PSI - Issue 13

Koji Uenishi et al. / Procedia Structural Integrity 13 (2018) 769–774 Uenishi and Goji / Structural Integrity Procedia 00 (2018) 000–000

770

2

Keywords: Wave propagation in granular media; Fracture of granular media; Dynamic slope failure

1. Introduction Earthquakes, i.e. fracture of our solid earth, are frequently investigated in light of continuum mechanics, and through our continuum mechanics-based analyses, for instance, the universal critical size for earthquake nucleation (Uenishi and Rice, 2003; Uenishi, 2018) and the crucial roles of the frequencies and types of incident seismic waves in generating unique dynamic structural failure patterns (Uenishi, 2010a, 2012) have been quantitatively indicated. However, there are other influential seismic phenomena that are hard to be explained through the concepts of continua. These phenomena include occurrence of landslides as well as formation of the geological flame structure with characteristic thickness 60 mm and periodic length 40 mm (Yasuda and Sumita, 2014), possibly caused by liquefaction and subsequent gravitational instability of sediments immersed in water. For these seismic phenomena, instead of mechanics of continua, mechanical properties of particles in granular media under dynamic impact may play some specific roles, but possible relation between waves and fracture in granular media, for example, does not seem to have been fully identified so far. Thus, in addition to the fundamental observations of transient granular mass flow from a (semi-)cylindrical column of dry glass beads (Uenishi and Tsuji, 2008; Uenishi et al., 2009), the mechanical characteristics of stress transfers in granular media that consist of penny-shaped photoelastic particles (diameter 20 or 40 mm, thickness 10 mm) made of epoxy resin and are subjected to dynamic impact (Uenishi et al., 2017) have been scrutinized by utilizing the experimental technique of dynamic photoelasticity in conjunction with high-speed photography. It has been found that in a single particle system where only one particle is situated on a horizontal rigid plane, dynamic wave propagation is identifiable inside that single particle, but in a layered (loosely packed) multi particle system stress is transferred rather quasi-statically from a particle to its neighbors and wave propagation is not clearly observed. Therefore, here, dynamic properties of two-dimensional granular media are further experimentally studied. Especially, dry granular slopes are considered and the wave and fracture development recognized in such slopes is compared with that in typical continuum media and the actual earthquake-induced slope failure mentioned in the next chapter. 2. Dynamic tensile cracking in slopes due to earthquakes and analytical speculations Just after the 2011 off the Pacific coast of Tohoku (Great East Japan) earthquake (moment magnitude M w 9.0), unique failure pattern was found in a fill slope in Sendai City where only open (tensile) cracks were produced in the top surface parallel to, but some meters away from, the edge of the slope. Although not widely known, this kind of slope failure has been repetitively caused, e.g. in the same slope by the 1978 Miyagi-ken-oki earthquake ( M w 7.5) (Fig. 1(a)), in the South Island of New Zealand by the 2011 Christchurch earthquake ( M w 6.2) (Hancox et al., 2011), and in California by the 1906 ( M w 7.8) and 1957 ( M w 5.7) San Francisco (Sitar et al., 1980) and the 1989 Loma Prieta ( M w 6.9) (Ashford and Sitar, 1997) seismic events. Efforts have been made to understand the generation mechanism of open cracks along but located at a small distance from the edge, but the continuum mechanics-based analyses of body wave interaction with a model slope (e.g. Sitar et al., 1980; Ashford and Sitar, 1997; Ashford et al., 1997) cannot straightforwardly reproduce the unique failure pattern. Even when granular slopes are presumed in the analyses, the effect of wave propagation on fracture in granular media is frequently ignored and in most cases only granular mass flow (translation of particles), i.e. nearly simultaneous collapse of slope face, edge and top surface, is depicted. That is, the mechanical reason for the only damage to the slope, open cracks in the top surface, cannot be rightly suggested with normal granular models, either. Only recently, it has been theoretically indicated that the influence of Rayleigh surface waves can be more significant than that of body waves in inducing the open cracks (Uenishi, 2010b) (Fig. 1(b)), and indeed, the transient stress development inside a two-dimensional model linear elastic slope obtained by a numerical particle method, the original version of the moving particle semi-implicit (MPS) method, shows that, at least in terms of stresses, it may be more appropriate to assume and trace the propagation of Rayleigh waves in a high frequency range so as to systematically describe the cause of the open cracks (Fig. 1(c)) (Uenishi and Sakurai, 2015). That is, body waves, even in a higher frequency range, may not be able to generate such a failure pattern, and the analyses handling only body wave interaction cannot thoroughly illustrate the slope dynamics and they may give