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Abstract
Clastogenic flows form by coalescing from accumulated spatter. Due to the viscous nature of spatter, agglutinate remobilization behaves according to the Bingham flow law. The two main factors controlling the onset of clastogenesis are yield strength and basal shear stress. These factors are dependent on concomitant factors including accumulation rate, cooling rate, cone height, and topographic slope. To model clastogenesis, yield strength and basal shear stress can be plotted together against time. When basal shear stress exceeds yield strength, clastogenesis may occur. Four spatter cones were investigated at Krafla, Iceland. Measurements of height and topographic slope from the Krafla cones were used to calculate basal shear stress. Yield strength was calculated as a function of the spatter cone’s internal temperature using the equation in Dragoni (1989), which itself is a function of the cooling rate times time. Experimental results from Rader and Geist (2015) were used to derive a linear statistical relationship between accumulation rate and cooling rate, since higher accumulation rates means greater insulation of the deposited clasts and thus slower cooling rates. The exterior of a spatter clast quenches in the air before landing, creating a glassy skin that binds the molten interior. Thus, a strength parameter that accounts for the strength of the vitreous interclastic framework formed by these rinds is added to the yield strength. Major oxide data was used to calculate the viscosity of the spatter as a function of temperature using the method of Giordano et al. (2008). These viscosities along with a vesicle strain analysis conducted using Geological Image Analysis Software (GIAS) were used to determine the amount of strain preserved in vesicles and to estimate the strain rates needed to initiate melt mobilization (Beggan and Hamilton, 2010; Rust et al., 2003). Only one of the four cones exhibited convincing evidence of clastogenesis, with a slope of 40° and a height of 3.5 m to 4 m. Major oxide and trace element data from XRF analysis indicate there is no geochemical control on clastogenesis. Viscosities calculated using Giordano et al.’s (2008) method were averaged across all the samples from each cone to construct a general viscosity versus temperature curve for Krafla lava. Compaction of vesicles is evident in thin section but there is no quantitatively consistent increase in strain towards the bottom of the cone according to GIAS. However, strain may be accommodated by deformation via viscous flow within the deposit (Grunder and Russell, 2005). The cones that did not produce clastogenic flows actually have slightly higher strain rates for given viscosities than the cone that did produce a clastogenic flow. In general, accumulation rates greater than or equal to 11 m/hr on 40° slopes, 14 m/hr on 30° slopes, and 18 m/hr on 20° slopes are capable of producing clastogenic flows. On 40° slopes, failure heights range from 4.5 m to 4.8 m depending on the accumulation rate, which are comparable to the height measured at the clastogenic cone at Krafla. Based on the strain rates for the clastogenic cone calculated from GIAS and those predicted by the model using the Bingham flow law, it appears that vesicles only accommodate a maximum of about 0.017% of the total strain. This model assumes a constant accumulation rate and constant linear cooling rate; however, real rates are likely not constant or linear. The cone will cool as a function of time, height, and accumulation rate, and the accumulation of material may occur episodically and still be high enough to generate clastogenesis. Future work on this model should address variations in these rates. Modeling the heat diffusion out of individual clasts and how it can potentially remelt the glassy rinds between clasts is also key to understanding the stability of a spatter cone and should be investigated in future studies. In general, the model presented is consistent with field observations.