US Army Corps of Engineers - Gravity Dam Design
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Figure C-4. Free body diagram of the i
th
wedge
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Figure C-5. Derivation of the general equation (Sheet 1 of 3)
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Figure C-5. (Sheet 2 of 3)
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Figure C-5. (Sheet 3 of 3)
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Figure C-6. Free body diagram of the i
th
wedge with anchor
The free body diagram above varies from that shown in
Figure C-4 in that the above free body diagram contains
an anchor force “A
i
” oriented at an angle, β
i
with the
vertical. The equilibrium equations and governing wedge
equation on the following pages will include this anchor
force.
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Figure C-7. Derivation of the general equation for a wedge containing an anchor force (Sheet 1 of 3)
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Figure C-7. Derivation of the general equation for a wedge containing an anchor force (Sheet 2 of 3)
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Figure C-7. Derivation of the general equation for a wedge containing an anchor force (Sheet 3 of 3)
Note: Solutions of factors of safety and forces on free
bodies determined by the above equations, or by computer
analyses should be verified by an independent method of
analysis. Vector diagrams may be used to check the
results graphically. In multi-wedge analyses, consider-
ation should be given to the stress-strain compatibility of
different rock materials on the failure plane.
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Appendix D
Example Problems - Sliding Analysis for
Single and Multiple Wedge Systems
D-1. Examples of typical static loading conditions for
single and multiple wedge systems are presented in this
appendix.
D-2. These examples are provided to clearly demon-
strate the procedure for applying the general wedge equa-
tion to the sliding analysis of single and multiple wedge
systems. The variations of uplift pressure, orientation of
failure planes, etc., used in the examples were only
selected to simplify the calculations and are not intended
to represent the only conditions to be considered during
the design of a hydraulic structure.
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D-2