Important Soil water Relationship

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$\large 1. \; W_{s}=\frac{W}{1+w}$

$w$ = water content

$w=\frac{W_{w}}{W_{s}}$

$\large 2. \; V_{s}=\frac{V}{1+e}$

$e=\frac{V_{v}}{V_{s}}$

V= V_v + V_s

$\large 3. \; \eta =\frac{e}{1+e}$

4. Most important relationship used every time:

eS=WG_s

$\large 5.\; \gamma _{t}= \frac{(G_{s}+Se)\times \gamma _{w}}{1+e}$

$\large 6.\; \gamma _{d}= \frac{G_{s}\times \gamma _{w}}{1+e}$

$\large 7.\; \gamma _{sub}= \frac{(G_{s}-1)\times \gamma _{w}}{1+e}$

$\large 8. \; \gamma _{}d=\frac{\gamma_{t}}{1+w}$

$\large 9. \; \gamma _{}d=\frac{(1-\eta _{a})\times G_{s}\gamma_{w}}{1+wG_{s}}$

$\large 10. \; S=\frac{w}{\frac{\gamma _{w}}{\gamma _{t}}(1+w)-\frac{1}{G_{s}}}$

This equation is valid if there is fresh water in the void space of the soil.

The volume of partially saturated soil will not change on drying.

Thus, $\gamma _{d}= constant$ .

The dry Unit Weight is used to measure the denseness of the soil

A higher value of $\gamma _{d}$ indicates that more solids are packed in a unit volume of soil and hence a more compact soil

In embankment, soil compaction is checked with respect to $\gamma _{d}$ .

11. Saturation Unit Weight ( $\gamma _{sat}$ ):

$\large {\color{DarkBlue} \gamma _{sat}=\frac{Wt. of the sat. soil}{Vol. of the soil}}$

Sat. unit weight of the soil will depend upon the water content of the soil.

12. Submerged unit weight ( $\large \gamma _{sub}$ ):

$\large {\color{DarkBlue} \gamma _{sub}=\gamma _{sat}-\gamma _{w}}$

All saturated conditions are not submerged conditions. Ex:- Capillary saturation zone will be called saturated zone but may not be treated as a submerged zone.

13. Specific Gravity of Solids (G_s):

$\large {\color{DarkBlue} G_{s}=\frac{\gamma _{s}}{\gamma _{w}}}$

G_sfor inorganic soil is 2.6 to 2.8

G_sfor organic soil is 1.5 to 2.0

14. Mass Specific Gravity (G_m):

$\large {\color{DarkBlue} G_{m}=\frac{unit wt. of soil}{unit wt. of water}}$

For Dry Soil:

$\large G_{m}=\frac{\gamma _{d}}{\gamma _{w}}$

For Sat. Soil:

$\large G_{m}=\frac{\gamma _{sat}}{\gamma _{w}}$

Partially Sat. soil:

$\large G_{m}=\frac{\gamma _{t}}{\gamma _{w}}$

Gs > Gm

$\large {\color{DarkBlue} \gamma_{s}> \gamma_{sat}> \gamma_{t}> \gamma_{d}> \gamma_{sub} }$

CE Masters-Civil Engineering Study Materials

Important Soil water Relationship