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# Controlling earthQuakes

## Periodic Reporting for period 3 - CoQuake (Controlling earthQuakes)

Reporting period: 2021-03-01 to 2022-08-31

Can earthquakes be avoided ?

Nowadays we know that we, humans, can cause earthquakes, but we don’t know if we can prevent them.

CoQuake tries to answer to this fundamental question using established mathematical theories and novel experimental tests.

Clearly, earthquakes are lethal and costly. Loss of life is a tragedy wherever it occurs and no matter how large the number of victims is. In addition, earthquakes have mid- and long-term consequences related to the future societal wellbeing and economic development. Earthquakes are also provoked by humans during energy production and geological storage. Wastewater disposal, enhanced oil recovery, hydraulic fracturing, CO2 sequestration and geothermal energy extraction are some of the recently used techniques that have as side/parasitic effects, the triggering of several uncontrollable seismic events. As a result earthquake control can lead to remarkable socio-economical benefits in the future.

CoQuake introduces a new field in earthquake engineering, which focuses on stimulating a fault in a controlled way, based on established mathematical methods and novel, sophisticated tools that are developed during the project. Instead of waiting passively an earthquake to trigger at high energy level and in an uncontrollable way, with all the related catastrophic consequences, CoQuake focuses on inducing it before, at a lower energy level, or even avoiding it completely by inducing a-seismic slip. In this manner it will be possible to mitigate the earthquake released energy and to reduce its impact.
The main objective of CoQuake is to explore whether it is possible or not to avoid earthquakes. Due to the significance of the underlying problem, the scientific developments that are carried out demand a high degree of scientific rigor. Having this in mind, one of the main achievements of the research in CoQuake, was to transform the problem of earthquake control to a concrete mathematical problem where rigorous proofs can provided.

Using the Mathematical Theory of Control we showed that earthquake-like instabilities can be prevented. We also showed, for the first time, how the slip velocity of faults can be controlled in order to drive the system in an a-seismic manner to a new stable equilibrium of lower energy. We prooved that this is possible even in the absence of detailed knowledge of the properties of the faults and of the surrounding rocks. Consequently, only rough estimations about the parameters of the geosystem are needed, which are available in-situ.

The experimental program went beyond our initial expectations. We conceptualized and developed an analogous experimental system using absorbent porous paper. This setup allowed us to identify key parameters that are related to anthropogenic seismicity and highlighted the importance of the more sophisticated and rigorous techniques developed in CoQuake. Moreover, we designed and constructed a new experimental apparatus that enabled us to put in evidence the theoretical developments of the project. Using 3D sand-printed samples and this novel device, we achieved total control of earthquake-like instabilities.

Focusing into the micro-mechanisms of fault friction, the application of stochastic DEM analyses allowed to unravel some new features of granular assemblies and backup our assumptions for new thermo-hydro-mechanical models with grain breakage that we developed based on the Cosserat theory for describing the friction of faults. In an effort to accelerate our simulations, we pushed further the use of Artificial Networks for constitutive modeling by proposing a novel thermodynamically consistent architecture (i.e. Thermodynamics-based Artificial Neural Networks - TANN). TANN assure more accurate predictions for unseen data, require less data and are robust to noise.

In the same time a novel versatile numerical framework was developed, i.e. the Numerical Geolab. This object-oriented code enables the simulation of complex systems under a variety of THMC couplings using micromorphic continua of arbitrary order, n-multi-scale simulations and TANN interaction.
It is worth mentioning that even though we are enthusiastic about these first results, we pay extreme attention in applying the scientific method with rigor. Our approach is based on the falsification of our theoretical findings. Therefore, the next steps are to increase the complexity of the studied geosystem in order to make it more realistic and to provide additional theoretical, numerical and experimental evidence in order to rigorously prove (or disprove) the possibility of earthquake control.

The mathematical proofs and the various tools that are under development, pave the way for designing earthquake control in a concrete realistic case study, which will be simulated numerically and experimentally in CoQuake.

Despite the apparent focus of the project on the main scientific question regarding earthquake control, CoQuake methodology aims at providing answers to several other open questions. These questions concern, among others, the modeling of multi-scale, multi-physics systems showing softening and strain localization, efficient computational modeling using higher order continua and machine learning, fault dynamics and discrete/continuous robust control of frictional systems. The theoretical, numerical and experimental methods that are under development go beyond the current state-of-the-art and are expected to be useful in many disciplines spanning from geosciences to mechanics and engineering.