Abstract: Upper bound solution of limit analysis with rigid blocks is widely applied to geotechnical engineering stability analysis. However, rigid blocks failure mechanism and complicated geometric relation are needed to assume and analyze for different geotechnical subjects. In order to banish these restrictions, a finite element upper bound solution with rigid translatory moving elements based on nonlinear programming is presented. And the key problem of determine initial value for nonlinear programming model is also solved. This method firstly discretizes computation domain into rigid elements, then defines the element velocities and nodes coordinate as decision variables, and uses upper bound theory to establish nonlinear programming model to acquire a solution. Corresponding finite element upper bound program is compiled to verify stabilities of slope and shallow tunnel to illustrate that velocity discontinuities of elements adjust automatically into best directions to acquire failure mechanism with distinct characteristics and upper bound solution with high accuracy. The method is expected to be applied widely to stability analysis for slopes, tunnels and other geotechnical subjects.

Key words: limit analysis, upper bound solution, rigid moving element, finite element method, nonlinear programming