A new analytical method is introduced for calculating displacements due to tunnelling. This is conceived within the framework of the bound theorems of plasticity, but allowing for soil strain-hardening. The ground displacements due to tunnelling are idealised by a simple displacement mechanism of distributed shearing in the plane of the tunnel cross-section. The tunnel support pressure corresponding to a certain volume loss is calculated from energy balances of the work dissipated in distributed shear, the potential energy loss of soil flowing into the tunnel, and the work done by this soil against the tunnel support pressure. The calculations are carried out in steps of small volume loss accompanying small reduction in support pressure, after each of which the tunnel geometry is updated. In this way, each reduced tunnel support pressure is related to a complete ground displacement field. A simplified closed-form solution is also provided for the prediction of maximum surface ground settlement for the particular case of deep tunnelling. This closed-form solution is obtained by integrating the vertical equilibrium equation on the tunnel centreline from the tunnel crown up to the ground surface. These two analytical solutions have been validated against five previously published centrifuge tests.
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