Static instability criterion and safety factor of tunnels based on loading/unloading response ratio

To obtain the method for static instability criterion of tunnels, the loading/unloading response ratio (LURR) theory is introduced into the analysis method. The nonlinear characteristics and the LURR variation laws of unlined circular tunnels under symmetrical loads are analyzed through the analytical method, and the results have proved their relevance. The research approach of LURR method is put forward based on the different loading characteristics of construction and operation tunnels. The critical conditions and the LURR variation laws of tunnels with and without linings are analyzed respectively through the finite element method. The results show that the nonlinear characteristics based on the LURR theory of tunnel deformation calculated by the analytical solution and the finite element solution are similar. The LURR variation laws of tunnel deformation are different in each loading and stability stages of tunnel system, the LURR variation rate in the weak area of the tunnel will be abnormal before its instability, and the abnormal variation trend is the precursor criterion of the instability of the tunnel system. Based on the determination of the ultimate bearing state of the tunnel system by the LURR method, the safety factor of the tunnel system is obtained by using the loading ratio. The static instability method based on the LURR theory of tunnels is proposed.