Water Pressures on Dams during Earthquakes

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.