تحلیل پاسخ یک بعدی و غیرخطی آبرفت دانه‌ای سیمانته تحت ارتعاش هارمونیک با استفاده از تکنیک اغتشاشات

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی کارشناسی ارشد، گروه مهندسی عمران، دانشکده فنی و مهندسی، دانشگاه خوارزمی، کرج، ایران.

2 دانشیار، گروه مهندسی مکانیک، دانشکده فنی و مهندسی، دانشگاه خوارزمی، کرج، ایران.

3 استاد، گروه مهندسی عمران، دانشکده فنی و مهندسی، دانشگاه خوارزمی، کرج، ایران.

چکیده

در این مطالعه به بررسی پاسخ آبرفت‌ تک لایه دانه‌ای سیمانته با سطح افقی تحت اثر ارتعاشات هارمونیک یک بعدی اعمالی در پایه پرداخته شد. مدلسازی به‌صورت یک لایه نیمه بینهایت درنظر گرفته شده و جابه‌جایی‌های افقی تنها در یک جهت و تنش‌ها و کرنش‌های برشی نیز روی صفحات افقی بطور یکنواخت لحاظ شده است. فرض بر آن است که وقتی خاک تحت تاثیر تحریک لرزه‌ای در پایه قرار می‌گیرد، تنها در آن تغییر شکل برشی ایجاد می گردد. رفتار غیرخطی خاک که ناشی از بارگذاری سیکلی می‌باشد، با استفاده از خصوصیات تغییرشکل دینامیکی یعنی نسبت میرایی و سختی نرمال شده تعیین می‌شود. این ویژگیهای دینامیکی به پارامترهای مختلفی مانند فشار همه جانبه و درصد سیمان وابسته هستند. در این مطالعه از یک مدل تجربی برای تعیین خصوصیات تغییرشکل دینامیکی خاک دانه‌ای سیمانته و غیر سیمانته استفاده شد. با تشکیل معادله یک درجه آزادی مرتبه اول غیرخطی حرکت تحت ارتعاش هارمونیک، امکان ارائه راه‌حل تقریبی این معادله با استفاده از تکنیک اغتشاشات مورد ارزیابی قرار گرفت. درنهایت، وقوع پدیده تشدید در آبرفت یک لایه سیمانته بررسی شد و دامنه در سطح زمین به روش تحلیلی و با دقت مناسب تعیین گردید. بر‌اساس نتایج، روش تحلیلی پیشنهادی برای تحلیل پاسخ سیستم یک درجه آزادی از سازگاری بسیار خوبی با روش‌های عددی مرسوم مانند رانج کوتا برخوردار است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

One-Dimensional Non-Linear Response Analysis of Granular Cemented Al-luvium Using Perturbation Method

نویسندگان [English]

  • Ali Shirzad 1
  • Seyed Ali Asghar Hosseini 2
  • Hamidi Amir 3
1 M.Sc. Student, Department of Civil Engineering, Faculty of Engineering, Kharazmi University, Karaj, Iran.
2 Associate Professor, Department of Mechanical Engineering, Faculty of Engineering, Kharazmi University, Karaj, Iran.
3 Professor, Department of Civil Engineering, Faculty of Engineering, Kharazmi University, Karaj, Iran.
چکیده [English]

In present study, the response of a cemented granular and horizontal layer is investigated under one-dimensional harmonic vibrations applied at its base. The modeling was performed considering an infinite horizontal layer with displacements occurred in one direction with uniform shear stress and strain distributions on horizontal planes. It is considered that only shear displacements occur when the soil layer is subjected to seismic excitation at base. The nonlinear behavior due to cyclic loading can be determined using dynamic characteristics of soil like shear modulus and damping ratio. These dynamic characteristics are dependent to different parameters like confining pressure and cement content. In present study, an empirical model was applied for determination of dynamic characteristics of cemented and uncemented soil. By deriving the one degree of freedom equation of motion, an approximate solution was suggested using perturbation method. Finally, the resonance phenomenon was studied for cemented granular layer and the amplitudes were predicted with a precise approximation. Based on the results, the suggested method was able to predict the response of soil layer with good consistency comparing to the results of numerical methods like Runge-Kutta.

کلیدواژه‌ها [English]

  • Perturbation method
  • Non-linear response analysis
  • One-layered cemented alluvium
  • Vibrations amplitude
  • Resonance frequency
[1] Ambraseys NN. On the shear response of a two-dimensional truncated wedge subjected to an arbitrary disturbance. Bulletin of the seismological society of America. 1960 Jan 1; 50(1): 45-56. doi: 10.1785/BSSA0500010045
[2] Gazetas G. Seismic response of earth dams: some recent developments. Soil dynamics and earthquake engineering. 1987 Jan 1; 6(1): 2-47. doi: 10.1016/0267-7261(87)90008-X
[3] Makdisi FI, Seed HB. Simplified procedure for evaluating embankment response. Journal of the Geotechnical Engineering Division. 1979 Dec; 105(12): 1427-1434. doi: 10.1061/AJGEB6.0000898
[4] Mononobe N, Takata A, Matumura M. Seismic stability of the earth dam, Trans. 2nd Congress on Large Dams, Washington DC, USA, 1936; 435-444.
[5] Seed HB, Wong RT, Idriss IM, Tokimatsu K. Moduli and damping factors for dynamic analyses of cohesionless soils. Journal of geotechnical engineering. 1986 Nov; 112(11): 1016-1032. doi: 10.1061/(ASCE)0733-9410(1986)112:11(1016)
[6] Feng T, Tang Y, Wang Q, Zhang J, Song J. Experimental Investigation of Dynamic Characteristics of Subsea Sand‐Silt Mixtures. Advances in Civil Engineering. 2019; 2019(1): 5619039. doi: 10.1155/2019/5619039
[7] Pestana JM, Salvati LA. Small-strain behavior of granular soils. I: Model for cemented and uncemented sands and gravels. Journal of geotechnical and geoenvironmental engineering. 2006 Aug; 132(8): 1071-1081. doi: 10.1061/(ASCE)1090-0241(2006)132:8(1071)
[8] Park D, Hashash YM. Soil damping formulation in nonlinear time domain site response analysis. Journal of earthquake engineering. 2004 Mar; 8(02): 249-274. doi: 10.1080/13632460409350489
[9] Phillips C, Hashash YM. A simplified constitutive model to simultaneously match modulus reduction and damping soil curves for nonlinear site response analysis. InGeotechnical earthquake engineering and soil dynamics IV. 2008; 1-10. doi: 10.1061/40975(318)9
[10] Sitar N, Clough GW. Seismic response of steep slopes in cemented soils. Journal of Geotechnical Engineering. 1983 Feb; 109(2): 210-227. doi: 10.1061/(ASCE)0733-9410(1983)109:2(210)
[11] Zhong Z, Ni B, Shi Y, Shen J, Du X. Convolutional neural network-based seismic fragility analysis of subway station structure considering spatial variation of site shear-wave velocity. Computers and Geotechnics. 2023 Nov 1; 163: 105741. doi: 10.1016/j.compgeo.2023.105741
[12] Reyes, S.F.Z. Advanced numerical modelling of the cyclic/dynamic response of offshore structures in inhomogeneous non-cohesive soils. PhD Thesis, University of Bristol, UK. 2023.
[13] Idriss IM, Seed HB. Seismic response of horizontal soil layers. Journal of the Soil Mechanics and Foundations Division. 1968 Jul; 94(4): 1003-1031. doi: 10.1061/JSFEAQ.0001163
[14] Menq FY. Dynamic properties of sandy and gravelly soils. The University of Texas at Austin; 2003.
[15] Senetakis K, Anastasiadis A, Pitilakis K. Normalized shear modulus reduction and damping ratio curves of quartz sand and rhyolitic crushed rock. Soils and Foundations. 2013 Dec 1; 53(6): 879-893. doi: 10.1016/j.sandf.2013.10.007
[16] Khodaparast M, Rajabi AM, Kabi A. The study of strength behavior of sandy soil mixed with plastic waste and cement slurry. Civil Infrastructure Researches. 2017 Mar 8; 2(2): 43-49. doi: 10.22091/CER.2017.828 [In Persian]
[17] Hamidi A, Abdoos S. Application of Lime and Portland Cement for Improvement of Clay Contaminated with Anthracene and Glycerol. Civil Infrastructure Researches. 2020 Feb 20; 5(2): 111-122. doi: 10.22091/CER.2020.5374.1198 [In Persian]
[18] Heidarli E, Ouria A. Laboratory Study of the Effect of Cement Stabilization of the Interface of Reinforcement and Sand on the Interface Shear Strength. Civil Infrastructure Researches. 2023 Aug 23; 9(1): 77-89. doi: 10.22091/cer.2022.8359.1415 [In Persian]
[19] Pakbaz MS, Alipour R. Influence of cement addition on the geotechnical properties of an Iranian clay. Applied Clay Science. 2012 Oct 1; 67: 1-4. doi: 10.1016/j.clay.2012.07.006
[20] Alipour R, Heidarzadeh H. Site response variations by ground improvement. In 8th International Conference on Seismology and Earthquake Engineering. Tehran, Iran. 2019. [In Persian]
[21] Haeri SM, Hamidi A. Constitutive modelling of cemented gravelly sands. Geomechanics and Geoengineering: An International Journal. 2009 May 28; 4(2): 123-139. doi: 10.1080/17486020902855696
[22] Torabipour A, Hamidi A. Ground Response Analysis of Cemented Alluviums Using Non-Recursive Algorithm. Journal of Earthquake Engineering. 2020 Sep 1; 24(9): 1390-1416. doi: 10.1080/13632469.2018.1481156
[23] Amini Y, Hamidi A, Asghari E. Shear strength–dilation characteristics of cemented sand–gravel mixtures. International Journal of Geotechnical Engineering. 2014 Oct 1; 8(4): 406-413. doi: 10.1179/1939787913Y.0000000026
[24] Hamidi A, Soleimani S. Shear strength-dilation relation in cemented gravely sands. International Journal of Geotechnical Engineering. 2012 Oct 1; 6(4): 415-425. doi: 10.3328/IJGE.2012.06.04.415-425
[25] Shirzad A, Hamidi A, Hosseini SA. Nonlinear free vibration analysis of granular soil layer using perturbation technique. Amirkabir Journal of Civil Engineering. 2021 Sep 23; 53(7): 2977-2994. doi: 10.22060/CEEJ.2020.17605.6614 [In Persian]
[26] Zhao MH, He W, Wang HH. Perturbation analysis on post-buckling behavior of pile. Journal of Central South University of Technology. 2007 Dec; 14(6): 853-857. doi: 10.1007/s11771-007-0162-5
[27] Hambleton JP, Sloan SW. Coordinate perturbation method for upper bound limit analysis. In2nd International symposium on computational geomechanics, Dubrovnik 2011; 373-84.
[28] Hambleton JP, Sloan SW. A perturbation method for optimization of rigid block mechanisms in the kinematic method of limit analysis. Computers and Geotechnics. 2013 Mar 1; 48: 260-271. doi: 10.1016/j.compgeo.2012.07.012
[29] Liu SJ, Wang HC. Interval back analysis on mechanical parameter of geotechnical engineering. Applied Mechanics and Materials. 2012 Sep 5; 170: 399-402. doi: 10.4028/ www.scientific.net/AMM.170-173.399
[30] Farah K, Ltifi M, Abichou T, Hassis H. Comparison of different probabilistic methods for analyzing slope stability. International Journal of Civil Engineering. 2014 Jul 10; 12(3): 264-268.
[31] Darendeli MB. Development of a new family of normalized modulus reduction and material damping curves. The university of Texas at Austin; 2001.
[32] Hashash YM, Park D. Non-linear one-dimensional seismic ground motion propagation in the Mississippi embayment. Engineering Geology. 2001 Oct 1; 62(1-3): 185-206. doi: 10.1016/S0013-7952(01)00061-8
[33] Hashash YM, Park D. Viscous damping formulation and high frequency motion propagation in non-linear site response analysis. Soil Dynamics and Earthquake Engineering. 2002 Sep 1; 22(7): 611-624. doi: 10.1016/S0267-7261(02)00042-8
[34] Hashash YM, Tsai CC, Phillips C, Park D. Soil-column depth-dependent seismic site coefficients and hazard maps for the upper Mississippi Embayment. Bulletin of the Seismological Society of America. 2008 Aug 1; 98(4): 2004-2021.‏ doi: 10.1785/0120060174
[35] Nayfeh AH. Introduction to perturbation techniques. John Wiley & Sons; 2011 Apr 8.
[36] Phillips C, Hashash YM. Damping formulation for nonlinear 1D site response analyses. Soil dynamics and earthquake engineering. 2009 Jul 1; 29(7): 1143-1158. doi: 10.1016/j.soildyn.2009.01.004
[37] Saxena SK, Avramidis AS, Reddy KR. Dynamic moduli and damping ratios for cemented sands at low strains. Canadian Geotechnical Journal. 1988 May 1; 25(2): 353-368. doi: 10.1139/t88-036
[38] Acar YB, El-Tahir ET. Low strain dynamic properties of artificially cemented sand. Journal of Geotechnical Engineering. 1986 Nov; 112(11): 1001-1015. doi: 10.1061/(ASCE)0733-9410(1986)112:11(1001).
[39] Sharma SS, Fahey M. Degradation of stiffness of cemented calcareous soil in cyclic triaxial tests. Journal of Geotechnical and Geoenvironmental engineering. 2003 Jul; 129(7): 619-629. doi: 10.1061/(ASCE)1090-0241(2003)129:7(619)
[40] Sharma SS, Fahey M. Deformation characteristics of two cemented calcareous soils. Canadian geotechnical journal. 2004 Dec 1; 41(6): 1139-1151. doi: 10.1139/t04-066
[41] Das BM, Ramana GV. Principles of soil dynamics. Boston, MA: PWS-Kent Publishing Company; 1993 Dec 4.
[42] Ishihara K. Soil behaviour in earthquake geotechnics. Oxford University Press; 1996 Jul 25.
[43] Kramer SL. Geotechnical earthquake engineering. Pearson Education India; 1996.
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