HR: 14:25h
AN: S13E-04    [Abstracts]
TI: Three-Dimensional Rupture Instability of a Slip-Weakening Fault Under Heterogeneous Loading
AU: * Uenishi, K
EM: uenishi@kobe-u.ac.jp
AF: Research Center for Urban Safety and Security, Kobe University, 1-1 Rokko-dai, Nada, Kobe, 657-8501 Japan
AU: Rice, J R
EM: rice@esag.harvard.edu
AF: Department of Earth and Planetary Sciences and Division of Engineering and Applied Sciences, Harvard University, 224 Pierce Hall, 29 Oxford Street, Cambridge, MA 02138 United States
AB: In previous studies [Rice and Uenishi, {\it EOS}, 2002; Uenishi and Rice, {\it JGR}, 2003], we considered slip initiation and rupture instability on two-dimensional faults that follow a slip-weakening relation and are subjected to a loading stress that is locally peaked spatially, the level of which changes quasi-statically in time. We showed that for the case in which the fault strength weakens linearly with slip, there exists a universal length of the slipping region at instability, independent of any length scales entering into the description of the shape of the loading stress distribution. Here, we study slip development and its (in)stability for three-dimensional planar faults that follow the linear slip-weakening relation. We employ an energy approach to give a Rayleigh-Ritz approximation for the dependence of size of the rupture zone and maximum slip on the level and shape of the loading stress distribution. The zone is assumed elliptical, $x^2/a^2 + z^2/b^2 \le 1$, with unknown axes $a, b$, where the fault coincides with the $x$-$z$ plane ($y = 0$). A loading stress $\tau_p + Rt - \kappa (x^2 + m^2 z^2) / 2$ is assumed on that plane; $\kappa$ and $m$ are positive constants and $Rt$ is the stress change from that for which the peak in the loading stress distribution equals the strength $\tau_p$. Results show this loading induces a rupture zone whose aspect ratio $a(t)/b(t)$ changes with time $t$ except for the cases of circular cracks ($m = a/b = 1$) for the opening (tensile) mode and $m = a/b \approx 1 / (1 - \nu)$ for the sliding mode (unidirectional shear in the $x$-direction). Here, $\nu$ is Poisson's ratio. These values of $m$ minimize the area of critical rupture zone at instability ($\pi a_c b_c$), and for the opening mode, the corresponding critical diameter is $2a_c = 2b_c \approx 1.960 \mu/[W(1 - \nu)]$, with $\mu$ being shear modulus and $W$ linear slip-weakening slope. For the sliding mode, the critical rupture size is written in terms of $\mu$, $\nu$ and $W$ (and the complete elliptic integrals of the first and second kinds). When, for example, $\nu = 0.25$, those critical lengths are $2a_c \approx 2.598\mu/W$ and $2b_c \approx 1.951 \mu/W$. Comparison of these results with the two-dimensional ones ($1.158 \mu/[W(1 - \nu)]$ for modes I and II; $1.158 \mu/W$ for mode III) shows that the critical lengths are of the same order for all cases, implying that the actual critical length associated with seismic nucleation may be of the order of up to few meters, as suggested by Uenishi and Rice [{\it JGR}, 2003].
DE: 7260 Theory and modeling
DE: 7209 Earthquake dynamics and mechanics
DE: 3210 Modeling
SC: Seismology [S]
MN: 2004 AGU Fall Meeting