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For fundamentally characterizing the effect of hierarchical structure ingranular matter, a set of compression-relaxation tests for dust particles andglass beads confined in a cylindrical cell was performed. Typical diameter ofboth grains is approximately 1~mm. However, dust particles are produced bybinding tiny ($\sim 5$~{\textmu}m) glass beads. The granular columns werecompressed with a piston until reaching a maximum load force of 20~N with aconstant compression rate $v$ ($0.17 \leq v \leq 2000$~{\textmu}m~s$^{-1}$).After that, the piston was stopped and the relaxation process was quantified.From the experimental results, we found that the compression force $F$nonlinearly increases with the increase of compression stroke $z$ depending onparticles. Besides, periodic undulation and sudden force drops were observed on$F(z)$ in dust particles and glass beads, respectively. The relaxation processwas characterized by an exponential decay of stress followed by a logarithmicdependence one in both kinds of particles. These experimental findings are themain point in this study. To understand the underlying physics governing thecompression mechanics, we assumed empirical forms of $F(z)$; $F\proptoz^{\alpha}$ for dust particles and $F \propto \exp(z/z_G)$ for glass beads($\alpha=2.4$ and $z_G=70$~{\textmu}m). Then, we found that the growing mannersof periodic undulation and force drops were identical to those of meancompression forces, i.e., power law in dust particles and exponential in glassbeads. In addition, the undulation amplitude and wavelength decreased as $v$increased in dust-particles compression. On the basis of experimental resultsand the difference between dust particles and glass beads, we also discuss theorigin of undulation and the physical meaning of granular-compression modelsused in engineering fields.

Undulating compression and multi-stage relaxation in a granular column consisting of dust particles or glass beads