Question

The laplacian form of equation for anisotropic soil is ______

(a) \(\frac{∂^2 h}{∂x^2}+\frac{∂^2 h}{∂y^2}=0\)

(b) \(k_x \frac{∂^2 h}{∂x^2}+\frac{∂^2 h}{∂y^2}=0\)

(c) \(\frac{∂^2 h}{∂x^2}+k_y\frac{∂^2 h}{∂y^2}=0\)

(d) \(\frac{k_x}{k_y}\frac{∂^2 h}{∂x^2}+\frac{∂^2 h}{∂y^2}=0\)

I had been asked this question in an online quiz.

Query is from Seepage through Anisotropic Soil topic in section Seepage Analysis of Geotechnical Engineering I

Answer 1

Correct option is (d) \(\frac{k_x}{k_y}\frac{∂^2 h}{∂x^2}+\frac{∂^2 h}{∂y^2}=0\)

The best I can explain: for anisotropic soil, kx≠ky

∴ \(k_x \frac{∂^2 h}{∂x^2}+k_y\frac{∂^2 h}{∂y^2}=0 \)

Rewriting it, \(\frac{k_x}{k_y}\frac{∂^2 h}{∂x^2}+\frac{∂^2 h}{∂y^2}=0. \)