Comments on “Characteristic Curves for Deep Circular Tunnels in Poroplastic Rock” by A. Bobet

Abstract

Bobet (2009), hereafter referred to as ‘‘the Paper’’, revisits the classic problem of the ground response curve by providing analytical solutions for the short-term and long-term responses of a porous medium with an elasto-plastic behaviour. Following the example of a number of earlier research works on poro-plastic behaviour (Lembo-Fazio and Ribacchi 1984; Giraud 1993; Wang and Dusseault 1994, 1995, Giraud et al. 2002), the Paper considers the general case of a non-unit Biot constant a. Furthermore, the assumed constitutive equations include the case of a sudden reduction in strength immediately after failure (brittle behaviour). This assumption represents a special case of the more general softening or hardening behaviour that has already been analysed by Lembo-Fazio and Ribacchi (1984), Izquierdo and Romana (1987), Wang and Dusseault (1994, 1995), Giraud et al. (2002). Besides two major problems concerning long-term and short-term behaviour, which will be discussed in the following two sections in detail, the Paper contains some errors and inaccuracies which make it difficult to follow the mathematical derivations. For example, the initial effective stress r0 should appear on the right hand side of Eq. 6 and, more specifically, the term (-1 ? 2m) r0 is missing within the brackets; the Abstract characterises the material behaviour as ‘‘elastic-perfectly plastic with brittle failure’’ which is a contradiction in itself; the parameter / introduced after Eq. 14 for characterising the associated flow rule should be probably replaced by the residual friction angle /; the short-term condition is characterised, strictly speaking, by a constant fluid mass rather than by a constant fluid volume; Sect. 3 introduces one parameter and three equations (np, Eqs. 11, 16 and 17) which are absolutely unnecessary for the definition of the constitutive model in the present case.