A model to describe precursory material-failure phenomena: applications to short-term forecasting at colima volcano, Mexico

Abstract

Some volcanoes exhibit at times accelerating strain and seismicity before eruptions. Different authors have used this behavior to predict eruptions and to develop materials-science models. Here, a linear Kelvin-Voigt viscoelastic model is proposed to describe the observed behavior. This model also has applications to other failure phenomena, such as landslides. The strain rate of a variety of materials under constant stress after an instantaneous elastic response is found to be well described by a general relaxation law: $\dot \varepsilon \left( t \right) = {B \over {1 + st}}$ , where B and s are parameters depending on the material and its creep state. Whether the creep regime is primary or tertiary depends upon the sign of s; s=0 corresponds to pseudoviscous flow. The creep behavior of the viscoelastic body is analyzed for different load histories. It is found that the body has an exponential distribution of retardation frequencies that may or may not converge, depending on the sign of s. According to the model, tertiary creep implies material degradation and a critical weakening of the medium leading to a runaway growth of the strain and seismic energy release rates. If tertiary creep is detected, time of failure predictions may be done from field data through determination of two model parameters for varying loads. The model response compare well with reported examples of pre-eruptive volcano behavior, and with reported results of landslide experiments. The model is tested with the July 1994 (in hindsight) and November 1998 (in foresight) Colima volcano eruptions. Although this method provides some guidance in estimating the time over which accelerating volcanic precursors may end in an eruption, it is emphasized that eruptions may fail to occur at the estimated time, or may not occur at all. On the other hand, eruptions may not be preceded by such a behavior.