Parameters of the surrounding rock.

In order to explore the distribution pattern of the plastic zone around a shallow tunnel, the elastoplastic analytical solutions for a shallow-buried circular tunnel in a semi-infinite medium were proposed in this study to calculate the plastic zone radius and stresses around a shallow-buried circular tunnel. Based on the Hoek-Brown yield criterion, the solutions were derived by using the bipolar coordinate system method under the influence of the geotechnical gravity. The rationality of the proposed calculation method was verified by comparing with the existing calculation methods and numerical simulation methods, and the proposed method was further used to analyze the influence of the mechanical parameters of the rock and soil mass and uniform ground load on the plastic zone radius and stresses around a shallow-buried circular tunnel. The results show that the theoretical calculation results obtained by the proposed method fit better with the numerical simulation results, and the maximum and average errors between the two are 1.63% and 1.35%, respectively, so the calculation accuracy of the proposed method is proven to be high. The quality and strength of the geotechnical medium and the uniform ground load are both the main influencing factors of the plastic zone radius and stresses around a shallow-buried circular tunnel, and the plastic zone radius is negatively correlated with the quality and strength of the geotechnical medium, and the stresses are also negatively correlated with the quality and strength of the geotechnical medium, but are positively correlated with the uniform ground load. Therefore, the mechanical parameters of the rock and soil mass and uniform ground load should be controlled strictly to ensure the safety of shallow tunnels under construction.

为探究浅埋隧道周边塑性区的分布规律，本研究提出半无限介质中浅埋圆形隧道的弹塑性解析解，用于计算浅埋圆形隧道周边的塑性区半径与应力分布。本研究基于霍克-布朗屈服准则(Hoek-Brown yield criterion)，考虑岩土自重的影响，采用双极坐标系法推导得到该解析解。通过与现有计算方法及数值模拟方法对比，验证了所提计算方法的合理性；并进一步利用该方法分析了岩土体力学参数与均布地面荷载对浅埋圆形隧道周边塑性区半径及应力的影响。研究结果表明，本方法得到的理论计算结果与数值模拟结果拟合度更高，二者的最大误差与平均误差分别为1.63%与1.35%，证明了本方法具备较高的计算精度。岩土介质的质量与强度、均布地面荷载均为影响浅埋圆形隧道周边塑性区半径及应力的主要因素；塑性区半径与岩土介质的质量、强度呈负相关，应力亦与岩土介质的质量、强度呈负相关，但与均布地面荷载呈正相关。因此，需严格管控岩土体力学参数与均布地面荷载，以保障在建浅埋隧道的施工安全。