A Model for Turbulent Hydraulic Fracture and Application to Crack Propogation at Glacier Beds
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 sma...
Published in: | Journal of Geophysical Research |
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ftharvardudash:oai:dash.harvard.edu:1/5027192 2023-05-15T16:21:32+02:00 A Model for Turbulent Hydraulic Fracture and Application to Crack Propogation at Glacier Beds Tsai, Victor C. Rice, James R. 2010 application/pdf http://nrs.harvard.edu/urn-3:HUL.InstRepos:5027192 https://doi.org/10.1029/2009JF001474 en_US eng American Geophysical Union doi:10.1029/2009JF001474 http://esag.harvard.edu/rice/236_TsaiRice_TurbHydraulicFract_JGR10.pdf Journal of Geophysical Research Tsai, Victor C. and James R. Rice. 2010. A model for turbulent hydraulic fracture and application to crack propagation at glacier beds. Journal of Geophysical Research 115:F03007. 0148-0227 http://nrs.harvard.edu/urn-3:HUL.InstRepos:5027192 Journal Article 2010 ftharvardudash https://doi.org/10.1029/2009JF001474 2022-04-04T12:43:27Z 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 \(\frac{7}{6}\), inversely as ice elastic modulus to the power \(\frac{2}{3}\), and as the ratio of crack length to wall roughness scale to the power \(\frac{1}{6}\). 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. 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. Earth and Planetary Sciences Engineering and Applied Sciences Version of Record Article in Journal/Newspaper glacier Greenland Ice Sheet Harvard University: DASH - Digital Access to Scholarship at Harvard Greenland Journal of Geophysical Research 115 F3 |
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Open Polar |
collection |
Harvard University: DASH - Digital Access to Scholarship at Harvard |
op_collection_id |
ftharvardudash |
language |
English |
description |
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 \(\frac{7}{6}\), inversely as ice elastic modulus to the power \(\frac{2}{3}\), and as the ratio of crack length to wall roughness scale to the power \(\frac{1}{6}\). 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. 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. Earth and Planetary Sciences Engineering and Applied Sciences Version of Record |
format |
Article in Journal/Newspaper |
author |
Tsai, Victor C. Rice, James R. |
spellingShingle |
Tsai, Victor C. Rice, James R. A Model for Turbulent Hydraulic Fracture and Application to Crack Propogation at Glacier Beds |
author_facet |
Tsai, Victor C. Rice, James R. |
author_sort |
Tsai, Victor C. |
title |
A Model for Turbulent Hydraulic Fracture and Application to Crack Propogation at Glacier Beds |
title_short |
A Model for Turbulent Hydraulic Fracture and Application to Crack Propogation at Glacier Beds |
title_full |
A Model for Turbulent Hydraulic Fracture and Application to Crack Propogation at Glacier Beds |
title_fullStr |
A Model for Turbulent Hydraulic Fracture and Application to Crack Propogation at Glacier Beds |
title_full_unstemmed |
A Model for Turbulent Hydraulic Fracture and Application to Crack Propogation at Glacier Beds |
title_sort |
model for turbulent hydraulic fracture and application to crack propogation at glacier beds |
publisher |
American Geophysical Union |
publishDate |
2010 |
url |
http://nrs.harvard.edu/urn-3:HUL.InstRepos:5027192 https://doi.org/10.1029/2009JF001474 |
geographic |
Greenland |
geographic_facet |
Greenland |
genre |
glacier Greenland Ice Sheet |
genre_facet |
glacier Greenland Ice Sheet |
op_relation |
doi:10.1029/2009JF001474 http://esag.harvard.edu/rice/236_TsaiRice_TurbHydraulicFract_JGR10.pdf Journal of Geophysical Research Tsai, Victor C. and James R. Rice. 2010. A model for turbulent hydraulic fracture and application to crack propagation at glacier beds. Journal of Geophysical Research 115:F03007. 0148-0227 http://nrs.harvard.edu/urn-3:HUL.InstRepos:5027192 |
op_doi |
https://doi.org/10.1029/2009JF001474 |
container_title |
Journal of Geophysical Research |
container_volume |
115 |
container_issue |
F3 |
_version_ |
1766009542777241600 |