The coefficient of compressibility
The coefficient of compressibility is a measure of how much a soil compresses under an applied load. It is an important parameter in geotechnical engineering, as it helps determine the settlement and consolidation behavior of soils.

Void ratio
Void ratio is defined as the ratio of the volume of voids (empty spaces) to the volume of solids in a soil sample. It is a measure of the degree of compactness or looseness of the soil. The void ratio can be calculated using the formula:

Void ratio (e) = volume of voids (Vv) / volume of solids (Vs)

Consolidating pressure
Consolidating pressure is the applied pressure on a soil sample during a consolidation test. In a consolidation test, a soil sample is subjected to a gradually increasing load to simulate the conditions experienced by the soil in the field. This load causes the soil particles to rearrange, resulting in settlement and compression.

Effect of consolidating pressure on coefficient of compressibility
The coefficient of compressibility is influenced by the magnitude of the consolidating pressure. It has been observed that the coefficient of compressibility increases with an increase in the magnitude of the consolidating pressure. This means that as the applied load on the soil sample increases, the compressibility of the soil also increases.

Explanation
When a soil sample is subjected to an increasing load, the voids in the soil are gradually reduced in size. This reduction in voids causes the soil particles to come closer together, resulting in compression and settlement. As the soil compresses under the applied load, the coefficient of compressibility increases.

The increase in the coefficient of compressibility with an increase in the magnitude of the consolidating pressure can be attributed to the rearrangement of soil particles. As the load is applied, the particles rearrange themselves to accommodate the new stress distribution. This rearrangement leads to a higher compressibility of the soil.

It is important to note that the coefficient of compressibility is specific to a given void ratio. Different soils with different initial void ratios will have different coefficients of compressibility. However, for a given void ratio, the coefficient of compressibility increases with an increase in the magnitude of the consolidating pressure.

In conclusion, the coefficient of compressibility increases with an increase in the magnitude of the consolidating pressure. This is because the applied load causes the soil particles to rearrange, resulting in compression and settlement of the soil.