Controlling Anthropogenic and Natural Seismicity: Insights From Active Stabilization of the Spring‐Slider Model

Abstract

We present a theoretical study focusing on exploring the possibility of controlling anthropogenic and natural seismicity. We actively control the pressure of injected fluids using a negative‐feedback control system. Our analysis is based on the spring‐slider model for modeling the earthquake instability. We use a general Coulomb‐type rheology for describing the frictional behavior of a fault system. This model leads to a nonautonomous system, whose steady state and stability are studied using a double‐scale asymptotic analysis. This approach renders the dominant order of the system time invariant. Established tools from the classical mathematical theory of control are used for designing a proper stabilizing controller. We show that the system is stabilizable by controlling fluid pressure. This is a central result for industrial operations. A stabilizing controller is then designed and tested. The controller regulates in real time the applied pressure in order to assure stability, avoid unwanted seismicity, and drive the system from unstable states of high potential energy, to stable ones of low energy. The controller performs well even in the absence of complete knowledge of the frictional properties of the system. Finally, we present two numerical examples (scenarios) and illustrate how anthropogenic and natural earthquakes could be, in theory, prevented.

A Cosserat Breakage Mechanics model for brittle granular media

“…The system is integrated in the Numerical Geolab framework (Stefanou, 2018), which provides a generalised continuum layer on top of the finite element solver FEniCS (Alnaes et al, 2015;Logg, Mardal and Wells, 2012). We use an implicit backwards Euler method, and select quadratic test functions for the displacements and linear test functions for the rotations (see Godio et al (2015) for a more thorough discussion of finite element implementation in the Cosserat continuum).…”

“…Particularly in a geological context, multi-physical couplings have a strong influence on the formation of localisation zones with temperature and pore fluid pressure interactions being well studied (e.g. Sulem, 2010;Sulem, Stefanou and Veveakis, 2011) and chemical changes such as decomposition and dehydration (Brantut and Sulem, 2012;Brantut, Sulem and Schubnel, 2011;Stefanou andSulem, 2013, 2014;Sulem and Famin, 2009;Veveakis, Alevizos and Vardoulakis, 2010;Veveakis, Stefanou and Sulem, 2013, among others) have also been shown to contribute towards forming but also potentially limiting the size of localisation zones. Recently, fully coupled systems that integrate the effects of temperature, pressurisation and chemical reactions have been explored (Platt, Rudnicki and Rice, 2014;Rattez, Stefanou and Sulem, 2018;Rattez et al, 2018a,b;Rice, Rudnicki and Platt, 2014;Sulem and Stefanou, 2016).…”

“…However, notably for the present study, the evolution of the size of the microstructure of the considered material also plays an important role in shear band development and apparent softening behaviour. The latter is connected to earthquake stability and control (Stefanou, 2019). Fault cores reveal that there are distinct zones within a more extensive damaged zone.…”

Absorbent Porous Paper Reveals How Earthquakes Could be Mitigated

“…However, this slip can be slow (aseismic) or sudden and abrupt (seismic), depending on the amount of slip weakening (Figure 1f). It can be shown that the condition for sudden, unstable slip is (Dieterich, 1979;Kanamori & Brodsky, 2004;Scholz, 2002;Stefanou, 2019):…”

Design of Sand‐Based, 3‐D‐Printed Analog Faults With Controlled Frictional Properties

“…where Δμ ⋅  n F is the frictional drop (corresponding to the static stress change of an earthquake) and sw c d is the characteristic slip-weakening distance (Di Toro et al, 2011;Dieterich, 1979;Kanamori & Brodsky, 2004;Scholz, 2002;Stefanou, 2019).…”