INDUSTRIAL ASSOCIATES PROGRAM
Center for Tectonophysics
Texas A&M University
HYDRAULIC CHARACTERISTICS
OF SELECTED FAULTS
The hydraulic character of a fault can be described in two ways that are interrelated. One can consider the fault to be a laterally extensive shear zone of finite thickness, t, with an average hydraulic conductivity, K*. Alternatively, one can ascribe to the fault a hydraulic conductance, C*, that combines the dimensional and physical characteristics of the fault. The hydraulic conductance relates the head change, dh, across the fault to the normal component of the specific discharge via the expression
Hydraulic conductance, as defined, has units of 1/time, e.g. dy-1 or sec-1. Use of the hydraulic-conductance characterization neglects the details of the fluid-flow field in the fault; instead, flow in the fault is considered to be of a 1-D nature. The hydraulic conductance is related to fault thickness and the average anisotropic hydraulic conductivity of the fault rock by the relation
where n is the direction vector normal to the fault. If the fault has an isotropic hydraulic conductivity, then the relation is
where K* is the average isotropic hydraulic conductivity of the fault rock in the shear zone. The hydraulic conductance of the fault can be related to the isotropic permeability of the shear zone fault rock, k*, by expressing the hydraulic conductivity in terms of permeability and fluid properties such that
where r and m are the fluid density and viscosity, respectively, and g is the gravitational acceleration.
Measurement of the hydraulic-head change across a fault is easier than determining the flow field within a fault. Thus, from a practical perspective, it is easier to determine the hydraulic conductance of a fault than to determine the average thickness of fault gouge and its average hydraulic conductivity. Determining the dimensional characteristics of the shear zone is difficult because of limited or non-existent exposure in the study area. At present, an empirical relationship between fault displacement and net gouge thickness is unavailable, primarily because in addition to displacement, other parameters, such as lithology, effective mean pressure, and structural position along the fault, also influence the thickness of sheared rock associated with a fault.
Various strategies can be used to determine the hydraulic conductance of a fault, but the easiest method utilizes a simple one-dimensional, steady-state model. In the absence of sources or sinks, under steady-state conditions the volumetric flow rate through any cross sections perpendicular to flow in the aquifer must be equal in order to satisfy mass balance constraints. If one further assumes a simple 1-D horizontal-flow model, then the specific discharge through the fault and the immediately adjacent reservoir interval are equal, which requires, using Darcy's law, that
where dh is the head change across the fault, K' is the hydraulic conductivity of the adjacent aquifer, and i is the hydraulic gradient in the aquifer adjacent the fault. Thus, an estimate of the conductance of fault can be determined if one has quasi-steady-state measures of the appropriate flow-field values and aquifer hydraulic conductivity.
Appropriate water-level data are available for calculating the hydraulic conductance of two faults within the study area: 1) fault F1, which separates Regions A and B and 2) fault F2, which separates the Western Region from Region C.
Fault F1
Fault F1 is an internal partition within the hydraulic compartment comprised of Regions A and B and is positioned such that all water flowing into Region B from Region A must cross fault F1. The water-level difference existing across the fault reflects the decrease of hydraulic head associated with flow through the fault. After a sufficient recovery interval, the head difference across the fault represents a dynamic equilibrium feature of the flow system, and the systems can be considered to be at a quasi-steady state.
The head change across the fault and the adjacent aquifer hydraulic gradient needed in Eq 5 can be determined from the water-level data for wells 404, 437 and 438, because of the favorable positions of the wells with respect to fault F1 and their alignment parallel to the groundwater flow direction (Figure, 20K). The hydraulic gradient, i, adjacent to the fault is assumed to be equal to that measured between wells 437 and 438. The head difference across the fault, dhf, is determined by an extrapolation of the water table as observed in wells 404 and 437 to the location of the fault by assuming the slope of the water table is equal and uniform on both sides of the fault (Figure 10) and is equal to the slope measured between wells 437 and 438. This is a conservative approach that underestimates the head-difference across the fault. The gradient on the up-stream side of the fault should be smaller because of the greater saturated thickness on that side of the fault. In order to satisfy the steady-state assumption of the model, the late-stage recovery data are most appropriate. Table 1 provides the appropriate data for a number of years. It shows that with time the gradient between wells 437 and 438 has decreased and that correspondingly, the calculated head difference across the fault has decreased. With these data, it is observed that the ratio of aquifer conductivity to fault conductance, K' / C*, ranges between 200 (ft) and 300 (ft), with an average value about 250 (ft), i.e.
| K' / C* = 250 (ft)
| or
| C* = 0.004 K' .
| (6)
|
Alternatively, in terms of permeability,
where t is in units of feet. The pump test for well 437 indicated an average aquifer hydraulic conductivity of 1.7 ft/dy, which is equivalent to an average permeability of 0.6 Darcy; thus, the hydraulic conductance of fault F1 and the shear zone permeability are estimated, respectively, to be
| C* =0.0068 /dy
| and
| k* =2.4 (mD/ft) t (ft) .
| (8)
|
Fault F1 is not exposed, hence the net gouge thickness associated with the fault is unknown, but based on other exposed faults in the area, a net thickness of about 1 ft (0.3 m) is probably an upper limit estimate of the fault gouge thickness, t. Consequently, the average permeability of the fault gouge associated with fault F1 is estimated to be 2.4 millidarcies, which is 250 times smaller than that of the neighboring undeformed sandstone. This nearly three orders of magnitude reduction of permeability relative to the undeformed rock compares favorably with several measurements of core-permeability of samples of fault gouge from outcrops of faults in the Hickory.
Fault F2
The hydraulic conductance of fault F2 is obtained using an analysis similar to that used for fault F1. In the analysis, the aquifer is assumed to exhibit no directional variation of permeability in the plane of the bedding. With this assumption, the normal component of the average specific discharge occurring across the fault, qn, is equal to
where "in" is the component of the hydraulic gradient normal to the fault and K' is the horizontal hydraulic conductivity in the aquifer adjacent to the fault. The orientation and magnitude of the hydraulic gradient is relatively well constrained in the western region adjacent the fault. The head difference occurring across the fault is determined by an extrapolation to the fault of the water table as observed in wells 430 and 429. In contrast with the analysis for fault F1, however, the slope of the water table is not assumed to be equal on both sides of fault F2. In contrast with the western side, the slope of the water table on the east side is unknown but is estimated using the steady state model. Under the assumptions of a 1-D model and identical hydraulic conductivities on either side of the fault, the hydraulic gradients on either side will be inversely proportional to the saturated thickness of each region. Hence, the gradient on the eastern side is estimated to be one third that on the western side due to the factor three difference in the saturated thicknesses.
As with fault F1, water-level data for times at the end of the recovery period provide best estimates of the hydraulic conductance of fault F2. Using Equation 5 and the data shown in Table 2, the hydraulic conductance of fault F2 is estimated to be
where K' is the hydraulic conductivity of the aquifer in the vicinity of the fault and the units of length are in feet. The value of the hydraulic conductivity is not known, but it is likely to be similar to that measured in the vicinity of fault F1. Thus, the hydraulic conductance of fault F2 is about 0.00058 dy-1, which is about 10 times smaller than the hydraulic conductance of fault F1. This difference reflects both an increase of net thickness and a lower average permeability of the fault gouge of fault F2 relative to that of fault F1. These differences, in turn, reflect the difference of magnitude and, possibly, the sense of displacement of the two faults. Fault F1 is a normal fault with between 50 to 75 ft (15 -23 m) of displacement, whereas fault F2 is an oblique-slip fault with about 150 ft (46 m) of dip-slip displacement and a discernible, but unknown, component of right lateral, strike-slip displacement.
