westergaard’s formula for point load:

It was proposed by Westergaard in 1938.

Westergard’s formula:

Example

Solved example to calculate effective stresses and water pressure is given below:

Faq