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%

The dry density (\( \rho_d \)) of soil can be calculated using the relationship between the specific gravity of soil particles (\( G_s \)), the water content (\( w \)), and the degree of saturation (\( S \)). The formula for dry density is:

\[
\rho_d = \frac{G_s \cdot \rho_w}{1 + w \cdot S \cdot G_s}
\]

Where:
- \( \rho_d \) is the dry density of the soil.
- \( G_s \) is the specific gravity of soil particles.
- \( \rho_w \) is the density of water (approximately \( 1000 \, \text{kg/m}^3 \)).
- \( w \) is the water content (expressed as a decimal, so \( 5\% = 0.05 \), etc.).
- \( S \) is the degree of saturation (also expressed as a decimal, so \( 70\% = 0.70 \), etc.).

We will compute the dry density for various values of \( w \) and \( S \), then plot the results.

Let's calculate and plot this now.

Learn how to calculate and plot the variation of dry density of soil at water contents of 5%, 10%, 15%, and 20%, and degrees of saturation of 70%, 80%, 90%, and 100%. Use the dry density formula incorporating specific gravity and water content. Includes step-by-step calculation and plotting guide.

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