There are several reasons to specify compaction moisture content. After all, the engineering properties of the completed works will depend on the compaction moisture content. Two identical soil samples, one compacted wet of optimum and one compacted dry of optimum (i.e., and to the same dry density) will have different values of friction angle, cohesion and permeability. Rarely do we consider such distinction, however - the exception being permeability. If you are concerned about the permeability of the completed works, then specifying compaction wet of optimum will be to your advantage. Refer to the work on clay liners by Jim Mitchell.
Now what's wet or dry of optimum? The reason I ask this rhetorical question is the industry is confused on this matter. Ask yourself, what the optimum moisture content to acheive 95 percent compaction? It's not the same value as the optimum moisture content for 100 percent relative compaction. Bear in mind running parallel to the ZAV is the LOO (Line of Optimums). It's not a vertical line, but that's how the industry perceives optimum moisture!
Outside of the technical answer to your question, I'll also say if you make compaction moisture content a specification requirement, you are a bit more likely to have the technician select the approprate proctor (or you are more likely to see in a forensic evaluation where the technical got off track.
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ípapß gordo ainÆt no madre flaca!