This paper proposes a procedure, involving block theory analysis, to minimize the support necessary to stabilize removable blocks around underground excavations. The limit equilibrium procedure involves contouring excess sliding forces on a stereo net for different excavation orientations. Data from a tunnel at Theodore Roosevelt Dam is used to demonstrate the procedure. Results indicate that stability of removable blocks is highly dependent on the exeavation's orientation and the roughness of joints. Estimated support forces are conservatively based on the maximum key block. The advantage of this technique is that the geometry and vector equations are easy to solve allowing many eases to be examined. Its application is limited to blocky rock masses with continuous jointing in low stress conditions. The main finding from this work is that additional research is necessary for characterizing the roughness of joints.

1.1 Need for a simple approach to stability analysis Support costs in blocky ground can be a significant portion of the outlay to develop underground tunnels or chambers. Often expenses for re-supporting excavations are hidden in maintenance budgets. As designers, we must ask whether there are ways to change the design so as to m'mimize support costs without increasing total project expenditures.

Sometimes the engineer has flexibility in selecting the heading of the excavation. The optimal orientation is influenced by factors such as (a) the orientation of in situ stresses, (b) the orientation of geologic structures relative to the excavation, and (c) the shape of the excavation. Often we use simple "rules of thumb" based on our experience to make the initial selection of orientation. Detailed numerical models that consider variations of the above factors are typically used only to verify the design. What is needed is a simple tool to quickly examine the amount of influence that the above factors have on stability of the excavation.

The principles of block theory (Goodman & Shi, 1985) are ideal for examining the effect of the geologic structures in blocky ground conditions. This is because it relies on analytic relationships between the geometry and applied forces. Block theory uses a limit equilibrium method to compute the stability of removable blocks formed by the intersection of joint sets. The resultant force acting on the block and strength of joints govern the block's stability. Slight adjustments of the excavation's orientation can have influence on the removability of blocks, and joints on which sliding occur. Since the joint pattern is repeated along the length of the excavation, so are the unstable blocks.

The advantage of using block theory principles for repetitive calculations of block stability include:

§ the equations are quickly solved by computer,

§ results can be shown graphically,

§ the mechanics of block behavior are simple, and

§ stability is indicated by a single parameter.

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