Permeability of highly fractured rock masses may be quantified as a tensor, which depends on the spacing, connectivity, orientation and aperture of fractures in the rock mass. Current models ignore dependency effects of connected fracture flow systems. A preliminary new model investigating the bed-normal permeability of two-dimensional stratified fractured rocks is proposed to quantify the dependence of flow on fracture/bedding relationships. In this model, fractures are assumed to be confined to single beds and located independently of fractures in adjacent layers. Bedding planes are modeled as [interlayers] to quantify head loss incurred during bed-normal flow. Two examples illustrate the effect of rock mass geometry on bed-normal permeability. The effect can range from quantitatively insignificant to order of magnitude differences in bed-normal permeability.
Predicting groundwater movement through fractured rock masses is important for contaminant plume remediation and containment. Fluid flow through fractured rock masses may be modeled by (1) a discrete approach, modeling flow through each fracture in the rock mass; or (2) a continuum approach, statistically averaging fracture parameters to quantify an equivalent porous medium (EPM). The continuum approach is practical in rock that is highly fractured with respect to the observation scale. The permeability of an anisotropic continuum is expressed as a tensor quantifying the directional permeability of a scale-dependent representative elemental volume (REV) that is statistically similar to the entire rock mass. This paper examines the bed-normal permeability of sedimentary rocks, which are characterized by parallel layers (the words) [bed] and [layer will be used interchangeably], with many fractures terminating on bedding planes. Such fracture patterns are very common in many rocks; for instance, in limestone, the pattern has been adopted as its international map symbol. Oda's tensor FÍJ extends Snow's tensor by allowing finite size fractures but does not explicitly incorporate fracture connectivity, crucial for establishing a flow network in fractured rocks. Assuming isotropy in the plane of the fracture is common and perhaps justified, but additional anisotropy in the REV may be introduced from head losses along a layer interface (e.g. bedding plane) that provides connecting flow pathways for fractures in successive layers. The permeability tensor for fractured rock has been further investigated by Long and Witherspoon (1985), Oda (1985) and Panda and Kulatilake (1995), but none of these have explicitly dealt with the effect of fracture connectivity on bed-normal permeability. The present work focuses on flow normal to layers (Fig. 1) and develops a novel, analytic solution practical for correcting permeability tensor models of two-dimensional fractured layered rock masses. Results are obtained for bed-normal fractures, confined to single beds, that occur with negative exponential and constant spacings. Analysis indicates that fracture permeability normal to stratification is a function of: (1) the fracture spacings; (2) layer thickness; (3) fracture apertures in each layer; (4) the layer interface (bedding plane) aperture; and (5) the product of fracture spacings of adjacent beds. An example is given in which the combined effect can result in REV anisotropy of several orders of magnitude.
