Elastoplastic Solutions for Surrounding Rock Masses of Deep-Buried Circular Tunnels with Non-Darcian Flow

The significant characteristics of the non-Darcian flow of groundwater seepage in a low-permeability rock mass have been reported, but there have been few studies on the analytical solutions for deep-buried circular tunnels comprising non-Darcian flow. In this study, based on the theory of non-Darcian flow and well pumping, an analytical solution was derived for the seepage field of rock masses surrounding a deep-buried circular tunnel. With consideration of seepage force due to non-Darcian flow as a volume pressure added to the stress field of the rock masses, an elastoplastic analytical solution was derived on the basis of the unified yield criterion. The analytical solutions were validated by comparing with those for the cases of Darcian flow and disregard for seepage, and the influences of various parameters on the plastic zone radius, radial displacement, and support characteristic curve were investigated. The results showed that under the condition of non-Darcian flow, the seepage forces had a slower increasing trend toward the tunnels. The plastic zone radius and radial displacement of the rock masses with non-Darcian flow remained between the upper limits in the condition of Darcian flow and the lower limits of disregard for seepage. With an increase in the head loss between the internal and external sections of a tunnel and a decrease in the united yield criterion parameter and the exponential parameter at low gradients, the plastic zone radius and radial displacement at the tunnel walls tended to gradually increase. As the hydraulic head loss between the internal and external sections of a tunnel increased, the influences of united yield criterion parameter, exponential parameter, and supporting pressure on the plastic zone radius and radial displacement were more significant. The analytical solution presented in this study can be used to design a tunnel excavated in a low-permeability rock mass below a water table.