is approximately equal to the initial normal stress 
. In the current configuration, the straightness of the interface as well as the uniformity of surface roughness ensure bilateral and symmetric propagation of the rupture (2).Lu et al. 10.1073/pnas.0704268104. |
SI Experimental Design and Methods
Rupture Initiation Procedure. A small hole of 0.1 mm in diameter is drilled in the center of a fault surface and a nickel wire with a diameter of 0.08 mm is cemented within. The ends of the nickel wire are connected to a charged capacitor whose stored energy is discharged, turning the wire into high-pressure plasma. This allows shear rupture to start in a small region around the explosion site under the action of the resolved shear traction due to far-field loading. The rupture concentrates shear stress ahead of its tips, allowing this stress to reach the static friction strength outside the area affected by the explosion, thus spreading the rupture farther. Interface locations behind the rupture front experience a dynamic reduction in frictional strength as would be expected from either a slip-weakening or velocity-weakening friction law, further promoting rupture growth. The nucleation procedure may result in some normal stress variation along the interface, due to waves radiated from wire explosion. That normal stress variation should be small outside the nucleation region compared with the value of the initial (resolved) normal stress. Xia et al. (1) estimates the variation to be <0.35 MPa at the location of particle velocity measurement at the time of rupture arrival, while initial normal stresses range from 7.50 MPa to 12.36 MPa for experimental parameters used in this study. Note that normal stress on the interface is not altered by sliding for times of observation, before the reflected waves arrive from the plate boundaries. Hence, we can assume that normal stress is approximately equal to the initial normal stress . In the current configuration, the straightness of the interface as well as the uniformity of surface roughness ensure bilateral and symmetric propagation of the rupture (2).
Criteria for Establishing Rupture Duration.
In order to consistently identify the timing of both interfacial sliding initiation and interfacial locking (or healing), and thus to determine the rupture duration, criteria are established which account for the elastodynamic shear deformation between the measurement points. Interfacial sliding starts if and only if shear stress
on the interface is equal to the static friction strength of the interface which, in turn, is equal to normal stress times the static friction coefficient 
. As already discussed, normal stress is approximately equal to the initial normal stress . The difference between the static friction resistance 
and initial shear stress 
at a point along the interface is overcome by the dynamic shear stress increase arriving with either the rupture tip or the shear wave front. Assuming uniform shear stress between the two measurement points, this difference in shear stress can be converted into a critical shear strain 
, and further into a critical relative displacement 
, which can be sustained between the two measurement points before interfacial sliding initiates. If 
is the shear modulus of Homalite-100 and D is the distance between the two measurement location, the critical displacement is given by: 
. [1]
The time of rupture initiation can be established by integrating the relative velocity records and determining the time at which displacement equal to is accumulated; this time is marked by green filled dots in Fig. 2. This time also corresponds to a particular value 
of the relative velocity which we call the elastic cut-off velocity. That value of relative velocity is plotted as the yellow dotted interface-parallel line in Fig. 2 b, d, and f. We demonstrate this procedure in relation to the results presented in Fig. 2 a and b. In that experiment, is calculated to be 0.72 mm, and the corresponding time of sliding initiation is determined to be 20 ms. This time coincides with the time of observed drastic velocity increase (Fig. 2a) and the arrival of the stress concentration (rupture tip) at the measurement location in photoelastic images. At 20 ms, the relative velocity is equal to 0.34 m/s and hence the elastic cut-off in this case is 
m/s. The yellow dotted line in Fig. 2b corresponds to that value of relative velocity. Non-zero relative velocities before the rupture initiation time of 20 ms in Fig. 2a correspond to elastodynamic shearing between the measurement points. Eq. 1 shows that the critical distance decreases significantly as the angle increases from 
to 
. Indeed, for 
we find 
mm, respectively. At the same time, the corresponding values of relative velocity vary only slightly, being 0.34, 0.32, and 0.42 m/s, respectively.
To find when the sliding stops, we employ two criteria. The first criterion, consistent with how the rupture initiation is determined, is to assume that sliding stops when the relative velocity becomes smaller than the elastic cut-off value . If the sliding velocity decreases below several times, we take the last time as the time of interface locking. Those times are marked by half-filled red dots in Fig. 2. The second, more conservative, criterion is to insist that the relative velocity drops to zero and that the integral of relative velocity from that time until the end of observation time is a small fraction (<5%) of the total accumulated relative displacement. The corresponding times are marked by fully filled red dots in those figures. The two different locking criteria produce the same qualitative results with respect to rupture mode identification, as discussed in the main text and shown in Figs. 2-4.
1. Xia KW (2005) Ph.D thesis (California Institute of Technology, Pasadena, CA).
2. Xia KW, Rosakis AJ, Kanamori H (2004) Science 303:1859-1861.