Dike modelling

Magma transport in brittle rock occurs by diking. Understanding the dy- namics of diking and its observable consequences is essential to deciphering magma propagation in volcanic areas. Furthermore, diking plays a key role in tectonic phenomena such as continental rifting and plate divergence at mid-ocean ridges. Physics-based models of propagating dikes usually involve coupled transport of a viscous fluid with rock deformation and fracture. But the behaviour of dikes is also affected by the exchange of heat with the sur- roundings and by interaction with rock layering, pre-existing cracks, and the external stress field, among other factors. This complexity explains why ex- isting models of propagating dikes are still relatively rudimentary: they are mainly 2D, and generally include only a subset of the factors described above. Here, we review numerical models on dike propagation focusing on the most recent studies (from the last 15–20 years). We track the influence of two main philosophies, one in which fluid dynamics are taken to control the behavior and the other which focuses on rock fracturing. It appear that uncertainties in the way that rock properties such as fracture toughness vary from labora- tory to field scale remains one of the critical issues to be resolved. Finally, we present promising directions of research that include emerging approaches to numerical modeling and insights from hydraulic fracturing as an industrial analogue.

A model of magma propagation in the crust is presented using a series of analogue experiments, where dyed water is injected at a constant flux into layers of solidified gelatine. The gelatine layers are transparent and, when intruded, deform in an almost ideal-elastic manner under the experimental conditions (low gelatine concentration: 2.5 or 3 wt%, and low temperature: 5–10◦C). The upper gelatine layer was 1.0 to 1.5 times stiffer than the lower layer, with either a ‘weak’ or ‘strong’ interface strength between the gelatine layers. The gelatine is seeded with 20–50μm-diameter PMMA-RhB neutrally buoyant particles that are fluoresced by a pulsed, vertical laser sheet centred on the injection point. Digital image correlation (DIC) is used to calculate incremental strain and finite strain in the deforming host material as it is intruded. This is mapped in 2D for the developing experimental volcanic plumbing system that comprises a feeder dyke and sill. Since the gelatine deforms elastically, strain measurements correlate with stress. Our results indicate that, for constant magma flux, the moment of sill inception is characterised by a significant magmatic pressure decrease of up to ∼60%. This is evidenced by the rapid contraction of the feeder dyke at the moment the sill forms. Sill propagation is then controlled by the fracture properties of the weak interface, with fluid from the feeder dyke extracted to help grow the sill. Pressure drops during sill inception and growth are likely to be important in volcanic systems, where destabilisation of the magmatic plumbing system could trigger an eruption.

Magma transport through dikes is a major component of the development of monogenetic volcanic fields. These volcanic fields are characterized by numerous volcanic centers, each typically resulting from a single eruption. Therefore, magma must be transported from source to surface at different places, which raises the question of the relative importance of (1) the self-propagation of magma through pristine rock and (2) the control exerted by pre-existing fractures. To address this issue, we have carried out a series of analogue experiments to constrain the interaction of a propagating dike through a medium with pre-existing fractures. The experiments involved the injection of air into an elastic gelatin solid, which was previously cut into its upper part to simulate pre-existing fractures. The volume of the dikes, their distance from the fractures, and the ambient stress field were systematically varied to assess their influence on potential dike-fracture interactions. The results show that distance and angle between dikes and fractures influence these interactions and the dike trajectory. Dike geometry and dynamics are also affected by both the presence of the fractures and the dike volume; dikes propagating in between fractures tend to decelerate. In nature, interactions are expected for dikes and fractures separated by less than about 200 m, and dikes with a volume less than about 10−2 km3 would experience a velocity decrease. These results highlight the influence of pre-existing fractures on the mechanics and dynamics of dikes. These heterogeneities must be considered when studying the transport of magmas within the crust.

The occurrence time of earthquakes can be anticipated or delayed by external phenomena that induce strain energy changes on the faults. ‘Anticipated’ earthquakes are generally called ‘triggered’, however it can be controversial to label a specific earthquake as such, mostly because of the stochastic nature of earthquake occurrence and of the large uncertainties usually as- sociated to stress modelling. Here we introduce a physical approach to quantify the probability that a given earthquake was triggered by a given stress-inducing phenomenon. As an example, we consider an earthquake that was likely triggered by a natural event: the M=6.2 13 Jan 1976 Ko ́pasker earthquake on the Gr ́ımsey Lineament (Tj ̈ornes Fracture Zone, Iceland), which occurred about three weeks after a large dike injection in the nearby Krafla fissure swarm. By using Coulomb stress calculations and the rate-and-state earthquake nucleation theory, we calculate the likelihood of the earthquake in a scenario that contains only the tectonic background and excludes the dike, and in a scenario that includes the dike but excludes the background. Applying the Bayes’ theorem, we obtain that the probability that the earthquake was indeed triggered by the dike, rather than purely due to the accumulation of tectonic strain, is about 60% to 90%. This methodology allows us to assign quantitative probabilities to different scenarios and can help in classifying earthquakes as triggered or not-triggered by natural or human-induced changes of stress in the crust.combined statistical and

World experiences reveal that catastrophic floods are posing a serious threat that comes not only from them as extreme events but also as the result of adaptation measures uncertainty, (i.e. dikes). In particularly old dikes constructed earliest at the north part of Albania, during the last floods demonstrated the high uncertainty and weak spots. In this paper, the significance of the seepage investigation and stability analysis are discussed. As a case study, parts of new dikes constructed last years along the Buna River located in north part of Albania are investigated. Filling materials for these dikes are represented mostly from silt and clay. Finite element method is used to perform seepage analysis while general limit equilibrium method is used to perform slope stability analysis. Both, seepage and slope stability analyses are done for three different scenarios: steady state, rapid filling, and rapid drawdown. Finally, it is concluded that silt-clay materials used in these dik...

World experiences reveal that catastrophic floods are posing a serious threat that comes not only from them as extreme events but also as the result of adaptation measures uncertainty, (i.e. dikes). In particularly old dikes constructed earliest at the north part of Albania, during the last floods demonstrated the high uncertainty and weak spots. In this paper, the significance of the seepage investigation and stability analysis are discussed. As a case study, parts of new dikes constructed last years along the Buna River located in north part of Albania are investigated. Filling materials for these dikes are represented mostly from silt and clay. Finite element method is used to perform seepage analysis while general limit equilibrium method is used to perform slope stability analysis. Both, seepage and slope stability analyses are done for three different scenarios: steady state, rapid filling, and rapid drawdown. Finally, it is concluded that silt-clay materials used in these dik...