Complex variable solutions for twin tunnelling at great depth in viscoelastic geomaterial considering the three-dimensional effects of tunnel faces

Abstract

Analytic solutions on twin tunnelling at great depth in viscoelastic geomaterial considering three-dimensional effects of tunnel faces are presented using the complex variable methods. According to the time interval between twin tunnel faces, the proposed solutions can be divided into two cases: A) newly constructing twin tunnels; and B) newly constructing single tunnel influencing an existing one. The analytic solutions can also consider sequential excavations and the mutual influence between twin tunnels. The three-dimensional effects of twin tunnel faces are transformed into equivalent plane-strain problems by introducing dimensionless coefficients. By means of a presented general case, the analytic solutions are verified via comparisons of both stresses and displacements with the numerical solution, in which a good agreement between these two solutions is observed. Subsequently, a parametric investigation is performed to study the influence of several parameters concerning twin tunnel geometry and excavation on stresses and displacements, together with the difference between Cases A and B. On the basis of the results, the analytic solutions provide quantitative insights into the essence of the three-dimensional effects of twin tunnel faces and would have certain values on the preliminary design stage of twin tunnels.