k (m2)

K (m/s)


10-17 to 10-15

10-10 to 10-8


10-15 to 10-13

10-8 to 10-6


10-12 to 10-10

10-5 to 10-3


10-9 to 10-8

10-2 to 10-1

Source: A. Verrjuit, 1982, Theory of groundwater How, 2d ed. (Macmillan Publishing Co.).

flow condition, which is expressed by Reynolds number R defined as

Experiments have shown the range of validity of Darcy's law to be

In practice, the specific discharge is always small enough for Darcy's law to be applicable. Only cases of flow through coarse materials, such as gravel, deviate from Darcy's law. Darcy's law is not valid for flow through extremely fine-grained soils, such as colloidal clays.

Generalization of Darcy's Law

In practice, flow is seldom one dimensional, and the magnitude of the hydraulic gradient is usually unknown. The simple form, Equation 9.2(2), of Darcy's law is not suitable for solving problems. A generalized form must be used, assuming the hydraulic conductivity K to be the same in all directions, as

For an anisotropic material, these equations can be written as qx


- Kxy


- Kxz



- Ky


- Kz



- Kzy


- Kzz

In the special case that Kxy = Kx Kzy = 0, the x, y, and z directions are the principal directions of permeability, and Equations 9.2(10) reduce to q = -K -- = -K^

This chapter considers isotropic soils since problems for anisotropic soils can be easily transformed into problems for isotropic soils.

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