# Primary Consolidation

**Courses > Foundation Analysis and Design > Settlement of Shallow Foundations > Primary Consolidation**

## Introduction on Primary Consolidation :

Primary compression results from changes in effective stress and is time-dependent. For general definitions, remarks and types of settlement refer to Settlement types, definitions, and general equation article.

## Concepts and Formulas of Primary Consolidation:

### Virgin Compression

Virgin compression occurs when the soil is normally consolidated and the effective vertical stress increases from the beginning to the end of the stress increment being analyzed. For virgin compression, the following equation is the primary consolidation settlement:

for each layer with constant parameters

In a more familiar way it can be rewritten as:

where

C_{c} = virgin compression index

H_{0} = height of the layer

e_{0} = void ratio

subscripts "0" and "f" for vertical stresses mean "initial" and "final", respectively.

### Decompression (Rebound)

Decompression (aka rebound or heave) occurs when the soil is either normally consolidated or overconsolidated and the effective vertical stress decreases from the beginning to the end of the stress increment being analyzed

for each layer with constant parameters

In a more familiar way it can be rewritten as:

where

C_{r} = decompression/recompression (rebound/reload) index

H_{0} = height of the layer

e_{0} = void ratio

subscripts "0" and "f" for vertical stresses mean "initial" and "final", respectively.

### Recompression plus Virgin Compression

Recompression plus virgin compression occurs when the soil is overconsolidated and the effective vertical stress increases from the beginning to the end of the stress increment being analyzed

for each layer with constant parameters

where

C_{c} = virgin compression index

C_{r} = decompression/recompression (rebound/reload) index

H_{0} = height of the layer

e_{0} = void ratio

subscripts "0", "f" and "p" for vertical stresses mean "initial", "final" and "preconsolidation", respectively.

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