A damage model for semi-brittle deformation of dome magmas from Colima volcano

The stability, collapse dynamics and/or eruption style of a lava dome is mainly controlled by the rheological response of its constituent magmas to a range of internal and external stresses of various magnitudes and rates. Laboratory experiments carried out on natural lava-dome samples with high crystallinity (>50%) have provided empirical relations between the viscosity of the samples and the applied temperature and strain rate. These experiments have also provided valuable insight into the complex link between the samples’ elastic parameters and physical properties, including porosity and microcrack density (damage). In order to incorporate this information into large-scale numerical models for lava dome deformations, it is crucial to quantify how different deformation mechanisms alter the elastic parameters and viscosity of dome magmas. We address this problem by applying a thermodynamically-based visco-poroelastic damage model to the deformation data from high-temperature uniaxial experiments involving lava samples from Colima volcano (Mexico). The experiments involve constant stresses (2.8-28 MPa) and constant temperatures (935-947°C) representing realistic lava dome conditions. For each experiment, we invert the deformation data using a nonlinear optimization scheme to constrain the optimal model parameters. Using the optimal parameters, we estimate the amount of damage, porosity and irreversible (inelastic) strain as a function of time throughout the experiments.

Our damage model establishes a quantitative link between the elastic parameters and the porosity and microcrack density of the magmas. We find that the rheological behavior of all three samples throughout the experiments is “semi-brittle” (brittle-ductile), and that the samples deform dominantly by pressure-driven compaction and cataclastic flow. We also find that the effective viscosity of the samples is a combination of two components: a ductile component with a constant viscosity, and a damage-induced viscosity, which depends on the strain-rate and the rate of damage increase; the damage-induced viscosity is responsible for the nonlinear variations of the apparent viscosity of the samples. The elastic parameters in all three models are determined by the competition between degradation (damage increase) and inelastic compaction (porosity decrease). Moreover, across the three models, the inferred kinetic parameters (e.g., damage rate, yield-cap parameters) decrease approximately linearly with the applied stress. Finally, the cumulative counts of the Acoustic Emissions (AEs), which were recorded for two of the experiments, match the evolution of the damage in the models. We discuss the implications of our damage model and the further theoretical, numerical and experimental work required for establishing large-scale numerical models for lava dome deformations.