1.5. For Sands

In sands, permeability can be empirically related to the square of some representative grain size from its grain-size distribution. For filter sands, Allen Hazen in 1911 found that k = 100 (D10)² cm/s where D10 = effective grain size in cm.

This chunk discusses how the permeability of sandy soils is fundamentally connected to the size of the grains. Specifically, Allen Hazen's empirical formula relates permeability (k) to the square of the effective grain size (D10). The D10 refers to the grain size at which 10% of the soil sample is finer. This means that as the grain size increases, the permeability increases quadratically, indicating that larger grains create more pathways for water to flow through the soil.

Think of sandy soil like a series of highways and side roads for water. If the sand grains are like large boulders — think of bigger highways — water can move quickly and easily, similar to high-speed traffic on a freeway. However, if the grains are much smaller — like tiny side roads — the water will have a harder time getting through, leading to slower flow.

Different relationships have been attempted relating void ratio and permeability, such as k ∝ e³/(1+e), and k ∝ e². They have been obtained from the Kozeny-Carman equation for laminar flow in saturated soils.

This chunk presents mathematical relationships that describe how the void ratio (e) affects the permeability (k) of soils. The void ratio is the ratio of the volume of voids (spaces) to the volume of solids in the soil. The relationships indicate that as the void ratio increases, the permeability increases in a non-linear fashion, suggesting that both factors are interdependent. The Kozeny-Carman equation provides a theoretical foundation for these observed relationships, particularly for calculating flow in saturated soils.

Imagine a sponge (representing soil) with different sized holes (voids). A sponge with larger holes allows water to seep through quickly (high permeability), while a sponge with smaller holes retains water longer (low permeability). As the sponge gets more holes (higher void ratio), there's a point where the overall speed of water flowing through changes, reflecting the mathematical relationships discussed.

where k and k are factors depending on the shape and tortuosity of the pores respectively, S is the surface area of the voids and γw are unit weight and viscosity of the pore water.

Here, the chunk explains additional factors that influence permeability. The shape and arrangement of soil particles can alter the paths water can take, affecting how easily it flows through the soil. 'Tortuosity' refers to how convoluted or twisted these paths are; more convoluted paths lead to lower permeability. Additionally, the properties of the water, such as its weight and viscosity (thickness), also play a role in determining how quickly it flows through the soil. These factors must be assessed for a more accurate prediction of permeability in various soils.

Think of the flow of traffic through a city. If the roads are straight and wide (high permeability), cars can move quickly. If the roads are narrow, winding through tight corners (high tortuosity), traffic slows down. Similarly, if the 'traffic' is thick, like honey (high viscosity), it will flow slower than water (low viscosity), affecting how quickly it can pass through the roads (pores).

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