Abstract: In order to understand the strength failure under complex stresses, and apply the strength theory to more materials, such as rocks and concrete, by the twin strength theory, the three-parameter twin strength criterion based on the hydrostatic pressure and the normal stress on the surface of main shear stress has been proposed, and the mathematical formula has been deduced. Then the comparative analyses between the theories under different stresses with the existing experimental data have been carried out. The results show that the ratios and under different ultimate stresses vary with different strength criteria respectively and the strength under condition of is less than that the strength under condition of . In the biaxial compressive stress , the biaxial compressive strength is larger than the uniaxial one . In triaxial compression stress, given fixed and smaller, increases gradually with the increase of , and given relatively larger, decreases gradually with the increase of . The theoretical predictions can reflect some experimental data of the granite, red sandstone, soft sandstone, concrete and other materials.

Key words: strength criterion, ultimate stress ratio, complex stress state, multiaxial strength, rock, concrete