An new elastic–plastic analytical solution of circular tunnel under non-axisymmetric conditions

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.