Limit load and failure mechanisms of a vertical Hoek-Brown rock slope

Abstract

The problem considered in this short note is the limit load determination of a vertical rock slope. The classical limit theorem is employed with the use of adaptive finite elements and nonlinear programming to determine upper and lower bound limit loads of a Hoek-Brown vertical rock slope. The objective function of the mathematical programming problem is such as to optimize a boundary load, which is known as the limit load, resembling the ultimate bearing capacity of a strip footing. While focusing on the vertical slope, parametric studies are carried out for several dimensionless ratios such as the dimensionless footing distance ratio, the dimensionless height ratio, and the dimensionless rock strength ratio. A comprehensive set of design charts is presented, and failure envelopes shown with the results explained in terms of three identified failure mechanisms, i.e. the face, the toe, and the Prandtl-type failures. These novel results can be used with great confidence in design practice, in particularly noting that the current industry-based design procedures for the presented problem are rarely found.

Keywords

• Bearing capacity
• Rock slope
• Vertical slope
• Finite element limit analysis
• Hoek-Brown yield criterion