# Bulk Unit Weight

Written by Jerry Ratzlaff on . Posted in Geotechnical

## Bulk Unit weight formulas

 $$\large{ \gamma_t = \frac{ W }{ V } }$$ $$\large{ \gamma_t = \frac{W_s \;+\; W_w}{V_s \;+\; V_v} }$$ $$\large{ \gamma_t = \frac{ \gamma_w \; V_w \;+\; \gamma_s \; V_s }{ V_v \;+\; V_s } }$$ $$\large{ \gamma_t = \frac{ \gamma_w \; V_w \;+\; G_s \; \gamma_w \; V_s }{ V_v \;+\; V_s } }$$ $$\large{ \gamma_t = \frac{ V_w \;+\; G_s \; V_s }{ V_v \;+\; V_s } \; \gamma_w }$$ $$\large{ \gamma_t = \frac{ S \; V_v \;+\; G_s \; V_s }{ V_v \;+\; V_s } \; \gamma_w }$$ $$\large{ \gamma_t = \frac{ S \; e \;+\; G_s }{ e \;+\; 1 } \; \gamma_w }$$ $$\large{ \gamma_t = \frac{ \left(G_s \;+\; S \; e \right) \; \gamma_w }{ e \;+\; 1 } }$$ $$\large{ \gamma_t = \frac{ \left(G_s \;+\; S \; w \right) \; \gamma_w }{ e \;+\; 1 } }$$

### Where:

$$\large{ \gamma_t }$$  (Greek symbol gamma) = bulk unit weight

$$\large{ S }$$ = degree of saturation

$$\large{ G_s }$$ = specific gravity of soil

$$\large{ \gamma_s }$$  (Greek symbol gamma) = unit weight of solid

$$\large{ \gamma_w }$$  (Greek symbol gamma) = unit weight of water

$$\large{ e }$$ = void ratio

$$\large{ V_s }$$ = volume of soil solid

$$\large{ V_v }$$ = volume of voids

$$\large{ V_w }$$ = volume of water

$$\large{ w }$$ = water content

$$\large{ W_s }$$ = weight of soil

$$\large{ W_w }$$ = weight of water