13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- normal stress acting perpendicular to the fault surface [5, 7−9]. However, the dynamic properties of shallow dip-slip faulting are not fully understood yet. Here, in order to give a possible physical explanation of the abovementioned observation, we numerically and experimentally study rupture (fracture) dynamics of a dip-slip fault (interface) situated in a two-dimensional, monolithic linear elastic medium. We employ the finite difference technique for numerical simulations on a PC basis, and in a series of experiments, we initiate rupture in the birefringent linear elastic material using a Q-switched Nd:YAG laser system or a projectile launched by a gun. We record the time-dependent evolution of the wave field induced by the crack-like rupture along the fault, and also monitor the particle motions on the free surface of the model. 2. Geometry and setting Our model contains a fault plane dipping either 90° (vertical) or 45° (nonvertical case) (Fig. 1) and in each case, the initial static shear stresses acting on the fault plane are set to be equal: For the vertical case (Fig. 1a), remote shear loading which increases linearly with depth is assigned; In the nonvertical case (Fig. 1b), compressive normal stress increasing with depth is given so that linearly increasing static shear stress acts on the fault plane (Fig. 1b). Using the finite difference technique [18], we study the seismic wave field (isochromatic fringe patterns) produced by rupture of this straight fault and try to gain insight into the free surface effect on dip-slip faulting. As we consider the problem in the framework of linear elasticity, we may assume, without loss of generality, the longitudinal (P) wave speed cP in the medium is 1. If Poisson’s ratio is 0.25, then the shear (S) wave speed cS becomes 1/ 3 (~ 0.58) and the Rayleigh (R) wave speed cR is about 0.53. We use the orthogonal 201 times 201 grid points and calculate displacements at each grid point with the second order accuracy. The uniform spacing between each orthogonal grid is 0.05, and the time step is also constant to be 0.025. We further assume the energy absorbing boundary conditions to the outer boundaries except for the upper free surface where the vertical normal and the tangential shear stresses are always zero. We simulate three different situations: finite fault that ruptures only at depth (Fig. 2); fault rupture (interface crack) starting at depth and arrested well below the free surface (Fig. 3); and fault rupture initiated at depth and reaching the free surface (Fig. 4). By showing the time-dependent dynamic (maximum in-plane shear) stress field, we suggest that the magnitudes of the stresses induced in the (a) Free surface (b) Footwall Free surface 45° Hanging wall Vertical section Figure 1. Schematic diagram of the geometry of the dip-slip fault model. For both (a) vertical and (b) nonvertical (45° dipping) situations, we assume a monolithic, linear elastic medium. The fault rupture (interface crack) starts at the bottom and in later simulations it propagates towards the free surface. While the geometrical symmetry is preserved in (a), the symmetry between the free surface and the two sides of the fault (hanging wall and footwall) is broken in (b).
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