When Does Magma Break?

Abstract

Geophysical signals arriving at the Earth's surface originate from a source mechanism at depth but are not necessarily directly observable. Therefore, well-posed experiments can provide insights into source mechanics and, importantly, the parameters required to model aspects of the sources of unrest signals. In this Chapter we detail one such example of how experimental laboratory work has improved our understanding of unrest signals. We focus on the failure of single-and multi-phase magmas, demonstrating that the liquid viscosity, and therefore the temperature and volatile content of a magma of a given composition, is the limiting parameter in determining whether a magma will ascend viscously or whether it can fracture during ascent. This critical threshold is characterized by a Deborah number, the ratio of the timescale of relaxation to the timescale of local flow. We show that for single-phase magmatic liquids and for vigorously vesiculating magmas, a local Deborah number of 10 À2 is the limit above which mixed viscoelastic behaviour including fracture propagation can be expected, and a Deborah number of 1 is the limit above which magma is dominantly elastic and responds in a brittle manner to applied stresses. These thresholds can be understood in terms of the onset and peak of the Debye relaxation process for viscoelastic liquids. The apparent validity of a Maxwell model permits us to predict the maximum stress that can be supported by a volcanic liquid deforming in the high Deborah number range. We use these constraints to provide a map of timescales on which we contour dominant system responses from viscous to purely brittle; valid for all magmatic liquids. Finally, we explore the scaling necessary to extend these conceptual insights to crystal-and bubble-bearing magmas valid under specific conditions. The competing timescales of deformation and relaxation in magma are relevant to unrest source mechanisms that originate from magma deformation, such as long-period seismic signals that are used to predict eruption timing. KeywordsRheology Á Strain rate Á Experimental volcanology Á Glass transition Á Failure forecasting Á Low frequency earthquakes Á Viscous dissipation Glossary RheologyThe study of the response of a material to an applied stress or deformation. In the volcano-sciences this typically refers to magma-rheology which is dominated by the rheology of the liquid phase (a viscous or viscoelastic melt) and the additional effect of suspended phases (crystals and gases). Viscoelasticity A material response to an applied stress in which both elastic and viscous components of the deformation are observed. In magma, as the temperature decreases or the local strain rate increases, the elastic component becomes more dominant. When the viscous component is negligible, purely elastic behaviour and material-rupture can readily occur. See Rheology.

Brittle‐Ductile Deformation and Tensile Rupture of Dome Lava During Inflation at Santiaguito, Guatemala

“…The role of Ф in decreasing rock strength during mixed mode and viscous deformation appears to be diminished, and pores may favor a certain degree of pervasive strain and stress relaxation. We may expect a stronger porosity dependence of the tensile strength during high‐temperature tests at strain rates close to and above the relaxation time of the silicate melt (e.g., above the fully brittle threshold where brittle deformation mechanics govern failure (Coats et al, ; Dingwell & Webb, ; Wadsworth et al, )).…”

A theoretical model of Surtseyan bomb fragmentation

“…As in the model presented in [12], we make no attempt here to model the development of vesicularity in rising magma or to consider viscous flow effects or changes in porosity due to compression. Instead, vesicular molten magma is treated as a competent porous rock matrix of constant porosity, owing to the high viscosity of the magma at temperatures at and below 1275 K [10,15,16]. The Deborah number De=tvistelas may be used to separate the time scales on which viscous (flowing) and elastic (brittle) responses occur in magma under stress.…”

“…Here t vis is the time required for viscous relaxation of magma and t elas is the time needed to deform magma as a competent solid. Brittle responses occur for De > 1 [16], and viscous flow is more important for relieving stress if De < 0.01. Viscous relaxation times are strongly dependent on temperature, and at 1275 K t vis ∼ 1 s. Then the assumption of brittle behaviour is good for De∼1telas>1, that is, for times t elas < 1 s. It will be seen in the numerical simulations that maximum pressure is reached in a millisecond or less, consistent with this assumption.…”

A theoretical model of Surtseyan bomb fragmentation

“…As in the model presented in [12], we make no attempt here to model the development of vesicularity in rising magma, or to consider viscous flow effects or changes in porosity due to compression. Instead, vesicular molten magma is treated as a competent porous rock matrix of constant porosity, due to the high viscosity of the magma at temperatures at and below 1275K [10,15,16]. The Deborah number De = t vis t elas may be used to separate the time scales on which viscous (flowing) and elastic (brittle) responses occur in magma under stress.…”

“…Here t vis is the time required for viscous relaxation of magma, and t elas is the time needed to deform magma as a competent solid. Brittle responses occur for De>1 [16], and viscous flow is more important for relieving stress if De<0.01. Viscous relaxation times are strongly dependent on temperature, and at 1275K t vis ∼ 1 s. Then the assumption of brittle behaviour is good for…”