Stress relaxation experiments are reported that culminate in energetic failure in rocks analogous to the loading cycle and subsequent localization or reactivation on brittle faults embedded in an elastic medium. Universally, rapid primary deformation arrests and transitions into a long secondary deformation phase that ultimately accelerates to catastrophic rupture. Primary deformation (u) conforms to Andrade's law as du/dt ~ (tc − t0)θ with a standard exponent of 2/3. In the long, and readily observable, secondary phase, the samples both deform and analogously shed load near linearly in time. This stress relaxation rate exhibits a robust power law dependency with time‐to‐rupture and exhibits the same 2/3 power law exponent observed in the primary phase. Similarly, the brittle strain energy released in the tertiary collapse scales with a normalized secondary stress relaxation rate. Together, these observations suggest a way to predict both the timing of rupture and its energetics from the observed stress (or strain) rate during the secondary relaxation stage.
A theoretical explanation of a time-to-failure relation is presented, with this relationship "Equation missing"<!-- image only, no MathML or LaTex --> then used to describe the failure of materials. This provides the potential to predict timing (tf − t) immediately before failure by extrapolating the trajectory "Equation missing"<!-- image only, no MathML or LaTex --> 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.
1 June 2013 in International Journal of Rock Mechanics and Mining Sciences