It is required to prepare a compacted cylindrical specimen of 40 mm diameter and 80 mm length from oven-dry soil. The specimen is required to have a water content of 10% and percent air voids of 18%. Taking , determine the mass of soil and mass of water required for the preparation of the above specimen.

Soil Mechanics Problems

Problem Statement

It is required to prepare a compacted cylindrical specimen of 40 mm diameter and 80 mm length from oven-dry soil. The specimen is required to have a water content of 10% and percent air voids of 18%. Taking \( G = 2.70 \), determine the mass of soil and mass of water required for the preparation of the above specimen.

Solution

1. Calculate the Total Volume

Total volume of the compacted sample:

\( V = \frac{\pi}{4} \cdot d^2 \cdot h = \frac{\pi}{4} \cdot (0.04)^2 \cdot 0.08 = 1.0053 \times 10^{-4} \, \text{m}^3 \)

2. Relationship Between Masses

Let the mass of solids (dry weight of soil) be \( M_d \):

\( M_w = w \cdot M_d = 0.10 \cdot M_d \)

Volume of solids:

\( V_s = \frac{M_d}{G \cdot \gamma_w} = \frac{M_d}{2.7 \cdot 1000} \)

Volume of water:

\( V_w = \frac{M_w}{\gamma_w} = \frac{0.10 \cdot M_d}{1000} \)

3. Volume of Air

Volume of air:

\( V_a = n_a \cdot V = 0.18 \cdot 1.0053 \times 10^{-4} = 1.8095 \times 10^{-5} \, \text{m}^3 \)

4. Total Volume Relationship

The total volume is the sum of the volumes of solids, water, and air:

\( V = V_s + V_w + V_a \)

Substituting values:

\( 1.0053 \times 10^{-4} = \frac{M_d}{2700} + \frac{0.10 \cdot M_d}{1000} + 1.8095 \times 10^{-5} \)

5. Solve for \( M_d \)

Rearranging and solving for \( M_d \):

\( M_d = 0.1554 \, \text{kg} = 155.4 \, \text{g} \)

Mass of water:

\( M_w = 0.16 \cdot M_d = 0.16 \cdot 0.1554 = 0.0249 \, \text{kg} = 24.9 \, \text{g} \)

Results:

Mass of dry soil: \( M_d = 155.4 \, \text{g} \)
Mass of water: \( M_w = 15.54 \, \text{g} \)

Explanation

This problem involves determining the mass of soil solids and water needed to prepare a compacted soil sample with specified dimensions, water content, and air voids. The relationships between volume, mass, and density are used to calculate these quantities.

The mass of soil solids \( M_d \) is determined based on the total volume and the proportions of solids, water, and air within the sample. Using the specific gravity of soil solids \( G \), the volume of solids can be expressed in terms of \( M_d \), enabling the equation for total volume to be solved.

Physical Meaning

Preparing a compacted soil sample with controlled water content and air voids is crucial for simulating field conditions in laboratory tests. The void ratio and degree of saturation affect the soil’s strength, permeability, and compressibility.

By determining the masses of soil and water, geotechnical engineers can ensure that the sample properties match the desired conditions, enabling accurate assessment of soil behavior under various loading and environmental conditions.