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GATE 2019 CE (CE2) – Question 27

Geotechnical Engineering · Permeability and seepage: flow nets, uplift pressure, piping, capillarity · 1 mark · Multiple choice

An anisotropic soil has vertical permeability $k_z$ and horizontal permeability $k_x$. To construct an isotropic flow net, by what factor is the horizontal dimension multiplied?

  1. $\sqrt{k_z/k_x}$
  2. $\sqrt{k_x/k_z}$
  3. $k_x/k_z$
  4. $k_z/k_x$

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Correct answer: (A) $\sqrt{k_z/k_x}$

Explanation

The anisotropic head equation is $k_xh_{xx}+k_zh_{zz}=0$. Set $x^\prime=x\sqrt{k_z/k_x}$. Then $k_xh_{xx}=k_zh_{x^\prime x^\prime}$ and both coefficients match. The horizontal multiplier is **√(kz/kx), A**.