Stability Analysis and the Stabilisation of Flexural Toppling Failure |
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| Authors: | Mehdi Amini Abbas Majdi Ömer Aydan |
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| Institution: | (1) School of Mining Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran;(2) School of Marine Civil Engineering, Tokai University, Shimizu, Japan; |
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| Abstract: | Flexural toppling is a mode of failure that may occur in a wide range of layered rock strata in both rock slopes and large
underground excavations. Whenever rock mass is composed of a set of parallel discontinuities dipping steeply against the excavated
face plane, the rock mass will have the potential of flexural toppling failure as well. In such cases, the rock mass behaves
like inclined superimposed cantilever beams that bend under their own weight while transferring the load to the underlying
strata. If the bending stress exceeds the rock column’s tensile strength, flexural toppling failure will be initiated. Since
the rock columns are “statically indeterminate,” thus, their factors of safety may not be determined solely by equations of
equilibrium. The paper describes an analytical model with a sequence of inclined superimposed cantilever rock columns with
a potential of flexural topping failure. The model is based on the principle of compatibility equations and leads to a new
method by which the magnitudes and points of application of intercolumn forces are determined. On the basis of the proposed
model, a safety factor for each rock column can be computed independently. Hence, every rock column will have a unique factor
of safety. The least factor of safety that exists in any rock column is selected as the rock mass representative safety factor
based on which simple equations are proposed for a conservative rock mass stability analysis and design. As a result, some
new relations are established in order to design the length, cross-sectional area and pattern of fully grouted rock bolts
for the stabilisation of such rock mass. Finally, the newly proposed equations are compared with the results of existing experimental
flexural toppling failure models (base friction and centrifuge tests) for further verification. |
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