Abstract: The upper bound limit analysis has broad application prospect as it has rigorous theoretical basis and clear physical meaning, and could give the safety factor as well as the critical velocity field at the same time. But it has slow convergence speed because of circumscribed polygon approximation (which is widely used) to Mohr-Coulomb yield circle. In view of this, we alleviated the requirement that all the points must strictly meet the limit properties, adopted the optimal square polygon approximation to the yield circle, and finally obtained the systematic calculation model of upper bound finite element based on optimal square polygon approximation. Numerical example shows that the method not only inherits the advantage circumscribed polygon have which approximates analytic solution from the upper, but also gets a precise result by less number of polygon edges, and also greatly improves the convergence speed.

Key words: limit analysis, upper bound finite element method, Mohr-Coulomb yield circle, optimal square approximation, analytical solution, slope stability