Soil parameters in terms of entropy coordinates

Abstract

In the ongoing research, an approximate, grading entropy based, advanced interpolation method is applied to establish empirical functions between the grading curves and the model parameters of sands. The space of the grain size distribution curves with N fractions is isomorphic to the space of the unit-sided simplex with dimension N-1. The traditional interpolation over the simplex with dimension N-1 is problematic since the number of the sub-simplexes (and the interpolation points) may increase exponentially with N. To overcome this difficulty, the function is approximately interpolated, which means that the interpolation is made on some 2-dimensional sections of the simplex and is extended to the whole simplex, using the grading entropy map. Two kinds of 2-dimensional sections can be used based on either fractal distributions or partly fractal partly on some maximal gap-graded distributions. In this paper the experiments were made on the artificial mixtures of natural sand grains earlier. Two kinds of functions were approximately interpolated for the minimum dry density using the measured data. One kind of function was determined for the parameters of an SWCC model directly from the level lines previously graphically interpolated from fractal distribution data.

The Finite Fractal Distributions as Mean Grain Size Distributions of Granular Matter

“…The use of grading entropy in assessing granular physical properties (eg., soil hydraulic conductivity, dry density, soil water retention model parameters [48][49][50][51] is more and more accepted and the measurements related to the statistical relations are worthy to be made on fractal grading curves.…”