We examine the ascent of volatile-rich basaltic magma through a vertical dike that intersects a horizontal tunnel of comparable cross-sectional area to the dike and located 300 $m$ below the surface and initially filled with air at atmospheric pressure. This process is a simplified representation of some aspects of the possible interaction of a basaltic fissure eruption with a man-made tunnel, as part of a risk assessment for the proposed high level waste repository at Yucca Mountain, Nevada, U.S.A. We study the decompression and flow that develops following breakthrough into the tunnel using a one-dimensional model averaged over the prescribed dike and tunnel geometry. The main volatile phase in the basaltic magma is water and this is exsolved from the melt as the mixture decompresses. We neglect any motion of the vapor bubbles relative to the mixture and use a parameterization of the bulk viscous resistance. The model predicts that for 2 $wt$% water, the magma-gas mixture decompresses rapidly into the tunnel, and generates a pressure jump in the air, which travels at a speed of order 500 $m/s$. Two end-members references simulations are investigated: one in which the dike-drift nozzle (about $20\,m^2$) opens instantly and is relatively smooth, and another one in which the dike-drift nozzle is opened from a small area ($< 1\,m^2$) to its steady opening (of about $20\,m^2$) in a minute. In either case the tunnel is eventually filled with high-pressure magma at about its initial dike-tip pressure within a few minutes. In the faster case the pressure jump is reflected and amplified by a factor of 20 - 45 thereby producing a high pressure region at the end of the tunnel away from the dike. In the slower case, the tunnel fills more gradually in about two minutes. Further flow behavior is investigated in a parameter study. The results suggest that this pressurization of the tunnel could lead to rock fracture and magma breakthrough to the Earth's surface.
|Publisher||Department of Applied Mathematics, University of Twente|
- hyperbolic equation
- decompressing magma flow
- Magma-repository interaction