Seepage properties Soil

For arithmetic calculation in case of rectangular soil element as shown with dimensions dx and dz in the following plane, and thickness dy with  perpendicular to this plane. Consider a planar type flow into the considered rectangular soil element.

In the x-direction , it was calculated that the net amount of the water entering and leaving the soil element.
Similarly in the z-direction, we can observe the basic difference between the water inflow and outflow is as s

Equation of soil element on considering three dimensional plane

In case of a two-dimensional steady flow of pore water condition , any imbalance in flow condition into and out of an soil element in the z-direction must be compensated by a corresponding opposite imbalance in the x-direction also. Combining the above equation , and dividing by , now the continuity equation is expressed as,

From Darcy’s law it can be expressed, where h is the head causing flow.

When the continuity equation is combined with Darcy’s law equation , the equation for flow of seepage water is expressed as:

For an isotropic soil material in which the permeability properties is the same in all directions (i.e. k x= k z), the flow equation is mentioned herewith. 

This is the Laplace equation with governing two-dimensional steady state flow condition. It can also be solved graphically, analytically, numerically, or analogically to solve the seepage equation of soil mass.