Progression of spontaneous in‐plane shear faults from sub‐Rayleigh to compressional wave rupture speeds

Abstract

We investigate numerically the passage of spontaneous, dynamic in-plane shear ruptures from initiation to their final rupture speed, using very fine grids. By carrying out more than 120 simulations, we identify two different mechanisms controlling supershear transition. For relatively weaker faults, the rupture speed always passes smoothly and continuously through the range of speeds between the Rayleigh and shear wave speeds (the formerly considered forbidden zone of rupture speeds). This, however, occurs in a very short time, before the ruptures reach the compressional wave speed. The very short time spent in this range of speeds may explain why a jump over these speeds was seen in some earlier numerical and experimental studies and confirms that this speed range is an unstable range, as predicted analytically for steady state, singular cracks. On the other hand, for relatively stronger faults, we find that a daughter rupture is initiated by the main (mother) rupture, ahead of it. The mother rupture continues to propagate at sub-Rayleigh speed and eventually merges with the daughter rupture, whose speed jumps over the Rayleigh to shear wave speed range. We find that this daughter rupture is essentially a "pseudorupture," in that the two sides of the fault are already separated, but the rupture has negligible slip and slip velocity. After the mother rupture merges with it, the slip, the slip velocity, and the rupture speed become dominated by those of the mother rupture. The results are independent of grid sizes and of methods used to nucleate the initial rupture.

Properties of the shear stress peak radiated ahead of rapidly accelerating rupture fronts that mediate frictional slip

“…Transporting significant energy ahead of the rupture front, the stress radiation amplitudes can reach the strength of the frictional interface and trigger supershear (5,9,(11)(12)(13)(14). The radiated shear stress peaks have a characteristic near-field signature: high-amplitude radiation (comparable to the dynamic stress drop) that is both localized and strongly focused in the direction of rupture propagation.…”

“…3A, Inset). To close the system, we choose the widely used (9,13,14,23) (1.4 μm). Spontaneous rupture nucleation in friction experiments and in natural faults has been the subject of extensive study (29)(30)(31)(32).…”

“…We first consider the effect of preimposed shear stress. Previous studies had suggested that once the shear stress peak, σ S xy , reaches the interfacial strength, σ p xy , a supershear secondary crack is born that propagates above C S (9) whose transition length has been numerically studied (9,(12)(13)(14). In Fig.…”

“…1 and later numerically observed in ref. 9, who found that a sufficiently strong shear stress peak can overcome interfacial strength and nucleate a daughter crack that will propagate at supershear velocities (10)(11)(12)(13)(14)(15). Such supershear ruptures have indeed been observed along natural fault planes (16,17) and in laboratory experiments (18)(19)(20)(21).…”

Recent developments in dynamic fracture: some perspectives

“…Super-shear cracks have long been considered in the fracture literature [3,199,200], but until they were observed in the beautiful experiments by Rosakis and coworkers [151], they were often considered to be of purely theoretical value. Since this first observation in weakly bonded homogeneous blocks that were ballistically loaded, mode II super-shear ruptures have been observed numerically [201][202][203] as well as in a variety of other scenarios that include frictional interfaces and quasi-static loading [141,146,149,152].…”