Use of fractal entropy to predict potential of internal instability of granular filters—a novel alternate to PSD-based methods

This study reports on a series of pressure gradient-controlled long-term hydraulic tests on ten sand-gravel mixtures. It is observed that the cumulative statistical distribution of soil particles expressed in terms of fractal entropy governed the erodibility of fines, based on which a more realistic criterion is proposed for prompt assessment of internal stability. For instance, the soil’s particle size distribution (PSD) is discretized into several fractions to extract maximum particle grading information through the principle of statistical/fractal entropy. Two normalized variables: base entropy ( h 0 ) and entropy increment (∆ h ) are determined directly from the particle size distribution curve. h 0 is then plotted against ∆ h to establish a plane, and maximum ∆ h line is drawn based on the principle of maximum entropy to obtain a semi-ellipse within plane formed by h 0 and ∆ h , wherein a PSD curve can be simply expressed as a point. Soils show internal stability on maximum ∆ h line; however, the stability at the vertex vicinity as a transition area corresponds to coefficient of uniformity and the number of fractions. A clear boundary between stable and unstable soils is visualized at maximum ∆ h line, and a simple criterion is proposed for prompt assessment of internal stability. A large body of published data is evaluated correctly and compared to several well-accepted existing methods.