ارايه ي روابط تعيين ظرفيت باربري شالوده هاي سطحي نواري واقع بر خاك هاي رسي دو لايه با استفاده از روش تفاضل محدود

Formulating the Bearing Capacity of Strip Footings Placed over Two-Layered Clays using the Finite Difference Method

در اين نوشتار از روش تفاضل محدود و مدل سازي دو بعدي به كمك نرم افزار FLAC براي تعيين ظرفيت باربري زهكشي‌نشده ي شالوده هاي نواري واقع بر خاك هاي رسي دو لايه استفاده شده است. همچنين براي مدل سازي رفتار خاك، از مدل رفتاري كشسان- خميري با سطح تسليم موهر- كولمب استفاده شده است. در اين پژوهش نسبت عمق لايه ي بالايي به عرض شالوده از 15/0 تا 3 و نسبت مقاومت برشي زهكشي‌نشده ي لايه ي بالايي به پاييني از 2/0 تا 5 تغيير كرده است. اين نسبت ها به گونه‌يي انتخاب شده اند كه مدل سازي و تحليل براي بيشتر حالات محتمل هندسه ي لايه ها و نيز مقاومت برشي زهكشي‌نشده ي آن ها انجام شود. در پايان با توجه به نتايج اين پژوهش، روابطي كاربردي براي تعيين ظرفيت باربري شالوده-هاي نواري واقع بر خاك هاي دو لايه ي رسي ارايه شده است، كه دقت بالايي دارند و مي توانند به صورت گسترده‌يي براي تعيين ظرفيت باربري شالوده هاي نواري در خاك هاي دو لايه ي رسي استفاده شوند.

This paper applies the finite difference method, using FLAC, to evaluate the undrained bearing capacity of rigid strip footings resting on two-layered clay deposits. For modeling the soil elastic-perfect plastic constitutive model, the Mohr-Coulomb failure criterion is used. Firstly, some numerical analyses are carried out and the results are compared with theoretical solutions in order to determine the accuracy of the model. In these analyses, values for elastic modulus, Poisson ratio, undrained soil shear strength, foundation width, element dimensions, boundary dimensions and loading velocity are changed, in order to identify the effect of each parameter on the final result and to free the modeling from numerical inaccuracies. Next, the ratio of depth of the upper layer to the width of the foundation (H/B) are varied from 0.15 to 3, while the ratio of undrained soil shear strength of the upper to the lower layer (cut/cub) is varied from 0.2 to 5, in order to model and analyze the most probable cases that could be encountered in practice. Results of analyses show that whilst, in the case of soft over strong clay, general failure usually occurs, in the case of strong over soft clay, as the top soil gets stronger, the soil will most likely experience punching failure, which is associated with a high amount of plastic settlement, before reaching its ultimate bearing capacity. Afterwards, the results of analyses are compared with the results obtained by other researchers using limit analysis, FEM, empirical and semi-empirical solutions. In the end, an equation is presented for each case (strong over soft clay and soft over strong clay), which represents the bearing capacity of two-layered clays, and their precision when describing the numerical results is examined. A comparison between the results of analyses and those given by the presented formula in this paper shows strong agreement between numerical results and the formula provided for each case (R2 > 0.99). This proves how reliable these equations are in determining the undrained bearing capacity of strip footings placed over two-layered clays, without needing to consult charts and figures.