Analytical study of groundwater flow field and inrush flux distribution for deeply-buried circular arched tunnels

With the development of transportation engineering, mining engineering, underground space engineering, and long-distance water diversion projects in China, the occurrence of tunnel water inrush disasters has become increasingly frequent. Due to the limited analytical study on the flow field of circular arched tunnels, an analytical solution for the water inrush and the flow field in the surrounding rock around a deep-buried circular arched tunnel was obtained using the conformal transformation method. Then the distribution of water inrush around the tunnel circumference was explored. The results reveal that the groundwater flow field near the tunnel is significantly influenced by the tunnel shape, while its influence on the groundwater flow field further away from the tunnel can be approximated as that of a tunnel with a circular cross-section. The maximum flow velocity around the circular arched tunnel occurs near the inflection points (i.e., the corners of the tunnel bottom), while the minimum flow velocity is located at the center of the tunnel floor. The flow velocity at the corners of the tunnel bottom can exceed three times the flow velocity at the center of the tunnel floor. As the tunnel shape approaches a circle, the relative differences of flow velocities at various points around the tunnel circumference gradually decrease. This study can provide a theoretical basis for estimating the water inrush flux and characterizing the groundwater flow field in the surrounding rock around circular arched tunnels, and support for tunnel construction planning and the design for tunnel groundwater seepage/drainage.