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

Some volcanoes exhibit at times accelerating strain and seismicity before e ruptions. Different authors have used this behavior to predict eruptions an d to develop materials-science models. Here, a linear Kelvin-Voigt viscoela stic model is proposed to describe the observed behavior. This model also h as 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 : epsilon over dot (t) = B/1+st, where B and s are parameters depending on the material and its creep state. Whether the creep regime is primary or te rtiary depends upon the sign of s; s=0 corresponds to pseudoviscous flow. T he creep behavior of the viscoelastic body is analyzed for different load h istories. It is found that the body has an exponential distribution of reta rdation 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 strai n and seismic energy release rates. If tertiary creep is detected, time of failure predictions may be done from field data through determination of tw o model parameters for varying loads. The model response compare well with reported examples of pre-eruptive volcano behavior, and with reported resul ts of landslide experiments. The model is tested with the July 1994 (in hin dsight) and November 1998 (in foresight) Colima volcano eruptions. Although this method provides some guidance in estimating the time over which accel erating volcanic precursors may end in an eruption, it is emphasized that e ruptions 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.