EGU General Assembly 2020
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Fully-coupled 3D modelling of magmatic dike propagation - finite pulse release from a point source

Andreas Möri, Brice Lecampion, and Haseeb Zia
Andreas Möri et al.
  • EPFL - École polytechnique fédérale de Lausanne, Lausanne , Switzerland (

Magmatic dikes are a naturally occurring type of fluid-driven fractures [1] propagating in the lithosphere driven by buoyancy (more precisely by the difference between the in-situ minimum horizontal stress gradient and the magma weight). Fully-coupled modelling of these 3D fractures is very challenging and most contributions until today have been restricted to 2D plane-strain. These 2D investigations have highlighted the importance of the head-tail structure, notably the fact that lubrication flow in the tail is driving the growth of the hydrostatic head [2, 3]. We investigate the 3D development of a buoyant dike from a point source, focusing on the case of a finite volume release under homogeneous conditions (homogeneous material properties and buoyancy contrast). We use the fully coupled planar 3D hydraulic fracture growth solver PyFrac based on the implicit level set algorithm [4].

This configuration shows an early time behaviour heavily dominated by the effects of the pulse release. The initially radial hydraulic fracture transitions toward a large time buoyant dike solution. At large time our simulations tends to the finger-like/constant breadth solution [5] albeit extremely slowly. Our results confirm the 3D toughness dominated head structure and the importance of the viscous tail as the driving mechanism for the dynamics of such a 3D Weertman’s pulse (form of the head). Depending on the initial phase of the pulse release, we observe an overshoot of the dike breadth when it is initially strongly dominated by viscous dissipation. Using a scaling analysis, we characterize the transition from the early time radial finite pulse fracture to the late dike constant breadth solution. Our simulations show, that the time when the buoyant force takes its full dominance is crucial and governs the existence (or not) of an overshoot. Mainly we show that the overshoot depends on a transitional time/lengthscale. A detailed understanding of the fracture propagation after the end of the finite volume release (yet without buoyancy) is key to quantify this lengthscale. We thus present scalings and semi-analytical solutions for this case and discuss its relevance for the transition toward a buoyancy driven dike propagation.

[1]  E. Rivalta, B. Taisne, A.P. Bunger, and R.F. Katz. Tectonophysics, 638:1–42, 2015.

[2]  J. R. Lister and R. C. Kerr. J. Geohpys. Res. Solid Earth, 96(B6):10049–10077, 1991.

[3]  S. M. Roper and J. R. Lister. J. Fluid Mech., 536:79–98, 2005.

[4]  A. P. Peirce and E. Detournay. Comput. Methods in Appl. Mech. Eng., 197(33-40):2858–2885, 2008.

[5]  L.N. Germanovich, D. I. Garagash, Murdoch, L., and Robinowitz M. AGU Fall meeting, 2014.

How to cite: Möri, A., Lecampion, B., and Zia, H.: Fully-coupled 3D modelling of magmatic dike propagation - finite pulse release from a point source , EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-21351,, 2020

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Presentation version 1 – uploaded on 06 May 2020
  • CC1: Questions and answers from the live chat during EGU2020, Michael Heap, 11 May 2020

    Q: Can you explain what you mean by “non-viscous shut-in”?

    A: We initiate the simulation with a radial Hydraulic fracture. These transition from Viscosity to toughness dominated regime when a constant injeciton rate is assumed. In our case the moment of shut-in (e.g. injection stops) is at a time much smaller than the transition time towards toughness dominated cases. So propagation after it is in a pulse regime which can be assumed purely viscous. If we alter this condition we might observe changes.

    Q: Could these numerical simulations be validated by analogue experiments? Would it be interesting?

    A: This is of course very interesting! We already tried to reproduce the experiments performed of Taisne & Tait, 2011. However, the configuration seems to be higlighy depend on the initialization procedure which makes it difficult to get satisfying result in reproducing experiments.

    Q: Stable breadth reached late; implications for dikes in natural cases?

    A: We are still at the beginning of our study but one implication is that the late time form of the dyke is prone to be a constant feature only after large distances of propagation (e.g. far away from the source). This could imply that for dikes propagating over limited distance the source conditions might play an important role.

    Q: The analytical shapes of fluid-driven fractures have been known for over 50 years. What is particularly new in your approach.

    A: The novelty of the approach is the linkage between the buoyant fracture and the radial one. Mainly regarding the shape and propagation form of the buoyant crack regarding specific source conditions. Additionally, the numerical scheme allows us to verify the 3D planar fracture solutions presented by Germanovich et al. 2014 with relatively good convergence. We thus seek to chracterize the condition (and mainly limitations) which allow an initially radial fracture to turn into a buoyant fracture or not. We couple this with an investigation of the final radius and shape of a injection pulse, which has obtained less interest until today.