A three-dimensional rotational failure mechanism for earth slope is extended from toe failure to include face failure and base failure. An efficient optimisation method is simultaneously employed to find the least upper bounds to the critical height in order to avoid missing the global minimum. Compared with the results from analysis based on toe failure alone, best estimates of the critical height and the critical failure mechanism are obtained. The calculated results are given in the form of graphs and tables for a wide range of parameters. The critical failure surfaces are also investigated to assess the influences of geometrical constraint and soil property on failure mechanism.

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Many constitutive models are available nowadays to predict soil-structure interaction problems. It is sometimes not very easier for engineers to select a suitable soil model to carry out their design analyses in terms of complexity versus accuracy. This paper describes the application of three constitutive models to back-analyse a well-instrumented centrifuge model test, in which the effect of basement excavation on an existing tunnel was simulated. These three models include a linear elastic-perfectly plastic model with the Mohr-Coulomb failure criterion (called MC model), a nonlinear elastic Duncan-Chang model (DC) and a hypoplastic model (HP), the last of which can capture path-dependent and strain-dependent soil stiffness even at small strains. By comparing with measured data from the centrifuge model test, it is found that the HP model yielded the best predictions of tunnel heave among the three models. Not only the gradient but also the magnitude of tunnel heave is predicted well by this HP model. This can be explained by the fact that the HP model can capture the path-dependent and strain-dependent soil stiffness even at small strains but not the MC and DC models. However, all three models underestimated the change in tunnel diameter and the maximum tensile bending strain in the transverse direction.