An analytical model considering interaction behavior of grouted rock bolts for convergence–confinement method in tunneling design

• Based on the convergence–confinement concept, a new approach is proposed to evaluate the rock bolting effect quantitatively considering the strain-softening behavior of ground.
• The theoretical predictions of displacement and axial force in rock bolt are consistent with the field measurement data.
• Case studies confirmed that the decoupling or friction behavior between ground and rock bolt has a significant influence on the rock bolting effect.
• Rock bolting effect is influenced by installing density, rock bolting length and ground condition interactively.

A new analytical model that represents the behavior of reinforced ground near a circular underground opening in a homogeneous, uniform stress field has been developed by considering the interaction behaviors between the grouted rock bolt and ground. Axial force distribution along the rock bolt has been analyzed at first. The coupling and decoupling behaviors of the interface between the ground and rock bolt are taken into account in the model. Thereafter, the mechanical behaviors of the reinforced mass are also evaluated according to the elasto-plasticity concept and the strain softening characteristic of ground. It highlights the influence of the different bolting patterns on the extent yield zone and tunnel deformation. The derivation of the analytical model and the influence of bolts on the stress and displacement field near an opening are illustrated in this paper. The theoretical predictions are verified with the measurement data in field, e.g. a Shinkansen tunnel named as Tawara Zaga Tunnel, which is planned to be open in 2022. Moreover, the applications of the proposed approach to tunnel design are discussed further according to the rock bolting effects of the standard supporting patterns of Japan Highway Public Corporation (JH) in different ground conditions.