تعيين ضريب باربري لرزه‌اي پي‌هاي سطحي تحت بار مايل با استفاده از معادله‌ي كوتر

Seismic Bearing Capacity Factor of Unit Weight Under Inclined Load Using the Kötter Equation

تعيين ظرفيت باربري پي‌‌هاي سطحي در هنگام زلزله يكي از موضوعات مهم ژيوتكنيك لرزه‌اي است. در اين تحقيق، با به‌كارگيري روش تعادل حدي، معادله‌ي كوتر و روش سعي و خطا، بهينه‌‌ترين ضريب باربري لرزه‌‌اي (N?E) روي خاك غير چسبنده براي پي سطحي، كه علاوه بر بار قايم تحت بار افقي نيز مي‌باشد، به دست آمده است. در اين روش، سطح گسيختگي خاك زير پي، به‌صورت مركب (صفحه‌اي و اسپيرال لگاريتمي) در نظر گرفته شده است. از مزاياي اين روش، تعيين سطح گسيختگي متناسب با ويژگي‌هاي خاك و ضرايب شتاب زلزله است. بر اساس نتايج به‌دست‌آمده از اين تحليل، با افزايش شتاب زلزله و افزايش بار افقي، ضريب باربري لرزه‌اي پي سطحي كاهش مي‌‌يابد. نتايج حاصل از اين تحقيق با ديگر نتايج موجود در متون علمي مقايسه شد و در اكثر حالات انطباق خوبي نشان داد.

Introduction Experimental and theoretical investigations indicate that the seismic bearing capacity of foundations is affected by earthquake excitation. In the present study, an analytical procedure is presented to obtain the seismic bearing capacity factor of shallow strip footing N?E for a foundation under inclined load on cohesionless soils. The limit equilibrium method with numerical iteration technique is utilized to calculate the seismic bearing capacity factor N?E. In the proposed analysis the K?tter’s equation and a failure surface consisting log-spiral and planar surface are employed. The results indicate that the seismic bearing capacity is reduced due to an increase in horizontal coefficient of earthquake acceleration. Besides, the results are in good agreement with solutions available in the literature. Methodology The failure pattern (Figure 1) is considered based on Budhu et al. work [1] with the difference that the pole of the log spiral is not fixed and varies with earthquake acceleration, friction angle, geometry etc. The failure surface has two passive parts, the log spiral of CD and DE. To obtain the distribution of soil reaction pressure for each of these two parts, the K?tter’s equation is employed. Asymmetrical elastic wedge with full mobilization of the passive resistance on one side (BC) of the footing and partial mobilization on the other side (AC) of the footing is assumed. In Figure (2), from the horizontal and vertical equilibrium: where QuE represents the ultimate seismic bearing capacity of the foundations, B is the inclination angle (tanB= horizontal load on the foundation/QuE), Ws is the weight of the triangular soil wedge ABC, ? is friction angle, pmp?E and pmp?E represent the seismic passive thrust and mobilized seismic passive thrust, m and ?m denotes the mobilization factor and mobilized friction angle: (3) In the above equations, m and ?m are unknown that can be determined by the trial and error. The trial and error continues until two calculated values for QUE from Eqs. (1) and (2) are approximately equal. Considering 2B, footing width: (4) Results Figure (3) clearly indicates that the seismic bearing capacity factor N?E is reduced with an increase in the inclination angle. The comparison of the developed seismic bearing capacity coefficients, N?E with those obtained from the other methods for ? = 30? are presented in Figure (4). It is observed that there is a good agreement between the N?E values of the proposed method and those reported by other researchers.