Li Guofeng, Li Ning, Bai Yue, Yang Min
Institute of Geotechnical Engineering, Xi'an University of Technology, Xi'an, 710048, China.
Top International Engineering Corporation, Xi'an, 710054, China.
Sci Rep. 2022 Mar 14;12(1):4367. doi: 10.1038/s41598-022-08353-3.
The surrounding rock is in the initial stress state before the tunnel excavation, and it undergoes the stress redistribution to reach the secondary stress state after the tunnel excavation. The surrounding rock is not only the main load source but also is an important part of the load bearing structure. Once the stress of some zone in the surrounding rock exceeds the strength of the rock mass, the part surrounding rock will enter into a state of plasticity or failure. Analytical solution is the most powerful mean to analyze this kind of underground cavern engineering problems. However, the existing solutions can not directly or simultaneously obtain the secondary stress field and excavation disturbance displacement field that we are concerned about. The implicit approximate solution cannot be degenerated to an accurate axisymmetric expression for the most existing non-axisymmetric elastic-plastic solutions. Therefore, this paper derives the elastic solution of a circular tunnel under the condition of the non-axisymmetric external load with the radial and shear inner loads. On this basis, the new elastic-plastic solution and the plastic zone radius equation of the circular tunnel under the conditions of the non-axisymmetric external load with radial inner load are derived. It can directly obtain the secondary stress field and excavation disturbance displacement field, and can degenerate to an accurate axisymmetric expression. The distribution characteristics of the analytical solution are in good agreement with the numerical test results, indicating that the new solution can provide a relatively accurate theoretical basis for the analysis and research of tunnel engineering.
隧道开挖前围岩处于初始应力状态，开挖后围岩经历应力重分布而达到二次应力状态。围岩既是主要的荷载源，又是承载结构的重要组成部分。一旦围岩中某区域的应力超过岩体强度，该部分围岩将进入塑性或破坏状态。解析解是分析这类地下洞室工程问题最有力的手段。然而，现有解无法直接或同时得到我们所关心的二次应力场和开挖扰动位移场。对于大多数现有的非轴对称弹塑性解，隐式近似解不能退化为精确的轴对称表达式。因此，本文推导了在非轴对称外荷载与径向及剪切内荷载作用下圆形隧道的弹性解。在此基础上，推导了非轴对称外荷载与径向内荷载作用下圆形隧道的新弹塑性解及塑性区半径方程。它能直接得到二次应力场和开挖扰动位移场，且能退化为精确的轴对称表达式。解析解的分布特征与数值试验结果吻合良好，表明新解能为隧道工程的分析研究提供较为准确的理论依据。
