Optimization-Based Simulation and Design of Tile Drainage Systems
Publication: Journal of Irrigation and Drainage Engineering
Volume 126, Issue 6
Abstract
Optimization-based models for simulation of tile drainage systems are formulated and solved with a finite-difference approximated Richard's equation as an embedded constraint. The solution methodology minimizes the sum of absolute violations of the discretized variably saturated porous media flow equations. The optimal design minimizes the sum of the pressure heads to obtain optimal drain locations and discharges for a given lateral spacing. The projected augmented Lagrangian method of nonlinear programming is used to solve the optimization models. The performance of the simulation is verified using the steady-state square embankment drainage problem. Thereafter, the simulation and design models are solved for a hypothetical tile drainage system. The results demonstrate the capability of the models.
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References
1.
Aguado, E., and Remson, I. (1974). “Groundwater hydraulics in aquifer management.”J. Hydr. Div., ASCE, 100(1), 103–118.
2.
Arora, J. S. ( 1989). Introduction to optimum design, McGraw-Hill, Singapore.
3.
Ayars, J. E., Grismer, M. E., and Guitjens, J. C. (1997). “Water quality as design criteria in drainage water management systems.”J. Irrig. and Drain. Engrg., ASCE, 123(3), 154–158.
4.
Bear, J. ( 1979). Hydraulics of groundwater, McGraw-Hill, New York.
5.
Brooks, R. H., and Corey, A. T. (1966). “Properties of porous media affecting fluid flow.”J. Irrig. and Drain. Div., ASCE, 92(2), 61–88.
6.
Celia, M. A., Bouloutas, E. T., and Varba, R. L. ( 1990). “A general mass-conservative numerical solution for the unsaturated flow equation.” Water Resour. Res., 26(7), 1483–1496.
7.
Chung, S. O., and Austin, T. A. (1987). “Modeling saturated-unsaturated water flow in soils.”J. Irrig. and Drain. Engrg., ASCE, 113(2), 233–250.
8.
Cohon, J. L., and Marks, D. H. ( 1975). “A review and evaluation of multiobjective programming techniques.” Water Resour. Res., 11(2), 208–220.
9.
Cooley, R. L. ( 1983). “Some new procedures for numerical solution of variably saturated flow problems.” Water Resour. Res., 19(5), 1271–1285.
10.
Das, A., and Datta, B. ( 1995). “Simulation of density dependent 2-d seawater intrusion in coastal aquifers using nonlinear optimization algorithm.” Proc., Am. Water Resour. Assn. Annu. Summer Symp. on Water Resour. and Envir. Hazards: Emphasis on Hydrologic and Cultural Insight in the Pacific Rim, 277–286.
11.
Das, A., and Datta, B. (1999a). “Development of multiobjective management models for coastal aquifers.”J. Water Resour. Plng. and Mgmt., ASCE, 125(2), 76–87.
12.
Das, A., and Datta, B. (1999b). “Development of management models for sustainable use of coastal aquifers.”J. Irrig. and Drain. Engrg., ASCE, 125(3), 112–121.
13.
Das, A., and Datta, B. (2000). “Optimization based solution of density dependent seawater intrusion in coastal aquifers.”J. Hydrologic Engrg., ASCE, 5(1), 82–89.
14.
Freeze, R. A., and Cherry, J. A. ( 1979). Groundwater, Prentice-Hall, Englewood Cliffs, N.J.
15.
Garcia, L. A., Manguerra, H. B., and Gates, T. K. (1995). “Irrigation-drainage design and management model: Development.”J. Irrig. and Drain. Engrg., ASCE, 121(1), 71–82.
16.
Gorelick, S. M. ( 1983). “A review of distributed parameter groundwater management modeling methods.” Water Resour. Res., 19(2), 305–319.
17.
Guitjens, J. C., Ayars, J. E., Grismer, M. E., and Willardson, L. S. (1997). “Drainage design for water quality management: Overview.”J. Irrig. and Drain. Engrg., ASCE, 123(3), 148–153.
18.
Hooghoudt, S. B. ( 1940). “Bijdragen tot de kennis van eenige naturkundige grootheden van den grond.” No. 7, Algemeene beschouwing van het probleem van de detailontwatering en de infiltratie door middel van parallel loopende drains, greppels, slooten en kanalen, Verslagen van Rijksuitgeverij Dienst van de Nederlandsche Staatscourant, S-Gravenhage, The Netherlands (in Dutch).
19.
Huyakorn, P. S., Springer, E. P., Guvanesan, V., and Wadsworth, T. D. ( 1986). “A three-dimensional finite-element model for simulating water flow in variably saturated porous media.” Water Resour. Res., 22(13), 1790–1808.
20.
Manguerra, H. B., and Garcia, L. A. (1995). “Irrigation-drainage design and management model: Validation and application.”J. Irrig. and Drain. Engrg., ASCE, 121(1), 83–94.
21.
Marino, M. A., and Tracy, J. C. (1988). “Flow of water through root-soil environment.”J. Irrig. and Drain. Engrg., ASCE, 114(4), 588–604.
22.
Murtagh, B. A., and Saunders, M. A. ( 1993). “MINOS 5.4 user's guide.” Tech. Rep. SOL 83-20R, Sys. Optimization Lab., Dept. of Operations Res., Stanford University, Stanford, Calif.
23.
Pan, L., Warrick, A. W., and Wierenga, P. J. ( 1996). “Finite element methods for modeling water flow in variably saturated porous media: Numerical oscillation and mass-distributed schemes.” Water Resour. Res., 32(6), 1883–1889.
24.
Simunek, J., Vogel, T., and van Genuchten, M. Th. ( 1994). “The SWMS-2D code for simulating water flow and solute transport in two dimensional variably saturated media.” Res. Rep. No.-132, U.S. Salinity Laboratory, Riverside, Calif.
25.
Willis, R. ( 1973). “Optimization of the assimilative waste capacity of the unsaturated and saturated zones of an unconfined aquifer system.” PhD thesis, University of California, Los Angeles.
26.
Willis, R. ( 1979). “A planning model for the management of groundwater quality.” Water Resour. Res., 15(6), 1305–1312.
27.
Willis, R., and Finney, B. A. ( 1985). “Optimal control of nonlinear groundwater hydraulics: Theoretical development and numerical experiments.” Water Resour. Res., 21(10), 1476–1482.
28.
Workman, S. R., Skaggs, R. W., Parsons, J. E., and Rice, J. ( 1990). DRAINMOD, user's manual, North Carolina State University, Raleigh, N.C.
Information & Authors
Information
Published In
Journal of Irrigation and Drainage Engineering
Volume 126 • Issue 6 • December 2000
Pages: 381 - 388
History
Received: Oct 6, 1998
Published online: Dec 1, 2000
Published in print: Dec 2000
Authors
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