Displacement process analysis of deep tunnels with grouted rockbolts considering bolt installation time and bolt length

This study investigates the interaction process between grouted bolts and tunnel surrounding rock, and establishes an analytical model for deep tunnels reinforced with active grouted rockbolts of the convergenceconfinement type. The rock mass is assumed to be elastic-perfectly plastic, obeying the Hoek-Brown criterion. The longitudinal displacement profile is introduced to represent the space effect of the tunnel face, based on which the fictitious pressure along the tunnel axis is determined. Because of delayed installation and limited length of the rockbolts, a rock mass may behave elastically or plastically at bolt installation with the rockbolts anchored in different zones. Six different evolution paths possibly encountered on the basis of the relative magnitude between the anchorage and plastic zones are proposed. The tunnel displacement, plastic radii, and stresses are determined. The analytical results are validated by comparing with those obtained from numerical simulations and an existing model. A parametric analysis shows that doubling bolt length from 2 to 4 m in a 14m-diameter tunnel reduces the tunnel wall displacement up to 20%. Installing rockbolts close to the tunnel face (less than 1 m) can reduce tunnel wall displacement up to 51%. Doubling the pretension load can reduce tunnel wall displacement up to about 20%. Increasing the support density can reduce the tunnel wall displacement by up to about 50%. The analysis shows that the proposed model outperforms Fahimifar's model, which deals with infinite rockbolts, in solving tunnel responses under grouted rockbolts, particularly in the case of large crosssectional tunnels excavated in poor geological conditions.