Evaluation of Eulerian and Lagrangian Method in Analysis of Concrete Gravity Dam Including Dam Water Foundation Interaction

Authors: L. Khan mohammadi, J. Vaseghi Amiri, B. Navayi neya , M. Davoodi

Abstract:

Because of the reservoir effect, dynamic analysis of concrete dams is more involved than other common structures. This problem is mostly sourced by the differences between reservoir water, dam body and foundation material behaviors. To account for the reservoir effect in dynamic analysis of concrete gravity dams, two methods are generally employed. Eulerian method in reservoir modeling gives rise to a set of coupled equations, whereas in Lagrangian method, the same equations for dam and foundation structure are used. The Purpose of this paper is to evaluate and study possible advantages and disadvantages of both methods. Specifically, application of the above methods in the analysis of dam-foundationreservoir systems is leveraged to calculate the hydrodynamic pressure on dam faces. Within the frame work of dam- foundationreservoir systems, dam displacement under earthquake for various dimensions and characteristics are also studied. The results of both Lagrangian and Eulerian methods in effects of loading frequency, boundary condition and foundation elasticity modulus are quantitatively evaluated and compared. Our analyses show that each method has individual advantages and disadvantages. As such, in any particular case, one of the two methods may prove more suitable as presented in the results section of this study.

Keywords: Lagrangian method, Eulerian method, Earthquake, Concrete gravity dam

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1061719

References:

[1] Westergaard H.M ,"Water pressure on Dams during Earthquakes", ASCE , 1931
[2] tsubo , S.,"Dynamic Water Pressure on Dam due to Irregular Earthquakes " Memoirs Faculty of Engineering , Kyushu University , Fukuoka , Japan , Vol. 18 ,No. 4 , 1959
[3] Brahtz, H. A., and Heilborn, C. H., discussion of "Water Pressure on Dams during Earthquakes," by H. M. Westergaard, Transactions, ASCE, Vol. 98, 1933
[4] Hoskins, L. M., and Jacobsen, L. S., Water Pressure in a Tank Caused by Simulated Earthquake," Bulletin, Seismological Society of America, Vol. 24, No. Jan.,1934
[5] Werner, P. W., and Sundquist, K. J., "On Hydrodynamic Earthquike Effects," Transactions, American Geophysical Union, Vol. 30, No. 5, Oct., 1949
[6] Bustamante J. I., Rosenblueth, E., Herrera, I., and Flores, A., "Presion hidrodynamica en presas y depositos, " Boletin Sociedad Mexicana de Ingenieria Sismica. Vol. 1, No. 2, Oct., 1963
[7] Zangar , C. N., "Hydrodynamic Pressures on Dams due to Horizontal Earthquake Effects," Engineering Monograph No. 11, U. S. Bureau of Reclamation, May , 1959
[8] Kotsubo, S., "External Forces on Arch Dams during Earthquakes," Memories Faculty of Engineering, Kyushu Univercity , Fukuoka, Japan, Vol. 20,No. 4, 1961
[9] Chopra A. K. ,Chakrabarti P., "Hydrodynamic Pressures And Response of Gravity Dams to Vertical Earthquake Component ", E.E. & D.D. Vol. 1, 1973
[10] Chopra A.K., Chakrabarti P., Gupta S. "Earthquake Response of Concrete Gravity Dams Including Hydrodynamic And Foundation Interaction Effects", Report No. UCB / EERC - 80/01 January 1980.
[11] Navaye nia B, "Hydrodynamic analysis of Gravity Dam-reservoir system with lagrangian method ", M.S thesis, mir Kabir university of technology,1990.
[12] Wilson E. L., Khalvati M., "Finite Elements for Dynamic Analysis of Fluid-Solid Systems", Int., J. Num. Meth. Eng. Vol. 19, 1983.
[13] Alijamshidi D, Navaye nia B, Vaseghi J, "Dynamic analysis of Concrete Gravity Dams with Eulerian and Lagrangian method",1997.
[14] Ahmadi M T, Gharebaghi B, "Earthquake analysis of Concrete Gravity Dams Including Hydrodynamic Interaction Effects with Eulerian method", International Institute Of Earthquake Engineering and Seimology,1983.