Off-fault deformation feedback and strain localization precursor during laboratory earthquakes

Earthquakes are highly destructive and reliable early warning remains elusive. Recent field observations indicate foreshock migration and progressive localization from broader damage zones onto narrow fault planes hours to years before mainshocks, suggesting spatial strain localization may presage large ruptures. Laboratory studies on intact rocks have long shown diffuse microcracking that localizes prior to failure (via acoustic emissions and in situ X-ray tomography), and some propose using localization to predict time to failure. However, most prior work concerns initially intact rocks, whereas natural earthquakes recur on established faults. Fault mechanics research using gouge and saw-cut samples and the rate-and-state (RS) framework generally treats faults as interfaces between elastic blocks, but natural faults are embedded in volumetric damage zones. Processes in the surrounding rock volume before, during, and after earthquakes likely control nucleation and recurrence. This study investigates whether off-fault deformation feeds back on fault stability, linking RS frictional properties to bulk processes, and tests if precursory off-fault strain localization accompanies stick-slip nucleation.

Field studies have reported foreshock migration and damage localization toward eventual rupture zones prior to main shocks (e.g., Oklahoma M_w 5.0; Landers 1992; Ridgecrest 2019), implying precursory spatial localization may be a harbinger of large earthquakes. Laboratory work on intact rocks has documented progressive localization via acoustic emissions and dynamic X-ray microtomography, with localization preceding catastrophic failure and enabling failure-time predictions. Fault friction experiments in triaxial, double-direct shear, and rotary setups underpin RS laws that capture transitions between stable and unstable slip with an interface-and-spring model. Yet, natural faults show kilometer-scale damage zones and altered properties, emphasizing volumetric effects. Prior studies on calcitic and silicic rocks report velocity dependence of RS parameters a and b; off-fault damage and postseismic relaxation are widely observed near major faults. Previous work also defined the localized-to-ductile transition (LDT) in rocks and showed strain partitioning between fault and bulk depends on the relative magnitudes of bulk yield and flow stresses versus fault frictional strength, motivating exploration of its role in earthquake nucleation on established faults.

Single-direct-shear friction experiments were conducted on bare Carrara marble surfaces using the HighSTEPS biaxial apparatus (EPFL, Switzerland) under oil confinement. To emulate different crustal depths (brittle to semi-brittle regimes), two confining pressures (P = 15 MPa and P = 50 MPa) and corresponding normal stresses (σ_N = 29 MPa and σ_N = 95 MPa) were applied, maintaining a ~2 ratio between normal and confining stresses to keep stress-shape ratio constant. Experiments were room dry at room temperature. The contacting surfaces (nominal area 34 × 20 mm²) were polished with P1200-grit diamond abrasive; each block was 11 mm thick. A double latex jacket isolated the fault from the silicon oil confining medium. Confining pressure and normal force were servo-controlled in closed loop; shear force was applied under displacement-rate control. After a run-in phase at v = 10⁻⁴ m/s for 5.5 mm to reach steady-state shear strength, velocity steps were performed across 10⁻⁴ to 10⁻² m/s. Forces FN and Fs were measured by load cells; total shear displacement by an external linear optical encoder (OE). Local bulk shear deformation was recorded with a strain gauge rosette (1.7 × 3 mm grids) centered 3 mm from the fault. Apparent friction coefficient μ was computed as Fs/FN. Frictional behavior was modeled with the Dieterich time-dependent RS law and evolution equation, μ(V,θ) = μ0 + a ln(V/V0) + b ln(θV0/D_c), coupled to elastic loading dτ/dt = k(V − V_f) with stiffness k; parameters a, b, and D_c were obtained by iterative least squares fitting of velocity-step transients. In stick-slip, (a − b) values were computed following a specific method ((a − b)_s) described in Supplementary S1; absolute values depend on constant machine stiffness, but relative changes are robust. Strain partitioning was quantified by comparing total shear strain (OE displacement divided by 11 mm) with local shear strain from strain gauges; the percentage of bulk-accommodated (elastic + inelastic) shear deformation at each velocity is the slope of the linear regression between ε_total and ε_s (stable and stick-slip cases treated as in Fig. 4c,d). Three experiments were performed: one at low P, σ_N (15, 29 MPa) and two repeats at high P, σ_N (50, 95 MPa) to assess reproducibility. An additional constant-stress, low-velocity experiment at high P and σ_N produced a thin section after 12 mm of slip to assess off-fault damage microstructures.

• Fault frictional stability depends on confining/normal stress and velocity. At low confining pressure and normal stress, sliding was stable across all tested load-point velocities, with a − b spanning conditionally unstable to stable values (approximately −0.005 to +0.01). At higher confining pressure and normal stress, the fault transitioned from unstable stick-slip to stable sliding as load-point velocity increased; two replicate experiments showed identical behavior.
• Rate-and-state parameter a − b increased with load-point velocity, ranging from about −0.014 to +0.015, in agreement with literature on calcitic and other rocks; values were reproducible between repeats.
• Off-fault bulk shear deformation was small at low confinement (≈0.5–2% of total shear deformation across velocities). At high confinement, the bulk contribution was initially about 10–12% at the lowest velocity step and rapidly decreased with increasing velocity to below about 4% at the higher velocities tested.
• Unstable slip (stick-slip) occurred only under high-stress conditions and only when a small but distinct fraction of shear strain delocalized in the bulk (∼10–12%), indicating that bulk deformation favors seismic slip when faults are conditionally unstable (a − b < 0).
• Over individual stick-slip cycles, shear strain partitioning varied systematically: after a slip event, bulk shear strain progressively delocalized during the interseismic (stick) phase and progressively re-localized onto the fault approaching the next rupture. This demonstrates unequivocal precursory localization of shear strain before nucleation of stick-slip events.
• A thin section from an additional constant-stress, low-velocity experiment revealed a ~100 μm damaged layer adjacent to the slip surface, with cracked and cloudy calcite grains suggestive of crystal plasticity, indicating off-fault damage proximal to the fault zone.
• Mechanistically, observations are consistent with off-fault inelastic deformation reducing the elastic modulus and effective surrounding stiffness, potentially dropping the system stiffness below the critical RS stability threshold and triggering unstable slip.

The experiments directly link off-fault deformation to fault stability, addressing whether volumetric processes in the damage zone can promote earthquake nucleation. When a − b < 0 (conditionally unstable friction), the onset of off-fault shear deformation at high stress delocalizes part of the shear, degrading the elastic properties of the surrounding rock (lower E, lower k) and potentially reducing the system stiffness below the RS critical stiffness, thereby enabling stick-slip. Increasing load-point velocity increases a − b and, via crystal plastic mechanisms in Carrara marble (twinning, dislocation slip), increases the bulk yield stress, suppressing delocalization (a ductile-to-localized transition) and stabilizing sliding. These results provide a volumetric framework for the depth-dependence of seismogenic behavior. Near the surface, stabilizing factors (gouge, dilatancy, low stress) yield a − b > 0 and aseismic slip. With depth, increasing normal stress tends to reduce a − b and eventually produce conditionally unstable behavior; the onset of delocalized shear strain near the localized-to-ductile transition (σ_y < σ_f < σ_flow) can further destabilize faults by lowering k, marking or advancing the onset of the seismogenic zone. The spectrum from slow to fast earthquakes can be understood via k/k_c; off-fault inelastic deformation likely increases with depth where σ_f approaches σ_flow, producing the greatest stiffness reduction (lowest k/k_c) and correlating with observed enhanced seismic activity. Past this minimum, behavior transitions rapidly, but mechanisms and limits remain uncertain. The observed cyclic precursory localization mirrors field reports of foreshocks and seismicity focusing toward mainshock epicenters, suggesting that monitoring off-fault strain localization may provide reliable warning signals. Additionally, surface geodetic signals typically attributed to aseismic fault slip may, in part, reflect off-fault inelastic deformation that does not relieve shear stress on the fault, potentially contributing to stress accumulation and eventual large earthquakes.

Confined velocity-stepping friction experiments on bare Carrara marble demonstrated that low load-point velocity promotes conditionally unstable friction (a − b < 0), but stick-slip occurred only when high-stress conditions enabled off-fault bulk shear deformation. The delocalization of shear strain reduces surrounding material stiffness, which can drop below the critical RS stiffness and trigger unstable slip. Extrapolated to the crust, the onset of the localized-to-ductile transition may destabilize conditionally unstable faults and catalyze seismicity. The experiments revealed cycles of strain delocalization and relocalization during repeating stick-slips, with unequivocal precursory localization of shear strain prior to rupture. These laboratory findings echo large-scale observations of foreshock localization and may inform earthquake early warning. Future research should (i) quantify the evolving volume and nature (elastic vs inelastic) of off-fault deformation throughout the seismic cycle, (ii) determine how stiffness reductions scale with depth and lithology, (iii) clarify mechanisms governing stability past the inferred stiffness minimum near the end of the LDT, and (iv) integrate volumetric damage evolution into predictive RS-based earthquake nucleation models.

• The strain gauges quantify local deviations from total strain but do not distinguish elastic from inelastic components; thus, the precise nature of the delocalized strain could not be determined.
• The ~100 μm damaged layer observed in a thin section cannot be uniquely attributed to interseismic partitioning versus coseismic damage created during stick-slip events.
• Absolute estimates of (a − b) in stick-slip depend on the apparatus stiffness; while constant during experiments (supporting relative comparisons), this limits direct comparison of absolute values across setups.
• Experiments were conducted on Carrara marble at room conditions over a limited velocity range, which may affect generalizability to other lithologies, temperatures, fluid conditions, and broader tectonic settings.
• The study does not fully resolve mechanisms or bounds governing the transition from unstable to conditionally unstable behavior beyond the inferred stiffness minimum with depth.