Soil is composed of three layers of height 'h' m each. The permeability of layers are k, 2k, and k respectively. The equivalent permeability in vertical direction is: 

Explanation:

Case 1: When the flow is along the bedding plane i.e. Horizontal flow

Equivalent permeability, \({{\rm{K}}_{{\rm{eq}}}} = \frac{{{{\rm{K}}_1}{{\rm{H}}_1} + {{\rm{K}}_2}{{\rm{H}}_2} + {{\rm{K}}_3}{{\rm{H}}_3}}}{{{{\rm{H}}_1} + {{\rm{H}}_2} + {{\rm{H}}_3}}}\)

Case 2: When the flow is perpendicular to the bedding plane i.e. Vertical flow

Equivalent permeability, \({{\rm{K}}_{{\rm{eq}}}} = \frac{{{{\rm{H}}_1} + {{\rm{H}}_2} + {{\rm{H}}_3}}}{{\frac{{{{\rm{H}}_1}}}{{{{\rm{K}}_1}}} + \frac{{{{\rm{H}}_2}}}{{{{\rm{K}}_2}}} + \frac{{{{\rm{H}}_3}}}{{{{\rm{K}}_3}}}}}\)

For the given case, we have three layers with the following properties:

First layer: $h_1 = h$ $k_1 = k$

Second layer: $h_2 = h$ $k_2 = 2k$

Third layer: $h_3 = h$ $k_3 = k$

 Equivalent permeability, \({{\rm{K}}_{{\rm{eq}}}} = \frac{{{{\rm{H}}_1} + {{\rm{H}}_2} + {{\rm{H}}_3}}}{{\frac{{{{\rm{H}}_1}}}{{{{\rm{K}}_1}}} + \frac{{{{\rm{H}}_2}}}{{{{\rm{K}}_2}}} + \frac{{{{\rm{H}}_3}}}{{{{\rm{K}}_3}}}}}\)

\({{\rm{K}}_{{\rm{eq}}}} = \frac{{{h} + {{h}} + {{\rm{h}}}}}{{\frac{{{{\rm{h}}}}}{{{{\rm{k}}}}} + \frac{{{{\rm{h}}}}}{{{{\rm{2k}}}}} + \frac{{{{\rm{h}}}}}{{{{\rm{k}}}}}}}\)

Keq = 6k/5