The Proctor maximum dry density is the laboratory benchmark for compaction: the peak dry unit weight a soil achieves in the standard (ASTM D698) or modified (ASTM D1557) Proctor test, reached at its optimum moisture content. Field control is a ratio against it — relative compaction RC = γd,field / γd,max × 100 — with earthwork specifications commonly demanding 90–95% of the modified Proctor maximum for structural fill and 98–100% for critical work like pavement subgrade.
The comparison must happen on a dry-mass basis, which is where field tests go wrong: a density gauge measures the bulk (moist) unit weight, and it has to be converted through γd = γbulk/(1 + w/100) before dividing by the Proctor maximum, or the moisture inflates the apparent compaction. A fill testing 20 kN/m³ bulk at 10% moisture is really γd = 18.18 kN/m³; against a modified Proctor maximum of 19 that is RC = 95.7% — a pass against a 95% target by less than a point.
Two companions complete the picture. The zero-air-voids curve, γzav = Gs·γw/(1 + (w/100)·Gs), is the fully saturated ceiling no legitimate data point can plot above — a built-in check on both field and lab numbers. And which side of optimum the fill was compacted on matters: dry of optimum tends stiffer but more prone to swelling and collapse on wetting; wet of optimum is more ductile and less permeable but weaker.