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One of the main distinctions between geomaterials and other engineering materials is the spatial variation of their properties in different directions inside them. This characteristic of geomaterials (so- called as heterogeneity) is studied herewith. Almost all natural soils are highly variable in their properties and rarely homogeneous. Soil heterogeneity can be classified into two main categories. The first is lithological heterogeneity, which can be manifested in the form of thin soft/stiff layers embedded in a stiffer/softer media or the inclusion of pockets of different lithology within a more uniform soil mass. The second source of heterogeneity can be attributed to inherent spatial soil variability, which is the variation of soil properties from one point to another in space due to different deposition conditions and different loading histories. Inherent spatial variability of geomaterials is itself devided into the random component, which is attributed to different depositioaln conditions, and the deterministic trends, which are attributed to the variation in soil properties, such as increase in soil strength with depth due to increase in confining pressure. Different elements of soil inherent spatial variability such as mean, variance, and spatial correlation characteristics were introduced with the main focus on the importance of spatial correlation distane and the way to handle it. Several spatial distributions introduced to describe the probabilistic variation of geotechnical properties of soils. Among all, absolute normal distribution was adopted as appropriate distribution, which best presents these properties in horizontal direction. Variation of geotechnical parameters in vertical direction is, however, conceived to follow a deterministic trend. Using random field theory, local average subdivisions (LAS) formulation and MATLAB Mathworks, virtual data with different correlations was produced, and by employing autocorrelation function, a trend for this function was invoked for different predetermined values of the scale of fluctuations. It was found that autocorrelation function has a deterministic trend as far as the scale of fluctuation has not been exceeded. It is clearly concluded that, for distances farther than the specific scale of fluctuation, the behavior is chaotic and this can be an index to calculate the scale of fluctuation of the experimental data.

Keywords: Local average subdivisions, Random field theory, Scale of fluctuation, Spatial variation, Heterogeneity

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