Question

The Hoek-Brown failure envelope is typically the segment of which one of the following?

• A. Straight line
• B. Ellipse
• C. Parabola
• D. Hyperbola

Answer 1

The Correct Option is C

The Hoek-Brown failure criterion is a widely used empirical criterion in geotechnical engineering, particularly in the study of rock mechanics. It is used to describe the failure of rocks under various conditions of stress. The failure envelope, which represents the limit of strength for a given material under different stress states, is typically parabolic in nature. The mathematical form of the Hoek-Brown criterion involves the relationship between the major and minor principal stresses, and the strength of the material, leading to a curve that is parabolic when plotted on a graph. This criterion allows engineers to predict when a rock mass will fail under shear and normal stress conditions.
In contrast to other failure criteria such as the Coulomb-Mohr criterion, which has a linear failure envelope, or more complex criteria that involve other shapes, the Hoek-Brown failure envelope is specifically known for being parabolic. Hence, the correct answer is (C) Parabola.
Key Concept: The Hoek-Brown failure envelope typically follows a parabolic shape, which is used to model the failure conditions of rock masses under different stress scenarios in geotechnical engineering. This failure envelope is particularly useful in the design of underground structures, tunnels, and foundations in rock.