Fig. 9

Oscillatory measurements of scoriae (a, b) and ash (c, d). a The friction coefficient calculated by the ratio of the shear to normal stresses, \(\mu =\sigma _{\tau }/\sigma _{\mathrm{N}}\), obtained by oscillatory measurements as a function of the angular frequency \(\omega\). The color of the curves indicates the imposed normal stress as shown in the legend. Crosses and circles indicate the fractured and unfractured samples, respectively. Solid and dotted curves indicate the increasing and decreasing angular frequency \(\omega\), respectively. b Q (inverse of the attenuation) calculated by the phase difference between the imposed strain and the measured stress. When the energy dissipation exceeds the elastic energy, \(Q<1\), and vice versa. Symbols and colors are the same as those in (a). c, d Same as (a, b) but for ash. The color of curves indicates the temperature, and symbols indicate the combinations of the size of the ash particles and the normal stresses. In these measurements, we use a strain amplitude of \(\gamma _{\mathrm{0}}=10^{-3}\)