The Role of Interpretation in the Observed Variability of Direct Shear Tests

Abstract

Understanding the behavior of discontinuities under shear stress is paramount for designing rock structures, as these discontinuities largely dictate stability. Discontinuities, which include fractures, are commonly assessed at a laboratory scale using direct shear tests. In this test, a rock core that is divided by the fracture of interest is placed in a shear holder, and a relatively constant normal force perpendicular to the fracture plane, is applied. Subsequently, an increasing force parallel to the fracture is applied to cause the displacement of one of the parts of the sample with respect to the other. Throughout the test, the machine records shear and normal forces and displacements.Various procedures exist for conducting direct shear tests, but this study focuses on multi-stage direct shear tests with repositioning. In this procedure, the sample is repositioned to its original position after reaching a specific horizontal displacement, and the normal force is increased. This process generates a series of traces or curves in the shear force vs. shear displacement space. To convert shear forces to shear stresses, the forces are divided by the contact area between the two surfaces of the sample. Two parameters are calculated based on the trace data described above (ASTM, 2016): the peak shear stress, which is associated with the maximum shear stress value along a sheared surface attained during a test, and the residual shear stress, which is associated with the point at which the shear stress remains essentially constant with increasing shear displacement. Once a shear stress value has been chosen from each of the traces that compound the test, these are matched to the corresponding normal stresses and depicted in a shear stress vs. normal stress plane. Then, applying any constitutive model or criterion to define a failure envelope and estimate peak and residual strengths is possible. In this study, the Mohr-Coulomb failure criterion is utilized, and the strength parameters are reported in terms of friction angle and cohesion. Identifying the peak shear stress and residual shear stress can be challenging, as these points may not be clearly defined or evident in specific direct shear test results. In such cases, the selection of points is left to the analyst's judgment. This is due to the lack of detailed guidance in current standards and suggested methods. Quantifying and understanding variability in engineering design is crucial for managing risk, ensuring safety and reliability, and optimizing designs for various conditions. The study further analyzed the impact of reported friction angle variations on the factor of safety of a mining bench through a basic modeling exercise using RocPlane of the Rocscience suite. This thesis contributes to quantifying uncertainty in an industry that often overlooks it. The coefficients of variation provided for different approaches can be used to quantify uncertainty in design, with potential applications in other rock mechanics problems.