In engineering practice, rock ledge stability analysis is often performed as a two-dimensional failure analysis, where the single sliding plane is defined by the problem geometry and not the actual joints geometry. This was the case with the Yard Trench Lead in Sunnyside Yard, an element of the East Side Access Project in NYC. A probabilistic wedge stability analysis, including surcharge load and rock bolt reinforcement, was presented and discussed as a design alternative. The transition from 2D to 3D and from a deterministic to a stochastic approach, with the use of the geological joint orientation data, was shown to provide a more realistic view of the initial support design and to have the potential of leading to reductions in the initial support costs.
Reinforcement and support requirements in blocky rock mass have commonly been assessed by means of a rigid blocks limit equilibrium stability analysis. This approach has been confirmed by site observations and proven in engineering practice when empirical, rock mass quality classification-based methods are unable to project structural failure. The relevant solutions have been presented, inter alia, by Wittke (1965), Priest (1980), Lucas (1980) and Bray & Brown (1976). The problem of arbitrary polyhedral block stability analysis was solved by Warburton (1981), Goodman and Shi (1985), Lin and Fairhurst (1988) and others. The method put forward by Goodman and Shi (1985) was used in this study for computations. It is popular and refers not only to a particular block, but to blocky rock mass in general, as well. While most of the methods consider the sliding and falling modes of failure, the problem of rotational failure has also been addressed (Mauldon 1995a,Wittke 1990).
As a result of the limited information on discontinuities and their highly stochastic nature, uncertainty constitutes the central problem of analyses and their interpretation in jointed, blocky rock mass. A solution to this problem is brought about by probabilistic methods, either analytical or simulation (for example, McMahon 1971, Priest & Brown 1983, Park et al. 2005, Hatzor 1993, Hoerger & Young 1990, Mauldon 1995b, Jakubowski & Tajdus 1995, Jakubowski 2011). The statistical description of a joint network is crucial for stochastic joint geometry modeling and probabilistic stability analysis in a blocky rock mass (Hudson & Priest 1983, Mauldon et al. 2001, Zhang & Einstein 2000, Kulatilake 2001, Shanley & Mahtab 1976, Chiles 1987, Dershowitz & Einstein 1988).