Analytical Solution for Determining Plastic Zones around Shallow Twin-Circular Tunnels Based on the Schwarz Alternation Method

In order to investigate the plastic yielding mode of surrounding rock caused by the excavation of shallow twin tunnels, the displacement and additional surface force joint controlling the Schwarz alternation method and complex function method are adopted to solve the elastic stress function of surrounding rock of shallow twin circular tunnels through iterative cycles as an example. The expression of plastic stress components of surrounding rock is obtained based on Mohr-Coulomb failure criterion. The elastoplastic solution of the radius of the plastic zone is determined preferentially by using the stress continuity condition at the interface of the elastic-plastic zones around the shallow twin circular tunnels. The analytical solution for the distribution range of the plastic zones around the shallow twin circular tunnels is established, according to the interconversion relationship between polar coordinates and right-angle coordinates. The rationality and applicability of the analytical solution are verified by numerical simulation results and field measurement results of engineering application. The influence of the center spacing of the twin tunnels on the plastic zones around shallow twin circular tunnels are also analyzed. The results show that the analytical solution in this study can be used to solve the problem of predicting the distribution range of the plastic zones around shallow twin tunnels in actual engineering, and meets the requirement of 20% engineering accuracy, fits well with the numerical simulation results, and has a high calculation accuracy. The distribution range of the plastic zones around shallow twin circular tunnels are positively correlated with the center spacing s of the twin tunnels. Based on the distribution pattern of the plastic zone around shallow twin circular tunnels under the influence of this factor, when the plastic zone reaches the critical state of penetration, the reasonableness of the calculation results of the distribution range of the plastic zones is preliminarily judged. It provides theoretical guidance for similar tunnel engineering design calculation and deformation control of surrounding rock.