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The eruptive activity of a volcano is controlled by the opening and closure of conduits through which magma ascends to the surface. Assuming that the conduit is filled with magma only immediately before and during an eruption, and disregarding any cooling of magma in this state, we develop a model to study the deformation of a cylindrical conduit surrounded by a viscoelastic cylindrical region in an infinite, elastic, homogeneous space. The viscoelastic behavior of the zone around the conduit is due to heat conduction from the hot magma, which raises the temperature beyond the brittle-ductile transition point. The effect of a tectonic regional stress which favors (compressive) or acts against (tensile) conduit closure is taken into account. The sensitivity of the model is checked with respect to the governing parameters, namely size of the viscoelastic region, ratio between its rigidity and that of the elastic medium, Poisson's ratio, and tectonic stress. Conduit closure is found to be ruled essentially by the extension of the viscoelastic region and by the ratio between its rigidity and the rigidity of the surrounding elastic medium, while tectonic stress is much less important. The model is applied to the last eruptive cycle of Mount Vesuvius. Using realistic values for the elastic and viscoelastic moduli, we find that an open conduit condition has been possible from 1631 to 1944, while the quiescence from 1944 on implies a closed conduit state.
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