Undrained stability of unsupported rectangular excavations in non-homogeneous clays

Abstract Solutions for the undrained stability of unsupported excavations are important in practice as they can be used for assessing the safety of temporary excavations associated with various civil works. Even though the previous stability solutions of unsupported excavations namely infinitely long trenches and circular excavations are available in the literature, there is a lack of the stability solution of unsupported rectangular ones. In this paper, the lower bound solutions for the undrained stability of unsupported rectangular excavations in non-homogeneous clays are presented for the first time. A three-dimensional lower bound finite element limit analysis is developed in order to investigate the stability of this problem. The undrained shear strength of non-homogeneous clays are considered as a linearly increasing one with depth. The effects of aspect ratios of rectangular excavations, excavated depth ratios, and normalized strength gradients on the stability number of the problem and its associated failure mechanisms are examined parametrically. A new design equation of the problem is also firstly presented for practical use by practising engineers.