A Generalized Analytical Model for Mechanical Responses of Rock during Multiple-Tunnel Excavation in Viscoelastic Semi-Infinite Ground

Abstract

The excavation of multiple tunnels at shallow depths has become increasingly common. The tunnel spacings, arrangements, buried depths, and excavation sequences significantly affect the ground responses. In addition, rock rheology makes the mechanical response of the ground a complex function of time. This study provides a generalized time-dependent analytical model by which the ground responses induced by the sequential excavation of multiple tunnels in a rheological rock can be addressed rapidly and precisely. The key factors, i.e., any viscoelastic characteristics of the surrounding rock, the real interactions between tunnels, and the tunnel sizes, arrangements, excavation times, and sequences, are fully taken into account. Using Schwartz's alternating method combined with complex variable theory, the elastic solutions of stress and displacement are first addressed for n tunnel excavations at shallow depths. Then, based on the elastic solutions and the corresponding extended principle for the viscoelastic problem, the general time-dependent analytical solutions in all the excavation stages are obtained for the ground assuming any viscoelastic model. The analytical solutions exhibit close agreement with the numerical results for models that are consistent, and they are qualitatively consistent with the numerical results of a real case. Then, parametric analyses are conducted for the sequential excavation of three tunnels to investigate the influences of tunnel arrangements, excavation sequences, and excavation times on displacements and stresses. The proposed analytical model can help to reveal the particular mechanical mechanisms of time-dependent ground responses due to sequential excavations combined with rock rheology. Moreover, an alternative approach is provided for the preliminary designs of future shallow tunnels in the rock.