Analytical solutions for interaction between existing and new tunnels parallel excavated in rheological rock mass

Owing to the interaction between the existing and new excavation tunnels in rheological rock, the distributions of stresses and displacements around twin tunnels are time-dependent and significantly different from thoes of single tunnel. For deeply buried twin circular tunnels sequentially excavated in viscoelastic rock, the complex variable function method, Laplace transform and superposition principle for viscoelastic cases are used in the derivation of excavation-induced displacements and stresses around tunnels. The solution is validated by FEM method through an example. Good agreement is demonstrated between the analytical and numerical solutions. Based on the analytical solutions, the analysis of induced displacements and total stresses distribution around the existing and new excavation tunnels, the variation of induced displacements versus time and the distance between tunnels are carried out. The solutions presented herein, which can be applied more conveniently in preliminary design and parametric investigation than numerical method, can be used to analyze the sequential excavation of twin tunnels in viscoelastic rock mass.