Abstract: Upper bound adaptive finite element method based on the six-node triangular high-order element has the advantages of high calculation accuracy and the ability to directly obtain structural failure mechanism from the refined mesh of the computational domain. However, if the linearization method of yield criterion is still used to establish the upper-bound finite element model, the calculation efficiency will be lower. Therefore, based on the previous research, a second-order cone programming method with higher computational efficiency is introduced to improve the computational efficiency of the upper bound finite element method. Upper bound adaptive finite element method based on second-order cone programming and the higher-order element is established. The analyses of slope stability and bearing capacity of strip foundation show that the proposed method improves the calculation efficiency of the upper bound finite element method, and the refined mesh of the computational domain can directly obtain the refine failure mechanism. It is also shown that the calculation time of the proposed method is significantly shorter than that of the linearization method of yield criterion under the same accuracy. Some examples are given in this paper to show the accuracy and effectiveness of the proposed method. This study can provide some references for theoretical research and engineering practice.

Key words: upper bound finite element method, second-order cone programming, higher-order triangular element, mesh adaptation, failure mechanism