Upper bound analysis for stability of a circular tunnel in heterogeneous clay

The stability of a shallow circular tunnel in undrained clay layer is examined in the framework of the limit analysis by means of the limit analysis upper bound method. Rigorous upper bounds of the face collapse pressure and failure envelopes are obtained using the rigid multi-block translational collapse mechanism. The multi-block failure mechanism has significant advantages with respect to the existing limit analysis: it takes into account the effect of cover-to-diameter ratio, gravity parameter and heterogeneous parameter. And the present results of the collapse pressure significantly improve the best available solution given by the solutions of other limit analysis. It is concluded that the collapse pressure increases linearly with the increase of gravity parameter, but decreases linearly with the increase of the heterogeneous parameter. Also the configuration of failure envelopes will vary as the cover-to-diameter ratio, gravity parameter and heterogeneous parameter differ. On the basis of those results, a simplified mechanism is obtained and a simplified solution is derived from the upper bound theory of plasticity. Finally the upper bound multi-block solution for the stability of TBM excavation in clays and its simplified solution are demonstrated by comparing with the centrifuge results.