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arxiv: 2607.01448 · v1 · pith:5TKHPC7Lnew · submitted 2026-07-01 · ⚛️ physics.geo-ph · cond-mat.soft

How effective normal stress oscillations advance failure in fault gouge: frequency dependence, non-failure window, and the role of dilation

Pritom Sarma , Einat Aharonov , Renaud Toussaint , Stanislav Parez This is my paper

Pith reviewed 2026-07-03 00:46 UTC · model grok-4.3

classification ⚛️ physics.geo-ph cond-mat.soft
keywords fault gougenormal stress oscillationsfrequency dependencedilationsub-critical failureacoustic fluidizationdiscrete element methodfluid-saturated granular material
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The pith

Effective normal stress oscillations trigger sub-critical failure in fault gouge at low and high frequencies but not in an intermediate window.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper uses a coupled discrete element-fluid dynamics model to simulate a sheared fluid-saturated or dry gouge layer under oscillating effective normal stress across frequencies from 0.5 Hz to 10 kHz while staying below the Mohr-Coulomb failure threshold. It reports failure in most cases, organized into four regimes ranging from repeated failure-and-arrest to continuous sliding, with a distinct non-failure window between roughly 30 and 200 Hz. The non-monotonic frequency dependence arises because low-frequency cycles permit shear-driven ratcheting dilation over each cycle while high-frequency cycles produce dynamic dilation through amplified seepage forces, stress gradients, and inertial effects. Pore-pressure and direct normal-stress oscillations yield the same regime structure, indicating they act as equivalent forcings with fluid coupling only adding a short delay from dilatant hardening.

Core claim

Sub-critical failure arises from dilation-induced strength deterioration via two mechanisms: low-frequency cycles allow sufficient time for shear-driven ratcheting dilation, while high-frequency cycles induce dynamic dilation via amplified seepage forces, stress gradients and inertial forces. The intermediate non-failure window represents the gap between these mechanisms. Pore-pressure and normal stress oscillations produce the same regime structure, confirming they act as equivalent forcings via Terzaghi's principle, with fluid coupling adding only a delay due to dilatant hardening.

What carries the argument

Frequency-dependent dilation mechanisms that reduce gouge strength under sub-critical effective normal stress oscillations, identified through the coupled discrete element-fluid dynamics simulations.

If this is right

  • Pore-pressure oscillations and direct normal stress oscillations produce equivalent effects on failure regimes through Terzaghi's principle.
  • The system exhibits four distinct regimes from cyclic failure-and-arrest to continuous sliding depending on oscillation frequency.
  • Frequency emerges as a controlling parameter for failure in granular materials under cyclic loading.
  • Fluid coupling introduces only a delay from dilatant hardening rather than changing the overall regime structure.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Real faults experiencing seismic waves or fluid injection at varying frequencies may exhibit stability bands that protect against triggering.
  • Cyclic injection protocols in subsurface engineering could be designed to operate inside the non-failure frequency window to reduce induced seismicity risk.
  • The same dilation mechanisms may operate in dry granular materials under rapid cyclic loading even without fluid.

Load-bearing premise

The coupled discrete element-fluid dynamics model accurately captures the grain-scale physics of fluid-saturated gouge without significant numerical artifacts.

What would settle it

Physical laboratory experiments on fluid-saturated gouge samples subjected to sub-critical normal stress oscillations at frequencies between 30 and 200 Hz that either produce or fail to produce the predicted non-failure window.

Figures

Figures reproduced from arXiv: 2607.01448 by Einat Aharonov, Pritom Sarma, Renaud Toussaint, Stanislav Parez.

Figure 1
Figure 1. Figure 1: Simulation setup and imposed forcing. (A) Dry control (Protocol 1): a prestressed granular layer under [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Periodicity and delay at ω = 1 Hz. Slip velocity V /V ∗ for the fluid-saturated (solid) and dry (dotted) layers, overlaid on the imposed forcing: pore pressure P/E (red) and normal stress σn/E (green). Slip recurs once per forcing cycle; saturated-layer slip is delayed relative to the dry layer by dilatant hardening (marked). time available for the layer to decelerate and re-jam between successive peaks. B… view at source ↗
Figure 3
Figure 3. Figure 3: Three failure modes and one non-failure window: slip velocity [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Maximum slip velocity V /V ∗ max versus oscillation frequency. Fluid-saturated (Protocol 2) at P0/σ0 = 0.25, ∆P/σ0 = 0.07 (blue) and P0/σ0 = 0.27, ∆P/σ0 = 0.05 (red), with the dry control (Protocol 1, ∆σn/σ0 = 0.07, green). All three share the same non-monotonic dependence, with the minimum in the non-failure window (30– 200 Hz, dashed box). 9 [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Porosity ϕ evolution at ω = 1 Hz (red), 100 Hz (blue), 1000 Hz (magenta), and constant injection (Sarma et al., 2025) (green). Time is normalized as t/tfail so failing runs reach failure at t/tfail = 1 (onset from [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Phase-space trajectories of ϕ versus V /V ∗ , colour-coded by time, for (A) constant injection (Sarma et al., 2025), (B) ω = 1 Hz, (C) ω = 100 Hz, (D) ω = 1000 Hz. (B) shows the ratchet: each cycle leaves a small irreversible dilation increment (loops drift upward in ϕ). (C) shows reversible loops with no drift. (D) shows dilation by grain agitation rather than ratcheting. All panels are pre-failure. P0/σ0… view at source ↗
Figure 7
Figure 7. Figure 7: Non-dimensional momentum-balance terms (normalized by [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Time-averaged magnitudes of the non-dimensional gradient terms (normalized by [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Normalized layer-thickness change ∆h/h0 for sheared (τ = 0.2 σ0, orange) and non-sheared (τ = 0, blue) layers under cyclic pore pressure at (A) 1 Hz, (B) 10 Hz, (C) 100 Hz, (D) 1000 Hz. (A, B): the sheared layer dilates more on each pressure rise and compacts more on each pressure drop than the non-sheared layer, its minima ratcheting upward, while the non-sheared traces stay symmetric, shear is essential … view at source ↗
read the original abstract

Cyclic pore-pressure or normal stress variations arise both in relation to natural earthquakes and in engineered subsurface systems, yet their effect on fault stability remains poorly constrained at the grain scale. Here we numerically model, using a coupled Discrete Element--fluid dynamics model, the response of a sheared, fluid-saturated or dry, gouge-filled fault to effective normal stress oscillations over a wide frequency range (0.5-10000 Hz). The effective normal stress is oscillated either by cycling the pore-pressure or by directly cycling the normal stress, while keeping the stress state below the Mohr-Coulomb threshold measured in continuous loading. Despite this sub-critical loading, we observe failure across most frequencies, with a non-monotonic frequency dependence. A distinct non-failure window emerges at intermediate frequencies (30-200 Hz), bounded by failure at both lower and higher frequencies; the system exhibits four regimes from cyclic failure-and-arrest to continuous sliding. Pore-pressure and normal stress oscillations produce the same regime structure, confirming that they act as equivalent forcings via Terzaghi's principle, with fluid coupling adding only a delay due to dilatant hardening. Sub-critical failure arises from dilation-induced strength deterioration via two mechanisms: (i) low-frequency cycles allow sufficient time for shear-driven ratcheting dilation, while (ii) high-frequency cycles induce dynamic dilation (acoustic fluidization) via amplified seepage forces, stress gradients and inertial forces. The intermediate non-failure window represents the gap between these mechanisms. These results identify frequency as a controlling parameter for failure in granular materials, with implications for dynamic earthquake triggering and cyclic injection protocols.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper uses a coupled Discrete Element Method-fluid dynamics model to simulate the response of sheared, fluid-saturated or dry fault gouge to sub-critical effective normal stress oscillations (via pore-pressure or direct normal stress cycling) over 0.5-10000 Hz. It reports failure at most frequencies with a distinct non-failure window at 30-200 Hz, four distinct regimes, and attributes sub-critical failure to dilation-induced strength loss via shear-driven ratcheting dilation at low frequencies and dynamic dilation (acoustic fluidization) at high frequencies, with pore-pressure and normal-stress forcings acting equivalently per Terzaghi's principle.

Significance. If the numerical results hold under validation, the work would establish frequency as a controlling parameter for granular failure under cyclic loading and identify two distinct dilation mechanisms separated by a non-failure window. This carries implications for dynamic earthquake triggering and cyclic injection protocols. The direct numerical integration approach and equivalence of forcing types are strengths, but the absence of experimental benchmarks limits immediate impact.

major comments (2)
  1. [Numerical methods and model validation] The central claim that sub-critical failure arises from two specific dilation mechanisms (ratcheting vs. acoustic fluidization) separated by the 30-200 Hz non-failure window rests on the fidelity of the coupled DEM-fluid model. The manuscript provides no quantitative validation against laboratory cyclic-loading experiments on fluid-saturated gouge, no error bars or statistical measures on the reported regimes, and no convergence or sensitivity tests to particle discretization, fluid-grid resolution, or boundary conditions. This is load-bearing for distinguishing physical mechanisms from possible numerical artifacts.
  2. [Loading protocol and failure criterion] The loading is described as sub-critical relative to the Mohr-Coulomb threshold measured in continuous loading, yet no details are given on how this threshold was determined (e.g., measurement protocol, number of realizations, or uncertainty), which is required to confirm that the observed failures are indeed sub-critical and not an artifact of threshold definition.
minor comments (2)
  1. [Abstract] The abstract states that four regimes are observed but does not enumerate them; a brief listing would improve clarity for readers.
  2. [Results] Consider adding a table or figure summarizing the frequency boundaries of each regime and the associated dilation mechanism for quick reference.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback, which highlights important aspects of model validation and methodological clarity. We respond to each major comment below and indicate where revisions will be made.

read point-by-point responses

  1. Referee: [Numerical methods and model validation] The central claim that sub-critical failure arises from two specific dilation mechanisms (ratcheting vs. acoustic fluidization) separated by the 30-200 Hz non-failure window rests on the fidelity of the coupled DEM-fluid model. The manuscript provides no quantitative validation against laboratory cyclic-loading experiments on fluid-saturated gouge, no error bars or statistical measures on the reported regimes, and no convergence or sensitivity tests to particle discretization, fluid-grid resolution, or boundary conditions. This is load-bearing for distinguishing physical mechanisms from possible numerical artifacts.

    Authors: We agree that the absence of direct quantitative benchmarks against laboratory cyclic-loading experiments on fluid-saturated gouge is a limitation for immediate impact, as noted in the referee summary. Our study is a numerical exploration of mechanisms using an established DEM-fluid coupling approach previously validated for quasi-static and dynamic regimes in our earlier work. To strengthen the manuscript, we will add: (i) error bars derived from at least five independent realizations per frequency, (ii) a new subsection reporting sensitivity tests (particle number doubled, fluid grid resolution varied by factor of two) confirming that the non-failure window and regime boundaries remain robust, and (iii) explicit discussion of how the two dilation mechanisms are distinguished from potential artifacts via consistency across forcing types and parameter sweeps. We cannot add new laboratory experiments within this revision but will expand the limitations section accordingly. revision: partial

  2. Referee: [Loading protocol and failure criterion] The loading is described as sub-critical relative to the Mohr-Coulomb threshold measured in continuous loading, yet no details are given on how this threshold was determined (e.g., measurement protocol, number of realizations, or uncertainty), which is required to confirm that the observed failures are indeed sub-critical and not an artifact of threshold definition.

    Authors: The Mohr-Coulomb threshold was obtained from separate monotonic shear simulations under constant normal stress until macroscopic failure, with the peak shear stress averaged over ten independent realizations using randomized initial particle packings. The oscillatory amplitude was set to 80% of this mean peak value, with the standard deviation across realizations being approximately 5%. We will insert a dedicated paragraph in the Methods section describing this protocol, the number of realizations, and the resulting uncertainty to confirm the sub-critical nature of the loading. revision: yes

Circularity Check

0 steps flagged

No significant circularity: results follow from direct numerical integration

full rationale

The paper reports outcomes of numerical integration of a coupled DEM-fluid model under imposed sub-critical stress oscillations. Failure regimes, frequency dependence, and the two dilation mechanisms are observed outputs of the simulation, not quantities defined in terms of themselves or obtained by fitting a target. No load-bearing step reduces by construction to an input, self-citation chain, or renamed empirical pattern. The model-validation concern raised by the reader is a question of external fidelity, not internal circularity of the derivation.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Abstract-only review limits visibility into exact parameter counts; standard granular-mechanics assumptions apply.

free parameters (1)
  • particle friction and stiffness parameters
    Typical DEM inputs that must be chosen; abstract does not state whether they were fitted to match a target failure threshold.
axioms (2)
  • domain assumption Terzaghi effective-stress principle equates pore-pressure and normal-stress oscillations
    Invoked to claim equivalence of the two forcings.
  • domain assumption Mohr-Coulomb failure criterion measured under continuous loading remains the relevant threshold under cyclic conditions
    Used to define the sub-critical regime.

pith-pipeline@v0.9.1-grok · 5848 in / 1379 out tokens · 34914 ms · 2026-07-03T00:46:05.551334+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

70 extracted references

  1. [1]

    and Sparks, D

    Aharonov, E. and Sparks, D. , title =. Physical Review E , volume =

  2. [2]

    and Goren, L

    Ben-Zeev, S. and Goren, L. and Toussaint, R. and Aharonov, E. , title =. Nature Communications , volume =

  3. [3]

    , title =

    Billi, A. , title =. Journal of Structural Geology , volume =

  4. [4]

    Boettcher, M. S. and Marone, C. , title =. Journal of Geophysical Research: Solid Earth , volume =

  5. [5]

    Bolton, M. D. , title =. G

  6. [6]

    Campbell, C. S. , title =. Powder Technology , volume =

  7. [7]

    and Scuderi, M

    Cappa, F. and Scuderi, M. M. and Collettini, C. and Guglielmi, Y. and Avouac, J.-P. , title =. Science Advances , volume =

  8. [8]

    and Spiers, C

    Chen, J. and Spiers, C. J. , title =. Journal of Geophysical Research: Solid Earth , volume =

  9. [9]

    and Niemeijer, A

    Chen, J. and Niemeijer, A. R. and Spiers, C. J. , title =. Geophysical Research Letters , volume =

  10. [10]

    Cochran, E. S. and Vidale, J. E. and Tanaka, S. , title =. Science , volume =

  11. [11]

    Collins, G. S. and Melosh, H. J. , title =. Journal of Geophysical Research: Solid Earth , volume =

  12. [12]

    Cundall, P. A. and Strack, O. D. L. , title =. G

  13. [13]

    and Chevoir, F

    da Cruz, F. and Chevoir, F. and Bonn, D. and Coussot, P. , title =. Physical Review E , volume =

  14. [14]

    Dieterich, J. H. and Linker, M. F. , title =. Geophysical Research Letters , volume =

  15. [15]

    Dijksman, J. A. and Wortel, G. H. and van Dellen, L. T. H. and Dauchot, O. and van Hecke, M. , title =. Physical Review Letters , volume =

  16. [16]

    Ellsworth, W. L. , title =. Science , volume =

  17. [17]

    and Griffa, M

    Ferdowsi, B. and Griffa, M. and Guyer, R. A. and Johnson, P. A. and Marone, C. and Carmeliet, J. , title =. Geophysical Research Letters , volume =

  18. [18]

    and Pouliquen, O

    Forterre, Y. and Pouliquen, O. , title =. Annual Review of Fluid Mechanics , volume =

  19. [19]

    Frank, F. C. , title =. Reviews of Geophysics , volume =

  20. [20]

    Frye, K. M. and Marone, C. , title =. Geophysical Research Letters , volume =

  21. [21]

    and Johnson, P

    Gomberg, J. and Johnson, P. , title =. Nature , volume =

  22. [22]

    and Aharonov, E

    Goren, L. and Aharonov, E. and Sparks, D. and Toussaint, R. , title =. Journal of Geophysical Research , volume =

  23. [23]

    and Aharonov, E

    Goren, L. and Aharonov, E. and Sparks, D. and Toussaint, R. , title =. Pure and Applied Geophysics , volume =

  24. [24]

    and Ferdowsi, B

    Griffa, M. and Ferdowsi, B. and Guyer, R. A. and Daub, E. G. and Johnson, P. A. and Marone, C. and Carmeliet, J. , title =. Physical Review E , volume =

  25. [25]

    and Cappa, F

    Guglielmi, Y. and Cappa, F. and Avouac, J.-P. and Henry, P. and Elsworth, D. , title =. Science , volume =

  26. [26]

    Hill, D. P. and Prejean, S. G. , title =. Treatise on Geophysics , publisher =

  27. [27]

    and Zimmermann, G

    Hofmann, H. and Zimmermann, G. and Zang, A. and Min, K.-B. , title =. Geothermal Energy , volume =

  28. [28]

    and Marone, C

    Hong, T. and Marone, C. , title =. Geochemistry, Geophysics, Geosystems , volume =

  29. [29]

    Hubbert, M. K. and Rubey, W. W. , title =. Geological Society of America Bulletin , volume =

  30. [30]

    Johnson, P. A. and Jia, X. , title =. Nature , volume =

  31. [31]

    and Brodsky, E

    Kanamori, H. and Brodsky, E. E. , title =. Reports on Progress in Physics , volume =

  32. [32]

    Keranen, K. M. and Weingarten, M. , title =. Annual Review of Earth and Planetary Sciences , volume =

  33. [33]

    Kuhn, M. R. and Bagi, K. , title =. Journal of Engineering Mechanics , volume =

  34. [34]

    and Saarno, T

    Kwiatek, G. and Saarno, T. and Ader, T. and Bluemle, F. and Bohnhoff, M. and Chendorain, M. and Dresen, G. and Heikkinen, P. and Kukkonen, I. and Leary, P. and others , title =. Science Advances , volume =

  35. [35]

    Linker, M. F. and Dieterich, J. H. , title =. Journal of Geophysical Research , volume =

  36. [36]

    and Sparks, D

    Makedonska, N. and Sparks, D. W. and Aharonov, E. and Goren, L. , title =. Journal of Geophysical Research , volume =

  37. [37]

    and Raleigh, C

    Marone, C. and Raleigh, C. B. and Scholz, C. H. , title =. Journal of Geophysical Research , volume =

  38. [38]

    , title =

    Marone, C. , title =. Annual Review of Earth and Planetary Sciences , volume =

  39. [39]

    and Flekk

    McNamara, S. and Flekk. Grains and gas flow: Molecular dynamics with hydrodynamic interactions , journal =

  40. [40]

    Mead, W. J. , title =. The Journal of Geology , volume =

  41. [41]

    Melosh, H. J. , title =. Journal of Geophysical Research: Solid Earth , volume =

  42. [42]

    Melosh, H. J. , title =. Nature , volume =

  43. [43]

    Evidence of earthquake triggering by the solid Earth tides , journal =

    M. Evidence of earthquake triggering by the solid Earth tides , journal =

  44. [44]

    On dense granular flows , journal =

  45. [45]

    and Byerlee, J

    Nur, A. and Byerlee, J. , title =. Journal of Geophysical Research , volume =

  46. [46]

    and Nicolas, M

    Pailha, M. and Nicolas, M. and Pouliquen, O. , title =. Physics of Fluids , volume =

  47. [47]

    and Pouliquen, O

    Pailha, M. and Pouliquen, O. , title =. Journal of Fluid Mechanics , volume =

  48. [48]

    and Aharonov, E

    Parez, S. and Aharonov, E. and Toussaint, R. , title =. Physical Review E , volume =

  49. [49]

    and Kozakovic, M

    Parez, S. and Kozakovic, M. and Havlica, J. , title =. Journal of Geophysical Research: Solid Earth , volume =

  50. [50]

    and Giorgetti, C

    Pignalberi, F. and Giorgetti, C. and No. The effect of normal stress oscillations on fault slip behavior near the stability transition from stable to unstable motion , journal =

  51. [51]

    , title =

    Reynolds, O. , title =. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science , volume =

  52. [52]

    , title =

    Reynolds, O. , title =. Proceedings of the Royal Institution of Great Britain , volume =

  53. [53]

    Rowe, P. W. , title =. Proceedings of the Royal Society of London A , volume =

  54. [54]

    and Oliver, C

    Vidal, V. and Oliver, C. and Lastakowski, H. and Varas, G. and G. Friction weakening by mechanical vibrations: A velocity-controlled process , journal =. 2019 , doi =

    2019

  55. [55]

    Rubinstein, J. L. and La Rocca, M. and Vidale, J. E. and Creager, K. C. and Wech, A. G. , title =. Science , volume =

  56. [56]

    and Aharonov, E

    Sarma, P. and Aharonov, E. and Toussaint, R. and Parez, S. , title =. Journal of Geophysical Research: Solid Earth , volume =

  57. [57]

    Savage, H. M. and Marone, C. , title =. Journal of Geophysical Research , volume =

  58. [58]

    Scholz, C. H. , title =

  59. [59]

    and Skoumal, R

    Schultz, R. and Skoumal, R. J. and Brudzinski, M. R. and Eaton, D. and Baptie, B. and Ellsworth, W. , title =. Reviews of Geophysics , volume =

  60. [60]

    and Rice, J

    Segall, P. and Rice, J. R. , title =. Journal of Geophysical Research , volume =

  61. [61]

    and Peck, R

    Terzaghi, K. and Peck, R. B. and Mesri, G. , title =

  62. [62]

    Thomas, A. M. and Nadeau, R. M. and B. Tremor-tide correlations and near-lithostatic pore pressure on the deep San Andreas fault , journal =

  63. [63]

    van der Elst, N. J. and Brodsky, E. E. , title =. Journal of Geophysical Research: Solid Earth , volume =

  64. [64]

    and Chen, J

    Yu, B. and Chen, J. and Spiers, C. J. and Ma, S. and Zhang, M. and Qi, W. and Chen, H. , title =. Journal of Geophysical Research: Solid Earth , volume =

  65. [65]

    and Zimmermann, G

    Zang, A. and Zimmermann, G. and Hofmann, H. and Stephansson, O. and Min, K.-B. and Kim, K. Y. , title =. Rock Mechanics and Rock Engineering , volume =

  66. [66]

    and Guyer, R

    Dorostkar, O. and Guyer, R. A. and Johnson, P. A. and Marone, C. and Carmeliet, J. , title =. Journal of Geophysical Research: Solid Earth , volume =

  67. [67]

    Scuderi, M. M. and Carpenter, B. M. and Johnson, P. A. and Marone, C. , title =. Journal of Geophysical Research: Solid Earth , volume =

  68. [68]

    Scuderi, M. M. and Carpenter, B. M. , title =. Geophysical Journal International , volume =

  69. [69]

    and Tullis, T

    Zhang, S. and Tullis, T. E. , title =. Tectonophysics , volume =

  70. [70]

    and Barchi, M

    Collettini, C. and Barchi, M. R. and De Paola, N. and Trippetta, F. and Tinti, E. , title =. Nature Communications , volume =