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A survey is presented of some recent developments of the numerical techniques for back analysis in the field of geomechanics, with particular reference to tunnelling problems. In the spirit of Terzaghi's observational design method, these techniques are seen as practical tools for interpreting the available field measurements, in order to reduce the uncertainties that in many instances affect the parameters governing the solution of complex geomechanics problems. Both deterministic and probabilistic viewpoints are considered and some significant applications to practical problems are illustrated

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SUMMARYThe pressure acting on tunnel support structures generally increases with lapse in time. The pressure increase may be caused by not only the time-dependent mechanical properties of the underground medium, but also by the progression of the tunnel face. In order to clarify these two effects, threedimensional analysis is required. In this study, however, a method which takes into account the three-dimensional effects of the tunnel face progression in two-dimensional plane strain analyses is proposed by introducing the 'equivalent initial stress'. The proposed method can be easily applied to time-dependent analyses of the behaviour of tunnel support structures installed in a visco-elastic medium.The tunnels considered here are circular in shape, being driven in homogeneous isotropic linear visco-elastic media having hydrostatic initial stresses.In the first part of this paper, detailed discussions of the proposed equivalent initial stress are given. The second deals with the mathematical formulations for obtaining closed-form solutions for the pressure acting on tunnel support structures. In the third, numerical results and discussions are given, and special attention is paid to the effects of both the time-dependent mechanical properties of the material and the tunnel face progression. Finally, the theoretical results obtained here are utilized for interpretation of field measurements.