Predicting 2D ground movements around tunnels in undrained clay

A new analytical method is introduced for calculating\uddisplacements due to tunnelling. This is conceived within\udthe framework of the bound theorems of plasticity, but\udallowing for soil strain-hardening. The ground displacements\uddue to tunnelling are idealised by a simple displacement\udmechanism of distributed shearing in the plane of\udthe tunnel cross-section. The tunnel support pressure\udcorresponding to a certain volume loss is calculated from\udenergy balances of the work dissipated in distributed\udshear, the potential energy loss of soil flowing into the\udtunnel, and the work done by this soil against the tunnel\udsupport pressure. The calculations are carried out in\udsteps of small volume loss accompanying small reduction\udin support pressure, after each of which the tunnel\udgeometry is updated. In this way, each reduced tunnel\udsupport pressure is related to a complete ground displacement\udfield. A simplified closed-form solution is also\udprovided for the prediction of maximum surface ground\udsettlement for the particular case of deep tunnelling. This\udclosed-form solution is obtained by integrating the vertical\udequilibrium equation on the tunnel centreline from\udthe tunnel crown up to the ground surface. These two\udanalytical solutions have been validated against five previously\udpublished centrifuge tests