An equivalent perfectly plastic model for estimating squeezing deformations in tunnelling through strain-softening ground.

A salient feature of stress analysis of strain-softening materials is the loss of solution uniqueness, i.e., the existence of several solutions with localisation of plastic deformations in thin shear bands in addition to a response with plastic deformations smoothly distributed over an extended zone. Although the non-localised response is only one among several possible solutions and may underestimate deformations to some extent, it remains of practical and scientific interest because it provides an indication of deformation magnitude and constitutes the basis of numerous analytical and semi-analytical solutions available in the literature. This paper investigates the adequacy of using the widely adopted linearly elastic, perfectly plastic constitutive model in combination with an appropriate strength value (hereafter referred to as "equivalent strength") to approximate the non-localised response of strain-softening materials to deep tunnel excavation. The equivalent strength lies between the residual strength and the peak strength and is determined such that the perfectly plastic model reproduces the tunnel convergence predicted by the non-localised solution of the classical rotationally symmetric plane-strain problem of an unsupported circular tunnel in softening ground. The proposed approach is subsequently evaluated through numerical analyses of non-rotationally symmetric problems involving non-circular tunnel geometries and anisotropic in-situ stress fields. The results show that the equivalent perfectly plastic model generally provides a good approximation of the magnitude and distribution of tunnel convergence predicted by the non-localised strain-softening response across different geometries and stress conditions. The proposed method offers a computationally efficient and numerically robust means for preliminary tunnel design and for estimating the non-localised response of strain-softening ground using constitutive models and analysis tools widely employed in engineering practice.