Estimation of the Scale of Fluctuation of Geotechnical Properties in Natural Deposits Using Random Field Theory

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.