Changes in lava effusion rate from a volcanic fissure due to pressure changes in the conduit

We calculate the change in effusion rate of lava from a volcanic fissure due to pressure changes in the volcanic conduit. The conduit is modelled as a cylinder with elliptical cross-section, embedded in an elastic medium. The elliptical shape can represent a wide range of cross-sections, according to the value of eccentricity, from almost circular vents to very long and narrow fissures. A 2-D problem is considered assuming invariance of pressure changes and conduit geometry with depth. The problem is solved analytically and expressions for the displacement and the stress fields in the elastic medium are provided. The displacement of the conduit wall is proportional to the ratio between the pressure change and the rigidity of surrounding rocks. The flow rate is a nonlinear function of the pressure change and increases with increasing pressure, due to the elastic deformation of the conduit wall.We consider flow rate oscillations with periods ranging from several minutes to hours, as are often observed during effusive eruptions. Assuming pressure oscillations with these periods, flow rate oscillations resulting from the elastic deformation of the conduit are calculated. The greatest oscillations in flow rate are obtained for very large values of the conduit eccentricity, corresponding to long and narrow volcanic fissures. For example, if a fissure is 100 m long and 2 m large, a pressure oscillation with an amplitude of 1 MPa yields a maximum displacement of the conduit wall equal to about 6 cm and an amplitude of flow rate oscillations of about 20 per cent.