Dynamic analysis of concrete gravity dam-reservoir systems by Wavenumber approach for the general reservoir base condition

Document Type : Article

Authors

Department of Civil and Environmental Engineering, Amirkabir University of Technology, Tehran, Iran

Abstract

Different approaches are utilized for dynamic analysis of concrete gravity dam-reservoir systems. The rigorous approach for solving this problem employs a two-dimensional semi-infinite fluid element (i.e., hyper-element). Recently, a technique was proposed for dynamic analysis of dam-reservoir systems in the context of pure finite element programming which was referred to as the Wavenumber approach. Of course, certain limitations were imposed on the reservoir base condition in the initial form of this technique to simplify the problem. However, this is presently discussed for the general reservoir base condition, contrary to the previous study which was merely limited to the full reflective reservoir base case. In this technique, the wavenumber condition is imposed on the truncation boundary or the upstream face of the near-field water domain. The method is initially described. Subsequently, the response of an idealized triangular dam-reservoir system is obtained by this approach, and the results are compared against the exact response. Based on this investigation, it is concluded that this approach can be envisaged as a great substitute for the rigorous type of analysis under the general reservoir base condition.

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Main Subjects


References
1. Hall, J.F. and Chopra, A.K. Two-dimensional dynamic
analysis of concrete gravity and embankment
dams including hydrodynamic e ects", Earthq. Eng.
Struct. D., 10(2), pp. 305-332 (1982).
2. Waas, G. Linear two-dimensional analysis of soil
dynamics problems in semi-in nite layered media",
Ph.D. Dissertation, University of California, Berkeley,
California (1972).
3. Khazaee, A. and Lot , V. Application of perfectly
matched layers in the transient analysis of damreservoir
systems", Soil Dynamics and Earthquake
Engineering, 60(1), pp. 51-68 (2014).
4. Sommerfeld, A., Partial Di erential Equations in
Physics, Academic Press, NY (1949).
5. Sharan, S.K. Time domain analysis of in nite
uid
vibration", Int. J. Numer. Meth. Eng., 24(5), pp. 945-
958 (1987).
M. Jafari and V. Lot /Scientia Iranica, Transactions A: Civil Engineering 25 (2018) 3054{3065 3065
6. Berenger, J.P. A perfectly matched layer for the absorption
of electromagnetic waves", J. Comput. Phys.,
114(2), pp. 185-200 (1994).
7. Chew, W.C. and Weedon, W.H. A 3D perfectly
matched medium from modi ed Maxwell's equations
with stretched coordinates", Microw. Opt. Techn. Let.,
7(13), pp. 599-604 (1994).
8. Basu, U. and Chopra, A.K. Perfectly matched layers
for time-harmonic elastodynamics of unbounded
domains: theory and nite-element implementation",
Comput. Meth. Appl. Mech. Eng., 192(11-12), pp.
1337-1375 (2003).
9. Jiong, L., Jian-wei, M., and Hui-zhu, Y. The study of
perfectly matched layer absorbing boundaries for SH
wave elds", Appl. Geophys., 6(3), pp. 267-274 (2009).
10. Zhen, Q., Minghui, L., Xiaodong, Z., Yao, Y., Cai, Z.,
and Jianyong, S. The implementation of an improved
NPML absorbing boundary condition in elastic wave
modeling", Appl. Geophys., 6(2), pp. 113-121 (2009).
11. Kim, S. and Pasciak, J.E. Analysis of cartesian PML
approximation to acoustic scattering problems in R2",
Wave Motion, 49, pp. 238-257 (2012).
12. Higdon, R.L. Absorbing boundary conditions for
di erence approximations to the multi-dimensional
wave equation", Math. Comput., 47(176), pp. 437-459
(1986).
13. Givoli, D. and Neta, B. High order non-re
ecting
boundary scheme for time-dependent waves", J. Comput.
Phys., 186(1), pp. 24-46 (2003).
14. Hagstrom, T. and Warburton, T. A new auxiliary
variable formulation of high order local radiation
boundary condition: corner compatibility conditions
and extensions to rst-order systems", Wave Motion,
39(4), pp. 327-338 (2004).
15. Givoli, D., Hagstrom, T., and Patlashenko, I. Finiteelement
formulation with high-order absorbing conditions
for time-dependent waves", Comput. Meth. Appl.
M., 195(29-32), pp. 3666-3690 (2006).
16. Hagstrom, T., Mar-Or, A., and Givoli, D. Highorder
local absorbing conditions for the wave equation:
extensions and improvements", J. Comput. Phys.,
227, pp. 3322-3357 (2008).
17. Rabinovich, D., Givoli, D., Bielak, J., and Hagstrom,
T. A nite element scheme with a high order absorbing
boundary condition for elastodynamics", Comput.
Meth. Appl. Mech., 200, pp. 2048-2066 (2011).
18. Samii, A. and Lot , V. High-order adjustable boundary
condition for absorbing evanescent modes of waveguides
and its application in coupled
uid-structure
analysis", Wave Motion, 49(2), pp. 238-257 (2012).
19. Lot , V. and Samii, A. Dynamic analysis of concrete
gravity dam-reservoir systems by wavenuber approach
in the frequency domain", Earthquakes and Structures,
3(3-4), pp. 533-548 (2012).
20. Lot , V. and Samii, A. Frequency domain analysis of
concrete gravity dam-reservoir systems by wavenumber
approach" , Proc. 15th World Conference on Earthquake
Engineering, Lisbon, Portugal (2012a).
21. Zienkiewicz, O.C., Taylor, R.L., and Zhu, J.Z., The Finite
Element Method, Butterworth-Heinemann (2013).
22. Chopra, A.K. Hydrodynamic pressure on dams during
earthquake", J. Eng. Mech.-ASCE, 93, pp. 205-223
(1967).
23. Chopra, A.K., Chakrabarti, P., and Gupta, S. Earthquake
response of concrete gravity dams including
hydrodynamic and foundation interaction e ects",
Report No. EERC-80/01, University of California,
Berkeley (1980).
24. Fenves, G. and Chopra, A.K. E ects of reservoir bottom
absorption and dam-water-foundation interaction
on frequency response functions for concrete gravity
dams", Earthq. Eng. Struct. D., 13, pp. 13-31 (1985).
25. Lot , V. Frequency domain analysis of gravity dams
including hydrodynamic e ects", Dam Engineering,
12(1), pp. 33-53 (2001).