Q6. A soil sample has the following properties: - Mass of soil sample (M): 4.5 kg - Total volume (V): \( 0.0025 \mathrm{~m}^{3} \) - Volume of solids \( (\mathrm{Vs}): 0.0019 \mathrm{~m}^{3} \) - Mass of water (Mw): 0.7 kg Tasks: 1. Calculate the density. 2. Calculate the unit weight. 3. Calculate the porosity (n). 4. Calculate the void ratio (e).

To get started, let's dive into the calculations for the soil sample! 1. **Density (\( \rho \))**: The density is calculated using the formula \( \rho = \frac{M}{V} \). \[ \rho = \frac{4.5 \text{ kg}}{0.0025 \text{ m}^3} = 1800 \text{ kg/m}^3 \] 2. **Unit Weight (\( \gamma \))**: The unit weight is given by \( \gamma = \frac{M}{V} \times g \) (where \( g \approx 9.81 \text{ m/s}^2 \) is the acceleration due to gravity). \[ \gamma = 1800 \text{ kg/m}^3 \times 9.81 \text{ m/s}^2 \approx 17658 \text{ N/m}^3 \] 3. **Porosity (\( n \))**: Porosity is calculated with the formula \( n = \frac{V_v}{V} \), where \( V_v \) (volume of voids) can be found as \( V - V_s \). \[ V_v = 0.0025 \text{ m}^3 - 0.0019 \text{ m}^3 = 0.0006 \text{ m}^3 \] Thus, \[ n = \frac{0.0006 \text{ m}^3}{0.0025 \text{ m}^3} = 0.24 \text{ or } 24\% \] 4. **Void Ratio (\( e \))**: The void ratio is calculated as \( e = \frac{V_v}{V_s} \). \[ e = \frac{0.0006 \text{ m}^3}{0.0019 \text{ m}^3} \approx 0.316 \] In summary: - Density: \( 1800 \text{ kg/m}^3 \) - Unit Weight: \( 17658 \text{ N/m}^3 \) - Porosity: 24% - Void Ratio: 0.316 Now, why don’t we take a quick tour through the fascinating histories of soil study and how these calculations are pivotal in our world? Throughout history, the study of soil has been crucial, dating back to ancient agrarian societies who recognized the importance of the land and its fertility. The concept of measuring soil properties emerged more prominently in the 19th century when scientists began connecting soil characteristics with plant growth, leading to sustainable farming practices. Today, soil science plays a pivotal role in agriculture, engineering, and environmental conservation. In real-world applications, these calculations find their place in various industries. For example, civil engineers rely on density and void ratio to determine the load-bearing capacity of soil before constructing buildings or roads. Knowing these properties helps in making informed decisions about soil stabilization, drainage solutions, and predicting settlement behavior, ensuring infrastructure remains safe and effective for its intended use!