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Important Relationships - Phase Diagram, Soil Mechanics | Soil Mechanics Notes- Agricultural Engineering PDF Download

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%.

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

1. What is a phase diagram in soil mechanics?
Ans. A phase diagram in soil mechanics is a graphical representation that shows the relationship between the different phases of soil (solid, liquid, and gas) at different combinations of temperature and pressure. It helps in understanding the behavior and characteristics of soil under different conditions.
2. How does a phase diagram help in agricultural engineering?
Ans. A phase diagram in agricultural engineering helps in understanding the physical properties of soil and its behavior under varying conditions. It allows engineers to analyze and predict the changes in soil structure, water content, and gas movement, which is crucial for making informed decisions related to irrigation, drainage, and soil management in agriculture.
3. What are the key components of soil mechanics in agricultural engineering?
Ans. The key components of soil mechanics in agricultural engineering include studying the physical properties of soil such as texture, structure, porosity, and permeability. It also involves analyzing soil-water relationships, understanding the behavior of soil under different loading conditions, and evaluating the stability and strength of soil for agricultural purposes.
4. How does soil mechanics impact soil fertility in agricultural engineering?
Ans. Soil mechanics plays a significant role in determining soil fertility in agricultural engineering. By understanding the physical properties and behavior of soil, engineers can assess the capability of soil to retain water, nutrients, and oxygen. This knowledge helps in designing irrigation systems, nutrient management strategies, and crop rotation plans to optimize soil fertility and improve agricultural productivity.
5. How can soil mechanics be applied to slope stability analysis in agricultural engineering?
Ans. In agricultural engineering, soil mechanics is used to evaluate the stability of slopes and prevent soil erosion. By studying the shear strength, cohesion, and frictional properties of soil, engineers can assess the stability of slopes and design appropriate measures to prevent landslides and soil erosion. This knowledge is crucial for maintaining the integrity of agricultural fields and preventing soil loss.
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