Abstract：It is proven that under assumption of the associated flow rule，the elasto-plastic matrix Dep is positive definite for hardening materials，positive semi-definite (the rank deficiency being one) for perfectly plastic materials and indefinite for softening materials，respectively. Based on the fact that Dep is singular for perfectly plastic materials，it is stated that if a slope arrives at the state of limit equilibrium，a layer of elements must go through the slope from the bottom of the slope to the top，each element in the layer being in plastic state. Hence，it is rational that the contour plots of the equivalent plastic strain or the plastic work are used to judge if slopes reach the limit equilibrium state. The paper makes a qualitative analysis for the abnormal phenomenon in which the plastic zones are usually overestimated in analyzing slope problems by FEM. The skill for overcoming such an abnormal phenomenon is proposed as well.
