Ground reaction curves for deep circular tunnels considering the effect of ground reinforcement

To investigate the behavior of tunnels in the presence of ground reinforcement, an analytical model of the convergence-confinement type is proposed. A deep circular tunnel with a far-field hydrostatic stress is considered. An equivalent reinforced region is introduced to represent the effect of ground improvement. Both the reinforced ground and the natural ground are assumed to be linear-elastic prior to the yield. They obey the linear Mohr–Coulomb yield criterion. Their post-yield behavior follows the non-associated flow rule defined by the dilation angle. Due to the different degrees of strengthening and the radius of the reinforced zone, the plastic zone(s), if any, may theoretically initiate from the inner boundary of the reinforced zone, the outer boundary of the reinforced zone, or both the inner and the outer boundaries simultaneously. In order to solve the proposed problem, six different configurations that can possibly be encountered according to the distribution and extent of the plastic zone(s) are solved. Additionally, seven critical unconfinement factors, each of which defines a possible transition between two consecutive configurations encountered, are also solved. Furthermore, a flow chart is designed to determine the actual configuration transitions with the input of the calculated critical unconfinement factors. The proposed analytical model is validated by a series of numerical simulations. A comparison reveals that the proposed model excels the classical Salençon's model in solving the mentioned problem.

► GRCs of a tunnel with various ground reinforcements are solved analytically.
► Derived solutions for six configurations and seven transitions possibly encountered.
► The proposed model excels the classical Salençon's model in solving GRC problem.