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
https://arxiv.org/abs/2607.01448 https://arxiv.org/pdf/2607.01448 https://arxiv.org/html/2607.01448
arXiv:2607.01448v1 Announce Type: new
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.
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A discrete Boltzmann model with state-dependent power-law relaxation time for nonequilibrium transport in compressible flows
Demei Li, Zhongyi He, Huilin Lai, Yanbiao Gan, Hailong Liu, Pengfei Lin
https://arxiv.org/abs/2605.18216 https://arxiv.org/pdf/2605.18216 https://arxiv.org/html/2605.18216
arXiv:2605.18216v1 Announce Type: new
Abstract: Thermodynamic nonequilibrium effects play a central role in momentum and energy transport in compressible flows. In conventional BGK kinetic models, the relaxation time $\tau$ is taken as a constant, which neglects the dependence of the relaxation process on local macroscopic states. To overcome this limitation, we develop a discrete Boltzmann model with a density- and temperature-dependent power-law relaxation time, termed DTRT-DBM, in which $\tau=\tau_0(\rho/\rho_0)^a(T/T_0)^b$. This formulation extends the discrete Boltzmann framework to flows with spatially varying nonequilibrium intensity. The model is validated by the Sod shock tube and by analytical solutions for viscous stress and heat flux, demonstrating accurate recovery of both macroscopic wave structures and nonequilibrium quantities across shock waves, rarefaction waves, and contact discontinuities. On this basis, phase diagrams of viscous stress and heat flux are constructed to examine how these quantities depend on the power-law exponents $a$ and $b$. The extrema of these quantities depend exponentially on the model parameters and exhibit regime-dependent behaviour. The roles of $a$ and $b$ are not symmetric: the nonequilibrium response is more sensitive to $a$ when density gradients dominate, but more sensitive to $b$ when temperature gradients dominate. Within the parameter range and flow configurations examined here, higher-order viscous stress increases the growth rate of the total viscous-stress extremum, whereas higher-order heat flux reduces the growth rate of the total heat-flux extremum. These results show that the proposed model can capture different higher-order nonequilibrium responses in compressible flows and provides a framework for the modelling and analysis of multiscale nonequilibrium processes.
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