In contrast with the level ground

which has a single symmetrical failure mode

foundation soil near the slope presents a variety of failure modes under different working conditions. Based on the upper bound finite element method

a nonlinear upper programming model is developed

in which a feasible arc interior point algorithm is used for solution. The calculation results are converted into the corresponding velocity field and the energy dissipation

and compared with the numerical results in the literature. It is shown that the upper bound finite element method can be used to effectively analyze the slope failure mode and obtain a reasonable solution. By converting the bearing capacity of slope into Terzaghi partial coefficient

and based on the variations of Nc、N? 、Nq

it is found that the variations of Nc and Nq are consistent with the existing monotonous change rule. As for N?

because the volume of the failure body changes due to the change of failure mode

a non-monotonous change rule of N? is observed. By defining the safe distance as the distance a0 /B completely unaffected by the slope

part of the calculation chart is developed

providing a useful reference for slope foundation design.