Soil parameters in terms of entropy coordinates

¹ EKIK HBM Research Centers and Bánki Donát Faculty of Mechanical and Safety Engineering, Óbuda University, H-1081, Budapest, Hungary
² Ybl Miklós Faculty of Architecture and Civil Engineering, Óbuda University, H-1174, Budapest, Hungary
³ Ruhr-Universität Bochum, 44801, Bochum, Germany
⁴ Institute of Mechanics and Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, 1113, Sofia, Bulgaria
⁵ School of Computing, Engineering and the Built Environment, Edinburgh Napier University, EH10 5DT, Edinburgh, United Kingdom
⁶ Birmingham City University, B42 2SU Birmingham and University of Bristol, BS8 1QU, Bristol, United Kingdom
⁷ Texas A&M University, College Station, TX 77843, United States of America

^* Corresponding author: imre.emoke@uni-obuda.hu

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.