Analytical Solution of Tunnel Surrounding Rock for Stress and Displacement Based on Lade–Duncan Criterion

The deformation and failure of tunnel surrounding rock is the result of tunnel excavation disturbance and rock stress release. When the local stress of surrounding rock exceeds the elastic limit of rock mass, the plastic analysis of surrounding rock must be carried out to judge the stability of tunnel. In this study, the Lade–Duncan yield criterion is used to calculate the analytic solutions for the surrounding rock in a tunnel, and the radius and displacement of the plastic zone are deduced using an equilibrium equation. The plastic zone radius and displacement based on Lade–Duncan criterion and Mohr–Coulomb criterion were compared by using single-factor analysis method under the different internal friction angles, in situ stresses, and support resistances. The results show that the solutions of the radius and displacement of plastic zone calculated by the Lade–Duncan criterion are close to those of Mohr–Coulomb criterion under the high internal friction angle and support resistance or low in situ rock stress; however, the radius and displacement of the plastic zone calculated by the Lade–Duncan criterion are larger under normal circumstances, and the Lade–Duncan criterion is more applicable to the stability analysis of the surrounding rock in a tunnel.

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