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Propagation of fluid-filled fractures by fluid buoyancy is important in a variety of settings, from magmatic dykes and veins to water-filled crevasses in glaciers. Industrial hydro-fracturing utilises fluid-driven fractures to increase the permeability of rock formations, but few studies have quantified the effect of buoyancy on fracture pathways in this context. Analytical approximations for the buoyant ascent rate facilitate observation-based inference of buoyant effects in natural and engineered systems. Such analysis exists for two-dimensional fractures, but real fractures are three-dimensional (3-D). Here we present novel analysis to predict the buoyant ascent speed of 3-D fractures containing a fixed-volume batch of fluid. We provide two estimates of the ascent rate: an upper limit applicable at early time, and an asymptotic estimate (proportional to$t^{-2/3}$) describing how the speed decays at late time. We infer and verify these predictions by comparison with numerical experiments across a range of scales and analogue experiments on liquid oil in solid gelatine. We find the ascent speed is a function of the fluid volume, density, viscosity and the elastic parameters of the host medium. Our approximate solutions predict the ascent rate of fluid-driven fractures across a broad parameter space, including cases of water injection in shale and magmatic dykes. Our results demonstrate that in the absence of barriers or fluid loss, both dykes and industrial hydro-fractures can ascend by buoyancy over a kilometre within a day. We infer that barriers and fluid loss must cause the arrest of ascending fractures in industrial settings.

International audience; The Asal-Ghoubbet Rift (AG Rift) in Djibouti lies in the subaerial continuation of the Aden ridge system, thereby constituting a unique location to study rifting processes and mechanisms involved in continental breakup and oceanic spreading. Continually upgraded and expanded geodetic technology has been used to record the 1978 Asal rifting event and postdiking deformation. In light of recent results obtained for the Manda Hararo-Dabbahu rifting event (2005–2010), we propose that the horizontal and vertical geodetic data can be modeled with a double source, involving a dike-like inflation component aligned along the rift axis and a spherical pressure source located at midsegment below the Fieale caldera. By revisiting the codiking data, we propose that the reservoir below Fieale could have fed, at least partially, the 1978 injection and the contemporaneous Ardoukôba eruption and potentially induced local subsidence due to magma draining out of the central reservoir. As an alternative to previously proposed viscoelastic relaxation models, we reinterpret postdiking observations using a purely elastic rheology. We determine the relative contribution of a midsegment reservoir inflation and a dike-like opening component, together with their respective time evolutions. Our results suggest that interactions between steadily accumulating tectonic strain and temporal variations in melt supply to the shallow magma plumbing system below the AG Rift may entirely explain the geodetic observations and that viscoelastic deformation processes played a minor role in the 30 years following the 1978 rifting event.

Precise characterization of the mechanical properties of gelatin, a classic analog of the elastic crust, is necessary for scaling the mechanical models of the Earth's crust behavior in laboratory experiments. Here we reassess how to accurately calculate the Young modulus (E) of gelatin contained in experimental tanks. By means of dedicated analog experiments and finite element simulations, we estimate the bias introduced by using equations appropriate for a half-space to interpret the subsidence due to a cylindrical surface load applied on the gelatin. In the case of a standard experimental setup with gelatin adhering to the tank wall, we find E is overestimated by at least 5% for a box with lateral size smaller than 20 times the cylinder diameter. In addition, we deduce a correction factor to be applied when using an analytical formula. We confirm that measuring the shear velocity leads to accurate estimates for the rigidity of gelatin. We also propose a new method for in situ Young's modulus estimation, relying on the length of air-filled propagating crack. Indeed, for a given injected volume, this length depends only on the density contrast between air and gelatin and on the Young's modulus of the gelatin. The fracture toughness of the gelatin is estimated independently. Direct comparison between fracture toughness and Young's modulus shows that for a given Young's modulus, salted gelatin has a higher fracture toughness than unsalted gelatin.