Fractal analysis of the fracture strength of lava dome material based on the grain size distribution of block-and-ash flow deposits at Unzen Volcano, Japan

A fractal theory of rock fragmentation is applied to block-and-ash flow deposits from the Fugendake dome, Unzen Volcano, Kyushu, Japan, in order to analyze the material strength and the energy required for size reduction of the source lava dome. Two fractal dimensions h and Ds, which are mutually interchangeable, represent the relative strength and energy for particles reduced to a given size. They can be theoretically estimated from the power relations of a reference grain size to the cumulative mass and number of fragments smaller than that size. The Unzen–Fugendake block-and-ash flow deposits have been further modified by size sorting and secondary fragmentation that occurred during flowage, so that the h value decreases (or Ds value increases) with increasing distance from the source. Coarse, reversely graded deposits are, however, found to retain the original size population relatively well. The Ds values estimated from deposits of this type are compatible with those previously reported from decompression–fragmentation experiments conducted on the same dome material. The employed fractal approach could thus give insights into the potential mode of dome collapse that generates block-and-ash flows.