Permeability and Seepage Flow - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 134

Figure 6.7 Types of laminar fl ow depending on relative roughness (Wittke 1990)

According to Lomize (1951), the streamlines in laminar fl ow of water between two parallel
glass plates remain parallel if k/D h 0.032. Such fl ow is referred to as “irrotational” (Fig. 6.7,

lower left). This implies that fl ow remains practically uninfl uenced by the discontinuity
walls if k/D h

≤

0.032. Such a discontinuity wall is denoted as “hydraulically smooth”. If
k/D h > 0.032, the streamlines diverge and sometimes whirl due to local rotation of wa-
ter particles. Flow is then denoted as “rotational” (Fig. 6.7, lower right). Lomize (1951)
found the following relationship between fl ow rate per unit width (specifi c fl ow) Q S and
mean aperture

≤

of rough fi ssures:

(6.14)

where f is a factor to account for surface roughness, and is known as “fl ow reduction
factor” or “friction factor”. Equation (6.14) is known as the “cubic law” since Q S is pro-
portional to the third power of the aperture (Witherspoon et al. 1980). This equation
refl ects the great infl uence of discontinuity aperture on fl ow rate.