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Fialko, YA, Rubin AM.  1999.  What controls the along-strike slopes of volcanic rift zones? Journal of Geophysical Research-Solid Earth. 104:20007-20020.   10.1029/1999jb900143   AbstractWebsite

We investigate the dynamics of viscous pressure losses associated with lateral magma transport in volcanic rift zones by performing (I) coupled elastic-hydrodynamic simulations of downrift magma flow in dikes and (2) analog experiments mimicking lateral dike propagation in the presence of an along-rift topographic slope. It is found that near-source eruptions are likely to be favored by shallow slopes while distant downrift eruptions may be encouraged by steeper slopes, provided that along-rift variations in the tectonic stress are negligible or uncorrelated on the timescale of multiple dike intrusions. This implies the existence of a critical slope to which a volcanic rift zone would naturally evolve. Such behavior is produced by three-dimensional (3-D) elastic effects and is controlled by the ratio of the driving pressure gradient due to the along-strike topographic slope to the vertical gradient in the excess magma pressure in the dike. This model may be viewed as complementary to commonly cited mechanisms that appeal to magma viscosity and the dynamics of freezing of lava flows at the surface to explain the low profiles of basaltic shield volcanoes. Our estimated values of the critical slopes are in general agreement with observations in Hawaiian rift zones, but further development of fully 3-D models is required for more accurate predictions.

Khazan, YM, Fialko YA.  1995.  Fracture Criteria at the Tip of Fluid-Driven Cracks in the Earth. Geophysical Research Letters. 22:2541-2544.   10.1029/95gl02547   AbstractWebsite

The effect of high confining pressure on fluid-filled crack growth is considered. Exact solutions are given for a two-dimensional horizontal crack in an infinite elastic body using the approximation of Dugdale-Barenblatt (DB) model. It is shown that for equilibrium cracks (i.e. for cracks on the verge of propagation) the large-scale crack characteristics, such as fluid overpressure, apparent fracture toughness, maximum opening of the crack and crack volume, grow with increase of confining pressure. These effects result from a pressure induced fracture resistance (PIFR). If basic parameters of the DB model (tensile strength and critical crack opening displacement) are independent of confining pressure then PIFR dominates over intrinsic rock strength starting from quite shallow depth (tens to hundreds of meters).