Permeability is a property of soil that describes its ability to allow the flow of fluids through its interconnected void spaces. Allen Hazen, an American engineer, conducted experiments to study the relationship between the permeability of soil and other factors. The equation derived from his experiments to express permeability is given as K = CD10.

Explanation:
- Allen Hazen conducted experiments to determine the relationship between the coefficient of permeability (K) and the particle size distribution of soil.
- He found that the coefficient of permeability is directly proportional to the square of the effective grain size (D10) and the coefficient of curvature (C) of the soil.
- The coefficient of permeability (K) is a measure of the ease with which water can flow through soil. It is expressed in units of velocity, such as cm/sec or ft/day.
- The effective grain size (D10) is the diameter of the soil particles such that 10% of the particles are finer than that size. It is determined using sieve analysis.
- The coefficient of curvature (C) is a measure of the uniformity of particle sizes in the soil. It is calculated using the formula C = (D30)^2 / (D60 * D10), where D30 and D60 are the particle sizes corresponding to 30% and 60% finer than them, respectively.
- Hazen's equation, K = CD10, suggests that the permeability of soil is influenced by both the effective grain size and the coefficient of curvature.
- The equation indicates that as the effective grain size (D10) or the coefficient of curvature (C) increases, the permeability of the soil also increases.
- The equation is widely used in geotechnical engineering to estimate the permeability of soil based on its particle size distribution.
- It is important to note that Hazen's equation is an empirical relationship and may not accurately predict the permeability of all types of soils. Other factors such as soil structure, compaction, and mineralogy also affect permeability. Therefore, it is recommended to perform laboratory tests to determine the actual permeability of a specific soil sample.