# Immediate settlement computations

**Courses > Foundation Analysis and Design > Settlement of Shallow Foundations > Immediate settlement computations**

## Introduction on Immediate settlement computations :

Immediate settlement results from distortion of soil mass caused by a change in total stress. For general definitions, remarks and types of settlement refer to Settlement types, definitions, and general equation article.

## Concepts and Formulas of Immediate settlement computations:

The settlement of the corner of a rectangular base of dimensions B' x L' on the surface of an elastic half-space can be computed from an equation from Theory of Elasticity as follows:

where

q_{0} = intensity of contact pressure in units of E_{s}

B' = least lateral dimension of contributing base area in units of S_{i}

I_{1} and I_{2} = influence factors, which depend on L'/B', thickness of stratum H. Poisson's ratio, and base embedment depth D

E_{s} = average modulus of elasticity of soil layer

Influence factors can be computed using:

where

I_{F} = embedment (or depth) factor which is equal to or less than 1.0 (for footings on the ground I_{F} = 1.0)

### Remarks

- For circular footings, convert to an equivalent square.
- Determine the point where the settlement is to be computed and divide the base so the point is
__at the corner__ or common corner of one or up to 4 contributing rectangles.
- The zone of influence is either of the following:
- Depth z = 5B where B is the least total lateral dimension of base
- Depth to where a hard stratum is encountered.

- Compute zone of influence based on the actual footing dimension.

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