Abstract
In order to study the water flow in the drainage layer of highway under steady-state condition, one-dimensional (1D) Boussinesq equation-based model with Dupuit-Forchheimer assumption was established and the semi-analytical solutions to predict the water-table height were presented. In order to validate the model, a two-dimensional (2D) saturated flow model based on the Laplace equation was applied for the purpose of the model comparison. The water-table elevations predicted by 1D Boussinesq equation-based model and 2D Laplace equation-based model match each other well, which indicates that the horizontal flow in drainage layer is dominated. Also, it validates the 1D Boussinesq equation-based model which can be applied to predict the water-table elevation in drainage layer. Further, the analysis was conducted to examine the effect of infiltration rate, hydraulic conductivity and slope of drainage layer on the water-table elevation. The results show that water-table falls down as the ratio of I s to K decreases and the slope increases. If the aquifer becomes confined by the top of drainage layer due to the larger ratio of I s to K or smaller slope, the solution presented in this work can also be applied to approximate the water-table elevation in unconfined sub-section as well as hydraulic head in the confined sub-section.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
RABAB’AH S, LIANG R Y. Finite element modeling of field performance of permeable bases under asphalt pavement [J]. Transportation Research Record, 2007, 2004: 163–172.
YANG X L, YIN J H. Slope stability analysis with nonlinear failure criterion [J]. Journal of Engineering Mechanics, 2004, 130(3): 267–273.
RAY M, CHRISTORY J P. Combating concrete pavement slab pumping: State-of-the-art and recommendations [C]// Proceedings of 4th International Conference on Concrete Pavement Design and Rehabilitation. West Lafayette: Purdue University, 1989: 725–733.
YANG X L, SUI Z R. Seismic failure mechanisms for loaded slopes with associated and nonassociated flow rules [J]. Journal of Central South University of Technology, 2008, 15(2): 276–279.
CHRISTOPHER B R, MCGUFFEY V C. Pavement subsurface drainage systems [M]. Washington D C: Transportation Research Record, 1997: 48–51.
MATHIS D M. Permeable base design and construction [C]// The 4th International Conference on Concrete Pavement Design and Rehabilitation. West Lafayette: Purdue University, 1989: 663–670.
MOULTON L K. Groundwater, seepage, and drainage: A Textbook on groundwater and seepage theory and its application [M]. New York, USA: Wiley, 1979: 201–322.
YANG X L. Seismic bearing capacity of a strip footing on rock slopes [J]. Canadian Geotechnical Journal, 2009, 46(8): 943–954.
YANG X L, YIN J H. Slope equivalent Mohr-Coulomb strength parameters for rock masses satisfying the Hoek-Brown criterion [J]. Rock Mechanics and Rock Engineering, 2010, 43(4): 505–511.
TOWNER G D. Drainage of groundwater resting on a sloping bed with uniform rainfall [J]. Water Resources Research, 1975, 11(1): 144–147.
YOUNGS E G, RUSHTON K R. Dupuit-Forchheimer analyses of steady-state water-table heights due to accretion in drained lands overlying undulating sloping impermeable beds [J]. Journal of Irrigation and Drainage Engineering, 2009, 135(4): 467–473.
CEDERGREN H R. Seepage, drainage and flow nets [M]. New York, USA: Wiley, 1967: 252–475.
YOUNGS E G. Horizontal seepage through unconfined aquifers with hydraulic conductivity varing with depth [J]. Journal of Hydrology, 1965, 3(3/4): 283–296.
YOUNGS E G. Exact analysis of certain problems of ground-water flow with free surface conditions [J]. Journal of Hydrology, 1966, 4: 277–281.
YOUNGS E G. Seepage through unconfined aquifers with lower boundaries of any shape [J]. Water Resources Research, 1971, 7(3): 624–631.
YOUGNS E G, RUSHTON K R. Steady-state ditch-drainage of two-layered soil regions overlying an inverted V-shaped impermeable bed with examples of the drainage of ballast beneath railway tracks [J]. Journal of Hydrology (Amsterdam), 2009, 377(3/4): 367–376.
MIZUMURA K. Theoretical boundary condition of groundwater flow at drawdown end [J]. Journal of Hydrologic Engineering, 2009, 14(10): 1165–1172.
RUSHTON K R, GHATAORA G. Understanding and modelling drainage of railway ballast [J]. Proceedings of the Institution of Civil Engineers-Transport, 2009, 162(4): 227–236.
HEYNS F J. Railway track drainage design techniques [D]. Department of Civil Environmental Engineering, Amherst: University of Massachusetts, 2000: 98–117.
MIZUMURA K. Approximate solution of nonlinear boussinesq equation [J]. Journal of Hydrologic Engineering, 2009, 14(10): 1156–1164.
BEAR J. Dynamics of fluids in porous media [M]. New York: American Elsevier Publishing Company, Inc., 1972: 361–362.
GMS. Groundwater modeling system [M]. Utah: Brigham Young University, 2002: 1–489.
STORMONT J, ZHOU S. Improving pavement sub-surface drainage systems by considering unsaturated water flow [R]. Albuquerque: University of New Mexico, 2001.
Author information
Authors and Affiliations
Corresponding author
Additional information
Foundation item: Project(511114) supported by the Natural Science Foundation of Hainan Province, China; Project(2009YBFZ05) supported by Postgraduate Award of Central South University, China; Project(200731) supported by Traffic Technology Fund of Hunan Province, China; Project(2008BAG10B01) supported by the National Key Technology R&D Program, China
Rights and permissions
About this article
Cite this article
Dan, Hc., Luo, Sp., Li, L. et al. Boussinesq equation-based model for flow in drainage layer of highway. J. Cent. South Univ. 19, 2365–2372 (2012). https://doi.org/10.1007/s11771-012-1283-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11771-012-1283-z