Soil Water Relationship

A soil mass is a complex structure consisting of soil solids, water and air or soil solids, water or air. It can be either a 3-phase system or 2-phase system depending on the constituent in the voids of the soil structure.
If the soil contains both water and air then it is called a 3-phase system and if it contains either water or air then it is called a 2-phase system.

To simplify the soil system all the 3 constituents are placed separately as shown above.
When the soil voids contain only water, it is called Saturated Soil and when voids contain only air then it is called dry soil.

${W}=$ Total Weight of Soil Sample
${{V}_{v}}=$ Volume of Void
${{V}_{s}}=$ Volume of Soil Solids
${V}=$ Total Volume of Soil Sample
${{V}_{w}}=$ Volume of water
${{W}_{s}}=$ Weight of Soil Solids
${V}_{a}=$ Volume of air voids
$W=$ Weight of Soil mass
${{W}_{w}}=$ Weight of water
${{W}_{a}}=$ Weight of air $=0$
${{W}_{sat}}=$ Weight of Saturated Soil

Important Terminologies

1. Water Content:
   The Water content of a soil is defined as a ratio of the weight of water to the weight of soil solids.
   $w=\frac{{W}_{w}}{{W}_{s}}$
   The water content of a soil is always greater than "ZERO" and it does not have any upper limit.


2. Void Ratio:
   The Void Ratio of a soil is defined as a ratio of the volume of voids to the volume of soil solids.
   $e=\frac{{V}_{v}}{{V}_{s}}$
   Its value is greater than "Zero" and it also does not have any upper limit.


3. Porosity:
   The Porosity of a soil is defined as a ratio of the volume of voids to the total volume expressed in percentage.
   $n=\frac{{V}_{v}}{V} \times 100$
   It varies from 0 to 100.


4. Degree of Saturation:
   The Degree of saturation of a soil is defined as a ratio of the volume of water to the volume of voids expressed in percentage.
   $S=\frac{{V}_{w}}{{V}_{v}}$
   It varies from 0 to 100
   If $S=0$, it means the soil is dry.
   If $S=100$, it means the soil is saturated


5. Air Content:
   The Air content of a soil is defined as a ratio of the volume of air voids to the volume of voids.
   ${a}_{c}=\frac{{V}_{a}}{{V}_{v}}$


6. Percentage Air Voids:
   The Air content of a soil is defined as a ratio of the volume of air voids to the total volume of soil.
   ${n}_{a}=\frac{{V}_{a}}{V} \times 100$


7. Bulk Unit weight:
   The bulk unit weight of a soil is defined as a ratio of the total weight of the soil to the total volume of the soil.
   ${\gamma}_{t}=\frac{W}{V}=\frac{{W}_{s}+{W}_{w}}{{V}_{a}+{V}_{w}+{V}_{s}}$
   It is generally expressed in $KN/m^3$


8. Unit weight:
   The unit weight of a soil is defined as a ratio of the weight of the soil solids to the volume of the soil solids.
   ${\gamma}_{s}=\frac{{W}_{s}}{{V}_{s}}$


9. Unit weight of water:
   The unit weight of water is defined as a ratio of the weight of the water to the volume of the water.
   ${\gamma}_{w}=\frac{{W}_{w}}{{V}_{w}}$


10. Dry Unit weight:
    The Dry unit weight of a soil is defined as a ratio of the weight of the soil solids to the total volume of the soil.
    ${\gamma}_{d}=\frac{{W}_{s}}{V}$


11. Saturated Unit weight:
    The saturated unit weight of a soil is defined as a ratio of the weight of the saturated soil to the volume of the soil.
    ${\gamma}_{sat}=\frac{{W}_{sat}}{V}$


12. Submerged Unit weight:
    The submerged unit weight of a soil is defined as a ratio of the submerged weight of the soil solids to the volume of the soil.
    ${\gamma}_{sub}=\frac{({W}_{s})_{sub}}{V}$


13. Specific Gravity of solids:
    The Specific Gravity of solids is defined as a ratio of the unit weight of the soil solids to the unit weight of water.
    $G=\frac{{\gamma}_{s}}{{\gamma}_{w}}$
    It is a unitless quantity.


14. Mass Specific Gravity of solids:
    The mass-specific gravity of solids is defined as a ratio of the bulk unit weight of the soil to the unit weight of water.
    ${G}_{m}=\frac{{\gamma}_{t}}{{\gamma}_{w}}$
    It is a unitless quantity.

Important relationships between soil and water (Click to expand)

$e=\frac{n}{1-n}$

$n=\frac{e}{1+e}$

${{W}_{s}}=\frac{W}{1+w}$

${eS}={wG}$

${\gamma}_{t}=\frac{G+eS}{1+e}{{\gamma }_{w}}$

${\gamma}_{d}=\frac{G}{1+e}{{\gamma }_{w}}$

${{\gamma }_{d}}=\frac{{{\gamma }_{t}}}{1+w}$ $=\frac{(1-{{n}_{a}})G{{\gamma }_{w}}}{1+wG}$

${\gamma}_{sat} =\frac{G+e}{1+e}{{\gamma }_{w}}$

$S=\frac{w}{\frac{{{\gamma }_{w}}}{{{\gamma }_{t}}}(1+w)-\frac{1}{G}}$

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