Understanding the response of a fault gouge, the granular material at the core of fault zones, can shed light on the way earthquakes are nucleated. For this purpose, in this paper, a series of particle-based simulations of a fault gouge, under conditions similar to the ones expected at deep down at the seismogenic zone, are conducted. A full scale fault with dimensions of the order of kilometers is almost impossible to be simulated at the grain-scale. In order to capture the inhomogeneities at this level, the response of several, small samples is combined in a stochastic-ensemble manner. The results suggest that local stick-slip events are vanishing with increasing number of tests thus, they are not critical for the macroscopic, global, material’s response. Contrary to this, the amount of slip needed to promote earthquake instabilities is shown to vary with respect to the mean particle size of the material. Finally, the granular polydispersity and the slip velocity do not seem to affect the system’s behavior. The later highlights possible important role of multiphysics on the rheology of fault gouges and provides evidence for the constitutive assumptions used in continuum models.
Two recent results on earthquake control are summarized in this conference presentation, with emphasis on sliding mode control. A simplified model of an earthquake instability is addressed by means of a cascade system of a 1D wave equation, representing the fault slip and wave propagation, and a 1D diffusion equation, representing the injection of fluid as a diffusion process. In order to avoid a fast slip (earthquake-like behavior), the control is designed to follow a slow reference in both systems despite model uncertainties and perturbations. Simulations are additionally conducted to support the robustness and stability properties of the proposed control algorithms, by separately, obtaining critical remarks that will lead to the design of the single control for the cascade system in a future stage.
Based on the mathematical developments presented in this paper and on others to follow, we show mathematically that fluid pressure can be used to stabilize and control the unstable fast seismic slip of a mature fault. In a more general framework, we discuss also the possibility of controlling complex systems exhibiting self-organized criticality due to frictional instabilities.
Please find enclosed the second of a series of three works on TANN that was recently published in Computer Methods in Applied Mechanics and Engineering (doi: 10.1016/j.cma.2022.115190, https://authors.elsevier.com/c/1fGS5AQEIzV-w).
In this paper we show how thermodynamics can be explicitly inserted into neural networks to guarantee thermodynamically consistent predictions of the behavior of complex materials with inelastic microstructure. We also show how internal state variables can be automatically discovered and give access to the salient micro-mechanisms that are related to the non-linear macroscopic behavior. Finally, based on a double-scale asymptotic homogenization scheme, we perform multiscale analyses achieving speed-ups of many orders of magnitude compared to micromechanical simulations.
I am very happy and proud of you Alexandre! Excellent work and presentation! For those that could not attend the defense here is the full recording: https://youtu.be/naSJC2cMEJs
Excellent work and presentation George! I am very happy and proud of you! For those that could not attend the defense here is the full recording: https://youtu.be/xyvAtueAmRU
Earthquakes nucleate when large amounts of elastic energy are suddenly released due to abrupt sliding over seismic faults. Besides physical causes, this energy release can be also triggered by injecting large amounts of fluids in the earth’s crust. Indeed, recent events show that injections can reactivate existing seismogenic faults and induce/trigger important earthquakes.
However, one can see the problem of fluid injections from another perspective. The dependence of fault friction on fluid pressure can be used as an input for stabilizing it. New results based on the mathematical theory of control show that it is indeed possible to stabilize and restrict chaos in this kind of non-linear unstable frictional systems and assure slow frictional dissipation toward desirable global asymptotic equilibria of lower potential energy.
Our mathematical derivations show that earthquake robust control is possible, provided that fault friction is bounded. Friction is a complex phenomenon involving several spatio-temporal scales and complex dynamics. In spite of complexity, the finiteness of energy of any physical process influencing friction as well as existing laboratory and in-situ experiments, support the boundedness of friction. However, the quantification of these bounds is challenging as experiments are difficult to perform deep down in the earth. As a result, we have to rely also on numerical simulations and digital twins of seismic faults, which until know are computationally very demanding.
To this end, we develop a novel deep learning approach for modeling complex materials, by enforcing the laws of thermodynamics. The method is accurate, fast and scalable, and will allow, in the near future, to derive reliable quantitative estimations of the bounds of fault friction under the effect of multiphyics couplings and complex grain/particle dynamics. In parallel, it will enable to optimize our earthquake control strategies by performing large scale simulations of real fault systems in a virtual, data- and physics-driven environment, that fits on a laptop.
