Question

For an anisotropic soil, permeability in $x$ and $y$ directions are $k_x$ and $k_y$ respectively, in a two-dimensional flow. The effective permeability ($k_{eff}$) for the soil is given by:

• A. $(k_x k_y)^{1/2}$
• B. $k_x / k_y$
• C. $(k_x^2 + k_y^2)^{1/2}$
• D. $k_x + k_y$

Hint:

For anisotropic soils in 2D flow, always use the geometric mean of directional permeabilities to find effective permeability.

Answer 1

The Correct Option is A

Step 1: Recall the formula for effective permeability.
For two-dimensional seepage in anisotropic soils, the effective permeability is calculated using the geometric mean: \[k_{eff} = \sqrt{k_x \cdot k_y}.\]

Step 2: Parameter substitution.
The formula is independent of specific values; the effective permeability is determined by the geometric mean.

Step 3: Final result.
Therefore, the effective permeability is $(k_x k_y)^{1/2}$.