A relation to predict the failure of materials and potential application to volcanic eruptions and landslides

Abstract

A theoretical explanation of a time-to-failure relation is presented, with this relationship then used to describe the failure of materials. This provides the potential to predict timing (tf − t) immediately before failure by extrapolating the trajectory as it asymptotes to zero with no need to fit unknown exponents as previously proposed in critical power law behaviors. This generalized relation is verified by comparison with approaches to criticality for volcanic eruptions and creep failure. A new relation based on changes with stress is proposed as an alternative expression of Voight’s relation, which is widely used to describe the accelerating precursory signals before material failure and broadly applied to volcanic eruptions, landslides and other phenomena. The new generalized relation reduces to Voight’s relation if stress is limited to increase at a constant rate with time. This implies that the time-derivatives in Voight’s analysis may be a subset of a more general expression connecting stress derivatives, and thus provides a potential method for forecasting these events.

An accelerating precursor to predict “time-to-failure” in creep and volcanic eruptions

“…This method works well in retrospective prediction for such laboratory experiments, landslides, and volcanic eruptions (Voight, 1988;Voight, 1994, 1995;Kilburn and Voight, 1998;Murray and Ramirez Ruiz, 2002;Budi-Santoso et al, 2013). Hao et al, 2016 However, the exponent α is not always equal to 2 but exhibits variation. Table 1 lists some values of α measured in laboratory and field for a range of loading conditions.…”

Catastrophic Failure and Critical Scaling Laws of Fiber Bundle Material

“…The damage fraction is widely described by a Weibull distribution of the form $D\left(\epsilon \right)=1-e^{-{\epsilon }^m}$ [11,17,18,19], where m is the Weibull index.…”

The Changeable Power Law Singularity and its Application to Prediction of Catastrophic Rupture in Uniaxial Compressive Tests of Geomedia

“…The accelerating behavior of some response quantities (e.g., deformation and seismic events) is widely observed before natural disasters such as volcanic eruptions (Bell et al, 2011(Bell et al, , 2013Boué et al, 2015;Hao et al, 2016;Kilburn, 2003;Kilburn & Voight, 1998;Voight, 1988), landslides (Helmstetter et al, 2004), and earthquakes, as well as in rupture experiments (Hao et al, 2013(Hao et al, , 2014Heap et al, 2009;Nechad et al, 2005a). This has been analyzed as a critical phenomenon (Abaimov & Cusumano, 2014;Bak & Tang, 1989;Girard et al, 2010;Rundle et al, 2003;Toussaint & Pride, 2002a, 2002b, 2002c, 2005 with a power law divergence of macroscopically observable quantities (Guarino et al, 1998(Guarino et al, , 2002Rundle et al, 2000;Weiss et al, 2014) at failure.…”

“…This has been analyzed as a critical phenomenon (Abaimov & Cusumano, 2014;Bak & Tang, 1989;Girard et al, 2010;Rundle et al, 2003;Toussaint & Pride, 2002a, 2002b, 2002c, 2005 with a power law divergence of macroscopically observable quantities (Guarino et al, 1998(Guarino et al, , 2002Rundle et al, 2000;Weiss et al, 2014) at failure. Such an accelerating behavior is usually accepted as a precursor for prediction of time to failure (Hao et al, 2016;Kilburn, 2003Kilburn, , 2012Kilburn & Voight, 1998;Main, 1999;Voight, 1988Voight, , 1989. For example, to quantitatively describe an acceleration process during the evolution to failure, Voight (1988Voight ( , 1989 suggested an empirical relationship, that is,…”