Flow through rock surface spillways, due to severe flood events, has the potential to erode spillway and cause a substantial headcut migration. That, in turn, may result in catastrophic releases from the reservoir. An effort towards developing a rational analysis methodology is presented. Specifically, a continuum-discrete combined analysis combined with the key block theory formed the basis of the approach. The first step of the approach is to numerically generate various realizations of a jointed system from the local joint and bedding plane characteristics. The second step is to derive an intrinsic vulnerability measure to damages based upon the problem topology. This is carried out by applying the removability criteria from the key block theory. The third step is mechanical analysis. For the objectives of assessing spillway stability, it is deemed important to incorporate block fracture into the analysis. The implications of the proposed approach are explored.


Water flows over unlined rock spillways, due to severe flood events, have the potential to erode spillway and cause a substantial headcut migration. That, in turn, may result in catastrophic releases from the reservoir [1]. At the present time, the stability analysis of spillways is semi-empirical in nature [2,3]: engineers would estimate an erodibility index and check if its value lies about an empirical critical threshold value that depends on energy dissipation rate of flowing water. But the physical basis of some of the contributing factors is not clear and it is not known how their ambiguity may affect the result of an assessment. Moreover, the resolution of the empirical method is not high, and that it is difficult to employ it for design. A desirable alternative is to have a methodology rooted in mechanical analysis. This is the objectives of the study. As the problem involved is fairly complex, this study represents only a first step toward developing a rational alternative based upon the computational mechanics. Since rocks are often delimited into blocks by discontinuities such as joints, it follows that a discrete analysis, not a continuum analysis, should be the basis of such efforts. The study employs a discrete analysis that falls within the general framework of the partition of unity method [4] that has roots in the manifold method [5,6]. Additionally, the key block concept [7] was included to assess the implications of topology on stability. One complicating factor may arise because problem topology can change as a consequence of being subjected to loads. Removal of blocks, and fracture or fragmentation are ways that topology can be dramatically altered. From this perspective, the incorporation of fracture is therefore essential. In the following, the various components of the approach are discussed. An example using simplified loading conditions to illustrate the benefits of the approach is presented at the end.


Mechanical modeling of discrete and continuum objects often follow different routes, and a coupling of these approaches often represents a mixture of different solution strategies. For instance, Cundall [8] combines the Lagrangian flow formulation [9] with the distinct element in creating the first coupled discrete-continuum code UDEC; Lemos [10] developed a hybrid distinct element-boundary element model; whereas Munjiza, Owen and Bicanic [11] have mixed distinct elements with finite elements. Shi [5] presented a manifold method that is unique in that it provides a possibility for developing a single framework.

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