Relative Density (Density Index) of a Cohesionless Soil
The right compaction measure for a CLEAN SAND, where a Proctor curve is poorly defined and relative compaction is the wrong spec. Dr = (e_max - e)/(e_max - e_min) on void ratios; substituting e = Gs gamma_w/gamma_d - 1 cancels the specific gravity and the unit weight of water entirely, leaving Dr = gamma_d,max (gamma_d - gamma_d,min)/(gamma_d (gamma_d,max - gamma_d,min)) - which is why no Gs is asked for. A field density of 117.6 pcf at 12% moisture is 105.0 pcf dry, and against index densities of 90 and 115 pcf that is 65.7%. Dr is measured against the LOOSEST and DENSEST index densities of that same soil, not a Proctor maximum, so the two scales are not interchangeable: a sand at 95% relative compaction can still be loose. Outside 0-100% means the field density falls outside the index-test range. A QC aid; the project geotechnical specification and the testing agency govern.
Formula and source
gamma_d = gamma_wet/(1 + w/100); Dr = 100 x gamma_d,max (gamma_d - gamma_d,min) / (gamma_d (gamma_d,max - gamma_d,min)), the dry-density reduction of Dr = (e_max - e)/(e_max - e_min).
Relative density (density index) as defined on void ratios and reduced to its dry-density form, standard soil-mechanics practice as compiled in Das, Principles of Geotechnical Engineering, and NAVFAC DM-7.01; the minimum and maximum index dry densities come from the laboratory index-density tests for that soil and are entered by the user.
Audience
This tile is built for trades and the adjacent professions in the Carpentry and Construction group. The interactive calculator runs entirely in your browser. No account, no fee, no advertising, no tracking.
Related tools
Posture
Rough Logic answers the math question the working professional asks on the job. The site is a calm, fast, ad-free, account-free, ever-free reference. It does not interpret code. It does not replace the licensed professional. It does not store your inputs. The Authority Having Jurisdiction governs all installations and inspections.