Seepage in Anisotropic soil
The Laplace equation presented in previous lesson (lesson 19) is valid for isotropic soil. If soil is anisotropic and coefficient of permeability in x andz direction is not same, the Laplace equation is modified as:
\[{k_x}{{{\partial ^2}h} \over {\partial {x^2}}} + {k_z}{{{\partial ^2}h} \over {\partial {z^2}}}=0\] (20.8)
where kx and kz are the coefficient of permeability in x and z direction, respectively. The Eq. (20.8) can be written as:
\[\frac{{{\partial ^2}h}}{{\frac{{{k_z}}}{{{k_x}}}\partial{x^2}}}+\frac{{{\partial^2}h}}{{\partial {z^2}}}=0\] (20.9)
Convert the x a new coordinate system x' such that
\[x'=x\sqrt {{{{k_z}} \over {{k_x}}}}\] (20.10)
and \[\partial {x'^2}=\partial {x^2}{{{k_z}} \over {{k_x}}}\] , Thus, Eq.(20.9) can be written as:
\[{{{\partial ^2}h} \over {\partial {{x'}^2}}} + {{{\partial ^2}h} \over {\partial {z^2}}}=0\] (20.11)
The Eq.(20.11) is Laplace equation for isotropic soil w.r.t x' and z coordinates. Here x coordinate is transformed to x' coordinate [as per Eq. (20.10)] for converting anisotropic soil medium into a fictitious isotropic medium (by keeping z coordinate unchanged). Thus, during the coordinate transformation horizontal dimension (x dimension) is multiplied by \[\sqrt {{{{k_z}} \over {{k_x}}}}\] . The value of coefficient of permeability for transformed section is taken as:
\[k'=\sqrt {{k_x}{k_z}}\] (20.12)
Thus, in this case the quantity of seepage (Q) is calculated as:
\[Q=\sqrt {{k_x}{k_z}} {h_L}{{{N_f}} \over {{N_d}}}\] (20.13
1. What is seepage in anisotropic soil? |
2. How can the flow net method be used to analyze seepage in anisotropic soil? |
3. What are some factors that affect seepage in anisotropic soil? |
4. How does seepage in anisotropic soil impact agricultural engineering? |
5. What are some methods to mitigate seepage in anisotropic soil? |
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