Two-dimensional simulations of magma-repository interactions reveal that the three phases --a shock tube, shock reflection and amplification, and shock attenuation and decay phase-- in a one-dimensional flow tube model have a precursor. This newly identified phase ``zero'' consists of the impact of magma against the drift roof, after breakthrough into the drift, which results into a large pressure pulse. This initial pressure pulse against the tunnel roof can be estimated using one-dimensional shock reflection models in the vertical direction. After phase zero there is a large-pressure region near the breakthrough and the subsequent phases: a shock tube phase, a shock reflection phase at the closed end of the drift and an attenuation phase are similar as in the one-dimensional flow tube model. The flow along the drift then becomes nearly one dimensional due to the large length to diameter ratio of the drift. Most notably, the pressure reflection pulse at the closed tunnel end is (much) larger than the initial pressure pulse at the tunnel roof. The presented simulations are preliminary in that they are purely two dimensional. Improved values of pressure pulses and volume fluxes of magma will be calculated in the future by incorporating the proper three-dimensional effects into averaged two-dimensional flow area models. The model considered herein is a necessary precursor of these future models.
|Publisher||Department of Applied Mathematics, University of Twente|