@article{MantiloniDavisGaeteRojasetal.2021,
  author    = {Mantiloni, Lorenzo and Davis, Timothy and Gaete Rojas, Ayleen Barbara and Rivalta, Eleonora},
  title     = {Stress inversion in a gelatin box},
  series = {Geophysical research letters : GRL / American Geophysical Union},
  volume    = {48},
  journal   = {Geophysical research letters : GRL / American Geophysical Union},
  number    = {6},
  publisher = {American Geophysical Union},
  address   = {Washington},
  issn      = {0094-8276},
  doi       = {10.1029/2020GL090407},
  pages     = {11},
  year      = {2021},
  abstract  = {Assessing volcanic hazard in regions of distributed volcanism is challenging because of the uncertain location of future vents. A statistical-mechanical strategy to forecast such locations was recently proposed: here, we further develop and test it with analog models. We stress a gelatin block laterally and with surface excavations, and observe air-filled crack trajectories. We use the observed surface arrivals to sample the distributions of parameters describing the stress state of the gelatin block, combining deterministic crack trajectory simulations with a Monte Carlo approach. While the individual stress parameters remain unconstrained, we effectively retrieve their ratio and successfully forecast the arrival points of subsequent cracks.},
  language  = {en}
}
@phdthesis{Davis2021,
  author    = {Davis, Timothy},
  title     = {An analytical and numerical analysis of fluid-filled crack propagation in three dimensions},
  doi       = {10.25932/publishup-50960},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-509609},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xi, 187},
  year      = {2021},
  abstract  = {Fluids in the Earth's crust can move by creating and flowing through fractures, in a process called `hydraulic fracturing'. The tip-line of such fluid-filled fractures grows at locations where stress is larger than the strength of the rock. Where the tip stress vanishes, the fracture closes and the fluid-front retreats. If stress gradients exist on the fracture's walls, induced by fluid/rock density contrasts or topographic stresses, this results in an asymmetric shape and growth of the fracture, allowing for the contained batch of fluid to propagate through the crust. The state-of-the-art analytical and numerical methods to simulate fluid-filled fracture propagation are two-dimensional (2D). In this work I extend these to three dimensions (3D). In my analytical method, I approximate the propagating 3D fracture as a penny-shaped crack that is influenced by both an internal pressure and stress gradients. In addition, I develop a numerical method to model propagation where curved fractures can be simulated as a mesh of triangular dislocations, with the displacement of faces computed using the displacement discontinuity method. I devise a rapid technique to approximate stress intensity and use this to calculate the advance of the tip-line. My 3D models can be applied to arbitrary stresses, topographic and crack shapes, whilst retaining short computation times. I cross-validate my analytical and numerical methods and apply them to various natural and man-made settings, to gain additional insights into the movements of hydraulic fractures such as magmatic dikes and fluid injections in rock. In particular, I calculate the `volumetric tipping point', which once exceeded allows a fluid-filled fracture to propagate in a `self-sustaining' manner. I discuss implications this has for hydro-fracturing in industrial operations. I also present two studies combining physical models that define fluid-filled fracture trajectories and Bayesian statistical techniques. In these studies I show that the stress history of the volcanic edifice defines the location of eruptive vents at volcanoes. Retrieval of the ratio between topographic to remote stresses allows for forecasting of probable future vent locations. Finally, I address the mechanics of 3D propagating dykes and sills in volcanic regions. I focus on Sierra Negra volcano in the Gal\'apagos islands, where in 2018, a large sill propagated with an extremely curved trajectory. Using a 3D analysis, I find that shallow horizontal intrusions are highly sensitive to topographic and buoyancy stress gradients, as well as the effects of the free surface.},
  language  = {en}
}