Discussion on Superposition Empirical Formula of Ultimate Bearing Capacity Based on the Upper Bound Limit Analysis Theory

Abstract

Traditional Terzaghi foundation bearing capacity superposition empirical formula dose not consider the nonlinear effect of the soil unit weight on the ultimate bearing capacity and its failure mode, which is only a kind of approximate method. Therefore, error occurs when unit weight is taken into account. The relatively complete two dimensional conversion velocity field based on slip-line field and the basic method and principle of corresponding failure mechanism were introduced in this paper. Compared with the existing upper bound failure mechanism, this failure mechanism adds a one-dimensional optimization freedom degree, which can reflect the real failure mode, and thus obtain better upper bound solutions. The results indicate that the traditional superposition empirical formula stress on safty, and the error caused by traditional superposition method will increase with the increase of the internal friction angle; the failure range derived from non-superposition method is between the failure range determined by using superposition method to solve the analysis coefficient Nγ and Nc (or Nq), which reflects the influence of soil unit weight on the failure mechanism.