This paper presents an extended three-dimensional discontinuous deformation analysis (3–D DDA) method for stability analyses of jointed rock tunnels. In the natural environment, rock masses are cut by finite joints into numerous polyhedral blocks with arbitrary shapes, including convex, concave, those with cavities and/or holes, and probably their unions. In stability analysis of rock-masses, especially for jointed rock tunnels, one of the primary bottlenecks is discontinuous computation of the contacts between arbitrarily shaped polyhedral blocks. The original contact detection approach proposed by the first author, entrance plane method (EPM), is extended to address this problem by integrating a novel method termed local convex decomposition (LCD). Rather than globally intersecting non-convex polyhedrons into a combination of convex polyhedrons, LCD only decomposes locally the non-convex vertex angles of polyhedrons into a set of convex vertex angles, which is much easier to implement. The decomposed vertices of these non-convex polyhedrons are separately detected for possible entrances in a geometrical way but then the whole polyhedron is treated as one in the mechanical calculation. The developed code is fully integrated in the original 3-D DDA program and then applied to a complex tunnel scenario. The whole failure process is exhibited dynamically, involving large displacement and rotation of multiple interaction blocks. Overall, the extended 3-D DDA could be potentially used to find the failure mechanism of jointed rock tunnels, such as to optimize the tunnel stabilization or protection design.
For structure design and disaster prevention, stability analyses are routinely performed to identify potentially unstable regions of tunnels, especially for those going through jointed rock masses. Practical rock tunnel stability problems are complicated because of complex topological geometry and mechanical behavior primarily resulting from joints. Numerical modeling techniques facilitate the approximate solutions, which would have never been possible by using the conventional techniques. However, the numerical methods for rock mechanics analysis are generally underdeveloped compared to its demand in practical rock tunnel engineering. Main barriers are as follows.
In the natural environment, there exist a great number of various joints, each with finite extensions. Consequently, these finite joints, which are assumed to be planar, cut the rock mass into numerous polyhedral blocks with arbitrary shapes, including convex, concave, those with cavities and/or holes (see Fig. 1), and probably their unions. For example, some nonconvex blocks usually exist in the tunnel surface, and the other potentially unstable regions formed by pre-existing joint planes (Shi and Goodman, 1989).
In most rock tunnel engineering cases, the behavior of rock masses is dominated by the geometrical configurations and mechanical properties of joints (Goodman, 1989). The numerical analysis accuracy depends mostly on properly treating interactions among joints, which can be referred to as a contact problem. Contact treatment is extremely difficult, especially in 3-D situations where the contacts between arbitrarily shaped polyhedral blocks can be highly non-linear, strongly non-smooth, and thus extremely indeterminable.
The rock tunnel failure is a complex process which involves sliding along and opening/closure of joints and large displacements, deformations and rotations of discrete blocks. The underlying continuum assumption within conventional continuum-based methods often leads to difficult parameters to define and oversimplified geometry to be realistic, making them almost impossible to realize the whole failure process (Jing, 2003).
