Relationship between Relative Compaction and Compression Strain
By Fred Yi, PhD, GE
November 9, 2012
Modified: 01/29/2018
When dealing with geotechnical investigations, it is usually the case that the geotechnical engineer needs to estimate shrinkage and provide recommendations for compacted fill. In geotechnical reports, you may read “the shrinkage is estimated as **%” and “soils should be compacted to a minimum relative compaction of **%.” However, the author of this note noticed that few publications can be found that contain a solid theoretical base for these recommendations. This technical note intends to provide a discussion with respect to the issue.
Figure 1 Phase diagram for derivation of void ratio, degree of saturation, etc.
Figure 1 shows the phase diagram for derivation of void ratio, degree of saturation, etc. When the soil changes from Status 1 (loose) to Status 2 (dense), the change of void ratio is
From this diagram, the void ratio can be calculated by 
Eq. (1) can then be rewritten as 
For compacted fill, 
The difference of void ratio between status of relative compaction of (RC)1 and (RC)2 can then be derived from Eqs. (3) and (4) as 
Comparing to the initial status of (RC)1 (loose), the volumetric compression strain is 
Δεv represents the change of volumetric strain and therefore is very useful for compacted fill recommendations.
Applications
1. Calculating Shrinkage
The first application of Eq. (6) is to estimate shrinkage. For example, if the native soil (bank, (RC)b) is of an average relative compaction of 80% and is compacted to a relative compaction of 90% (compacted, (RC)c), the shrinkage can then be calculated as
2. Calculating Swell
For example, if the native soil (bank, (RC)b) is of an average relative compaction of 93% and is compacted to a relative compaction of 90% (compacted, (RC)c), the shrinkage can then be calculated as
3. Calculating Anticipated Settlement
The second application is that Eq (6) can be used to directly estimate additional settlement for grading quality control because under confined condition the volumetric strain equals the axial strain. As such, if the recommended relative compaction is 90% while the achieved average field density is only 88%, the anticipated compression strain relative to the recommended 90% relative compaction will be
For 10 feet of fill, the soil layer would have a potential for an additional 2.7 inches of settlement if compacted to 88% instead of 90% relative compaction.
