The Structural Engineer's Corner

Eng. Onorio Francesco Salvatore

Hydrodynamic effects during earthquakes on dams and retaining walls: von Karman’s theory

Written By: Lexatus - Oct• 27•13

Von Karman for dams 2 - Onorio

In a previous post we went through the Westergaard’s theory for the analysis of gravity dams under seismic actions (“Hydrodynamic effects during earthquakes on dams and retaining wall: Westergaard’s theory“). In this post we’ll see the von Karman’s theory of the same subject.

Following the discussions on Westergaard’s theory, there were some proposals by different Authors on the same subject. Experts like von Karman, Bauman, Rowe, Pearce, Brahtz and Heilbron, Bakhmeteff, etc. agreed on the Westergaard’s solution.

Among the various proposals, the one from Theodor von Karman was judged particularly interesting as he introduced some simplifications on the theory and hence defining very easy and practical formulas to solve the problem.

Von Karman proposed to neglect the compressibility of the water, at least in the range of frequencies that happens during seismic motions. In this way, the volume of water interested by the problem is equal to one quadrant of ellipse and it moves in solidarity with the dam.

With the simplified equations, he defined the following practical formulas for the pressure at the bottom (p0), the overall thrust (S) and the moment on the dam (M0):

Von Karman for dams 1 - Onorio

The above formulas give values so similar to the ones from Westergaard that the difference is only around a couple of percentage units.

For any issues or questions, you can contact the author at:

onorio@strutturista.com

Eng. Onorio Francesco Salvatore

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