بررسی فشار هیدرودینامیکی در سدها با مخزن بی‌نهایت با در نظر گرفتن اثر تعامل سد و مخزن

نوع مقاله : مقاله پژوهشی

نویسندگان

گروه مهندسی عمران، دانشکده مهندسی و فناوری، دانشگاه مازندران، بابلسر، ایران

چکیده

سد‌ها به‌دلیل اهمیت فراوانی که برای زیر ساخت‌های یک کشور دارند، باید به‌طور دقیق تحلیل و بررسی شوند. از مهم‌ترین بحث‌های مورد نیاز برای تحلیل سدها در مناطق لرزه‌ای، برآورد فشارهای هیدرودینامیکی و تغییر شکل سد می‌باشد. در‌‌این پژوهش، یک روش تحلیلی برای ارزیابی پاسخ‌های دو نوع سد صلب و انعطاف‌پذیر با مخزنی به طول بی‌نهایت انجام شد. فرکانس‌ها، معادله فشار و تغییر شکل برای یک سیستم سد-مخزن با شاره تراکم ناپذیر، ناچرخشی و بدون چسبندگی با کمک روش تبدیل دیفرانسیلی محاسبه شد. در سدهای مورد بررسی، از امواج سطحی صرف‌نظر و کف مخزن کاملا صلب و بدون شیب در نظرگرفته شده است. تحلیل‌ها با درنظر گرفتن اثرات اندرکنش سد-مخزن انجام شد. اثرات پارامترهای نظیر ارتفاع سد، چگالی جرمی سیال، ضریب شتاب افقی زمین و ضریب کشسانی برای سدهای صلب و منعطف بر فشار هیدرودینامیکی و تغییرشکل سدها مورد ارزیابی قرار گرفت. مهم‌ترین اثرات اندرکنش سد و مخزن بر فشار هیدرودینامیکی عدم رخداد فشار بیشینه در تراز کف سد منعطف می‌باشد. همچنین نتایج نشان می‌دهد که در سد منعطف با افزایش 40 درصدی از ضخامت سد، مقدار جابه‌جایی کاهش‌یافته ولی بیشینه فشار وارده به سد بیش از 150 درصد افزایش یافت. با افزایش 20 درصدی از ضریب کشسانی سد، بیشینه فشار حدودا 22 درصد افزایش یافت. همچنین با افزایش ارتفاع، با توجه به نرم‌تر شدن سد، جابه‌جایی افزایش می‌یابد و در نتیجه فشارهیدرودینامیکی، کمتر شد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Hydrodynamic Pressure Analysis in Dams with Infinite Reservoirs Considering Dam–Reservoir Interaction

نویسندگان [English]

  • Ali Mohammadi Kordkheyli
  • Mohsen Bozorgnasab
  • Ali Asgari
  • Reza Taghipour
Department of Civil Engineering, Faculty of Engineering and Technology, University of Mazandaran, Babolsar 47416-13534, Iran.
چکیده [English]

Dams, due to their critical importance for a country's infrastructure, must be analyzed and evaluated with high precision. One of the key considerations for dam analysis in seismic regions is the estimation of hydrodynamic pressures and dam deformations. In this study, an analytical method was developed to assess the responses of two types of dams—rigid and flexible—connected to a reservoir of infinite length. Frequencies, pressure distribution, and deformation for a dam–reservoir system with an incompressible, irrotational, and non-adhesive fluid were calculated using the differential transform method. In the analyzed dams, surface waves were neglected, and the reservoir floor was assumed to be perfectly rigid and horizontal. The analyses considered the effects of dam–reservoir interaction. The influences of parameters such as dam height, fluid density, horizontal ground acceleration, and elasticity modulus on the hydrodynamic pressure and dam deformation were evaluated for both rigid and flexible dams. The most significant effect of dam–reservoir interaction on hydrodynamic pressure was the absence of maximum pressure at the base of the flexible dam. Results also indicate that, in the flexible dam, a 40% increase in dam thickness reduces displacement, while the maximum pressure on the dam increases by more than 150%. Increasing the elasticity modulus by 20% leads to an approximately 22% increase in maximum pressure. Moreover, with increasing dam height, displacement increases due to the softer behavior of the dam, resulting in a reduction in hydrodynamic pressure.

کلیدواژه‌ها [English]

  • Hydrodynamic Pressure
  • Dam–Reservoir Interaction
  • Differential Transform Method
  • Rigid Dam
  • Flexible Dam
[1] J. Ahadian, A.R. Afzalian, Applied Analysis of Piano Key Weir (PKW) Structures as a Diversion Dam, Amirkabir Journal of Civil Engineering, 49(3) (2017) 463-476, https://doi.org/10.22060/ceej.2016.694.
[2] A. Jafari, A. Aftabi Sani, Solving two classical fluid-structure interaction problem utilizing differential transform method, Journal of Solid and Fluid Mechanics, 10(3) (2020) 17-30, https://doi.org/10.22044/jsfm.2020.9854.3213.
[3] H.M. Westergaard, Water pressures on dams during earthquakes, Transactions of the American society of Civil Engineers, 98(2) (1933) 418-433, https://doi.org/10.1061/TACEAT.0004496.
[4] S. Kotsubo, Dynamic water pressure on dams due to irregular earthquakes, Transactions of the Japan Society of Civil Engineers, 1957(47) (1957) 38-45, https://doi.org/10.2208/jscej1949.1957.47_38.
[5] A.K. Chopra, Hydrodynamic pressures on dams during earthquakes, Journal of the Engineering Mechanics Division, 93(6) (1967) 205-223, https://doi.org/10.1061/JMCEA3.0000915.
[6] J. Avilés, X. Li, Analytical–numerical solution for hydrodynamic pressures on dams with sloping face considering compressibility and viscosity of water, Computers & Structures, 66(4) (1998) 481-488, https://doi.org/10.1016/S0045-7949(97)00091-6.
[7] M. Zingales, Seismically induced, non-stationary hydrodynamic pressure in a dam-reservoir system, Probabilistic Engineering Mechanics, 18(2) (2003) 151-163, https://doi.org/10.1016/S0266-8920(02)00056-5.
[8] B. Navayineya, J.V. Amiri, M.A. Ardeshir, A closed form solution for hydrodynamic pressure of gravity dams reservoir with effect of viscosity under dynamic loading, World Academy of Science, Engineering and Technology, 58 (2009) 416-420, https://doi.org/10.5281/zenodo.1080840.
[9] G. Lin, Y. Wang, Z. Hu, Hydrodynamic pressure on arch dam and gravity dam including absorption effect of reservoir sediments, IOP Conference Series: Materials Science and Engineering, 10(1) (2010) 012234, https://doi.org/10.1088/1757-899X/10/1/012234.
[10] R. Attarnejad, A. Bagheri, Dam-reservoir interaction including the effect of vertical component of earthquake acceleration on hydrodynamic pressure, Advanced Materials Research, 255-260 (2011) 3493-3499, https://doi.org/10.4028/www.scientific.net/AMR.255-260.3493.
[11] M.A. Karaca, S. Küçükarslan, Analysis of dam-reservoir interaction by using homotopy analysis method, KSCE Journal of Civil Engineering, 16(1) (2012) 103-106, https://doi.org/10.1007/s12205-012-0870-8.
[12] B. Navayi Neya, M.A. Ardeshir, An analytical solution for hydrodynamic pressure on dams considering the viscosity and wave absorption of the reservoir, Arabian Journal for Science and Engineering, 38(8) (2013) 2023-2033, https://doi.org/10.1007/s13369-013-0566-5.
[13] N. Bouaanani, S. Renaud, Effects of fluid–structure interaction modeling assumptions on seismic floor acceleration demands within gravity dams, Engineering Structures, 67 (2014) 1-18, https://doi.org/10.1016/j.engstruct.2014.02.004.
[14] R. Tarinejad, S. Pirboudaghi, Legendre spectral element method for seismic analysis of dam-reservoir interaction, IJCE, 13(2) (2015) 148, https://doi.org/10.22068/IJCE.13.2.148.
[15] R.-A. Jafari-Talookolaei, S. Lasemi-Imani, Free vibration analysis of a delaminated beam–fluid interaction system, Ocean Engineering, 107 (2015) 186-192, https://doi.org/10.1016/j.oceaneng.2015.07.053.
[16] M. Rezaiee-Pajand, A. Aftabi S, M.S. Kazemiyan, Analytical solution for free vibration of flexible 2D rectangular tanks, Ocean Engineering, 122 (2016) 118-135, https://doi.org/10.1016/j.oceaneng.2016.05.052.
[17] M. Jafari, V. Lotfi, Dynamic analysis of concrete gravity dam-reservoir systems by a wavenumber approach for the general reservoir base condition, Scientia Iranica, 25(6) (2018) 3054-3065, https://doi.org/10.24200/sci.2017.4227.
[18] M. Rezaiee-Pajand, M.S. Kazemiyan, A. Aftabi S, Solving coupled beam-fluid interaction by DTM, Ocean Engineering, 167 (2018) 380-396, https://doi.org/10.1016/j.oceaneng.2018.04.020.
[19] H. Mazighi, M.K. Mihoubi, Study of the effect of upstream slope on water pressure in concrete gravity dam, Procedia Structural Integrity, 13 (2018) 1438-1441, https://doi.org/10.1016/j.prostr.2018.12.298.
[20] M. Wang, J. Chen, L. Wu, B. Song, Hydrodynamic pressure on gravity dams with different heights and the westergaard correction formula, International Journal of Geomechanics, 18(10) (2018) 04018134, https://doi.org/10.1061/(ASCE)GM.1943-5622.0001257.
[21] H. Xu, D. Zou, X. Kong, Z. Hu, X. Su, A nonlinear analysis of dynamic interactions of CFRD–compressible reservoir system based on FEM–SBFEM, Soil Dynamics and Earthquake Engineering, 112 (2018) 24-34, https://doi.org/10.1016/j.soildyn.2018.04.057.
[22] Y. Wang, Z. Hu, W. Guo, Hydrodynamic pressures on arch dam faces with irregular reservoir geometry, Journal of Vibration and Control, 25(3) (2018) 627-638, https://doi.org/10.1177/1077546318791013.
[23] M. Pasbani Khiavi, A. Feizi, M. Jalali, Frequency analysis of concrete gravity dam with finite element model and LHS method Numerical Methods in Civil Engineering, 3(3) (2019) 13–19, https://doi.org/10.29252/nmce.3.3.14.
[24] M. Pasbani Khiavi, A. Sari, Evaluation of hydrodynamic pressure distribution in reservoir of concrete gravity dam under vertical vibration using an analytical solution, Mathematical Problems in Engineering, 2021(1) (2021) 6669366, https://doi.org/10.1155/2021/6669366.
[25] M.A. Hariri-Ardebili, J.W. Salamon, S.M. Seyed-Kolbadi, Discussion of “hydrodynamic pressure on gravity dams with different heights and the westergaard correction formula” by Mingming Wang, Jianyun Chen, Liang Wu, and Bingyue Song, International Journal of Geomechanics, 22(8) (2022) 07022006, https://doi.org/10.1061/(ASCE)GM.1943-5622.0002396.
[26] J. Ye, H. Zhou, X. Zhou, Hydrodynamic pressure on lateral side of dam excited by harmonic seismic vibration: A novel formulation, Soil Dynamics and Earthquake Engineering, 164 (2023) 107626, https://doi.org/10.1016/j.soildyn.2022.107626.
[27] M. Pasbani Khiavi, A. Ferdousi, A. Moallemi Khiavi, A probabilistic model for evaluation of the dynamic behavior of a concrete gravity dam considering the fluid-structure interaction, Advances in Civil Engineering, 2023(1) (2023) 9927608, https://doi.org/10.1155/2023/9927608.
[28] D. Ouzandja, M. Messaad, A.T. Berrabah, M. Belharizi, Seismic analysis of Fractured Koyna Concrete Gravity Dam, Archives of Hydro-Engineering and Environmental Mechanics, 70 (2023) 29-47, https://doi.org/10.2478/heem-2023-0003.
[29] R. Kouhdasti, N. Bouaanani, Response spectrum and modal dynamic analyses of gravity dams using ground motion accelerations modified to account for hydrodynamic effects, Earthquake Spectra, 40(4) (2024) 2761-2804, https://doi.org/10.1177/87552930241246016.
[30] F. Şermet, M.E. Kartal, M.E. Yiğit, E. Hökelekli, The effect of the gravity on the earthquake performance of roller compacted concrete dams, 2024, 15(1) (2024) 20-29, https://doi.org/10.20528/cjcrl.2024.01.003.
[31] A. Asgari, Extended power series solution for Perkins-Kern-Nordgren model of hydraulic fracture, AUT Journal of Civil Engineering, 6(4) (2022) 461-468, https://doi.org/10.22060/ajce.2023.19737.5814.
[32] M. Nourifar, A.A. Sani, A. Keyhani, Efficient multi-step differential transform method: Theory and its application to nonlinear oscillators, Communications in Nonlinear Science and Numerical Simulation, 53 (2017) 154-183, https://doi.org/10.1016/j.cnsns.2017.05.001.