Upper bound of tunnel face stability using asymmetric yielding

Although significant advancement has been made over recent years with respect to three-dimensional upper bound calculations of tunnel facing, a considerable difference still exists between analytically and empirically based stability values. The current work suggests that the difference may well be the outcome of the traditional use of Tresca yield criterion for the upper bound calculations, which, by definition, does not distinguish among the shearing modes (compression, extension, plane strain). Consequently, this paper suggests and discusses a new yield function, which allows for asymmetric yielding. Such yielding is only beneficial in the case of three-dimensional and continuous velocity fields, and therefore a numerical procedure that generates relevant kinematically admissible fields for classical upper bound calculation is suggested. The procedure involves conversion from a load controlled boundary value problem to a velocity controlled problem at the limit state of collapse. The analysis results in significantly lower upper bound values than those presented earlier (for Tresca material), and the values are much closer to the stability curves of Kimura and Mair (1981), which are commonly used in design.