Masters Theses

Date of Award

8-1994

Degree Type

Thesis

Degree Name

Master of Science

Major

Civil Engineering

Major Professor

Matthew Mauldon

Committee Members

Edwin G. Burdette, Eric C. Drumm

Abstract

The study of problems related to the stability of wedge failure in rock cuts began approximately in the early nineteen sixties. At that time, only a few mathematical approaches in two dimensions and some graphical methods had been developed to understand the slope stability characteristics of a rock dissected by fractures and discontinuity planes, and subject to seepage and water pressures. The first studies concerning the three-dimensional stability analysis of rock slopes were made by Wittke (1965), John (1968), and Londe et al. (1969 and 1970). Years later, with the development of better computational systems, more complex analyses combining vector and graphical methods were made by Goodman (1980), Hoek and Bray (1981), Goodman and Shi (1985), Warburton (1993), and Priest (1993) among others. In the classic wedge stability problem the active resultant force R→ (the vector sum of weight, rock bolt forces, hydraulic forces, etc.), is resolved into components R→N and R→T, respectively, perpendicular to and parallel to the potential sliding direction along the line of intersection (Z-axis). R→N is then resolved onto each of the contact planes so as to satisfy the conditions for static equilibrium. Virtually all authors assume that shear forces vanish on the XY plane. A factor of safety against sliding can then be obtained directly, either by graphical techniques (stereographic projection) or by vector analysis.

This study is based on the development of an analytical model for sliding stability analysis of prismatic blocks in rock slopes. A prismatic block is a rock block bounded by a number n of contact planes, where the lines of intersection of these contact planes are all parallel. If the number of these contact planes (n) approaches infinity, the surface formed approaches a cylindrical shape, such as occurs in cylindrically-folded rocks. When the number of these contact planes is three or more, the distribution of normal forces on those planes is statically indeterminate. If the orientation of the active resultant is such that the block will attempt to move parallel to the line of intersection, the stability with respect to sliding is in addition indeterminate. To deal with these kinds of cases (n≥3), a mathematical approach is developed to determine of stability using the concept of minimum potential energy. This new model is then used to evaluate the factor of safety against sliding of prismatic blocks as a function of friction angles, block geometry, and loading conditions. The model developed is quite general and includes wedge sliding (n=2) and plane sliding (n=1) as special cases. To validate the model the factor of safety is calculated by the new energy-based method and the result compared with the solution for the limiting equilibrium approach, obtaining an answer that remained the same to 2 significant figures by both methods.

This analysis was used in sliding stability investigations of two road cuts with cylindrically-folded rocks located between Walland and Kinzel Springs, Blount County, Tennessee. The rock formations of these two rock cuts display conditions of instability such as rockslides, rockfalls, and dip slope failure that are barely controlled by different means such as retaining walls, steel mesh, or anchor bolts. The initial results using the new energy-based approach in these rock cuts show a significant reduction in the factor of safety of up to 14% when compared with the solution for the same type of folded rock taken as a wedge failure. Therefore, it was possible to determine that there is a reduction in the factor of safety compared with the typical wedge failure model when three or more planes of discontinuity are taken into account to form the prismatic rock.

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