# Bulk Density

Written by Jerry Ratzlaff on . Posted in Geotechnical Engineering Bulk density, abbreviated as Y, also called apparent density or volumetric density, is the ratio total weight of soil to the total volume of soil.

## Bulk Density formulas

 $$\large{ Y = \frac{ W_t }{ V_t } }$$ $$\large{ Y = \frac{ M_t }{ V_t } }$$ $$\large{ Y = \frac{ SG_s \; \left( 1 \;+\; w \right) }{ 1 \;+\; e } \; \rho_w }$$ $$\large{ Y = \frac{ SG_s \; \left( 1 \;+\; w \right) \; \gamma_w }{ 1 \;+\; e } }$$ $$\large{ Y = \frac{ SG_s \;+\; S \; e }{ 1 \;+\; e } \; \rho_w }$$ $$\large{ Y = \frac{ \left( SG_s \;+\; S \; e \right) \; \gamma_w }{ 1 \;+\; e } }$$

### Where:

 Units English Metric $$\large{ Y }$$ = bulk density $$\large{ \frac{lbm}{ft^3} }$$ $$\large{ \frac{kg}{m^3} }$$ $$\large{ S }$$ = degree of saturation (expressed as %) $$\large{dimensionless}$$ $$\large{ \rho_w }$$  (Greek symbol rho) = density of water $$\large{ \frac{lbm}{ft^3} }$$ $$\large{ \frac{kg}{m^3} }$$ $$\large{ SG_s }$$ = specific gravity of soil $$\large{dimensionless}$$ $$\large{ M_t }$$ = total mass of soil $$\large{lbm}$$ $$\large{kg}$$ $$\large{ V_t }$$ = total volume of soil $$\large{ft^3}$$ $$\large{m^3}$$ $$\large{ W_t }$$ = total weight of soil $$\large{lbf}$$ $$\large{N}$$ $$\large{ \gamma_w }$$  (Greek symbol gamma) = unit weight of water $$\large{ \frac{lbm}{ft^3} }$$ $$\large{ \frac{N}{m^3} }$$ $$\large{ e }$$ = void ratio $$\large{dimensionless}$$ 