Abstract: Drainage is one of the most cost-effective and important seepage control measures in high-dam engineering. The multiple levels of drainage tunnels and the upwards- and downwards-drilled drainage holes constitute the 3D cross-connected drain system, but accurately modeling the drains has been one of the difficulties in the seepage analysis in hydraulic engineering. Long-term studies have shown that drains function by presenting discharge boundaries, which can be characterized by water head, no-flux, unilateral or mixed water head-unilateral boundary condition. However, it may result in erroneous modeling of the drains and the seepage field when the drain boundary conditions are incorrectly prescribed, or there lacks reliable transition algorithm for drain boundary conditions. Based on a proposed 200-m roller compacted concrete gravity dam, the control mechanism of the 3D cross-connected drain system on the seepage field is summarized, the self-equilibrated relationship of flow rate characterized by the water head-unilateral boundary condition is clarified, and the automatic transition algorithm of the boundary conditions for downwards-drilled drainage holes is presented. The simulation results of the transient seepage flow in the dam foundation show that, the core of accurately modeling the 3D cross-connected drain system is to locate the downwards-drilled drainage holes that characterized by the water head-unilateral boundary condition. When these boreholes are erroneously prescribed with no-flux boundary condition (i.e., recognized as failed), the phreatic surface is overestimated by 1.7−10.6 m; when they are erroneously prescribed with water head boundary condition (i.e., overflow occurs through their upper ends), the phreatic surface is overestimated by up to 29.4−94.5 m. Different from previous studies, the boreholes still perform well in lowering the groundwater level and pore water pressure in the dam foundation by their own self-equilibrated relationship of flow rate, where the seeped water is collected and discharged to lower boreholes, even no overflow occurs. Besides, the optimization analysis of the drain spacing implies that a drain spacing of 3 m commonly used in engineering practices is suitable, but a larger spacing of drainage holes could be suggested for those drilled downwards from the longitudinal drainage tunnel at elevation 2 928 m on the right bank. The research results are of great significance for the design and seepage safety evaluation of seepage control system of high dams.

Key words: drainage hole, boundary condition, concrete dam, transient seepage flow, design optimization