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Force chains play an important role in linking the macro- and micro-mechanisms of powder in high velocity compaction (HVC). Force chain lengths, as an important quantitative characteristic, can describe the geometry of force chains. In this study, force chain lengths and their relation to other force chain characteristics in HVC were investigated by discrete element method. Results revealed that force chain length decreased and it can be related to the densification process of ferrous powder in HVC. Moreover, long force chains extended from top to bottom and may play a major role in supporting load, although the percentage of long force chains was low. Probability density functions of force chain lengths further showed the exponential decay. The proportion of short force chains increased and the proportion of long force chains decreased. Long force chains had high strength and can be aligned to the direction of the external load, but force chain lengths did not have clear relation to straightness. These relations were confirmed by Pearson correlation coefficients.

We treat the earth crust and mantle as large scale discrete matters based on the principles of granular physics and existing experimental observations. Main outcomes are: A granular model of the structure and movement of the earth crust and mantle is established. The formation mechanism of the tectonic forces, which causes the earthquake, and a model of propagation for precursory information are proposed. Properties of the seismic precursory information and its relevance with the earthquake occurrence are illustrated, and principle of ways to detect the effective seismic precursor is elaborated. The mechanism of deep-focus earthquake is also explained by the jamming–unjamming transition of the granular flow. Some earthquake phenomena which were previously difficult to understand are explained, and the predictability of the earthquake is discussed. Due to the discrete nature of the earth crust and mantle, the continuum theory no longer applies during the quasi-static seismological process. In this paper, based on the principles of granular physics, we study the causes of earthquakes, earthquake precursors and predictions, and a new understanding, different from the traditional seismological viewpoint, is obtained.

An initially homogeneous freely evolving fluid of inelastic hard spheres develops inhomogeneities in the flow field u(r, t) (vortices) and in the density field n (r, t)(clusters), driven by unstable fluctuations, δa = {δn, δu}. Their spatial correlations, <δa(r, t)δa(r′,t)>, as measured in molecular dynamics simulations, exhibit long range correlations; the mean vortex diameter grows as ; there occur transitions to macroscopic shearing states, etc.

The Cahn–Hilliard theory of spinodal decomposition offers a qualitative understanding and quantitative estimates of the observed phenomena. When intrinsic length scales are of the order of the system size, effects of physical boundaries and periodic boundaries (finite size effects in simulations) are important.

The contact network of a frictionless polydisperse granular packing is isostatic in the limit of low applied pressure. It is argued here that, on disordered isostatic networks, displacement–displacement and stress–stress static Green functions are described by random multiplicative processes and have a truncated power-law distribution, with a cut-off that grows exponentially with distance. If the external pressure is increased sufficiently, excess contacts are created, the packing becomes hyperstatic, and the abovementioned anomalous properties disappear because Green functions now have a bounded distribution. Thus, the low-pressure, isostatic, limit is a critical point.