# 5.6 Hydraulic Conductivity in Fractured Rocks

Hydraulic conductivity of a fractured rock is dependent on its unfractured hydraulic conductivity (called matrix hydraulic conductivity) as well as the spacing between fractures, their aperture (width of the fracture opening), roughness of the fracture walls, and their interconnectedness.

When fracturing is extensive relative to the volume of material that a K values is assigned to, groundwater flow in the fracture network can be treated as a continuum and the hydraulic conductivity of the system can be used in Darcy’s law to estimate flow rates (Figure 41). In that case, the transmission properties of the fractured medium are assumed to behave as an equivalent porous medium represented by a hydraulic conductivity value in each primary direction.

The site can be conceptualized as an equivalent porous medium as long as the smallest unit of interest exceeds the volume of the REV. Figure 42 presents a conceptual model of a fractured volume of rock. Fractured rocks are typically anisotropic because of the directional variations in fractures and joints (Figure 42). In some cases, it is quite common for Kz to be greater than Kx because fractures oriented in the near vertical direction are common and tend to have larger apertures than those that are not as steep. Vertical fractures tend to have larger apertures because they do not respond to the weight of overlying material to the same degree as horizontal or fractures occurring at less than vertical orientations.

When the matrix hydraulic conductivity is minimal and groundwater is flowing through a sparse network of fractures or when groundwater transport of dissolved substances through fractures is of interest, it can be useful to determine the hydraulic conductivity of individual fractures or a fracture network (Figure 42b). For example, Snow (1968) developed an equation to estimate the equivalent hydraulic conductivity (and intrinsic permeability) of a medium with a parallel array of planar fractures (Equations 41 and 42) as shown in Figure 43. The aperture of the fractures, b, and the number of fractures per unit distance of rock face, N, are required to estimate K of the fractured system.

 (41)

where:

 Kfracture set = equivalent hydraulic conductivity of a fracture set (L/T) N = the number of fractures per unit distance of rock face, N = 1/spacing (s) where spacing is the average distance between fractures (1/L) b = fracture aperture (L) ρ = fluid density (M/L3) g = gravitational constant (L/T2) μ = Dynamic viscosity M/(LT)
 (42)

where:

 kfracture set = equivalent intrinsic permeability of a fracture set (L2)

In general, when conducting groundwater resource investigations, fractured rock systems are treated as equivalent pores media. When representations of flow in a fracture network are required, specialized groundwater modeling tools are applied.