True Triaxial Data Research Articles

A conceptual three-dimensional frictional model to predict the effect of the intermediate principal stress based on the Mohr-Coulomb and Hoek-Brown failure criteria

The intermediate effective principal stress has a considerable influence on rock strength as shown by true-triaxial data on intact rock. Therefore, a failure criterion that incorporates all three principal stresses may provide an improved prediction of failure than one that considers only the major and minor effective principal stresses. This study introduces a generalisation method, which converts two-dimensional failure criteria (i.e., Mohr-Coulomb and Hoek-Brown failure criteria) to three-dimensional failure criteria, for the prediction of this true-triaxial data. This method is based on a physical mechanism, and it assumes that the potential failure surface of a material has roughness, which provides additional frictional resistance when the intermediate effective principal stress is greater than the minor effective principal stress. This roughness is introduced theoretically by assuming a repeating diamond-shaped element over the failure surface. These roughness elements have the same dip as predicted by the Mohr-Coulomb and Hoek-Brown failure criteria but are offset by the dip direction angle which is assumed similar to that calculated traditionally from the major effective principal stress direction to the failure surface. With this roughness, it is shown that the major effective principal stress at failure can be predicted using an explicit solution that uses the intermediate and minor effective principal stresses and the Mohr-Coulomb or Hoek-Brown parameters as inputs. This generalisation predicts the same strength as the Mohr-Coulomb or Hoek-Brown failure criteria under conventional triaxial loading conditions, when the intermediate and minor effective principal stresses are equal. Under general stress conditions, this generalisation produces results that are aligned closely with the true-triaxial data as well as other previous theoretical predictions. This method importantly gives a possible physical mechanism for the strengthening influence of the intermediate effective principal stress. This may lead to a more accurate prediction of the rock strength under general stress conditions.

Failure Criteria for Isotropic Rocks Using a Smooth Approximation of Modified Mohr–Coulomb Failure Function

It is reported that strength of rocks is a function of three-dimensional (3D) stress state as observed from the large sets of experimental results under the true-triaxial condition. Triaxial compression test data in general is readily available for rocks, but in practice true-triaxial facilities are seldom used. This creates a requirement for 3D failure criterion, which can be used to predict the true-triaxial strength using simple triaxial compression test data. We have proposed three criteria by altering the deviatoric function of modified Mohr–Coulomb criterion (Singh et al. in Int J Rock Mech Min Sci 48(4):546–555, 2011). The proposed criteria represent the behaviour of rock from lower to very high confining pressures. The criteria have unique yield surfaces. The yield surface changes its shape with the change in the mean stress. It is observed beyond certain value of the mean stress; the yield surfaces converge to von-Mises yield surface which means the shape of the yield surface is independent of pressure beyond the certain value of mean normal stress. The criteria require three parameters that can be easily calculated from the triaxial compression test results. The proposed criteria also satisfy the Drucker stability postulate, hence could be adopted as a plastic potential function. For the assessment of the criteria, true-triaxial data from twelve rocks are considered. Results of the criteria are compared with the modified Mohr–Coulomb criteria both 2D and 3D proposed by Singh et al. (Int J Rock Mech Min Sci 48(4):546–555, 2011). Performance of the new failure criteria for the considered rocks are observed to be better than the modified Mohr–Coulomb criteria (2D and 3D).

Implicit Algorithm for Modeling Unsaturated Soil Response in Three-Invariant Stress Space

An implicit integration algorithm has been refined to predict the stress–strain–strength response of unsaturated soil under suction-controlled, multiaxial stress paths that are not achievable in a conventional cylindrical cell. The algorithm supports numerical analyses in a deviatoric plane by using a mixed control constitutive driver, in conjunction with a generalized Cam-Clay model that also incorporates the influence of a third stress invariant, or Lode-angle θ , within a constant-suction scheme. True triaxial data from a previously accomplished series of suction-controlled triaxial compression, triaxial extension, and simple shear tests on 10-cm cubical specimens of silty sand, were used for the tuning and validation of the refined algorithm. The elliptical Willam–Warnke surface was adopted for simulation of unsaturated soil response in three-invariant stress space. Reasonably satisfactory agreement was observed between experimental and predicted deviatoric stress versus principal strain response for ...