PSI - Issue 37

Koji Uenishi et al. / Procedia Structural Integrity 37 (2022) 397–403 Uenishi and Nagasawa / Structural Integrity Procedia 00 (2022) 000 – 000

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1. Introduction In seismology, an earthquake source model usually assumes one single, relatively large fracture region in a brittle solid that may expand quasi-statically or dynamically and may radiate seismic waves. However, such a single large scale fracture model causes most likely one sole seismic event, and may not be useful in clarifying the physical mechanisms of a cluster of earthquakes and earthquake swarms, for example, the 2016 Kumamoto, Japan, earthquakes that consist of a very strong quake (moment magnitude M w 6.2) at 9:26 pm on 14 April and even stronger second shaking ( M w 7.0) at 1:25 am on 16 April (local time). In order to comprehend the physical background behind the complex seismicity, here, quasi-static and dynamic fracture development as well as generation of waves is observed in a two-dimensional framework experimentally and numerically. Our attention is paid to the mechanics behind shallow dip-slip faulting that has not been fully grasped yet owing to the insufficient amount of the near-field seismological recordings and the analytical complexity (Uenishi, 2015). Hence, linear elastic brittle specimens that have sets of pre-existing small-scale (local) parallel fracture regions are prepared where each of the small-scale fracture regions or cracks is set to model a large-scale (global) geological normal fault plane that dips vertically or with some angle to the horizontal free surface. 2. Vertically dipping small-scale cracks For the laboratory experiments, transparent photoelastic polycarbonate specimens having small-scale parallel cracks are prepared with a digitally controlled laser cutter. Every specimen is under external tensile load that is exerted by a testing machine and acting parallel to the free surfaces, and the initiation and evolution of fractures and possibly the fracture-induced waves are observed using a high-speed video camera at a frame rate of 50,000 frames per second. A variety of different distribution patterns of pre-existing cracks with various dip angles are examined, and in this contribution, typical four cases are introduced. In the first case (Uenishi et al., 2020), a set of vertically dipping cracks are subjected to tensile loading (Fig. 1(a)). The photographs taken by the high-speed camera clearly indicate that the dynamic fracture evolution is composed of three stages: (1) Upward propagation of the main fracture and total split of the specimen into two; (2) Jump of fracture on the top free surface to remote positions, and the initiation of the downward secondary fractures and their sudden arrest; and (3) Reactivation of downward propagation of the secondary fracture after a short temporal interval (in this example, 200  s) (one of the photographs is shown in Fig. 1(b)). Note that the cluster of the secondary and further fractures (2 and 3 in Fig. 1(b)) are induced even without applying further external load and they are obviously guided by the dynamic, main fracture-induced waves. Finite difference simulations with the spatiotemporally second order accuracy can reinforce the idea of such considerable effect of the main fracture-induced waves. In Fig. 1(c), contours of the maximum in-plane shear stress, normalized with regard to the external constant, uniform static tensile stress, are depicted for a geometrically simpler, homogeneous, isotropic and linear elastic polycarbonate specimen with the mass density 1,200 kg/m 3 , shear modulus 820 MPa and Poisson’s ratio 0.37 (1,201  361 orthogonal grids). For graphical clarity, the specimen here has small-scale cracks only on the line of the main fracture. In the figure, the so called rupture front wave around the tip of the main fracture as well as regions of stress amplification are identifiable at positions away from the main fracture. At these larger stress regions that are induced by the reflection of the main fracture-induced body waves, the secondary fractures can be initiated. Similarly, further numerical simulations can indicate that reflection and diffraction of the Rayleigh surface waves generated upon a complete split of the specimen by the main fracture can govern the resumption process of the arrested secondary fracture (Uenishi et al., 2020; Uenishi and Nagasawa, 2021). Thus, the local fracture development can be dynamically controlled by the global propagation of the main fracture-induced waves. 3. Inclined small-scale cracks Other three different experiments illustrate the significant dependency of the fracture behavior on the initial inclination (dip) angle and distribution pattern of the set of parallel cracks. In the second case with a relatively large dip angle, 70 degrees (Fig. 2), the fracture evolution looks similar to the case with the dip angle of 90 degrees (Fig. 1). The upward main fracture dynamically moves and links the pre-existing inclined cracks, followed by the downward secondary fracture. This time, the secondary fracture seems to be initiated before the total split of the