Optimization of Quadrilateral Infiltration Trench Using Numerical Modeling and Taguchi Approach
Publication: Journal of Hydrologic Engineering
Volume 24, Issue 3
Abstract
Infiltration trenches can help to accelerate infiltration of water into the deep vadose zone and groundwater table. A two-dimensional model was developed to characterize the performance of arbitrarily shaped infiltration trenches. This model employs a mixed form of Richards’ equation, which was solved using the coordinate transformation technique, and the reservoir equation to describe the effects of water ponding and evaporation through the soil–air interface. The model was validated using numerical and experimental test cases in the literature, and in all cases, acceptable results were obtained. Subsequently, the shape of an infiltration trench was optimized with respect to the amount of inflow water using the Taguchi technique. Running 25 combinations which were representative of 125 different trench shapes and volume of inflow water showed that a rectangular trench with a capacity of about 36% of the volume of inflow water is the best cross section of a trench. The predicted normalized recharge obtained by the Taguchi method and that of numerical modeling showed perfect agreement (about 0.01% error) for the combination that resulted in the most normalized recharge value.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The third author expresses his special appreciation and thanks to his wife for her support and guidance.
References
An, H., Y. Ichikawa, Y. Tachikawa, and M. Shiiba. 2010. “Three-dimensional finite difference saturated-unsaturated flow modeling with nonorthogonal grids using a coordinate transformation method.” Water Resour. Res. 46 (11): W11521. https://doi.org/10.1029/2009WR009024.
An, H., Y. Ichikawa, Y. Tachikawa, and M. Shiiba. 2011. “A new Iterative Alternating Direction Implicit (IADI) algorithm for multi-dimensional saturated-unsaturated flow.” J. Hydrol. 408 (1–2): 127–139. https://doi.org/10.1016/j.jhydrol.2011.07.030.
An, H., Y. Ichikawa, Y. Tachikawa, and M. Shiiba. 2012. “Comparison between iteration schemes for three-dimensional coordinate-transformed saturated–unsaturated flow model.” J. Hydrol. 470: 212–226. https://doi.org/10.1016/j.jhydrol.2012.08.056.
An, H., and S. Yu. 2014. “Finite volume integrated surface-subsurface flow modeling on nonorthogonal grids.” Water Resour. Res. 50 (3): 2312–2328. https://doi.org/10.1002/2013WR013828.
Aravena, J. E., and A. Dussaillant. 2009. “Storm-water infiltration and focused recharge modeling with finite-volume two-dimensional Richards equation: Application to an experimental rain garden.” J. Hydraul. Eng. 135 (12): 1073–1080. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000111.
Azari Rad, M., A. N. Ziaei, and M. R. Naghedifar. 2017. “Three-dimensional numerical modeling of submerged zone of Qanat hydraulics in unsteady conditions.” J. Hydrol. Eng. 23 (3): 04017063. https://doi.org/10.1061/(ASCE)HE.1943-5584.0001607.
Berardi, M., F. Difonzo, M. Vurro, and L. Lopez. 2018. “The 1D Richards’ equation in two layered soils: A Filippov approach to treat discontinuities.” Adv. Water Resour. 115: 264–272. 10.1016/j.advwatres.2017.09.027.
Browne, D., A. Deletic, G. M. Mudd, and T. D. Fletcher. 2008. “A new saturated/unsaturated model for stormwater infiltration systems.” Hydrol. Processes 22 (25): 4838–4849. https://doi.org/10.1002/hyp.7100.
Browne, D., A. Deletic, G. M. Mudd, and T. D. Fletcher. 2013. “A two-dimensional model of hydraulic performance of stormwater infiltration systems.” Hydrol. Processes 27 (19): 2785–2799. https://doi.org/10.1002/hyp.9373.
Brunone, B., M. Ferrante, N. Romano, and A. Santini. 2003. “Numerical simulations of one-dimensional infiltration into layered soils with the Richards equation using different estimates of the interlayer conductivity.” Vadose Zone J. 2 (2): 193–200. https://doi.org/10.2136/vzj2003.1930.
Celia, M. A., E. T. Bouloutas, and R. L. Zarba. 1990. “A general mass-conservative numerical solution for the unsaturated flow equation.” Water Resour. Res. 26 (7): 1483–1496. https://doi.org/10.1029/WR026i007p01483.
Davis, A. P., W. F. Hunt, R. G. Traver, and M. Clar. 2009. “Bioretention technology: Overview of current practice and future needs.” J. Environ. Eng. 135 (3): 109–117. https://doi.org/10.1061/(ASCE)0733-9372(2009)135:3(109).
Durbin, T., and D. Delemos. 2007. “Adaptive underrelaxation of Picard iterations in ground water models.” Groundwater 45 (5): 648–651. https://doi.org/10.1111/j.1745-6584.2007.00329.x.
Dussaillant, A. R., C. H. Wu, and K. W. Potter. 2004. “Richards equation model of a rain garden.” J. Hydrol. Eng. 9 (3): 219–225. https://doi.org/10.1061/(ASCE)1084-0699(2004)9:3(219).
Farahi, G., S. R. Khodashenas, A. Alizadeh, and A. N. Ziaei. 2017. “New model for simulating hydraulic performance of an infiltration trench with finite-volume one-dimensional Richards’ equation.” J. Irrig. Drain. Eng. 143 (8): 04017025. https://doi.org/10.1061/(ASCE)IR.1943-4774.0001176.
Farthing, M. W., and F. L. Ogden. 2017. “Numerical solution of Richards’ equation: A review of advances and challenges.” Soil Sci. Soc. Am. J. 81 (6): 1257. https://doi.org/10.2136/sssaj2017.02.0058.
Huang, K., B. P. Mohanty, and M. T. van Genuchten. 1996. “A new convergence criterion for the modified Picard iteration method to solve the variably saturated flow equation.” J. Hydrol. 178 (1–4): 69–91. https://doi.org/10.1016/0022-1694(95)02799-8.
Jiménez-Martínez, J., T. H. Skaggs, M. T. Van Genuchten, and L. Candela. 2009. “A root zone modelling approach to estimating groundwater recharge from irrigated areas.” J. Hydrol. 367 (1–2): 138–149. https://doi.org/10.1016/j.jhydrol.2009.01.002.
Kolivand, F., and R. Rahmannejad. 2017. “Estimation of geotechnical parameters using Taguchi’s design of experiment (DOE) and back analysis methods based on field measurement data.” Bull. Eng. Geol. Environ. 77 (4): 1763–1779. https://doi.org/10.1007/s10064-017-1042-3.
Kosugi, K. I. 2008. “Comparison of three methods for discretizing the storage term of the Richards equation.” Vadose Zone J. 7 (3): 957–965. https://doi.org/10.2136/vzj2007.0178.
Mamourian, M., K. M. Shirvan, R. Ellahi, and A. B. Rahimi. 2016. “Optimization of mixed convection heat transfer with entropy generation in a wavy surface square lid-driven cavity by means of Taguchi approach.” Int. J. Heat Mass Transfer 102: 544–554. https://doi.org/10.1016/j.ijheatmasstransfer.2016.06.056.
Matthews, C. J., R. D. Braddock, and G. C. Sander. 2004. “Modeling flow through a one-dimensional multi-layered soil profile using the Method of Lines.” Environ. Model. Assess. 9 (2): 103–113. https://doi.org/10.1023/B:ENMO.0000032092.10546.c6.
Pan, L., and P. J. Wierenga. 1995. “A transformed pressure head-based approach to solve Richards’ equation for variably saturated soils.” Water Resour. Res. 31 (4): 925–931. https://doi.org/10.1029/94WR03291.
Paniconi, C., and M. Putti. 1994. “A comparison of Picard and Newton iteration in the numerical solution of multidimensional variably saturated flow problems.” Water Resour. Res. 30 (12): 3357–3374. https://doi.org/10.1029/94WR02046.
Peaceman, D. W., and H. H. Rachford. 1955. “The numerical solution of parabolic and elliptic differential equations.” J. Soc. Ind. Appl. Math. 3 (1): 28–41. https://doi.org/10.1137/0103003.
Rathfelder, K., and L. M. Abriola. 1994. “Mass conservative numerical solutions of the head-based Richards equation.” Water Resour. Res. 30 (9): 2579–2586. https://doi.org/10.1029/94WR01302.
Richards, L. A. 1931. “Capillary conduction of liquids through porous mediums.” Physics 1 (5): 318–333. https://doi.org/10.1063/1.1745010.
Roy, R. K. 2010. A primer on the Taguchi method. Dearborn, MI: Society of Manufacturing Engineers.
Sasidharan, S., S. A. Bradford, J. Šimůnek, B. DeJong, and S. R. Kraemer. 2018. “Evaluating drywells for stormwater management and enhanced aquifer recharge.” Adv. Water Resour. 116: 167–177. https://doi.org/10.1016/j.advwatres.2018.04.003.
Schaap, M. G., F. J. Leij, and M. T. van Genuchten. 2001. “ROSETTA: A computer program for estimating soil hydraulic parameters with hierarchical pedotransfer functions.” J. Hydrol. 251 (3–4): 163–176. https://doi.org/10.1016/S0022-1694(01)00466-8.
Šimůnek, J. 2005. “Models of water flow and solute transport in the unsaturated zone.” In Encyclopedia of hydrological sciences. New York: Wiley.
Šimůnek, J., M. Šejna, H. Saito, M. Sakai, and M. T. van Genuchten. 2013. The HYDRUS-1D software package for simulating the one-dimensional movement of water, heat, and multiple solutes in variably-saturated media, version 4.17. Riverside, CA: Dept. of Environmental Sciences, Univ. of California Riverside.
Siriwardene, N. R., A. Deletic, and T. D. Fletcher. 2007. “Clogging of stormwater gravel infiltration systems and filters: Insights from a laboratory study.” Water Res. 41 (7): 1433–1440. https://doi.org/10.1016/j.watres.2006.12.040.
Taguchi, G., S. Chowdhury, and Y. Wu. 2005. Taguchi’s quality engineering handbook. Hoboken, NJ: Wiley.
van Genuchten, M. T. 1980. “A closed-form equation for predicting the hydraulic conductivity of unsaturated soils.” Soil Sci. Soc. Am. J. 44 (5): 892–898. https://doi.org/10.2136/sssaj1980.03615995004400050002x.
Vázquez-Suñé, E., X. Sánchez-Vila, and J. Carrera. 2005. “Introductory review of specific factors influencing urban groundwater, an emerging branch of hydrogeology, with reference to Barcelona, Spain.” Hydrogeol. J. 13 (3): 522–533. https://doi.org/10.1007/s10040-004-0360-2.
Xiao, Q., and E. G. McPherson. 2011. “Performance of engineered soil and trees in a parking lot bioswale.” Urban Water J. 8 (4): 241–253. https://doi.org/10.1080/1573062X.2011.596213.
Yang, H., W. A. Dick, E. L. McCoy, P. L. Phelan, and P. S. Grewal. 2013. “Field evaluation of a new biphasic rain garden for stormwater flow management and pollutant removal.” Ecol. Eng. 54: 22–31. https://doi.org/10.1016/j.ecoleng.2013.01.005.
Yang, H., E. L. McCoy, P. S. Grewal, and W. A. Dick. 2010. “Dissolved nutrients and atrazine removal by column-scale monophasic and biphasic rain garden model systems.” Chemosphere 80 (8): 929–934. https://doi.org/10.1016/j.chemosphere.2010.05.021.
Zha, Y., J. Yang, L. Shi, and X. Song. 2013. “Simulating one-dimensional unsaturated flow in heterogeneous soils with water content-based Richards equation.” Vadose Zone J. 12 (2), in press. https://doi.org/10.2136/vzj2012.0109.
Zha, Y., J. Yang, L. Yin, Y. Zhang, W. Zeng, and L. Shi. 2017. “A modified Picard iteration scheme for overcoming numerical difficulties of simulating infiltration into dry soil.” J. Hydrol. 551: 56–69. https://doi.org/10.1016/j.jhydrol.2017.05.053.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 24 • Issue 3 • March 2019
Copyright
©2018 American Society of Civil Engineers.
History
Received: May 27, 2018
Accepted: Oct 4, 2018
Published online: Dec 20, 2018
Published in print: Mar 1, 2019
Discussion open until: May 20, 2019
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.