About the critical height of a vertical cut

The iconic problem of the stability analysis of a vertical cut is revisited after Drucker’s celebrated contribution, in order to assess the sensitivity of the analysis to the soil tensile resistance. Within the framework of the exterior approach of the theory of yield design, the same virtual mechanisms as introduced by Drucker are reconsidered and thoroughly implemented. It is observed that, whatever the value of the friction angle, the drastic drop of the non-dimensional stability factor observed by Drucker when the constituent soil does not sustain tension remains confined within the immediate vicinity i.e., a few percent, of zero tensile resistance. Despite the fact that this conclusion cannot be considered as a final one since it is only based upon a full implementation of Drucker’s virtual collapse mechanisms, we believe it may bring some relief as to the reliability of classical analyses that do not take any tension cutoff into account, as a response to Drucker’s warning about “the consequences of assuming soil unable to take tension”.