The essence of geotechnical/geological engineering is understanding, characterizing and quantifying networks or systems of natural materials or phenomena and their behavior. New insights, understanding and practical applications may be possible using conceptual mathematical and physics breakthroughs that incorporate power-law relationships, including fractals, self-ordered criticality and percolation theory. Where a soil or rock mass is considered a disordered system or network of many different size particles, these concepts are especially useful. Simple power-law characterization may include logarithmic plotting of event or particle size along an abscissa (x-axis) and cumulative number of occurrences along an ordinate (y-axis). Resulting size-frequency logarithmic trends tend to plot as approximately straight lines (power laws), and frequently include at least two power law trends. Example practical applications are presented. These include summarizing ground vibration data, and particle size distributions for excavatability and rippability.
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