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Formulas are derived for the changes of water pressures during an earthquake for the case of a straight dam with a vertical up-stream face. The vibrations in the earthquake are assumed horizontal in a direction perpendicular to the darn. A formula is obtained involving a series of sines (Equation (31)). This series, however, may be replaced with satisfactory approximation by a simpler formula (Equation (49)). The results are also expressed in the following manner: The pressures are the same as if a certain body of water were forced to move back and forth with the dam while the remainder of the reservoir is left inactive; Fig. 3 shows approximately the shape of this body of water. The influence of the dynamic action of the water is found to be neither excessively large nor negligible.
Harald Westergaard (Sun,) studied this question.