A rigorous formulation of drain boundary conditions for groundwater flow modeling in geotechnical engineering

Drains play an important role in seepage control in geotechnical engineering. The enormous number and one-dimensional (1D) geometry of drainage holes make their nature difficult to be accurately modeled in groundwater flow simulation. It has been well understood that drains function by presenting discharge boundaries, which can be characterized by water head, no-flux, unilateral or mixed water head-unilateral boundary condition. It has been found after years of practices that the flow simulation may become erroneous if the transitions among the drain boundary conditions are not properly considered. For this, a rigorous algorithm is proposed in this study to detect the onset of transitions among the water head, no-flux and mixed water head-unilateral boundary conditions for downwards-drilled drainage holes, which theoretically completes the description of drain boundary conditions. After verification against a numerical example, the proposed algorithm is applied to numerical modeling of groundwater flow through a gravity dam foundation. The simulation shows that for hundreds of downwards-drilled drainage holes used to be prescribed with water head boundary condition, 56% and 2% of them are transitioned to mixed water head-unilateral and no-flux boundary conditions, respectively. The phreatic surface around the drains will be overestimated by 25–33 m without the use of the mixed boundary condition. For the first time, this study underscores the importance of the mixed water head-unilateral boundary condition and the proposed transition algorithm in drain modeling, which may become more essential for simulation of transient flow because of groundwater dynamics.