Theoretical Characterization of Brittle Zone Development in Arbitrarily Arranged Unequal-Circular Double-Holes Tunnels Considering Out-of-plane Principal Stress

This study investigates the mechanism of out-of-plane principal stress in brittle zone development around asymmetrically arranged double-holes tunnels with unequal diameters. Based on the two-dimensional and three-dimensional Hoek-Brown yield criteria, The radius increment method and numerical iteration were employed to establish the stress model. Parameter relationships were derived based on the conformal mapping extension and the stress continuity characteristics on elastic-brittle interface. Combined with the 2D interpolation and differential evolution methods, a semi-analytical approach was finally established for determining the brittle-plastic zones of two unequal circular tunnels with arbitrary arrangements under the biaxial in-situ stress field. The accuracy of the theoretical solution was validated through comparing with the numerical simulation and the verification of the stress continuity conditions on the elastic-brittle interfaces. Numerical verification showed 95.2% accuracy in plastic zone prediction. Based on the developed solutions, further analysis was conducted on the effects of tunnel arrangement and initial out-of-plane in-situ stress q on the brittle expansion of double-holes tunnels. It is found that the tunnel spacing was found to transform brittle-plastic zone shapes from oval to teardrop patterns, and the out-of-plane stress reduced brittle-plastic zones by approximately 20%. The proposed theoretical model can provide important guidance for the fast prediction of the loosening zones of elastic-brittle-plastic rock surrounding double-holes tunnels and the reinforcement zones for bolts and grouting reinforcement.