Estimating Parameters from a Single Test for the Three-Dimensional Failure Criterion for Frictional Materials

The three-dimensional failure criterion for soils was expanded to include concrete and used for rocks. The failure criterion is expressed in terms of the first and the third invariants of the stress tensor and it requires two parameters for characterization of the strength of soils and three parameters for concrete and rocks. For soils, one parameter is used to describe the opening angle of the failure surface, i.e., similar to the friction angle, and the second parameter is employed to describe the curvature of the failure surface in meridian planes that contain the hydrostatic axis. The third parameter, used for concrete and rocks, is slightly higher than the uniaxial tensile strength and is used to capture the cohesion and tensile strength. Typically, the results of three triaxial compression tests and the tensile strength from a Brazilian test or from an estimate are required for the determination of these three parameters. Careful inspection of parameters, determined from numerous high-quality tests on soils, concrete, and rocks presented in the literature, revealed that two of the parameters relate to each other. Therefore, it is possible to obtain the two parameters from the results of a single triaxial compression test. The relation between the two parameters is demonstrated, and it is shown how the results from a single test are used to determine the parameters to describe the three-dimensional failure surface for soils, concrete, and rocks.