Thickness of Etnean Lavas

Walker1 has reported observations made on the volcano Etna of the thickness of solid lava flows and the inclination of the slopes on which they lie. He also made estimates of the viscosity of the lava flowing down the slopes of Etna in May 1966, by measuring the thickness and velocity of flow of the lava and the angle of inclination of the slope. The formulae used to determine the viscosity are those for a Newtonian fluid exhibiting laminar flow. Walker sought a relation between the viscosity of fluid lava, the thickness of solid lava and the inclination of the slopes on which the solid lava lies. It seems, however, that such a relation is unlikely because a lava flow having the properties of a Newtonian fluid would continue to flow until no lava at all remained on the sloping surface. Hot lava is observed to flow and cold lava is found to rest on sloping surfaces, however, so we may surmise that flowing lava is not Newtonian in its behaviour, at least as it approaches a fully solid state. Walker's valuable observations enable these questions to be investigated. If the thickness of solid lava flows were determined by the viscosity of the lava when liquid, if this had the properties of a Newtonian fluid, and if the flow were laminar, we should expect to observe a relation between angle of slope, α, and solid thickness, h, of the form where K is a constant. In practice, Walker's observations do not support a relationship of this form but, rather, one of the form where (hν max) is the maximum vertical thickness of lava found on any slope (see Table 1). Now hν sin α is proportional to the shear at the base of the flow caused by the weight of the overlying lava. That (hν max) sin α should be constant for the solid lava flows on Etna suggests that in the final stages of solidification, as the final thickness is determined, the lava is non-Newtonian and approximates in its behaviour to a Bingham plastic2. If the stress acting on a Bingham plastic is smaller than a critical value, which is called the yield stress, no flow occurs, but if the stress acting on it exceeds this value then flow does occur. In the case of lava we may suppose that, as solidification occurs, flow continues until the thickness reaches a value such that, for the slope in question, the shear at the base of the lava caused by the weight of the overlying material becomes smaller than the yield stress, and that at this point flow ceases. If lava flows in the final stages of solidification do behave as Bingham plastics, it is clear that no lower limit to the thickness of a flow is set by this property and so flows may be of any thickness up to the limit set by the yield stress characteristic of the lava concerned and the inclination of the slope on which the lava lies. Walker's observations are consistent with these conclusions if the yield stress of Etnean lava in the final stages of solidification is about 2.5 × 106 dynes/cm2. It follows that, in general, in the case of lavas tilted after their solidification, it is only the maximum thickness of lava at any locality which may supply information about the original slope.