Forerunning, Sub- and Supershear Rupture in Dry and Fluid-Saturated Media

This six day advanced course presents recent theoretical and numerical advances in dynamic fracture mechanics, focusing on sub , inter , and supershear rupture in dry and fluid saturated media. Emphasis is placed on mode I tensile fracture, mode II shear rupture, forerunning (mother–daughter crack mechanisms), and the role of poroelastic coupling in accelerating rupture beyond classical wave speed limits. The course integrates theory, experiments, numerical modeling, and geophysical relevance.

Classical fracture mechanics predicts an upper limit for crack speed: Rayleigh for tensile fractures and shear wave speed for shear ruptures. Yet experiments, earthquake observations, and modern simulations show that fractures can exceed these limits, sometimes surpassing even the compressional wave speed. Supershear ruptures are crucial in earthquake physics because rupture speed controls seismic radiation, ground motion amplification, and Mach cone formation. About 15–20% of large earthquakes (Mw > 7) involve supershear rupture, but the mechanisms governing the transition remain incompletely understood, especially in fluid saturated faults.

Mode I fracture is examined first, using FEM, XFEM, phase field, peridynamics, and hybrid FEM/PD models. Tensile cracks can propagate faster than shear and even compressional waves. Numerical results reveal a progressive transition with increasing loading or injection rate: smooth propagation, stepwise advancement, and forerunning, where cracks nucleate ahead of the main tip. Importantly, forerunning also occurs under subsonic conditions, such as in beams on elastic foundations under sinusoidal loading, showing it is not inherently tied to supersonic motion. In saturated media, increasing injection rates promote transitions from smooth to stepwise to forerunning, highlighting strong coupling between pore pressure diffusion, stress waves, and fracture dynamics. Relevant cases are solved with XFEM, phase field, and a new 2 D hybrid FEM/PD model.

The second part addresses mode II rupture, relevant to earthquakes and dams under seismic loading. The hybrid FEM/PD model (extended to mode II and III) and phase field examples reproduce sub Rayleigh and supershear rupture, Mach cones, and both direct transitions and Burridge–Andrews mother–daughter mechanisms. A key result is that in saturated media, poroelastic effects near the rupture front strongly favor direct supershear transitions, unlike dry media where both direct and indirect mechanisms occur depending on loading and heterogeneity.

Across both modes, supersonic rupture emerges as a robust outcome of wave–fracture interaction and fluid–solid coupling. Forerunning provides a unifying mechanism for tensile and shear supershear rupture, while the stepwise regime reveals a previously unexplored transitional behavior.

The mechanisms explored here are directly relevant to rupture along fluid rich faults, slab tearing, volcanic tremors, dams under seismic loading, and hydro demolition. Understanding how fluids promote rapid rupture acceleration is essential for seismic hazard assessment and interpretation of high frequency ground motions.