Weight to Volume relationships in soils

Calculation

Input

Output

Explanation

Weight-Volume Relationships



Soil mass and it's three phases [Adapted from Source]

1. Volume of soil solids,
   

   $V_s=M_s/G{\gamma }_w$
   which is derived using the definition of solid unit weight
   

   ${\gamma }_s=M_s/V_s$
   and the definition of soil specific gravity,
   

   $G={\gamma }_s/{\gamma }_w$
   . Therefore,
   

   ${\gamma }_s=M_s/V_s\to G{\gamma }_w=M_s/V_s\to V_s=M_s/G{\gamma }_w$
   

1. Volume of voids,
   

   $V_v=V_t-V_s$
   

1. Volume of water,
   

   $V_w=M_s{\gamma }_w$
   
2. Volume of air,
   

   $V_a=V_v-V_w=V_t-V_w-V_s$
   

1. Void ratio,
   

   $e=V_v/V_s$
   
2. Porosity,
   

   $n=V_v/V_t$
3. Degree of saturation,
   

   $s=V_w/V_v$
   which can range between zero for a completely dry soil, to 1 for a fully saturated soil

1. Moisture content,
   

   $w=M_w/M_s$
   
2. Unit weight,
   

   ${\gamma }_t=M_t/V_t$
   , also known as moist unit weight or total unit weight since it includes weight of water and soil solids
3. Dry unit weight,
   

   ${\gamma }_d=M_s/V_t$
   
4. Solid unit weight,
   

   ${\gamma }_s=M_s/V_s$
   
5. Saturated unit weight,
   

   ${\gamma }_{sat}={\gamma }_t$
   for
   

   $s=100\%$
   (i.e.
   

   $V_a=0$
   ) is when the soil is completely saturated
6. Submerged (buoyant) unit weight,
   

   ${\gamma }_b={\gamma }_{sat}-{\gamma }_w$
   for
   

   $s=100\%$
   is when the soil is below the ground water table

Weight-Volume Relationships for



$V_s=1$





Weight-volume relationships for



$V_s=1$

[Adapted from Source]

1. Moist unit weight,
   

   ${\gamma }_t={\gamma }_w\times G(1+w)/(1+e)$
   
2. Dry unit weight,
   

   ${\gamma }_d={\gamma }_w(G)/(1+e)$
   
3. Degree of saturation,
   

   $S=wG/e$
   

1. Saturated unit weight,
   

   ${\gamma }_{sat}={\gamma }_w(G+e)/(1+e)$
   
2. Submerged unit weight,
   

   ${\gamma }_b={\gamma }_w(G-1)/1+e)$
   

Weight-Volume Relationships for



$V_t=1$





Weight-volume relationships for



$V=1$

[Adapted from Source]

1. Moist unit weight,
   

   ${\gamma }_t={\gamma }_w\times G(1-n)(1+w)$
   
2. Dry unit weight,
   

   ${\gamma }_d={\gamma }_{w}G(1-n)$
   

1. Saturated unit weight,
   

   ${\gamma }_{sat}={\gamma }_w[G-n(G-1)]$
   

References

1. Advanced Soil Mechanics by Braja M. Das
2. Soil Phase Diagram and Relationship Formulas

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