Bulk Unit Weight

Written by Jerry Ratzlaff on . Posted in Geotechnical

partially saturated soil 1Bulk 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

 

Tags: Equations for Weight Equations for Soil