Massachusetts-Rhode Island Water Science Center
U.S. Geological Survey, Open-File Report 98-415A
By Paul M. Barlow and Allen F. Moench
A product of the Ground-Water Resources Program
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1. Titles and Contacts (2 pages)Analytical solutions to the ground-waterflow equation are derived for ten cases of hydraulic interaction between a stream and a confined, leaky, or water-table aquifer. The ten aquifer types for which analytical solutions are derived are: a semi-infinite or finite-width confined aquifer; a semi-infinite or finite-width leaky aquifer with constant head overlying the aquitard; a semi-infinite or finite-width leaky aquifer with an impermeable layer overlying the aquitard; a semi-infinite or finite-width leaky aquifer overlain by a water-table aquitard; and a semi-infinite or finite-width water-table aquifer. All aquifer types allow for the presence or absence of a uniform semipervious streambank. Of primary interest are newly derived solutions for water-table aquifers and for leaky aquifers overlain by water-table aquitards.
Two computer programs are described that evaluate the analytical solutions for time-varying stream-stage or recharge stresses that are specified by the user. The programs can simulate the effects of stream-stage fluctuations for all aquifer types. However, simulation of basin-wide recharge or evapotranspiration at the water table is permitted only for water-table aquifers and leaky aquifers overlain by a water-table aquitard. For these aquifer types, effects of recharge or evapotranspiration can be simulated alone or in combination with stream-stage fluctuations. The computer programs use the convolution relation to calculate changes in ground-water levels at an observation well or observation piezometer, seepage rates at the stream-aquifer boundary, and bank storage. The program designated STLK1 was developed for application to confined and leaky aquifers, and the program designated STWT1 was developed for application to water-table aquifers. The programs can be applied to the analysis of a passing flood wave, determination of ground-water discharge rates in response to recharge, determination of aquifer hydraulic properties, design of streamaquifer data-collection networks, and testing of numerical-model computer codes. Instructions are provided for constructing the necessary data-input files for the programs, and three sample problems are described to provide examples of the uses of the programs.
Abstract
Introduction
Purpose and Scope
Description of Stream-Aquifer Systems
Previous Studies
General Theoretical Background
Governing Differential Equation and Initial and Boundary Conditions
Convolution Relations
Presentation of Analytical Solutions
Confined and Leaky Aquifers
Assumptions
Boundary-Value Problems
Laplace Transform Analytical Solutions
Water-Table Aquifers
Assumptions
Boundary-Value Problems
Laplace Transform Analytical Solutions
Evaluation of Analytical Solutions for Step Input
Confined and Leaky Aquifers
Water-Table Aquifers
Computer Programs STLK1 and STWT1—Implementation of Analytical Solutions for Time-Varying Inputs
Discretization of Convolution Relations
Instructions for Preparing Data-Input Files
Program STLK1
Program STWT18
Result and Plot Files
Sample Problems
Sample Problem 1—Response of a Confined Aquifer to a Sinusoidal Flood Wave
Sample Problem 2—Response of a Water-Table Aquifer to a Sinusoidal Flood Wave
Sample Problem 3—Response of a Water-Table Aquifer to Recharge
Summary
References Cited
Attachment 1. Derivation of Analytical Solutions
Step Response for Flow from a Semi-Infinite Confined or Leaky Aquifer
Head Distribution Due to a Step Change in Stream Stage
Dimensionless Seepage at Streambank Due to Step Change in Stream Stage
Step Response for Flow from a Finite-Width Confined or Leaky Aquifer with a
Semipervious Streambank
Head Distribution Due to a Step Change in Stream Stage
Dimensionless Seepage at Streambank Due to Step Change in Stream Stage
Step Response for Flow from a Semi-Infinite Water-Table Aquifer
Head Distribution Due to a Step Change in Stream Stage
Dimensionless Seepage at Streambank Due to Step Change in Stream Stage
Step Response for Flow from a Finite-Width Water-Table Aquifer with a Semipervious Streambank
Head Distribution Due to a Step Change in Stream Stage
Dimensionless Seepage at Streambank Due to Step Change in Stream Stage
Attachment 2. Documentation of Programs STLK1 and STWT177
Program STLK1
Narrative
List of Program Variables
Program STWT1
Narrative
List of Program Variables
1-4. Schematic diagrams showing:
1. Ground-water discharge from a water-table aquifer to a partially penetrating, hydraulically connected stream: (A) laterally extensive (semi-infinite) aquifer; and (B) narrow aquifer of finite width
2. Types of aquifers for which analytical solutions are derived: (A) confined; (B) leaky, with a constant head overlying the aquitard; (C) leaky, with an impermeable layer overlying the aquitard; (D) leaky, overlain by a water-table aquitard; and (E) water table (unconfined)
3. Response of stream-aquifer system to flood wave: (A) rise of stream stage and seepage of streamflow into aquifer as bank storage; (B) stream-stage hydrograph; (C) seepage hydrograph; (D) ground-water-head hydrograph; and (E) bank-storage-volume hydrograph
4. Response of stream-aquifer system to a gradual recharge event: (A) rise of water table; (B) recharge hydrograph; (C) ground-water-head hydrograph; and (D) ground-water-discharge hydrograph
5-14.Schematic sections showing:
5. Semi-infinite, confined aquifer (A) without semipervious streambank material and (B) with semipervious streambank material
6. Finite-width, confined aquifer (A) without semipervious streambank material and (B) with semipervious streambank material
7. Semi-infinite, leaky aquifer with constant head overlying the aquitard (case 1) (A) without semipervious streambank material and (B) with semipervious streambank material
8. Finite-width, leaky aquifer with constant head overlying the aquitard (case 1) (A) without semipervious streambank material and (B) with semipervious streambank material
9. Semi-infinite, leaky aquifer with impermeable layer overlying the aquitard (case 2) (A) without semipervious streambank material and (B) with semipervious streambank material
10. Finite-width, leaky aquifer with impermeable layer overlying the aquitard (case 2) (A) without semipervious streambank material and (B) with semipervious streambank material
11. Semi-infinite, leaky aquifer overlain by a water-table aquitard (case 3) (A) without semipervious streambank material and (B) with semipervious streambank material
12. Finite-width, leaky aquifer overlain by a water-table aquitard (case 3) (A) without semipervious streambank material and (B) with semipervious streambank material
13. Semi-infinite, water-table aquifer (A) without semipervious streambank material and (B) with semipervious streambank material
14. Finite-width, water-table aquifer (A) without semipervious streambank material and (B) with semipervious streambank material
15-20. Graphs showing change in (A) ground-water head and (B) seepage rate to aquifer, for 1-foot increase in stream stage:
15. Semi-infinite confined aquifer with and without semipervious streambank material
16. Finite-width confined aquifer with and without semipervious streambank material
17. Finite-width and semi-infinite confined aquifers
18. Semi-infinite leaky aquifer with constant head overlying the aquitard
19. Semi-infinite leaky aquifers
20. Semi-infinite water-table aquifer without semipervious streambank material
21-22. Graphs showing:
21. Change in ground-water head for 1-foot increase in stream stage at several vertical positions in a semi-infinite water-table aquifer
22. (A) Change in ground-water head and (B) seepage rate to aquifer, for 1-foot increase in stream stage; semi-infinite water-table aquifer and leaky aquifer overlain by water-table aquitard
23. Schematic diagram showing continuous and discretized (A) stream-stage and (B) recharge hydrographs
24-27. Representations showing:
24. Example data-input file for program STLK1
25. Example data-input file for program STWT1
26. Example result file for program STLK1
27. Example plot file for program STLK
28-29. Graphs showing (A) ground-water head at observation well, (B) seepage rate between stream and aquifer, and (C) bank storage in aquifer, for a one-day sinusoidal flood wave:
28. Semi-infinite confined aquifer
29. Semi-infinite water-table aquifer
30. Graph showing ground-water discharge for a one-day recharge event, finite-width water-table aquifer
31. Representation showing example data-input file for program STWT1 for recharge event (sample problem 3)
1. Dimensionless variables and variable groupings for confined and leaky aquifers
2. Dimensionless variables and variable groupings for water-table aquifers
3. Parameters and dimensions of the hypothetical confined and leaky aquifers
4. Parameters and dimensions of the hypothetical water-table aquifer
5. Input data format for program STLK1
6. Input data format for program STWT1
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Suggested Citation:
Barlow, P.M., Moench, A.F., 1998, Analyitical Solutions and Computer Programs for Hydraulic Interaction of Stream-Aquifer Systems, United States Geological Survey, Open-File Report 98-415A, 85 p.
U.S. Department of the Interior | U.S. Geological Survey
Persistent URL: https://pubs.usgs.gov/of/1998/ofr98-415A
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Page Last Modified: Monday, 02-Oct-2006 13:43:34 EDT
