Usually

stress state of the soil is replaced by plane strain state when slope stability is analyzed

which leads to conservative results adopting triaxial tests. Based on fully considering the physical meanings and mechanisms of the intermediate principal stress

this paper proposes a modified relationship of intermediate principal stress in plane strain state when soil approaches ultimate strength making. Mises strength criterion identical to the circle internally tangent to M-C strength criterion

and we further derive the ratio of maximum principal stress to minor principal stress

which is a constant associated with internal frictional angle under plane strain state. The ratio has been proved by tests

which demonstrates the modified relationship of intermediate principal stress is reasonable. Based on the ratio and the modified relationship

the stress path under plane strain state is derived. Combined with Lade-Duncan strength criterion

the strength formula transformation between plane strain state and triaxial state is established. Then

comparisons between internal frictional angle derived from plane strain experiment and strength formula transformation show that the errors between the two frictional angle are only about 2%

which largely decrease the errors caused by triaxial test. Two different strength parameters

one of which is derived from triaxial test and another of which is derived from strength formula transformation

are used to evaluate the stability of a homogeneous slope. The results show that

when the internal friction angle in triaxial test state is between 10°-20°

the difference of safety factor based on the two different strength parameters is small; if it beyond 20°

the safety factor in plane strain state is about 19% larger than that under triaxial state. However

the results are only effective in this study

a further study is needed. Furthermore

the critical slip surface depth becomes shallower and shape becomes steeper with larger strength of soil under plane strain state.