Scientific Investigations Report 2008–5002
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Ground-water flow was simulated using variable-direction anisotropy in hydraulic conductivity to represent the folded, fractured sedimentary rocks that underlie the Shenandoah Valley in Virginia and West Virginia. The anisotropy is a consequence of the orientations of fractures that provide preferential flow paths through the rock, such that the direction of maximum hydraulic conductivity is oriented within bedding planes, which generally strike N30°E; the direction of minimum hydraulic conductivity is perpendicular to the bedding. The finite-element model SUTRA was used to specify variable directions of the hydraulic-conductivity tensor in order to represent changes in the strike and dip of the bedding throughout the valley.
The folded rocks in the valley are collectively referred to as the Massanutten synclinorium, which contains about a 5-km thick section of clastic and carbonate rocks. For the model, the bedrock was divided into four units: a 300-m thick top unit with 10 equally spaced layers through which most ground water is assumed to flow, and three lower units each containing 5 layers of increasing thickness that correspond to the three major rock units in the valley: clastic, carbonate and metamorphic rocks. A separate zone in the carbonate rocks that is overlain by colluvial gravel—called the western-toe carbonate unit—was also distinguished.
Hydraulic-conductivity values were estimated through model calibration for each of the four rock units, using data from 354 wells and 23 streamflow-gaging stations. Conductivity tensors for metamorphic and western-toe carbonate rocks were assumed to be isotropic, while conductivity tensors for carbonate and clastic rocks were assumed to be anisotropic. The directions of the conductivity tensor for carbonate and clastic rocks were interpolated for each mesh element from a stack of “form surfaces” that provided a three-dimensional representation of bedrock structure. Model simulations were run with (1) variable strike and dip, in which conductivity tensors were aligned with the strike and dip of the bedding, and (2) uniform strike in which conductivity tensors were assumed to be horizontally isotropic with the maximum conductivity direction parallel to the N30°E axis of the valley and the minimum conductivity direction perpendicular to the horizontal plane. Simulated flow penetrated deeper into the aquifer system with the uniform-strike tensor than with the variable-strike-and-dip tensor. Sensitivity analyses suggest that additional information on recharge rates would increase confidence in the estimated parameter values.
Two applications of the model were conducted—the first, to determine depth of recent ground-water flow by simulating the distribution of ground-water ages, showed that most shallow ground water is less than 10 years old. Ground-water age distributions computed by variable-strike-and-dip and uniform-strike models were similar, but differed beneath Massanutten Mountain in the center of the valley. The variable-strike-and-dip model simulated flow from west to east parallel to the bedding of the carbonate rocks beneath Massanutten Mountain, while the uniform-strike model, in which flow was largely controlled by topography, simulated this same area as an east-west ground-water divide. The second application, which delineated capture zones for selected well fields in the valley, showed that capture zones delineated with both models were similar in plan view, but differed in vertical extent. Capture zones simulated by the variable-strike-and-dip model extended downdip with the bedding of carbonate rock and were relatively shallow, while those simulated by the uniform-strike model extended to the bottom of the flow system, which is unrealistic. These results suggest that simulations of ground-water flow through folded fractured rock can be constructed using SUTRA to represent variable orientations of the hydraulic-conductivity tensor and produce a physically realistic flow system that accurately reflects the pattern of bedrock structure.
Abstract
Introduction
Purpose and Scope
Previous Investigations
Hydrogeology of the Shenandoah Valley
Physiography
Bedrock Geology
Stratigraphy
Structure
Surficial Geology
Hydrology
Ground-Water Discharge
Ground-Water Withdrawals
Recharge
Transmissivity
Anisotropy in Inclined, Fractured Sedimentary Rocks
Simulation of Flow in Inclined, Fractured Sedimentary Rocks
Representation of Bedrock Structure in Shenandoah Valley
Conceptual Fracture Framework
Form Lines, Form Surfaces, and Computation of Conductivity Tensor
Ground-Water Flow Model
Model Design
Mesh and Layering
Boundary Conditions
Hydraulic Conductivity
Model Calibration
Observations
Parameters
Model Fit
Model Applications
Ground-Water Age Distributions
Capture Zones of Well Fields
Summary
Acknowledgments
References Cited
Appendix 1. Modifications to SUTRA
1–3. Maps showing—
1. Geologic and physiographic provinces in eastern North America showing the Great Valley and Mesozoic Rift basins
2. Geographic features of the Shenandoah Valley, Virginia and West Virginia
3. Bedrock geology of the Shenandoah Valley, Virginia and West Virginia
4. Photograph showing bedrock surface exposed near quarry operation in Cambrian-Ordovician carbonate rock, Shenandoah Valley, Virginia and West Virginia
5. Graph showing long-term water-level hydrographs for two observation wells in the Shenandoah Valley in Augusta and Rockingham Counties, Virginia
6. Map showing watersheds and streamflow-gaging stations where base flow was estimated, and locations of wells with long-term hydrographs
7. Graph showing relation between base flow estimated from streamflow measurements and computed as a function of the percentages of the basin area underlain by rock unit
8–14. Diagrams showing—
8. Box plots of transmissivity values by rock unit estimated from specific capacity of pumped wells
9. Schematic diagram showing alternative designs to represent ground-water flow through inclined fractured sedimentary rocks with an orthogonal finite- difference grid
10. Formation of fractures in response to contractional deformation and folded bedding
11. Generalized geologic sections showing rock units and form lines of bedding and faults in rocks underlying the Shenandoah Valley, Virginia and West Virginia
12. Model domain showing map view of finite-element mesh and four rock units represented by the model
13. Generalized section D–D’ showing units used to define model layers
14. Perspective three-dimensional views along sections C–C’ and E–E’ showing attitude of bedding represented in ground-water flow models A and B: (A) strike direction (maximum conductivity direction, Kmax), and (B) dip angle (medium conductivity direction, Kmed)
15. Graph showing estimated relations used to compute maximum hydraulic conductivity with depth in carbonate, clastic, and metamorphic rocks in model A
16–18. Diagrams showing—
16. Block diagrams along sections C–C’ and E–E’ showing spatial distribution of maximum hydraulic conductivity (Kmax) used in models A and B
17. Block diagrams along sections C–C’ and E–E’ showing spatial distribution of simulated ground-water velocity in model A
18. Box plots of hydraulic conductivity values by rock unit estimated from specific capacity of pumped wells and through calibration with model A
19–21. Graphs showing—
19. Residual plots for simulated heads in model A: (A) relation between simulated and observed values, and (B) relation between simulated values and residuals
20. Residual plots for simulated flows in model A: (A) relation between residuals and drainage-area size, and (B) relation between simulated and observed base flow and drainage-area size
21. Composite-scaled sensitivities of optimal parameters in model A. [Kmax: maximum hydraulic conductivity, Kmed: medium hydraulic conductivity, Kmin: minimum hydraulic conductivity]
22–26. Diagrams showing—
22.Block diagram along section D–D’ showing spatial distribution of simulated ground-water age and flow directions with (A) model A (variable strike and dip), and (B) model C (uniform strike)
23.Capture zones (plan view of contributing area) delineated with model A (variable strike and dip) to (A) the Martinsburg water supply in Berkeley County, W.Va., and (B) industrial well fields in Rockingham County, Va.
24. Capture zones (plan view of contributing area) delineated with model C (uniform strike) to (A) the Martinsburg water supply in Berkeley County, W.Va., and (B) industrial well fields in Rockingham County, Va.
25. Three-dimensional perspective views of capture zones to the Martinsburg water supply in Berkeley County W.V. delineated with (A) model A (variable strike and dip), and (B) model C (uniform strike)
26. Capture zones (plan view of contributing area) delineated with model A (variable strike and dip) with recharge decreased by one-half to simulate drought conditions at (A) the Martinsburg water supply in Berkeley County, W.Va., and (B) industrial well fields in Rockingham County, Va.
Suggested citation: Yager, R.M., Southworth, Scott, and Voss, C.I., 2008, Simulation of ground-water flow in the Shenandoah Valley, Virginia and West Virginia, using variable-direction anisotropy in hydraulic conductivity to represent bedrock structure: U.S. Geological Survey Scientific Investigations Report 2008-5002, 54 p.
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