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The soil formation consists of complex and longtime processes in which many different chemical and physical changes occur in soil deposit, or in its original source rock. This processes cause the soil to show nonhomogeneous characteristics and to have spatial variation in its mechanical properties. The spatial variation of soil properties lead to many uncertainties in prediction of soil mechanical behavior; subsequently the design of structure which depend on soil deposits becomes troublesome. For dealing with such problem the probabilistic and statistical tools are proposed as convenient methods for choosing appropriate design soil parameters and estimating the uncertainties in design. The coupled utilization of random field theory and Monte Carlo simulation technique yield probability distribution functions for geotechnical problems in which different cases of soil distribution is assumed for analyses. In such problems the soil properties are distributed into the field according to the assumptions of random field theory by consideration of a probability distribution (with the given mean and standard deviation) and scale of fluctuations. This distribution of soil properties with the use of random field theory is performed repeatedly until a desired statistical distribution for the results is obtained. This distribution can be used as a basis for extracting the statistical characteristics for the problem in hand. In this paper the effect of spatial variability parameters on the bearing capacity of strip foundations on clayey soils were investigated. The soil un-drained shear strength (Cu) was assumed as spatial variable parameter with the use of logarithmic distribution and the so-called coupled random field theory; the Monte Carlo simulation technique was used for obtaining probability distribution of bearing capacity of foundation on nonhomogeneous clayey soil. The Mohr Coloumb elastic perfectly plastic constitutive model and the Finite Difference Method (FDM) were used for modelling soil behavior and calculating the bearing capacity of foundation. The spatial variability of un-drained shear strength was investigated using three parameters: coefficient of variation of un-drained shear strength (Cov(Cu((, and the scale of fluctuation of shear strength in horizontal and vertical directions (x, and y directions). The range of these parameters were chosen such that the results of current research can be generalized to any field problem. The results obtained from this study, were investigated by average and coefficient of variation of NC parameter which is the cohesion factor in classic bearing capacity equations (i.e. as Terzaghi, Meyerhof, Hansen and Vesic bearing capacity equations). It can be interpreted from the results that by increasing the coefficient of variation of soil un-drained shear strength the average bearing capacity decreases and the coefficient of variation of bearing capacity increases; also the average bearing capacity of foundation has an approximately increasing trend with increasing the scale of fluctuations in both horizontal and vertical directions. Finally at the end of this paper two practical simplified equations were suggested using multiple regression method for estimation of average and coefficient of variation of bearing capacity factor NC, given the spatial variation parameters of soil un-drained shear strength. These equations can be implemented by geotechnical experts for applying the variability of cohesion in the design of foundations on nonhomogeneous clayey soil formations.

Keywords: Bearing Capacity, Spatial Variability, Finite Difference Method, Multiple Regression Method, Monte Carlo Simulation.

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