2. Range of relative density and corresponding range of angle of friction for coarse-grained soil

Relative density is a measure of the density of a soil sample in relation to its maximum and minimum possible densities.

Relative density provides a way to quantify how densely packed the soil particles are. It is expressed as a percentage and helps us understand the compactness of the soil. The formula for relative density (Dr) is:

Dr = (emax - e) / (emax - emin) × 100  

where e is the void ratio of the soil sample, emax is the maximum void ratio, and emin is the minimum void ratio.

Think of relative density like a packed suitcase. If you only have a few clothes in the suitcase, it’s not very full—that's a low relative density. If you stuff it full of clothes, that’s a high relative density. Just as you can measure how full a suitcase is, we measure how densely packed soil particles are.

Coarse-grained soils, such as sandy or gravelly soils, have larger particle sizes that affect their density and friction properties.

Coarse-grained soils typically allow water to drain through them more easily than fine-grained soils because of the larger spaces (voids) between the particles. This property influences both the relative density and the angle of friction, which is the measure of how resistant the soil is to sliding under load. The angle of friction can vary based on how dense the soil is—more dense conditions result in a higher angle of friction.

Consider coarse-grained soil like a pile of rocks. When you push on a loose pile of rocks, they may slide easily. However, if you pack the rocks closely together, they become harder to push. Here, the packed arrangement reflects a higher angle of friction compared to the loose arrangement.

The range of relative density for coarse-grained soils varies from loose (Dr < 25%) to dense (Dr > 75%).

Understanding the range of relative density is crucial for classifying coarse-grained soils. Loose soils, which have a relative density of less than 25%, tend to have lower strength and stability. In contrast, dense soils with a relative density greater than 75% have higher strength and can better support structures. The middle range, between 25% and 75%, indicates moderate packing and strength characteristics which are significant for engineering applications.

Think of a trampoline. When it’s very loose, it’s difficult to bounce—this is like soil with low relative density. When the trampoline is tightly stretched and firm, it’s easy to jump high—that’s like soil with high relative density. Finding the right balance is key to understanding how to build over different types of soil.

The angle of friction for coarse-grained soils corresponds to the relative density—typically ranging from about 25° to 45°.

The angle of internal friction (C6) is a representation of the shear strength of the soil and how it can resist sliding. For coarse-grained soils that are loose (low relative density), the angle of friction is typically smaller (around 25°). As the density increases, the angle of friction also increases, reaching up to about 45° for very dense soils. This relationship is fundamental in geotechnical engineering, as it helps in estimating the stability of slopes and the bearing capacity of soil.

Envision trying to push a large cardboard box on different surfaces. On a smooth floor, it slides easily, similar to loose soil with low friction angle. On a rough floor, it requires more force to push—that's akin to dense soil with a high friction angle. The force needed directly relates to how the soil behaves under load.

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