Calculate and plot the variation of dry density of a soil in kg/m (G, = 2.65) at w = 5, 10, 15, and 20% for degree of saturation, S = 70, 80, 90, and 100%

To calculate and plot the variation of dry density of a soil, we need to use the formula for dry density (\(\rho_d\)) in soil mechanics. 

The dry density \(\rho_d\) of a soil can be calculated using the following formula:

\[
\rho_d = \frac{\rho}{1 + w}
\]

where:
- \(\rho_d\) = dry density of the soil (kg/m³)
- \(\rho\) = bulk density of the soil (kg/m³)
- \(w\) = water content (decimal form)

The bulk density \(\rho\) can be found using:

\[
\rho = \frac{G_s \cdot \rho_w (1 + w)}{1 + \frac{S \cdot w}{G_s}}
\]

where:
- \(G_s = 2.65\) is the specific gravity of soil solids
- \(\rho_w = 1000 \, \text{kg/m}^3\) is the density of water
- \(S\) = degree of saturation (decimal form)
- \(w\) = water content (decimal form)

Given:
- \(G_s = 2.65\)
- Water content (\(w\)) values = 5%, 10%, 15%, 20%
- Degree of saturation (\(S\)) values = 70%, 80%, 90%, 100%

We will calculate the dry density for each combination of \(w\) and \(S\) and plot the results. Let's proceed with the calculations and plotting.

Learn how to calculate and plot the variation of dry density of soil using specified water contents and degrees of saturation. This problem involves formulas for bulk density and dry density in soil mechanics, with calculations performed for various combinations of water content and degree of saturation.

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