Abstract: Fractured geomaterials contain complex networks of natural fractures that influence hydro-mechanical behaviors through unsaturated flow. This study investigates droplet dynamics at fracture intersections using phase-field modeling, focusing on geometric controls (aperture ratio, tilt angle, and intersection angle) about splitting behavior. XGBoost-based feature importance analysis reveals the relative impacts of these parameters. Validated against experimental data, the work identifies four distinct flow regimes: complete splitting, partial splitting (with/without dragging), and non-splitting. When the droplet length is 2 cm, increasing the fracture aperture ratio W_\textb, the tilt angle \alpha of the fracture relative to the horizontal plane, and the intersection angle \beta leads to a decrease in the droplet splitting ratio \eta , and in some cases, no splitting occurs. At the condition W_\textb > 0.4 , a noticeable dragging phenomenon is observed; at the condition 20^ \circ \leqslant \alpha \leqslant 35^ \circ , the droplet completely splits into another channel; and at the condition \alpha \leqslant 15^ \circ , the droplet ceases to flow and gets stored in the fracture at the intersection. Feature importance analysis reveals that the tilt angle \alpha of the fracture relative to the horizontal plane and the intersection angle \beta have a far greater impact on droplet splitting behavior than the aperture ratio W_\textb. The model is then extended to a fracture network structure to analyze the unsaturated infiltration of surface water in fracture systems in nature. It is found that unsaturated flow phenomena caused by the "blocking effect" of air in the fractures are common. The "preferred channel" chosen by the droplet is closely related to factors such as the straightness and flow area between the inlet and outlet of the channels. These results provide theoretical insights and methodological references for simulating flow in fractured structures and design engineering solutions involving random fractures.