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%.
1. What is a phase diagram in soil mechanics? |
2. How does a phase diagram help in agricultural engineering? |
3. What are the key components of soil mechanics in agricultural engineering? |
4. How does soil mechanics impact soil fertility in agricultural engineering? |
5. How can soil mechanics be applied to slope stability analysis in agricultural engineering? |
|
Explore Courses for Agricultural Engineering exam
|