تحلیل ارتعاش آزاد غیرخطی لایه خاک دانه‌ای با استفاده از تکنیک اغتشاشات

نوع مقاله : مقاله پژوهشی

نویسندگان

1 مهندسی عمران،فنی و مهندسی،خوارزمی،تهران،ایران

2 گروه مهندسی عمران دانشگاه خوارزمی، تهران، ایران

3 گروه مهندسی مکانیک دانشکده مهندسی دانشگاه خوارزمی، تهران،ایران

چکیده

در این تحقیق یک مدل تجربی به منظور تعیین خصوصیات تغییرشکل دینامیکی خاک دانه‌ای سیمانته و غیرسیمانته ارائه گردیده است. سپس به مطالعه و بررسی فرکانس طبیعی آبرفت‌های یک لایه، همگن و با سطح افقی تحت اثر ارتعاشات هارمونیک یک‌بعدی پرداخته شده است. مدل ارائه شده سازگاری بسیار خوبی با نتایج آزمایشگاهی در محدوده گسترده‌ای از انواع خاک دانه‌ای دارد. اگر سطح زمین، سطح سنگ بستر زیر خاک و مرز بین لایه خاک و سنگ به صورت افقی در نظر گرفته شود، محدوده جانبی رسوبات آبرفت یک لایه تأثیری در پاسخ ندارد و در این صورت لایه رسوبات ممکن است به صورت یک لایه افقی نیمه‌بی‌نهایت در نظر گرفته شود. در چنین مواردی وقتی خاک تحت تأثیر تحریکات لرزه‌ای در پایه قرار می‌گیرد، تنها تغییرشکل‌های برشی در خاک ایجاد می‌شوند. رفتار غیرخطی خاک که ناشی از بارگذاری سیکلی می‌باشد، از طریق اصلاح در خصوصیات تغییرشکلی دینامیکی خاک دانه‌ای یعنی نسبت میرایی و سختی نرمال شده، با استفاده از رویکرد جدیدی در معادله تعادل دینامیکی حرکت حاکم بر رفتار سیستم یک درجه آزاد تحت ارتعاش آزاد، قرار داده شده است. پس با تشکیل معادله یک درجه آزادی مرتبه اول غیرخطی حرکت تحت ارتعاش آزاد، امکان ارائه راه‌حل تقریبی این معادله با تکنیک اغتشاشات وجود خواهد داشت. فرکانس طبیعی این سیستم یک درجه آزاد به روش تحلیلی تعیین گردید و نتایج نشان می‌دهد که دقت لازم را دارا می‌باشد. روش تحلیلی برای تعیین پاسخ سیستم یک درجه آزاد از سازگاری بسیار خوبی با روش عددی مانند روش رانج کوتا برخوردار است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Nonlinear Free Vibration Analysis of Granular Soil Layer Using Perturbation Technique

نویسندگان [English]

  • Ali Shirzad 1
  • Amir Hamidi 2
  • S.A.A. Hosseini 3
1 Civil engineering, engineerin,kharazmi,Tehran,Iran
2 civil engineering department, Kharazmi University, Tehran, Iran
3 Mechanical engineering department, faculty of engineering, Kharazmi University, Tehran, Iran.
چکیده [English]

In this study, an experimental model has been proposed to determine the dynamic deformation properties of cemented and non-cemented granular soils and then the natural frequency of one-layered, homogeneous and horizontal surface alluvium under the influence of one-dimensional harmonic vibrations was studied. The proposed model is very compatible with laboratory results in a wide range of grain soils. The natural frequency of a one-degree-of-freedom system was determined analytically, and the results showed that it has careful accuracy. The analytical method to determine the response of a one-degree-of-freedom system has a very good agreement with the numerical method such as the Runge-Kutta method. In the present study, considering the one-layered alluvium as a lumped mass system and nonlinear spring and nonlinear damping, a clear solution of this system of a one-degree-of-freedom has been proposed. On the other hand, the natural frequency can not only be a function of the depth of the alluvium layer and can be considered as a function of time.

کلیدواژه‌ها [English]

  • Perturbation techniques
  • Natural frequency
  • nonlinear effects
  • experimental formulations
  • One-layer deposit surface response
[1] Pestana, J. M. and L. A. Salvati (2006). "Small-strain behavior of granular soils. I: Model for cemented and uncemented sands and gravels." Journal of geotechnical and geoenvironmental engineering 132(8): 1071-1081.
[2] Idriss, I. M. and H. B. Seed (1968). "Seismic response of horizontal soil lauers." Am Soc Civil Engring J Soil Mech.
[3] Nayfeh, A. H. (2011). Introduction to perturbation techniques, John Wiley & Sons.
[4] Chen, C. and Z.-m. Zhou (2013). "Nonlinear cross-anisotropic model for soils at various strain levels." International Journal of Geomechanics 14(4): 04014012.
[5] Zhang, J., et al. (2005). "Normalized shear modulus and material damping ratio relationships." Journal of Geotechnical and Geoenvironmental Engineering 131(4): 453-464.
[6] Groholski, D. R., et al. (2016). "Simplified model for small-strain nonlinearity and strength in 1D seismic site response analysis." Journal of Geotechnical and Geoenvironmental Engineering 142(9): 04016042.
[7] Hardin, B. O. and V. P. Drnevich (1972). "Shear modulus and damping in soils: measurement and parameter effects." Journal of Soil Mechanics & Foundations Div 98(sm6).
[8] Hashash, Y. M. and D. Park (2001). "Non-linear one-dimensional seismic ground motion propagation in the Mississippi embayment." Engineering Geology 62(1-3): 185-206.
[9] Hashash, Y. M. and D. Park (2002). "Viscous damping formulation and high frequency motion propagation in non-linear site response analysis." Soil Dynamics and Earthquake Engineering 22(7): 611-624.
[10] Hashash, Y. M., et al. (2008). "Soil-column depth-dependent seismic site coefficients and hazard maps for the upper Mississippi Embayment." Bulletin of the Seismological Society of America 98(4): 2004-2021.
[11] Ishibashi, I. and X. Zhang (1993). "Unified dynamic shear moduli and damping ratios of sand and clay." Soils and foundations 33(1): 182-191.
[12] Iwasaki, T., et al. (1978). "Shear moduli of sands under cyclic torsional shear loading." Soils and Foundations 18(1): 39-56.
[13] Kokusho, T., et al. (1982). "Dynamic properties of soft clay for wide strain range." Soils and Foundations 22(4): 1-18.
[14] Richart, F. E., et al. (1970). "Vibrations of soils and foundations."
[15] Park, D. and Y. M. Hashash (2004). "Soil damping formulation in nonlinear time domain site response analysis." Journal of Earthquake Engineering 8(02): 249-274.
[16] Phillips, C. and Y. M. Hashash (2008). A simplified constitutive model to simultaneously match 1modulus reduction and damping soil curves for nonlinear site response analysis. Geotechnical Earthquake Engineering and Soil Dynamics IV: 1-10.
[17] Phillips, C. and Y. M. Hashash (2009). "Damping formulation for nonlinear 1D site response analyses." Soil Dynamics and Earthquake Engineering 29(7): 1143-1158.
[18] Saxena, S. K., et al. (1988). "Dynamic moduli and damping ratios for cemented sands at low strains." Canadian Geotechnical Journal 25(2): 353-368.
[19] Seed, H. B., and Idriss, I. M. (1970). “Soil moduli and damping factors for dynamic response analysis.” Rep. No. EERC 70-10, Earthquake Engineering Research Center, Berkeley, Calif.
[20] Seed, H. B., et al. (1986). "Moduli and damping factors for dynamic analyses of cohesionless soils." Journal of geotechnical engineering 112(11): 1016-1032.
[21] Stokoe, K., et al. (1999). Dynamic soil properties: laboratory, field and correlation studies. Proceednings of the 2nd international conference on earthquake geotechnical engineering 1999., AA Balkema.
[22] Stokoe, K., et al. (2004). Development of a new family of normalized modulus reduction and material damping curves. International Workshop on Uncertainties in Nonlinear Soil Properties and their Impact on Modeling Dynamic Soil Response.
[23] Vucetic, M. and R. Dobry (1991). "Effect of soil plasticity on cyclic response." Journal of geotechnical engineering 117(1): 89-107.
[24] Vucetic, M., et al. (1998). "Damping at small strains in cyclic simple shear test." Journal of geotechnical and geoenvironmental engineering 124(7): 585-594.
[25] Zen, K., Umehara, Y., and Hamada, K. ~1978!. “Laboratory tests and in situ seismic survey on vibratory shear modulus of clayey soils with various plasticities.” Proc., 5th Japanese Earthquake Engineering Symp., Japan, 721–728.
[26] Lee, M. K. W., and Finn, W. D. L. (1978). “DESRA-2, dynamic effective stress response analysis of soil deposits with energy transmitting boundary including assessment of liquefaction potential.” Soil Mech. Series No. 38, Univ. of British Columbia, Vancouver, Canada.
[27] Yasuda, N. and N. Matsumoto (1993). "Dynamic deformation characteristics of sands and rockfill materials." Canadian Geotechnical Journal 30(5): 747-757.
[28] Yasuda, N., et al. (1996). "Dynamic deformation characteristics of undisturbed riverbed gravels." Canadian geotechnical journal 33(2): 237-249.
[29] Menq F.-Y., 2003. Dynamic Properties of Sandy and Gravelly Soils (Ph.D. dissertation). University of Texas, Austin, USA.
[30] Senetakis, K., et al. (2013). "Normalized shear modulus reduction and damping ratio curves of quartz sand and rhyolitic crushed rock." Soils and Foundations 53(6): 879-893.
[31] Feng, T., et al. (2019). "Experimental Investigation of Dynamic Characteristics of Subsea Sand-Silt Mixtures." Advances in Civil Engineering 2019.
[32] Darendeli, M. B. (2001). "Development of a new family of normalized modulus reduction and material damping curves."
[33] Zhao, M.-h., He, W., & Wang, H.-h. (2007). Perturbation analysis on post-buckling behavior of pile. Journal of Central South University of Technology, 14(6), 853-857.
[34] Hambleton, J., & Sloan, S. (2011). Coordinate perturbation method for upper bound limit analysis. Paper presented at the 2nd International symposium on computational geomechanics, Dubrovnik.
[35] Hambleton, J., & Sloan, S. (2013). A perturbation method for optimization of rigid block mechanisms in the kinematic method of limit analysis. Computers and Geotechnics, 48, 260-271.
[36] Liu, S. J., & Wang, H. C. (2012). Interval back analysis on mechanical parameter of geotechnical engineering. Paper presented at the Applied Mechanics and Materials.
[37] Farah, K., Ltifi, M., Abichou, T., & Hassis, H. (2014). Comparison of different probabilistic methods for analyzing slope stability. International Journal of Civil Engineering, 12(3), 264-268.
[38] Acar, Y. B. and E.-T. A. El-Tahir (1986). "Low strain dynamic properties of artificially cemented sand." Journal of Geotechnical Engineering 112(11): 1001-1015.
[39] Kokusho, T. (1980). "Cyclic triaxial test of dynamic soil properties for wide strain range." Soils and foundations 20(2): 45-60.
[40] Sharma, S. S., & Fahey, M. (2003). Degradation of stiffness of cemented calcareous soil in cyclic triaxial tests. Journal of Geotechnical and Geoenvironmental engineering, 129(7), 619-629.
[41] Sharma, S. S. and M. Fahey (2004). "Deformation characteristics of two cemented calcareous soils." Canadian geotechnical journal 41(6): 1139-1151.
[42] Iwasaki, T., Tatsuoka, F. and Takagi, Y. (1976) :"Dynamic shear deformation properties of sand for wide strain range," Report of Civil Engineering Institute, No. 1085, Ministry of Construction (in Japanese).
[43] Ambraseys, N. (1960). On the shear response of a two-dimensional truncated wedge subjected to an arbitrary disturbance. Bulletin of the seismological society of America, 50(1), 45-56.
[44] Gazetas, G. (1987). Seismic response of earth dams: some recent developments. Soil dynamics and earthquake engineering, 6(1), 2-47.
[45] Makdisi, F. I., & Seed, H. B. (1979). Simplified procedure for evaluating embankment response. Journal of Geotechnical and Geoenvironmental engineering, 105(ASCE 15055).
[46] Mononobe, N., Takata, A., & Matumura, M. (1936). Seismic stability of the earth dam. Paper presented at the Proc. 2nd Congress on Large Dams.
[47] Das, B. M., & Ramana , G. V. (2011). Principles of soil dynamics: Cengage Learning.
[48] Ishihara, K. (1996). Soil behaviour in earthquake geotechnics.
[49] Kramer, S. L. (1996). Geotechnical earthquake engineering: Pearson Education India.