Abstract: Most of the strength criteria for soils should satisfy the Coulomb’s law on the failure surface, and the effective stress strengh indices of isotropic soil are unique under different drainage conditions. The mathematical and physical meanings of triaxial total stress strength indices are investigated based on the relationship between the excess pore pressure at failure in Coulomb's law under undrained conditions and that in consolidated undrained (CU) triaxial tests. The results show that, in view of the linear envelope of the Coulomb's law under drained and undrained conditions, the pore pressure coefficient D_f is proved to be constant, which is related to the normal stress state on the failure surface. The existence of linear total stress failure envelop of CU is based on the certain relationship among Skempton’s pore pressure coefficients A_f , D_f , cohesion and deviator stress at failure. The corresponding expression is also obtained. Furthermore through the strength parameters of CU tests, the secant strength indices, φ_R and c_R, are obtained. It provides more reasonable and operational method for engineering problems with known sliding surfaces. However if the total stress tangent strength indices of CU are used, the strength will be overvalued by more than 10%, which will cause great security risk.