Modares Civil Engineering journal مهندسی عمران مدرس MCEJ Engineering & Technology http://mcej.modares.ac.ir 1 admin 2476-6763 2476-6763 fa jalali 1397 8 1 gregorian 2018 11 1 18 4 online 1 fulltext
fa بررسی عددی اثر زبری بر ضریب ظرفیت باربری Nγ به روش المان محدود مرز پایین Numerical study on the effect of roughness of shallow foundations on bearing capacity factor Nγ using lower bound finite element analysis به علت پیچیده بودن تعیین مقدار دقیق N&gamma;محققان مختلف، مقادیر متفاوتی را برای این ضریب با استفاده از روش‌های گوناگون پیشنهاد داده‌اند. با توجه به تأثیرگذار بودن زبری پی، بر مقدار این ضریب، بررسی اثرات زبری بر مقادیرN&gamma; امری ضروری می‌باشد. در این پژوهش مقادیر ضریب ظرفیت باربریN&gamma; برای پی‌های سطحی، با در نظر گرفتن اثر زبری پی، به روش آنالیز حدی المان محدود مرز پایین مورد بررسی قرار گرفته است. برای این منظور، یک برنامه کامپیوتری در محیط MATLAB نوشته ‌شده است که با استفاده از روش آنالیز حدی مرز پایین به کمک المان محدود و برنامه‌ریزی خطی ضریب ظرفیت باربری N&gamma;را در حالت‌های پی صاف و زبر تعیین می‌نماید. مقادیر محاسبه شده N&gamma;توسط برنامه تدوین شده، با نتایج دیگر محققین مورد مقایسه قرار گرفته است. به دلیل اینکه روش بکار گرفته شده در حد پایین قضایای حدی قرار دارد، نتایج به دست آمده دارای شاخص اطمینان مناسب بوده و برآورد ایمن از ظرفیت باربری ارائه می‌کند. Due to the complexities associated with the determination of bearing capacity coefficient N&gamma;, researchers have proposed different values for this coefficient. As the roughness of foundation influences the value of this parameter, it is essential to consider its effect on N&gamma;. In the present research, the values of bearing capacity factor N&gamma;, has been determined by lower bound finite element method. The problem has been solved for a two-dimensional domain of the soil beneath a strip foundation. The domain was discretized into a three-nodded linear triangular element. In this method, in contrast to the conventional finite element analyses, the primary variables are three components of two-dimensional stress matrix. Differential equations of stress equilibrium in horizontal and vertical directions are the governing equations of problem. The bearing capacity is defined as the maximum load which can be applied to the foundation while not violating the stress constraints. The constraints include stress discontinuity and yield condition constraints. The stress components at a node common in adjacent elements are not essentially equal. The stress at adjacent element can be discontinuous. The condition of stress discontinuity means that the stress components should be such that the tangential and normal forces at common border lines of adjacent elements are in equilibrium. Moreover, the stress components should be such that they do not violate the Mohr-Coulomb failure criterion. The failure criterion was linearized into definite linear segments. The aforementioned equality and non-equality conditions construct a set of linear equations. The maximum load can be applied to the foundation was determined by linear programming as an optimization technique. The N&gamma; factor was calculated at two conditions of rough and smooth conditions. For the smooth foundation, an additional constraint was applied. The horizontal at the soil-foundation interface was imposed zero. The values of N&gamma; were compared at different values of soil friction angles. The values of the factor obtained from the current research were compared with the results of other relevant researchers including the results obtained from limit equilibrium, slip line method, upper bound solutions and lower bound solutions. The results indicate that the roughness of foundation affects the value of N&gamma; factor and consequently affect the bearing capacity. Therefore, in order to calculate the precise and reliable bearing capacity of a foundation, it is essential to take the effect of foundation roughness into account. The results of comparisons with the relevant studies indicate that the results of different methods do not differ substantially for the friction angles less than 30 degrees. On the other hand, the values of factors obtained from different methods differ substantially from each other for the friction angles higher than 30 degrees. This divergence increases by increasing the friction angle. The factors obtained from upper bound solutions are essentially higher than those obtained from the present research which is a lower bound solution. As the exact solution is higher than what obtained from lower bound solution, it could be stated that the reliability index of the factors obtained from the current study is higher than other methods. It could be concluded that the proposed factors can be regarded as a safe estimate for N&gamma; factor. زبری پی سطحی,المان محدود,مرز پایین,آنالیز حدی,ضریب ظرفیت باربریNγ, Roughness,Shallow Foundation,Lower Bound,Bearing Capacity Factor,Nγ, 37 45 http://mcej.modares.ac.ir/browse.php?a_code=A-16-10827-2&slc_lang=fa&sid=16 1 1 علی رضا باقریه `1003194753284600107805` 1003194753284600107805 Yes 1 دانشگاه ملایر Somaye Safiyari سمیه صفیاری `1003194753284600107806` 1003194753284600107806 No Department of Civil Engineering, Malayer University, Malayer, Iran گروه مهدسی عمران، دانشگاه ملایر، ایران