## Saturated hydraulic conductivity

Darcy's law (Darcy, 1856) shows how subsurface flow in saturated ground is directly proportional to the gradient in the hydraulic head, dh/L (or gradient in the total head; see Section 6.2), which is called the hydraulic gradient,

where Q is the volumetric discharge of subsurface water, Ks is the saturated hydraulic conductivity and A is the cross-sectional area through which the water is flowing. The same equation also defines the term saturated hydraulic conductivity of the soil, regolith or rock, namely the subsurface water velocity per unit cross-sectional area and unit hydraulic gradient; however, this is conventionally written as,

The hydrological characteristic of the saturated hydraulic conductivity is sometimes called the coefficient of permeability, and models of subsurface flow are typically most sensitive to spatial variations in this property. Where only saturated rock is under study, the term saturated hydraulic conductivity is sometimes simply described as hydraulic conductivity or K. Some typical values of saturated hydraulic conductivity are given in Table 5.1.

 Strata Ks (cmh-1) Reference Well-drained topsoil 1-100 Chappell and Ternan (1992) Well-drained subsoil 1-100 Chappell and Ternan (1992) Poorly drained subsoil 0.001 Chappell and Ternan (1992) Rock (highly weathered) >10000 Bear (1972) Rock (unweathered granite) <0.000 001 Bear (1972)

There are many ways of measuring the saturated hydraulic conductivity, though they can be divided into techniques for testing undisturbed cores, and those undertaken on cased or uncased holes. Tests on repacked soil or repacked regolith give Ks values not normally considered representative of the field situation.

### 5.1.1 Tests on undisturbed cores

Undisturbed cores of soil, regolith or rock can returned to the laboratory and the saturated hydraulic conductivity determined using a laboratory permeameter. With a constant-head laboratory permeameter (Fig. 5.1, left), terms within this last equation are measured and the equation solved directly. Alternatively, a falling-head laboratory permeameter (Fig. 5.1, right) can be used and the saturated hydraulic conductivity derived using,

Ks = (rt 2L/rc 2t)ln h1 h where rt is the radius of the tube used to apply water to the core, rc is the radius of the soil core, L is the length of the soil core, t is the time taken for the pressure head

Fig. 5.1 Laboratory permeameters.

0.15m

0.3m

Transparent polycarbonate reservoir

0.15m

Ball-valve control

Ventilation tube

Steel sample ring

Ball-valve control

Ventilation tube

Steel sample ring

Reservoir

Ball-valve

Ventilation tube

Soil core

Steel ring