بررسی و مقایسه دو مکانیسم انتقالی و دورانی در تحلیل سه‌بعدی پایداری لرزه‌ای شیروانی‌ها به روش تحلیل حدی مرز بالا

نوع مقاله : Articles

نویسندگان

1 پردیس دانشکده‌های فنی، دانشگاه تهران، تهران، ایران

2 دانشکده عمران، پردیس دانشکده‌های فنی، دانشگاه تهران، تهران، ایران

3 پژوهشکده مهندسی ژئوتکنیک، پژوهشگاه بین المللی زلزله‌شناسی و مهندسی زلزله، تهران، ایران،

چکیده

در این مقاله بر مبنای روش تحلیل حدی مرز بالا به بررسی پایداری سه‌بعدی شیروانی­ها در مقابل زلزله بر اساس مکانیسم­های گسیختگی دورانی و انتقالی و نیز مقایسه نتایج آنها پرداخته شده است. تعریف سطوح جانبی مکانیسم­های گسیختگی سه‌بعدی در روش مرز بالا مستلزم رعایت قانون جریان وابسته است که تشکیل صفحات جانبی مسطح را در مکانیسم انتقالی بسیار مقید می­کند و در حالت مکانیسم دورانی لازم است معادلات این سطوح، معادله دیفرانسیل خاصی را ارضا کنند. در ادامه تحقیقات مربوط به پایداری سه‌بعدی شیروانی­های خاکی به روش مرز بالا با استفاده از مکانیسم­های انتقالی و دورانی،  تحقیق حاضر به مقایسه نتایج حاصل از یک مکانیسم انتقالی با یک مکانیسم دورانی که الگوریتم آن در این تحقیق بر اساس حل نهایی میخالوفسکی و به روشی ساده­تر تدوین شده است، می­پردازد. به‌طورکلی روند تغییرات ضریب پایداری شیروانی با افزایش ضریب زلزله برای هر دو مکانیسم دورانی و انتقالی تقریباً مشابه است. همچنین اهمیت تحلیل‌های سه‌بعدی در حالت لرزه‌ای نسبت به حالت استاتیکی بیشتر است. نتایج حاصل از این تحقیق نشان می­دهد که مکانیسم دورانی در اکثر موارد و به‌خصوص در شیب­های قائم نتایج بهتری ارائه می­دهد، اگرچه  مکانیسم انتقالی برای خاک‌های چسبنده و با مکانیسم­های مقید نتایج بهتری دارد.

کلیدواژه‌ها


عنوان مقاله [English]

Comparison of Three Dimensional Translational and Rotational Mechanisms in Seismic Slope Stability Analyses by Upper Bound Limit Analysis

نویسندگان [English]

  • Behzad Amirloo 1
  • Orang Farzaneh 2
  • Faradjolla Askari 3
1 School of Civil Engineering, University of Tehran, Tehran, Iran
2 School of Civil Engineering, University of Tehran, Tehran, Iran
3 Geotechnical Engineering Research Center, International Institute of Earthquake Engineering and Seismology (IIEES), Tehran, Iran
چکیده [English]

In this paper, seismic stability of slopes in three dimensional cases is investigated, using rotational and translational failure mechanisms and compared based on the upper bound limit analysis method. Definition of lateral surfaces of three dimensional failure mechanisms in upper bound method requires considering the associated flow rule, which makes it necessary that particular equations be satisfied. To develop further studies on three dimensional stability of slopes using translational and rotational mechanisms, the present work compares the results of a translational mechanism with a rotational one.
In order to compare the factor of safety in slopes stability problems between translational and rotational mechanisms under body forces due to the weight of the soil mass and horizontal acceleration of the earthquake, the parameter λφc   is used, where γ is the unit weight of the soil, H is the height of slope and c and ϕ are the soil shear strength parameters.
This comparison is carried out for different slope inclination angles (30, 60, 90), two ratios of the width of the failure mechanism (L) to the slope height (H), i.e. 1 and 8, and for cohesive (λφc = 0) and non-cohesive soils (λφc ≠ 0). L/H = 1 and L/H = 8 are used to model the three dimensional and two dimensional mechanisms, respectively. By an increase in the parameter of λφc, the soil behaves more frictional.
Some of the most important results of this research are as follows:
- Generally, the importance of three dimensional analyses is more in seismic states.
- The trend of variations of the safety factor of slopes is almost the same by increase in the coefficient of horizontal earthquake acceleration for both rotational and transitional mechanisms.
-  The results of this study show that in rotational mechanisms, in most cases, especially in vertical slopes, the safety factors are smaller than translational mechanisms.
- Translational mechanisms results (safety factors) are usually lower in cohesive soils.
-  The difference between the results of two translational and rotational mechanisms is less in cohesive soils and more in frictional soils.
- By an increase in inclination angle of the slope, the difference between the results of the two mechanisms becomes more.
Regardless of the kind of the mechanism, in assessing the effect of different parameters on the factor of safety of slopes stability, the following general points can be noted:
- The increase in the coefficient of horizontal earthquake acceleration (from 0 to 0.3) contributes to the decrease in the factor of safety. The reductions for cohesive soils and inclination angle equal to 30 degrees are about 69 and 40 percent, respectively for two dimensional and three dimensional mechanisms. The mentioned reductions for frictional soils in vertical slopes, are about 35 and 20 percent. These results indicate that the effect of earthquake is more in lower slopes with cohesive soil.
- As the failure mechanism widens, the safety factor decreases, and at higher kh values, this decrease becomes more pronounced. This indicates the greater impact of earthquakes on reducing the stability of two-dimensional mechanisms.
- The difference between the results of two dimensional and three dimensional mechanisms in cohesive soils is more than frictional soils.
- The factors of safety of slopes in three dimensional mechanisms are more than two dimensional. This is due to the fact that the contribution of lateral surfaces in 3D mechanisms is more outstanding than the bottom logarithmic spiral surface. It contributes to the increase in the rate of dissipated work and consequently the factor of safety of the slope increases.

کلیدواژه‌ها [English]

  • Three Dimensional Slope Stability
  • Rotational Mechanism
  • Translational Mechanism
  • Upper Bound Limit Analysis
  • Factor of safety
  1. - Amirloo, B. (2017) Analysis of Three-Dimensional Soil Slopes Stability Based on Upper Bound Limit Analysis Using Rotational Failure Mechanisms. Master’s Thesis, University of Tehran, Iran (In Persian).
  2. - Askari, F. (1999) Three-Dimensional Analysis of Homogeneous and Nonhomogeneous Slopes in Static and Dynamic Mode Using Upper Bound Theorem of Limit Analysis. Ph.D. Dissertation Thesis, University of Tehran, Iran (in Persian).
  3. - Giger, M.W. & Krizek, R.J. (1975) Stability analysis of vertical cut with variable corner angle. Soils and Foundation, 15(2), 63-71.
  4. - DeBuhan, P. and Garnier, D. (1998) Three dimensional bearing capacity analysis of a foundation near a slope. Soil and Foundations, 38(3), 153-163.
  5. - Fazelinia, M. (2006) Analysis of Three-Dimensional Slopes Stability Based on Rotational Failure Mechanisms. Master’s Thesis, University of Tehran, Iran (in Persian).
  6. - Michalowski, R.L. and Drescher, A. (2009) Three-dimensional stability of slopes and excavations. Geotechnique, 59(10), 839-850.
  7. - Michalowski, R.L. (1989) Three-dimensional analysis of locally loaded slopes. Geotechnique, London, 39(1), 27-38.
  8. - Farzaneh, O. and Askari, F. (2003) Three-dimensional analysis of nonhomogeneous slopes. ASCE, Journal of Geotechnical and Geoenviromental Engineering, 129(2), 137-145.
  9. - Chen, W.F. and Liu (1990) Limit Analysis in Soil Mechanics, Elsevier Science Publishers, B.V.
  10. - Askari, F. and Farzaneh, O. (2003) Upper-bound solution for seismic bearing capacity of shallow foundations near slopes. Geotechnique, 53(8), 697-702.
  11. - Ganjian, N. (2002) Analysis of Three-Dimensional Stability of Arch Slopes in Plan Based on Upper Bound Limit Analysis. Master’s Thesis, University of Tehran, Iran (in Persian).