Analytical solutions to ground settlement induced by ground loss and construction loadings during curved shield tunneling

This paper focuses on the ground settlement induced by the construction of a curved shield tunnel.Ground loss and construction loadings are the two factors causing ground settlement,and two corresponding analytical models were developed.First,the ground settlement due to ground loss was analyzed based on 3D image theory.The"integrative gap at shield tail"(IGST)and overcutting gap of a curved tunnel were considered.Second,the ground settlement due to construction loadings was analyzed by modifying Mindlin's solutions.The additional thrust,frictional force,and grouting pressure were considered.Subsequently,a case study and a parameter analysis were conducted.Finally,the obtained solutions were compared with a classical analytical solution,numerical simulations,and monitored results.The proposed model could effectively predict the ground settlement in-duced during curved shield tunneling.

Ground reaction curves for circular excavations in non-homogeneous,axisymmetric strain-softening rock masses

Fast methods to solve the unloading problem of a cylindrical cavity or tunnel excavated in elasto-perfectly plastic, elasto-brittle or strain-softening materials under a hydrostatic stress feld can be derived based on the self-similarity of the solution. As a consequence, they only apply when the rock mass is homogeneous and so exclude many cases of practical interest. We describe a robust and fast numerical technique that solves the tunnel unloading problem and estimates the ground reaction curve for a cylindrical cavity excavated in a rock mass with properties depending on the radial coordinate, where the solution is no longer self-similar. The solution is based on a continuation-like approach(associated with the unloading and with the incremental formulation of the elasto-plastic behavior), fnite element spatial discretization and a combination of explicit sub-stepping schemes and implicit techniques to integrate the constitutive law, so as to tackle the diffculties associated with both strong strain-softening and elasto-brittle behaviors. The developed algorithm is used for two practical ground reaction curve computation applications. The frst application refers to a tunnel surrounded by an aureole of material damaged by blasting and the second to a tunnel surrounded by a ring-like zone of reinforced(rock-bolted) material.