# HOW TO CALCULATE DEPTH OF SHALLOW FOUNDATION?

Deciding the right depth of foundation for a building structure is an important step in the process of building design. Information given in this post will help you decide the proper depth of foundation for a building.

After reading this post you will be able to answer the following questions.

- What is a foundation?
- What are the factors affecting depth of foundation?
- How to calculate depth of foundation?

# What is Foundation?

Foundation is that part of the structure which receives load of the superstructure and then transmits that load to soil underneath in such a manner so that the soil never fails in shear or never goes through excessive settlement of differential settlement.

# Factors Affecting Depth of Foundation

Before calculating depth of shallow foundation, the following factors have to be considered well in advance.

- Foundation should be placed at such a depth so that it is safe against damages due to swelling, shrinkage or freezing of sub soil.
- Bearing capacity of soil beneath the foundation must be adequate to support the load coming from foundation.
- If foundation has to be placed on cohesive soil then the settlement due to consolidation should not be excessive.
- Never place foundation on loose or disturbed soils which have a tendency to erode by wind or flood.
- If possible then foundation should be placed above ground water table as this can avoid cost of pumping, and can prevent instability of soil due to seepage of water into the bottom of an excavation.
- Make an investigation on foundation soil to know its physical and chemical properties, because presence of sulphate can damage foundation.

# Calculation of Depth of Foundation

The minimum depth of shallow foundation for a soil can be calculated using the following formula as suggested by Rankine. This is called **Rankine’s Formula**.

**D _{min} = (q/**

**g) * [(1 – sin**

**Ø) / (1 + sin**

**Ø)]**

^{2}Where,

**D _{min}** = Minimum depth of foundation in

**m**

**g** = Density of unit weight of soil in **kN/m ^{3}**

**Ø** = Angle of repose in **Degrees**

**q** = Intensity of load or Safe bearing capacity of soil in **kN/m ^{2}**

## Example Calculation

Calculate the minimum depth required for a foundation to transmit a pressure 55 kN/m^{2} in a cohesionless soil having density 16 kN/m^{3} and angle of repose 20^{0}?

__Given Data__

Intensity of pressure (q) = 55 kN/m^{2}

Density of soil (g) = 16 kN/m^{3}

Angle of repose (Ø) = 20^{0}

__Calculation__

Minimum depth of foundation, according to Rankine,

**D _{min} = (q/**

**g) * [(1 – sin**

**Ø) / (1 + sin**

**Ø)]**

^{2}D_{min} = (55/16) * [(1 – sin20^{0}) / (1 + sin20^{0})]^{2}

D_{min} = 0.82 m

## Helpful Points

For preliminary calculation of depth of foundation, the values of density and angle of repose, as given in the following table can be used.

Soil Type |
Angle of Repose (in Degree) |
Unit weight (in kN/m^{3}) |

Dry sand | 25 – 35 | 16.0 |

Moist sand | 30 – 35 | 18.4 |

Wet sand | 15 – 25 | 19.2 |

Dry & compacted sand | 35 | 19.2 |

Clean gravel | 30 – 40 | 17.9 |

Mixture of gravel & sand | 25 – 40 | 19.2 |

Rubble stone | 45 | 19.2 |

Dry clay | 30 | 17.6 |

Wet clay | 15 | 19.2 |

Ash | 40 | 6.4 |

### NOTE:

- The values given the table above are approximate value.
- To know the density of soil on site you have to test it onsite. There are two common methods which are widely used for determination of density of soil on site. Click the following two links to read the test procedure.

**How to calculate density of soil onsite using core cutter method?**

**How to calculate density of soil onsite using sand replacement method?**

- To know the safe bearing capacity of soil, perform Plate Load Test on site and calculate safe bearing capacity from the plate load test data. Read the following two posts on PLT.

**How to perform plate load test on site?**

**How to calculate safe bearing capacity of soil from PLT?**

- For a quick determination of safe bearing capacity of soil, read the following post.

How to determine Pile depth.. step to determine or formula to be used..

The information provided was very useful. but I still have a question. I have designed a reinforced concrete slab with a thickness of 30cm. the soil underneath the slab is dry compacted sand. the slab will be used as base for bigbags filed with sand. the total load of one bigbag is 2.7T. 10bigbags =27T.

if I calculate the depth I get 0.07m. is this correct