For the undrained shear failure of saturated clay, designing methods based on the strength parameters of c_cu and φ_cu obtained by the triaxial consolidated-undrained shear test (CU test) were developed in domestic engineering field. In contrast, the φ=0 method with the total strength S_u is commonly used internationally. Based on the mechanical intrinsity of Coulomb's law of friction and the Mohr circle analysis method in solid mechanics, it was pointed out that the strength envelope and the corresponding strength parameters (c_cu, φ_cu or the transformed parameters c_cq, φ_cq) obtained by the triaxial CU test do not have the intrinsic nature of Coulomb's law of friction and it is prefer to be regarded as the dependency of total strength S_u on the effective consolidation stress ${{\sigma }^{\prime }}_{\text{c}}$. The advantages of the application of the φ=0 method in practice and the principle of determination of total strength S_u were discussed, and the misleading of the mechanical principle of this method in domestic researchers were clarified. Based on several analysis examples of slope stability, earth pressure and foundation bearing capacity, the problems caused by mistaking the c_cu and φ_cu as the Coulomb's strength parameters in practice were discussed in detail.