Soil Foundations & Soil Capacity Mathematics


Soil Foundations

Soil is predominately a mixture of minerals, dead or decaying matter, and liquids. The composition of soil varies significantly from place to place. The climate, relief, and the ecosystem that resides on top all play a part in shaping the earth. Soil is the part of the foundations for every land based building therefore, it is extremely important that all the properties of the soil are obtained before building takes place. Soil foundations come in all shapes and sizes and it is important that you consider all the variables before constructing your structure

What are the Important Soil properties?

Terzaghi’s Bearing Capacity Theory is used for calculating the final bearing capacity, on the tipping point of disaster, of the rough shallow foundations. After the bearing capacity has been calculated, safety guidelines and regulations can be incorporated into the parameters to calculate the safe bearing limit of the soil. The theory defines shallow foundations as structures that are less than or equal to their width. However, more recent studies have found that a foundation may still be shallow for foundations with depths equal to three or four times their width. Terzaghi’s theory takes into account the soil friction, cohesion, embedment surcharge, and the self-weight. Terzaghi was an influential pioneer and he left a huge impact in geotechnical engineering.

The Mathematics

Square foundations utilise the following equation:


However, for circular foundations, the equation changes as the factor for the combined multiplication of the width, B, effective unit weight, Y’, and .the modified bearing factors, is reduced from 0.4 to 0.3.                                                           2

Foundations that are continuous require the following;




The other symbols are defined as ;

5  modified bearing capacity

C’ is the effective cohesion,

Y’ is the effective unit weight when saturated or the total unit weight if not fully saturated,

123 Is the vertical effective stress at the foundation depth,

B is the width of the foundation (diameter for circular foundations).

6 is the internal angle of friction,

8  Is obtained via a graph

Due to the issues that arise from trying to obtain the 9Value from a graph the equation has been sought to be simplified over the years with the most successful alteration carried out by Coduto resulting in an accuracy of within 10%.

However, it is extremely important to remember that the equation calculates the maximum possible bearing capacity at ‘tipping point’. Therefore, it is important to remember the safety constraints.

The safety constraint is defined as:


The FS is the factor of safety which is used to determine the gross ultimate bearing capacity.

There have been improvements and alterations to Terzaghi’s formula in an attempt to simplify or improve the accuracy. A worthwhile alteration was that of Meyehof who included a shape factor so that the same equation could be used for all calculations. Terzaghi also improved his equation for situations where the soil has a local shear failure. The final product caused a change in the coefficient for the factor of effective cohesion and bearing capacity factors. The bearing capacity factors were also redefined for this situation with sigma’ being altered to:


The following video is a good online learning source that will educate you on everything you need to know about soil foundations: