According to the elastic-ideal plastic assumption and associated flow rule

the intermediate principal stress equation and the strength equation in plane strain condition are proposed on the basis of Lade-Duncan criterion. The shear strength parameter under plane strain condition is connected with that under conventional triaxial condition. Therefore

the equivalent internal friction angle and the cohesion in plane strain condition can be determined by a conventional triaxial test

which can effectively reflect the effect of intermediate principal stress on the increase of internal friction angle under plane strain condition. It is proved that the friction angle at the condition of strength failure of non-cohesive soil under plane strain is that of the maximum value of the equivalent friction angle

which is the mathematical meaning of the new strength equation. The mathematical meaning of the new strength equation is also shown by drawing the geometric relationship of three criteria on the π plane. The effectiveness of the strength equation is confirmed with experimental results of bearing capacity. In the calculation of plane strain using the standard method or the finite element method

the new strength equation can choose shear strength parameter more efficiently

considering the influence of the intermediate principal stress.