Dynamic Rupture, Fault Opening, and Near Fault Particle Motions along an Interface between Dissimilar Materials

Dynamic rupture propagation along an interface between two different elastic solids under shear dominated loading is studied numerically by a 2-D lattice particle model (LPM). The configuration of the lattice particle model consists of two solid blocks of different elastic properties connected along a planar interface. Each block is characterized as an isotropic elastic material and the interface strength is described as a composite elastic modulus of a mismatch function of the elastic properties of two dissimilar materials. The particle interaction between the two blocks with pair inter-particle potential also takes account of normal stress variations.

💡 Research Summary

The paper investigates dynamic rupture propagation along a planar interface separating two elastic solids with contrasting material properties, using a two‑dimensional lattice particle model (LPM). The authors construct two blocks—one softer, one harder—each represented by a triangular lattice of particles interacting via a modified Lennard‑Jones pair potential. The elastic constants of the blocks differ, while density is kept equal, and the interface stiffness K is defined as a mismatch function of the two blocks’ shear moduli, following the formulations of Comninou (1977) and Weertman (1980). This choice reproduces realistic material contrasts observed in natural faults, where shear‑wave speed ratios range from 0.7 to 1.0.

Boundary conditions impose a constant far‑field shear stress τ∞ and compressive normal stress σ∞, and friction on the interface follows Coulomb’s law (τ = f σ) with a coefficient f between 0.6 and 0.85. To trigger rupture, a rough segment of about 200 particle spacings is introduced at the left edge of the fault; the remainder of the interface is perfectly smooth. The system is driven by a shear strain rate of 5 × 10⁻⁴ and a constant compressive strain of 0.002, mimicking tectonic loading. Time integration is performed with a velocity‑Verlet scheme.

Key findings from the simulations are:

1. Rupture Speed and Directionality – When the rupture propagates toward the softer material, it travels at a speed close to the slower Rayleigh wave speed of that material. The rupture is self‑sustaining, forming a slip pulse that does not decay.

2. Interface Separation (Fault Opening) – Simultaneous with slip, a localized normal displacement discontinuity appears. At the point of opening, the shear stress on the fault drops to zero instantaneously, and the normal stress also collapses, indicating a temporary loss of contact.

3. Asymmetric Particle Motions – Normal‑direction particle velocities and accelerations are markedly larger than those in the slip direction. Moreover, the softer block exhibits normal displacements roughly twice as large as those in the harder block. When the material contrast exceeds about 40 %, the normal motion in the hard block becomes negligible, and the waveform resembles a Schallamach detachment wave observed in rubber friction experiments.

4. Pulse Sharpening with Propagation – As the rupture front moves away from the nucleation zone, the slip‑pulse and opening‑pulse become sharper and increase in amplitude, consistent with the “traveling‑wave radiation” mechanism described by Andrews and Ben‑Zion (1997).

5. Radiated Seismic Energy – Synthetic seismograms show that the dominant energy is carried by surface waves excited by the combined slip‑opening‑healing process. The radiated energy therefore originates from the work done in pulling the interface apart (opening) as well as from the subsequent re‑contact (healing). The shear stress on the fault therefore experiences a partial stress drop rather than a full release.

These observations align closely with laboratory foam‑rubber experiments (Anooshehpoor and Brune, 1994, 1999) and with theoretical predictions from Weertman’s dislocation model. Notably, the authors extend Weertman’s original analysis— which allowed only continuous normal displacement—by incorporating a climb (opening) component. This extension demonstrates that self‑sustaining slip pulses can exist even when the shear‑wave speed contrast far exceeds the 19 % limit originally identified by Weertman. The inclusion of normal displacement also bridges the model to Haskell’s (1964) formulation for identical half‑spaces and to Schallamach waves for large contrasts.

The broader implication is a potential resolution of the “heat‑flow paradox” on major faults. Normal vibration and transient fault opening reduce the effective normal stress, thereby limiting frictional heating during slip. This mechanism also explains anomalously high P‑wave radiation observed in some earthquakes, as the normal stress fluctuations generate tensile normal stresses that radiate compressional energy.

In summary, the study provides a robust numerical demonstration that dynamic rupture on dissimilar material interfaces can be accompanied by significant fault opening, asymmetric particle motions, and surface‑wave dominated radiation. By coupling slip and climb dislocations within a lattice‑particle framework, the authors reconcile laboratory observations, analytical dislocation theory, and seismic phenomenology, offering a comprehensive picture of how material contrast influences earthquake rupture dynamics.