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# Important Relationships - Phase Diagram, Soil Mechanics Agricultural Engineering Notes | EduRev

## Agricultural Engineering : Important Relationships - Phase Diagram, Soil Mechanics Agricultural Engineering Notes | EduRev

The document Important Relationships - Phase Diagram, Soil Mechanics Agricultural Engineering Notes | EduRev is a part of the Agricultural Engineering Course Soil Mechanics Notes- Agricultural Engineering.
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Important Relationships

Followings are the important relationships between the various quantities defined in the previous section.

$n={e \over {1 + e}}$                          (2.11)

${V_s}={V \over {1 + e}}$                (2.12)

${V_v}={e \over {1 + e}}V$              (2.13)

$e={{{G_s}w} \over S}$                    (2.14)

${\gamma _{bulk}}={\gamma _t}={{{G_s} + Se} \over {1 + e}}{\gamma _w}$                 (2.15)

For completely saturated soil, S =1, Thus,

${\gamma _{sat}}={{{G_s} + e} \over {1 + e}}{\gamma _w}$                          (2.16)

For completely dry soil, S =0, Thus,

${\gamma _d}={{{G_s}} \over {1 + e}}{\gamma _w}$                                       (2.17)

$\gamma '={{{G_s} - 1} \over {1 + e}}{\gamma _w}$                                         (2.18)

${\gamma _d}={{{\gamma _{bulk}}} \over {1 + w}}$                                         (2.19)

Problem 1: In a partially saturated soil, moisture or water content is 20% and ${\gamma _{bulk}}$ = 18 kN/m3. Determine the degree of saturation and void ratio. Gs = 2.65. Take the unit weight of the water as 10 kN/m3.

Solution:

${\gamma _d}={{{\gamma _{bulk}}} \over {1 + w}}={{18} \over {1 + 0.2}} = 15\;kN/{m^3}$

${\gamma _d}={{{G_s}} \over {1 + e}}{\gamma _w}$

Thus, $e={{{G_s}{\gamma _w}} \over {{\gamma _d}}}-1={{2.65 \times 10} \over {15}}-1=0.767$

Thus, the void ratio is 0.767.

$e={{{G_s}w} \over S}$

Thus, $S={{{G_s}w} \over e}={{2.65 \times 0.2} \over {0.77}}=0.691$

Thus, the degree of saturation is 69.1%.

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