New Design Criteria for Subsurface Drainage System Considering Heat Flow Within Soil

  • Mahmoud A. M. AbdelrahmanEmail author
Part of the The Handbook of Environmental Chemistry book series (HEC, volume 75)


Land drainage is defined as the removal of excess surface and subsurface water from the soil. The drainage design criteria are classified into agricultural, technical, environmental, and economic design criteria. Traditional drainage design formulae, though easy to implement, do not take into account the various soil properties, heat flow within porous media (soil), and its impact on evaporation rate, root water uptake, and design process. Therefore, the effect of the evaporation and root water uptake on the water table drawdown and consequently on the lateral drain spacing should be considered. Finite element models utilized to simulate water and heat flow in variably saturated soil under unsteady-state condition. The finite element models were linked together with coupling terms to be exploited as one model.

Four case studies were applied on clay, clay loam, sandy clay loam, and loamy sand soils cultivated with maize crop. The results of the applied case studies demonstrated that considering evaporation and root water uptake in the design process results in wider lateral drain spacing which leads to a more economical drainage system. It was proven that the percentage increase in lateral drain spacing varies between 22.4 and 50% regarding to soil type.


Design criteria Evaporation Heat transfer Modeling Subsurface drainage system 

Symbols and Abbreviations


Volumetric water content (L3 L−3)


Saturated soil water content (L3 L−3)


Residual water content (L3 L−3)


Volumetric fraction of liquid phase (L3 L−3)


Flow domain


Volumetric weight of water (ML−2 T−2)


Coefficient in the soil water retention function (L−1)


Temperature scaling factor for the hydraulic conductivity (−)


Piezometric head


Piezometric head at soil column entrance


Piezometric head at soil column exit


Energy loss (L)


Average thermal conductivity (ML/T3 °C)

λij (θ)

Apparent thermal conductivity of the porous media (ML/T3 °C)


Cross-sectional area (L2)

b1, b2, b3

Empirical parameters to calculate thermal conductivity (−)

C (θ)

Volumetric heat capacities of the porous medium (M/LT2 °C)


Calcium carbonate


Volumetric heat capacity solid phase (M/LT2 °C)


Volumetric heat capacity organic matter (M/LT2 °C)


Volumetric heat capacities liquid phase (M/LT2 °C)


Digital elevation model


Drainage Research Institute


Maximum potential evaporation rate (LT−1)


Potential evaporation rate function of time (LT−1)


Evapotranspiration rate (LT−1)


Pressure head (L)


Initial pressure head (L)


Haress pilot area


International Commission on Irrigation and Drainage


International Institute for Land Reclamation and Improvement


Unsaturated hydraulic conductivity (LT−1)


Components of an anisotropy tensor


Saturated hydraulic conductivity (LT−1)


Darcy’s soil column length (L)


Exponent in soil water retention function (−)


National Water Research Center


Organic matter


Pressure (ML−1 T−2)


Darcian fluid flux (LT−1)


Volume of water per unit time (L3/T)


Sink term (L3 L−3 T−1)


Temperature degree (°C)


Time (T)


Initial time


Prescribed initial temperature (°C)


Potential transpiration (LT−1)


Gravitational head


Zankalon pilot area



I wish to express my deep gratitude to Prof. Dr. Osama Waheed El-Din, Professor Emeritus, Water Structures Department, Faculty of Engineering, Zagazig University for his significant review and constructive comments and are gratefully acknowledged and sincerely appreciated.


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Drainage Research Institute (DRI), National Water Research Centre (NWRC), Delta BarragesCairoEgypt

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