Final answer:
To calculate the porosity, degree of saturation, and bulk specific gravity of the sand sample, we need to first determine the volume of solids using the specific gravity and dry weight of the sand, then find the volume of voids and use it to calculate the porosity and degree of saturation. Lastly, we calculate the bulk specific gravity using the total weight of the sand and water and the total volume of the container.
Step-by-step explanation:
To determine the porosity, degree of saturation, and bulk specific gravity of a sand sample, we must use several measures and properties of the material. The porosity (n) of a material is the ratio of the volume of voids to the total volume, given by the equation n = Vv/Vt, where Vv is the volume of voids and Vt is the total volume. The degree of saturation (Sr) is the ratio of the volume of water to the volume of voids, calculated using Sr = Vw/Vv, with Vw being the volume of water. Lastly, the bulk specific gravity (G) is determined using the equation G = (Ws/(Ww + Vs)), where Ws is the weight of solids, Ww is the weight of water, and Vs is the volume of solids.
Given:
- Volume of container (Vt) = 0.30 ft3
- Dry weight of sand (Ws) = 31 lb
- Volume of water (Vw) = 0.051 ft3
- Specific gravity of sand (Gs) = 2.72
- Density of water = 62.4 lb/ft3 (since 1 gallon of water is approximately 8.34 pounds and 1 cubic foot contains 7.48 gallons, thus
To find the volume of solids in the sand (Vs), we use the specific gravity formula:
, where ρw is the density of water (62.4 lb/ft3).
Once we have Vs, we can calculate the volume of voids (Vv) as Vv = Vt - Vs. With Vv, we can then determine the porosity n using the formula n = Vv/Vt. The degree of saturation Sr is obtained by Sr = Vw/Vv. Finally, we can calculate the bulk specific gravity G using the combined weight of water and solids in relation to the total volume through
