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 convergence-confinement 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 14-m-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 cross-sectional tunnels excavated in poor geological conditions.

本研究研究了注浆锚杆与隧道围岩的相互作用过程，建立了收敛约束型活动注浆锚杆加固深部隧道的分析模型。岩体被假定为完全弹性塑性，遵守 Hoek-Brown 准则。引入纵向位移剖面来表示隧道掌子面的空间效应，在此基础上确定沿隧道轴线的虚拟压力。由于锚杆的安装延迟和长度有限，当锚杆锚固在不同的区域时，岩体在锚杆安装时可能表现出弹性或塑性。根据锚固区和塑性区之间的相对大小，提出了可能遇到的六种不同的演化路径。隧道位移，塑性半径和应力被确定。通过与从数值模拟和现有模型中获得的结果进行比较来验证分析结果。参数分析表明，在直径 14 米的隧道中，将螺栓长度从 2 米加倍到 4 米，可将隧道壁位移减少 20%。在靠近隧道掌子面（小于 1 m）处安装岩栓可以将隧道壁位移减少 51%。将预紧载荷加倍可将隧道壁位移减少约 20%。增加支护密度可使隧道壁位移减少约 50%。分析表明，所提出的模型在求解注浆岩栓下隧道响应方面优于 Fahimifar 模型，该模型处理无限岩栓，特别是在地质条件较差的大断面隧道的情况下。