Improved Boussinesq Equation–Based Model for Transient Flow in a Drainage Layer of Highway: Capillary Correction
Publication: Journal of Irrigation and Drainage Engineering
Volume 139, Issue 12
Abstract
Currently, time to drain and depth of flow are the two basic concepts for designing the drainage layer of highway, both of which are based on the saturated flow and cannot reasonably evaluate the drainage efficiency of drainage layer. A recent study demonstrated that capillary effects could become significant with unsaturated flow playing an important role in conducting water out of the drainage layer in some cases. In view of the disadvantages of the two methods, it is reasonable to combine them to guide the design of a drainage layer. Here, a model was established based on the one-dimensional (1D) transient Boussinesq equation with a capillary correction. The general solution to the governing equation was obtained using the method of separation variables. Furthermore, the presented model was validated against numerical simulations predicted by a finite-difference method (the MATLAB program) and the finite-element method (SUTRA program). A comparison was conducted to demonstrate the difference between the saturated drainage and unsaturated drainage processes. The results showed that the time to drain the same water volume based on the saturated model is much less than that based on the unsaturated model. The present model with capillary correction performs better than the saturated model in predicting time to drain in the drainage layer.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This research has been supported by the Fundamental Research Funds for the Central Universities of P.R. China (Grant No. 2012QNZT048), National Natural Science Foundation (Grant No. 51248006 and 51308554), and China Postdoctoral Science Foundation (Grant No. 2012M521563) to the first writer. The research is also assisted by the Special Financial Grant from the China Postdoctoral Science Foundation (Grant No. 2013T60865), the Hainan Natural Science Foundation (Grant No. 511114), Traffic Technology Fund of Guizhou Province of P.R. China (Grant No. 2013-121-013).
References
AASHTO. (1998). Guide for design of pavement structures, Washington, DC.
Al-Qadi, I. L., Lahouar, S., Louizi, A., Elseifi, M. A., and Wilkes, J. A. (2004). “Effective approach to improve pavement drainage layers.” J. Transp. Eng., 130(5), 658–664.
Bakker, M. (2004). “Transient analytic elements for periodic Dupuit-Forchheimer flow.” Adv. Water Resour., 27(1), 3–12.
Barber, E. S., and Sawyer, C. L. (1952). “Highway subdrainage.” Proc., Highway Research Board, 643–666.
Bear, J., and Verruijt, A. (1987). Modeling groundwater flow and pollution, D. Reidel, Dordrecht, The Netherlands.
Casagrande, A., and Shannon, W. L. (1952). “Base course drainage for airport pavements.” ASCE Trans., 117(2516), 792–820.
Cedergren, H. R. (1974). Drainage of highway and airfield pavements, Wiley, New York.
Dan, H.-C., Xin, P., Li, L., Li, L., and Lockington, D. (2012a). “Boussinesq equation-based model for flow in the drainage layer of highway with capillarity correction.” J. Irrig. Drain. Eng., 138(4), 336–348.
Dan, H.-C., Xin, P., Li, L., Li, L., and Lockington, D. (2012b). “Capillary effect on flow in the drainage layer of highway pavement.” Can. J. Civ. Eng., 39(6), 654–666.
Dawson, A. (2008). Water in road structure, Springer, Berlin, Germany.
FHWA. (1992). “Demonstration project no. 87: Drainage pavement system participant notebook.”, Washington, DC.
Gardner, W. R. (1958). “Some steady-state solutions of the unsaturated moisture flow equation with application to evaporation from a water table.” Soil Sci., 85(4), 228–232.
Gardner, W. R. (1962). “Approximate solution of a non-steady state drainage problem.” Soil Sci. Soc. Am. Proc., 26(2), 129–132.
Gureghian, A. B. (1978). “Solutions of Boussinesq equation for seepage flow.” Water Resour. Res., 14(2), 231–236.
Hogarth, W. L., Parlange, J. Y., Parlange, M. B., and Lockington, D. (1999). “Approximate analytical solution of the Boussinesq equation with numerical validation.” Water Resour. Res., 35(10), 3193–3197.
Li, L., et al. (2005). “Similarity solution of axisymmetric flow in porous media.” Adv. Water Resour., 28(10), 1076–1082.
Mallela, J., Titus-Glover, L., and Darter, M. I. (2000). “Considerations for providing subsurface drainage in jointed concrete pavements.”, Transportation Research Board, Washington, DC, 1–10.
Ministry of Transport of the People's Republic of China (MOTPRC). (2006). Specifications for design of highway asphalt pavement, China Communications Press, Washington, DC.
Moulton, L. K. (1979). Groundwater, seepage, and drainage: A textbook on groundwater and seepage theory and its application, Federal Highway Administration (FHWA), Washington, DC.
Rabab’an, S. R. (2007). “Integrated assessment of free draining base and subbase materials under flexible pavement.” Ph.D. thesis, Univ. of Akron, Akron, OH.
Richards, L. A. (1931). “Capillary conduction of liquids through porous mediums.” J. Appl. Phys., 1(5), 318–333.
Russo, D. (1988). “Determining soil hydraulic-properties by parameter-estimation—On the selection of a model for the hydraulic-properties.” Water Resour. Res., 24(3), 453–459.
Serrano, S. E., and Workman, S. R. (1998). “Modeling transient stream/aquifer interaction with the non-linear Boussinesq equation and its analytical solution.” J. Hydrol., 206(3–4), 245–255.
Smith, R. E. (2002). Infiltration theory for hydrologic applications, American Geophysical Union, Washington, DC.
Srivastava, R., and Yeh, T. C. J. (1991). “Analytical solutions for one-dimensional, transient infiltration toward the water-table in homogeneous and layered soils.” Water Resour. Res., 27(5), 753–762.
van Genuchten, M. Th. (1980). “A closed-form equation for predicting the hydraulic conductivity of unsaturated soils.” Soil Sci. Soc. Am. J., 44(5), 892–898.
Verhoest, N. E. C., and Troch, P. A. (2000). “Some analytical solutions of the linearized Boussinesq equation with recharge for a sloping aquifer.” Water Resour. Res., 36(3), 793–800.
Voss, C. I., and Provost, A. M. (2008). “A model for saturated-unsaturated, variable-density ground-water flow with solute or energy transport.”, Reston, VA.
Youngs, E. G., and Rushton, K. R. (2009). “Dupuit-forchheimer analyses of steady-state water-table heights due to accretion in drained lands overlying undulating sloping impermeable beds.” J. Irrig. Drain. Eng., 135(4), 467–473.
Information & Authors
Information
Published In
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Aug 17, 2012
Accepted: May 27, 2013
Published online: May 29, 2013
Discussion open until: Oct 29, 2013
Published in print: Dec 1, 2013
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.