FLOW PARALLEL TO SOIL LAYERS
When the fl ow is parallel to the soil layers (Figure the hydraulic gradient is the same at all points. The fl ow through the soil mass as a whole is equal to the sum of the fl ow through each of the layers. There is an analogy here with the fl ow of electricity through resistors in parallel. If we consider a unit width (in the y direction) of fl ow and use Equation , we obtain
where Ho is the total thickness of the soil mass, kx(eq) is the equivalent permeability in the horizontal (x) direction, z1 to zn are the thicknesses of the fi rst to the nth layers, and kx1 to kxn are the horizontal hydraulic conductivities of the fi rst to the nth layer. Solving Equation for kx(eq), we get
Flow through stratifi ed layers.
FLOW NORMAL TO SOIL LAYERS:
For fl ow normal to the soil layers, the head loss in the soil mass is the sum of the head losses in each layer:
where DH is the total head loss, and Dh1 to Dhn are the head losses in each of the n layers. The velocity in each layer is the same. The analogy to electricity is fl ow of current through resistors in series. From
Darcy’s law, we obtain
where kz(eq) is the equivalent hydraulic conductivity in the vertical (z) direction and kz1 to kzn are the vertical hydraulic conductivities of the fi rst to the nth layer. Solving Equations leads to
Values of kz(eq) are generally less than kx(eq)—sometimes as much as 10 times less.