Dynamic Analysis of Concrete Gravity Dams due to Nonuniform Translation and Rotational Components of Earthquake Considering Reservoir interaction

Document Type : Research Article


1 Phd candidate, Department of Civil Engineering, Noshirvani University of technology, Babol, Iran

2 Associate professor, Department of Civil Engineering, Noshirvani University of technology, Babol, Iran


The main purpose of this paper is presentation of proper finite element formulation for dynamic analysis of concrete gravity dams under nonuniform translational and rotational components of earthquake considering dam- reservoir interaction. Time delay of travelling waves is considered to generate the nonuniform ground motion and the rocking component of earthquake has been obtained using the corresponding translational components based on classical elasticity and elastic wave propagation theories in term of wave frequency functions. The translation and rocking components of ground motion are applied to support points of dam-reservoir bottom and analyses have done using finite element method base on Lagrangian-Lagrangian approach. Results show that the rocking component and time delay of travelling translation waves can be effect considerably on linear dynamic response of concrete gravity dams in some cases.


[1] احمدی، محمد تقی؛ نوائی نیا، بهرام، تحلیل دینامیکی سد و مخزن به روش لاگرانژی، مجله بین المللیمهندسی)دانشگاه علم و . صنعت(. جلد 6، شماره 1،1374
[2] علی جمشیدی، داوود؛ نوائی نیا، بهرام؛ واثقی امیری، جواد؛ تحلیل دینامیکی سدهای بتنی وزنی با مدلسازی مخزن به روش های ، لاگرانژی و اویلری؛ نشریه دانشکده فنی دانشگاه تهران، شماره 6.1386 ،709- جلد 41 ، صفحه 724
[3] معظمی گودرزی، خسرو؛ لرزه شناسی، انتشارات وزارت علوم و. آموزش عالی، 1351
[4] نوائی نیا، بهرام؛ تحلیل هیدرودینامیک سد و مخزن به روش لاگرانژی، پایان نامه کارشناسی ارشد، دانشگاه صنعتی
. امیرکبیر، 1369
[5] کلانی ساروکلایی، لیلا؛ نوائی نیا، بهرام؛ واثقی امیری، جواد؛ توکلی،حمیدرضا؛ اثر مولفه دورانی زلزله بر پاسخ دینامیکی سدهای بتنی وزنی با احتساب اندرکنش سد و مخزن، مجله علمی و پژوهشی . دانشگاه صنعتی شریف، 1390
[6] Chopra, A. K.; “Earthquake Behavior of Reservoir-Dam Systems”, Journal of the Engineering Mechanics
Division, ASCE, Vol. 94, EM6, PP. 1475-1500, 1968.
[7] Bayraktar, A.; Dumanogluand, A. A.; Calayir, Y.;“Asynchronous dynamic analysis of dam-reservoirfoundation
system by the Lagrangian approach”,Journal of Computer and Structure, Vol. 58, No. 5, PP.925-935,1996.
[8] Kojic, S.; Trifunac, M. D.; “Earthquake response of arch dams to nonuniform canyon motion”, University
of Southern California, Department of Civil Engineering, Report No. CE 88-03, 1988.
[9] Mirzabozorg, H.; Varmazyari, M.; Ghaemian,M.; “Dam- reservoir- mass foundation system and traveling wave along reservoir bottom”, Soil Dynamics and Earthquake Engineering, Vol. 30, No.8, PP. 746-756, 2009.
[10] Alves, S. W.; “Nonlinear analysis of Pacoima dam with spatially nonuniform ground motion”, Ph.D thesis, California Institute of Technology, 2005.
[11] Bilici, Y.; et al.; “Stochastic dynamic response of dam– reservoir– foundation systems to spatially varying earthquake ground motions”, Soil Dynamics and Earthquake Engineering, Vol. 29, PP. 444-458,2009.
[12] Newmark, N. M.; “Torsion in Symmetrical Buildings”, Proceeding of the 4th World Conference
on Earthquake Engineering, Santiago, Chile; A3, PP.19-23, 1969.
[13] Ghafory Ashtiani, M.; Singh, M. P.; “Structural response for six correlated earthquake components”
Journal 0f Earthquake Engineering and Structural Dynamics, Vol. 14, No. 1, PP. 103-119, 1986.
[14] Huang, B. S.; “Ground rotational motions of the 1999 Chi Chi, Taiwan earthquake as inferred from
dense array observations”, Geophysical Research Letters, Vol. 30, No. 6, PP. 1307-1310, 2003.
[15] Ghayamghamian, M. R.; Nouri, G. R.; “On the characteristics of ground motion rotational components using Chiba dense array data”,Earthquake Engineering and Structural Dynamics,Vol. 36, No. 10, PP. 1407-1442, 2007.
[16] Spudich, P.; et al. “Transient stresses at Parkfield,California, produced by the M 7.4 Landers earthquake
of June 28, 1992: Observations from the UPSAR dense seismograph array”, Journal of geophysical research, Vol. 100, No. B1, PP. 675-690, 1995.
[17] Ghayamghamian, M. R.; et al.; “A comparison among different methods in the evaluation of torsional
ground motion”, Journal of Iran geophysics, Vol. 4,No. 3, PP.2-44, 2010.
[18] Trifunac, M.D.; “A note on rotational components of earthquake motions on ground surface for incident
body waves”, Soil Dynamic and Earthquake Engineering, Vol. 1, No. 1, PP. 11-19, 1982.
[19] Lee, V.W.; Trifunac, M.D.; “Rocking strong earthquake accelerations”, Soil Dynamic and Earthquake Engineering, Vol. 6, No. 2, PP. 75-89,1987.
[20] Lee, V. W.; Liang, L.; “Rotational components of strong motion earthquakes”, The 14th world conference on earthquake engineering. Beijing,China, 2008.
[21] Li, H. N.; Sun, L. Y.; Wang, S. Y.; “Improved approach for obtaining rotational components of seismic
motion” Nuclear Engineering and Design. Vol. 232,No. 2, PP. 131-137, 2004.
[22] Nigbor, R. L.; “Six- degree- of- freedom ground motion measurement”, Bulletin of the Seismological
Society of America, Vol. 84, No. 5, PP. 1665-1669,1994.
[23] Suryanto, W.; et al.; “First comparison of arraydirect ring laser measurements”, Bulletin of the
Seismological Society of America, Vol. 96, No. 6, PP.2059-2071, 2006.
[24] Liu, C. C.; et al.; “Observation rotational and translational ground motion at the HGSD station in
Taiwan from 2007 to 2008”, Bulletin of Seismological Society of America, Vol. 99, No. 2B, PP. 1228-1236,
[25] Kalab, Z.; Knejzlik, J.; “Examples of rotational component records of mining induced seismic events
from the Karvina region”, ACTA Geodynamicia and Geomaterialia, Vol. 9, No. 2, PP. 173- 178, 2012.
[26] Kalab, Z.; Knejzlik, J.; Lednicka, M.; “Observation of rotational component in digital data of mining
induced seismic events” Gornictwo, Vol. 7, No. 1, PP.59- 74, 2012.
[27] Calayir, Y.; Dumanoglu, A.; Bayraktar, A.; “Earthquake analysis of gravity dam-reservoir systems using the
Eulerian and Lagrangian approaches”, Journal of Computers and Structures, Vol. 59, No. 5, PP. 877-890, 1996.
[28] Hamdi, M. A.; Ousset, Y.; Verchery, G.; “A displacement method for the analysis of vibrations of coupled fluid -structure systems” International Journal for Numerical Methods in Engineering, Vol.13, No. 1, PP. 139-150, 1978.
[29] Wilson, E. L.; Khalvati, M.; “Finite elements for the dynamic analysis of fluid-solid systems” International
Journal for Numerical Methods in Engineering, Vol. 19, No. 11, PP. 1657-1668, 1983.
[30] Ahmadi, M. T.; Ozaka, Y.; “A simple method for the full- scale 3- D dynamic analysis of arch dams” 9th
World Conference on Earthquake Engineering Japan,Tokyo, 1988.
[31] Navayi Neya, B.; “Mathematical modeling of concrete gravity dams under earthquake loading considering
construction joints”, Ph.D thesis, Moscow Power Engineering Institute, 1998.
[32] Sadd, M. H.; “Elasticity, Theory, Applications and Numerics”, Academic Press, Elsevier, 2009.
[33] Chopra, A. K., “Dynamic of structures, Theory and application to earthquake engineering”, 3rd Ed.,
Prentice all of India, 2008.
[34] Hinton, E.; et al.; “A note on mass lumping and related processes in the finite element”, Earthquake
Engineering and Structural Dynamic, Vol.4, No. 3,PP. 245-249, 1976.
[35] Merriam, J. L.; Kraige, L. G.; “Engineering Mechanics-Dynamic”, 6th Ed., John Wiley& Sons,2008.
[36] Chopra, A. K.; “Earthquake Response Analysis of concrete Gravity Dams”, ASCE, Vol. 96, No. EM4,