Kinematic constraints may greatly affect the stability of a jointed rock mass. While traditional limit equilibrium methods typically do not adequately incorporate kinematics, the Discontinuous Deformation Analysis (DDA) method actually models the kinematics of motion along discontinuities. Analysis of the two block sliding problem shows the importance of accounting for kinematic effects. In addition, DDA analyses of slopes with hinged failure surfaces show that the initiation and mode of failure are highly sensitive to the location and spacing of discontinuities within the rock mass.
Kinematics is well recognized as an important element in the analysis of discontinuous rock masses (Goodman, 1995). In this paper we present the results of kinematic analyses using Discontinuous Deformation Analysis. DDA is a numerical method developed to model the behavior of discontinuous media, such as jointed rock masses (Shi, 1988 and 1993). The rock mass is modeled as a system of deformable blocks that can move and interact with one another. One of the strengths of this method is the fact that it models the kinematics of motion along discontinuities. This is accomplished through a complex contact detection algorithm which prevents the blocks from penetrating and facilitates calculation of the contact forces and friction between the blocks. The influence of kinematics on several aspects of rock slope stability problems is addressed in this paper. The specific class of problems we are concerned with is that in which the failure surface consists of two intersecting planes, a "hinged" failure surface. This type of slope geometry was chosen for several reasons: kinematic solutions exist for single-plane failure surfaces and the logical progression is to consider two intersecting planes, and more importantly, a non-kinematic solution exists for two intersecting planes which can be used for comparison and validation of the DDA method. Our results show that kinematics is indeed a major factor in stability analyses, and that the initiation of failure and failure mode are very sensitive to the location and spacing of the discontinuities.
The importance of modeling kinematics of motion is illustrated through analysis of the "two block sliding problem." An analytical solution for initiation of sliding, without kinematic constraints, is presented by Goodman (1989), as follows. An upper "active" block is separated by a vertical discontinuity from a lower "passive" block. Figure Ia shows the configuration of the problem and the symbols used. Wi and Wi are the weights of the upper and lower blocks, áú and 0.2 are the upper and lower slope angles (30° and 5° in this case), and öé, öé, and ö3 are the friction angles on the upper and lower slopes and the vertical discontinuity, respectively. However, if the kinematics is taken into account, the active block immediately transfers its load to the lower surface and the driving force changes accordingly. Thus, a solution which accounts for kinematics will not give a result identical to that of the limit equilibrium analysis.