A Model for Turbulent Hydraulic Fracture and Application to Crack Propagation at Glacier Beds
Abstract. Glaciological observations of under-flooding suggest that fluid-induced hydraulic fracture of an ice sheet from its bed sometimes occurs quickly, possibly driven by turbulently flowing water in a broad sheet flow. Taking the approximation of a fully turbulent flow into an elastic ice mediu...
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| Format: | Text |
| Language: | English |
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| Online Access: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.5906 http://esag.harvard.edu/rice/TsaiRice_TurbHydraulicFract_toJGR_Jul09.pdf |
| Summary: | Abstract. Glaciological observations of under-flooding suggest that fluid-induced hydraulic fracture of an ice sheet from its bed sometimes occurs quickly, possibly driven by turbulently flowing water in a broad sheet flow. Taking the approximation of a fully turbulent flow into an elastic ice medium with small fracture toughness, we derive an approximate expression for the crack-tip speed, opening displacement and pressure profile. We accomplish this by first showing that a Manning-Strickler channel model for resistance to turbulent flow leads to a mathematical structure somewhat similar to that for resistance to laminar flow of a power-law viscous fluid. We then adapt the plane-strain asymptotic crack solution of Desroches et al. [1994] and the power-law self-similar solution of Adachi and Detournay [2002] for that case to calculate the desired quantities. The speed of crack growth is shown to scale as the overpressure (in excess of ice overburden) to the power 7/6, inversely as ice elastic modulus to the power 2/3, and as the ratio of crack length to wall roughness scale to the power 1/6. We tentatively apply our model by choosing parameter values thought appropriate for a basal crack driven by the rapid drainage of a surface meltwater lake near the margin of the Greenland Ice Sheet [Das et al., 2008]. Making various approximations perhaps relevant to this setting, we estimate fluid inflow rate to the basal fracture and vertical and horizontal surface displacements, and find order-of-magnitude agreement with observations by Das et al. [2008] associated with lake drainage. Finally, we discuss how these preliminary estimates could be improved. 1. |
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