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A gravity dam may fail in following ways:
(i) By overturning
(ii) By crushing or compression
(iii) By development of tension
(iv) By shear failure or sliding
(i) By overturning
(ii) By crushing or compression
A dam may fail due to failure of materials, i.e., the compression stress produced may exceed allowable stress and dam material may get crushed.
$P=\text{Direct stress + Bendng stress}=\cfrac{\sum Y}{B}+\cfrac{M}{I}Y=\cfrac{\sum Y}{B}\pm \cfrac{M \cdot e}{B^{2}/6}Y$
$\cfrac{P_{max}}{P_{min}}= \cfrac{\sum Y}{B}\left [ 1 \pm \cfrac{6e}{B}\right]$
If $P_{min}$ comes out to be negative, it means tension shall be produced at the appropriate end.