Fracture toughness of ice and firn determined from the modified ring test

Fischer, Mark P.; Alley, Richard B.; Engelder, Terry

doi:10.3189/s0022143000016257

Cited by 18 publications

(9 citation statements)

References 27 publications

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“…negligible energy required to add new crack area). As will be shown in Section 3, with estimates of ice fracture toughness from Ashby [1989] (see also Schulson and Duval [2009, p. 208]), Fischer et al [1995], and Rist et al [1999] showing K Ic ≈ 0.1–0.2 MPa m 1/2 , and guidelines like those of Savitski and Detournay [2002] and Bunger and Detournay [2008], this approximation is reasonable for the glacial application considered.…”

Section: Model Setup: Turbulent Hydraulic Fracturementioning

confidence: 72%

“…The hydraulic head gradient is given by S ≈ Δ p in /( ρgL ) ≈ 0.1 so that bed slopes ≪5° can be safely ignored. Taking ice fracture toughness of K Ic ≈ 0.16 MPa m 1/2 [ Rist et al , 1999], which is slightly on the high side of estimates by Ashby [1989] and Fischer et al [1995], and surely higher than for the ice‐rock interface (regardless of whether the ice is frozen to the bedrock or not), we can compare the total energy lost in the pressure gradient (per unit surface area of the crack), e loss ≡ E loss / Area ≈ Δ p in h ≳ 0.9 · 10 5 J/m 2 , with the fracture energy K Ic 2 / E ≈ 4.1 J/m 2 . Since the pressure gradient energy loss is much greater than the fracture energy (except at the very earliest stages of crack growth, when h ≲ 10 −5 m or equivalently L ≲ 0.1 m), it is reasonable to neglect the fracture energy.…”

Section: Understanding Glacial Crack Propagationmentioning

confidence: 99%

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A model for turbulent hydraulic fracture and application to crack propagation at glacier beds

Tsai¹,

Rice²

2010

J. Geophys. Res.

143

215

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[1] 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. 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.Citation: Tsai, V. C., and J. R. Rice (2010), A model for turbulent hydraulic fracture and application to crack propagation at glacier beds,

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Section: Model Setup: Turbulent Hydraulic Fracturementioning

confidence: 72%

Section: Understanding Glacial Crack Propagationmentioning

confidence: 99%

A model for turbulent hydraulic fracture and application to crack propagation at glacier beds

Tsai¹,

Rice²

2010

J. Geophys. Res.

143

215

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“…First, the fracture mechanics model relies on critical parameters, such as crevasse spacing and ice fracture toughness, which must be prescribed a priori and are not readily available in most numerical flow models. For example, the fracture toughness of glacier ice is generally assumed to span a factor of 4, between 0.1 and 0.4 MPa m 1/2 , but a paucity of observational data limits the parameterization of variations in ice fracture toughness with density (and thus depth) and temperature [ Fischer et al ., ; Rist et al ., ]. Additionally, both laboratory and field evidence suggest that temperature, sediment and liquid water contents, and crystal size can all substantially affect the fracture toughness of ice [ Dempsey , ; Petrovic , ; Moore , ].…”

Section: Crevasse Modelsmentioning

confidence: 99%

Glacier crevasses: Observations, models, and mass balance implications

Colgan

Rajaram

Abdalati

et al. 2016

Reviews of Geophysics

175

199

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We review the findings of approximately 60 years of in situ and remote sensing studies of glacier crevasses, as well as the three broad classes of numerical models now employed to simulate crevasse fracture. The relatively new insight that mixed-mode fracture in local stress equilibrium, rather than downstream advection alone, can introduce nontrivial curvature to crevasse geometry may merit the reinterpretation of some key historical observation studies. In the past three decades, there have been tremendous advances in the spatial resolution of satellite imagery, as well as fully automated algorithms capable of tracking crevasse displacements between repeat images. Despite considerable advances in developing fully transient three-dimensional ice flow models over the past two decades, both the zero stress and linear elastic fracture mechanics crevasse models have remained fundamentally unchanged over this time. In the past decade, however, multidimensional and transient formulations of the continuum damage mechanics approach to simulating ice fracture have emerged. The combination of employing damage mechanics to represent slow upstream deterioration of ice strength and fracture mechanics to represent rapid failure at downstream termini holds promise for implementation in large-scale ice sheet models. Finally, given the broad interest in the sea level rise implications of recent and future cryospheric change, we provide a synthesis of 10 mechanisms by which crevasses can influence glacier mass balance. Field ObservationsBy virtue of providing relatively easy access to a glacier's interior, crevasses can be an asset to observational glaciologists, permitting, for example, the efficient examination of glacier stratigraphy. Annual accumulation

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“…Doyle et al, 2013). The fracture toughness of ice, K IC , is the critical stress at which a pre-existing flaw will begin to propagate, for which we prescribe a fracture toughness of 150 kPa m 1/2 as an average of values calculated by Fischer et al (1995) and Rist et al (1999). We prescribe an initial crevasse depth, or preexisting flaw, of 1 × 10 −7 m to ensure initiation of fracture propagation.…”

Section: Appendix C: Calculation Of Crevasse Depthsmentioning

confidence: 99%

Modelling the transfer of supraglacial meltwater to the bed of Leverett Glacier, Southwest Greenland

et al. 2015

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Abstract. Meltwater delivered to the bed of the GreenlandIce Sheet is a driver of variable ice-motion through changes in effective pressure and enhanced basal lubrication. Ice surface velocities have been shown to respond rapidly both to meltwater production at the surface and to drainage of supraglacial lakes, suggesting efficient transfer of meltwater from the supraglacial to subglacial hydrological systems. Although considerable effort is currently being directed towards improved modelling of the controlling surface and basal processes, modelling the temporal and spatial evolution of the transfer of melt to the bed has received less attention. Here we present the results of spatially distributed modelling for prediction of moulins and lake drainages on the Leverett Glacier in Southwest Greenland. The model is run for the 2009 and 2010 ablation seasons, and for future increased melt scenarios. The temporal pattern of modelled lake drainages are qualitatively comparable with those documented from analyses of repeat satellite imagery. The modelled timings and locations of delivery of meltwater to the bed also match well with observed temporal and spatial patterns of ice surface speed-ups. This is particularly true for the lower catchment ( < 1000 m a.s.l.) where both the model and observations indicate that the development of moulins is the main mechanism for the transfer of surface meltwater to the bed. At higher elevations (e.g. 1250-1500 m a.s.l.) the development and drainage of supraglacial lakes becomes increasingly important. At these higher elevations, the delay between modelled melt generation and subsequent delivery of melt to the bed matches the observed delay between the peak air temperatures and subsequent velocity speed-ups, while the instantaneous transfer of melt to the bed in a control simulation does not. Although both moulins and lake drainages are predicted to increase in number for future warmer climate scenarios, the lake drainages play an increasingly important role in both expanding the area over which melt accesses the bed and in enabling a greater proportion of surface melt to reach the bed.

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Fracture toughness of ice and firn determined from the modified ring test

Cited by 18 publications

References 27 publications

A model for turbulent hydraulic fracture and application to crack propagation at glacier beds

A model for turbulent hydraulic fracture and application to crack propagation at glacier beds

Glacier crevasses: Observations, models, and mass balance implications

Modelling the transfer of supraglacial meltwater to the bed of Leverett Glacier, Southwest Greenland

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