Dynamic Analysis of Gravity Dams by Employing Efficient Fluid Hyper-Element

Document Type : Research Article



Fluid hyper-element is usually utilized to model semi-infinite region in dynamic analysis of concrete gravity dams. This part of water domain is assumed to have constant depth that extends to infinity in the upstream direction. The accurate dynamic analysis of concrete gravity dam is obtained by employing two dimensional semi-infinite fluid element.
The usual method for calculating the impedance matrix of fluid hyper-element is dependent on the solution of a complex eigen-value problem for each frequency. In the present study, an efficient technique is proposed which simplifies this procedure significantly, and results in great computational time savings. The accuracy of this method is tested under various conditions thoroughly and concluded that efficient technique is accurate under all practical conditions.


[1]Chopra, A. K.; Chakrabarti, P. and Gupta, S.; including hydrodynamic and foundation interaction effects”, Report No EERC-80/01, University of California, Berkeley, January, 1980.
[2]Fenves, G.; Chopra, A.K.; “Effect of reservoir bottom absorption and dam-water-foundation rock interaction on frequency response functions for concrete gravity dams”, Earthquake Engineering and Structural Dynamics, vol.13,.p.p. 13-31, 1985.__
[3]Lotfi, V.; “Frequency domain analysis of concrete gravity dams including hydrodynamic effects”, Dam Engineering, vol. XII, Issue 1, p.p. 33-53,2002._
[4]Lotfi, V.; “Significance of rigorous fluid- foundation interaction in dynamic analysis of concrete gravity dams”, Structural Engineering and Mechanics, vol. 21, No. 2, p.p. 137-150, July.2005)
[5]Sommerfeld, A.; “Partial differential equations in  physics”, Academic Press, NY. 1949._
[6]Hall, J.F.; Chopra, A.K..; “Two dimensional dynamic analysis of concrete gravity and embankment dams including hydrodynamic
effects”, Earthquake Engineering and Structural Dynamics, vol. 10, p.p. 305-332, 1982._
[7]Tan, H.; Chopra, A.K.; “Earthquake Analysis of Arch Dams Including Dam-Water-Foundation Rock Interaction”, Earthquake Engineering and Structural Dynamics, vol.24, p.p. 1453-1474, 1995._
[8]Fok, K.L.; Chopra, A.; “Earthquake Analysis and response of concrete arch dams”, Report No EERC-85/07, University of California, Berkeley,US, July, 1985.__
[9]Tajirian, F.F.; “Impedance matrices and interpolation_ techniques 3-D_ interaction analysis by the flexible volume method”, Ph.D.
Dissertation, Department of_ Civil Engineering,University of California, Berkeley_ .CA, Sept.,1981._
[10]Lotfi, V.; “An efficient three dimensional fluid  hyper-element for dynamic analysis of concrete arch dam”, Structural Engineering and_Mechanics,vol.24, No.6, p.p.683-698, 2006.
[11]Fok, K.L.; Chopra, A.; “Earthquake Analysis of arch dams including dam- water interaction reservoir boundary absorption and foundation flexibility”, Earthquake_Engineering and Structural Dynamics, vol. 14, p.p.155-184, 1986._
[12]Lotfi, V.; “Direct frequency domain analysis of concrete arch dams based on FE-(FE-HE)-BE technique”, Journal of Computers and Concrete,vol. 1, ,Issue 3, p.p. 285-302, 2004._
[13]Lotfi, V.; Rosset, J.M. and J. Tassoulas;, “A Technique for the analysis of the response of dams to earthquakes”, Earthquake Engineering and Structural Dynamics, vol. 15, p.p. 463-490, 1987.