ALBERT

Description: Recent high-resolution pan-Arctic sea ice simulations show fracture patterns (linear kinematic features or LKFs) that are typical of granular materials but with wider fracture angles than those observed in high-resolution satellite images. Motivated by this, ice fracture is investigated in a simple uni-axial loading test using two different viscous–plastic (VP) rheologies: one with an elliptical yield curve and a normal flow rule and one with a Coulombic yield curve and a normal flow rule that applies only to the elliptical cap. With the standard VP rheology, it is not possible to simulate fracture angles smaller than 30∘. Further, the standard VP model is not consistent with the behavior of granular material such as sea ice because (1) the fracture angle increases with ice shear strength; (2) the divergence along the fracture lines (or LKFs) is uniquely defined by the shear strength of the material with divergence for high shear strength and convergent with low shear strength; (3) the angle of fracture depends on the confining pressure with more convergence as the confining pressure increases. This behavior of the VP model is connected to the convexity of the yield curve together with use of a normal flow rule. In the Coulombic model, the angle of fracture is smaller (θ=23∘) and grossly consistent with observations. The solution, however, is unstable when the compressive stress is too large because of non-differentiable corners between the straight limbs of the Coulombic yield curve and the elliptical cap. The results suggest that, although at first sight the large-scale patterns of LKFs simulated with a VP sea ice model appear to be realistic, the elliptical yield curve with a normal flow rule is not consistent with the notion of sea ice as a pressure-sensitive and dilatant granular material.

Description: Recent high resolution pan-Arctic sea ice simulations show fracture patterns (Linear Kinematic Features – LKFs) that are typical of granular materials but with intersection (fracture) angles wider than those observed from high-resolution satellite images (with a modal value of θ = 20°). In this article, We investigate the mechanism of formation and parameter dependencies of ice fracture in simple numerical bi-axial test on a 8 km x 25 km ice floe at an unprecedented resolution of 25m for two different yield curves: an elliptical (VP) and a Coulombic yield curve both with normal flow rule. In the standardVP model, the simulated angle of fracture is θ = 33.9°, compared to 20° in observations. The dependence of the angle of fracture on the ice shear strength is also contrary to that of typical granular materials with larger angle of fracture for higher shear strength – think of a wet sand castle with steeper walls than a dry sand castle. In this model, the divergence along the fracture lines (or LKFs) is entirely dictated by the ice shear strength used in the model with high shear strength resulting in convergence along LKFs and low shear strength resulting in divergence along LKFs. This is again contrary to typical granular materials where divergence (or dilation) is linked with the orientation of contacts normals that oppose the flow with divergence present for larger shear resistance and convergence for lower shear resistance. Moreover, the angle of fracture depends on the confining pressure in the uni-axial test with more convergence as the confining pressure increases, again contrary to granular material that have an angle of fracture that is independent of the confining pressure. We note that all three behaviors of the VP model are linked with the use of an associative (normal) flow rule. In the Coulombic model, the angle of fracture is smaller (θ = 23.5°), but the solution is unstable when the compressive stresses are too large because of the discontinuity between the straight limbs of the yield curve and the elliptical capping. Our results show that while the VP model gives angles of fracture that are visually correct, the bias in the magnitude of the angle of fracture and the physical dependencies of the angle of fracture on mechanical strength parameters and stress fields couple the sea ice mechanical strength parameters, the sea-ice drift, sea-ice deformation (strain-rate) field in an inconsistent way. We consider this evidence to move away from the elliptical yield curve and associative (normal) flow rule, a deformation law that is not applicable to pressure-sensitive and dilatant granular material such as sea ice.

Description: High-resolution viscous-plastic (VP) sea ice models reproduce the narrow deformations lines observed in the Arctic sea ice, called the Linear Kinematic Features (LKFs). Recent studies showed that standard VP models overestimate the intersection angles between the LKFs when compared to observations. We investigate fracture angles in a uniaxial compression test and two different VP rheology. The first one uses an elliptical yield curve and a normal flow rule. In contrast, the second rheology uses a different elliptical plastic potential that creates a non-normal flow rule. Results show that the non-normality of the flow rule changes the angles of fracture. This new rheology can create fracture angles as low as 22º when the rheology with normal flow rule is limited to angles above 30º. A newly adapted theory – based on one developed from granular material observations – predicts the modeled fracture angles accurately. Using a non-normal flow rule takes longer to solve numerically, but allow reductions of the fracture angle to values within the range of satellite observations and decouples the angle of fracture from the shape of the yield curve.

Description: Sea-ice observations and models show zones of high deformation typical of granular medium (linear kinematic features (LKFs)). Recent high-resolution simulations feature fractures that mimic the observed pattern but with wider intersection angles. Motivated by this, we investigate the dependence between conjugate faults intersection angles and different viscous–plastic rheologies. Using an idealized uniaxial setting, the ice fracture is modeled with different confinement ratios and two different VP rheologies: one with an elliptical yield curve and a normal flow rule, and one with a Coulombic yield curve and a normal flow rule that applies only to the elliptical cap. Modeling fracture angles smaller than 30° is not possible with an elliptical yield curve in a pure compression setting. Further several modeled behaviors are inconsistent with the granular nature of sea ice : (1) the fracture angle increases with ice shear strength; (2) the divergence along the fracture lines (or LKFs) is uniquely defined by the shear strength of the material with divergence for high shear strength and convergence follow shear strength; (3) the angle of fracture depends on the confining pressure with more convergence as the confining pressure increases. With Mohr’s circle, this behavior is shown to be linked to the convexity of the yield curve. The Coulombic yield curve is able to model smaller angles but the solution is unstable because of non-differentiable corners between the straight limbs of the Coulombic yield curve and the elliptical cap. The results show that, although the fracture patterns at first appear realistic, the yield curve should be revised to take into account the nature of sea ice as a pressure-sensitive and dilatant granular material.

Description: Fracture lines dominate the dynamics of sea ice. They affect the ice mass balance and the heat transfer between the atmosphere and the ocean. Therefore, climate modeling and sea ice prediction require an accurate fracture representation. Most sea ice models use viscous-plastic (VP) rheologies to simulate sea ice internal stresses. One of the issues with these rheologies is that they overestimate the intersection angles between fracture lines, with consequences for the subsequent sea ice drift. In idealized experiments, we investigate the mechanisms linking VP rheologies and fracture angles and assess alternative rheologies for high-resolution modeling. Results show that the definition of the transition between viscous and plastic states is essential for the creation of sharp fracture lines. The fracture angles with Mohr-Coulomb yield curves agree with the Arthur fault orientation theory. Further, rheologies with Mohr-Coulomb yield curves or teardrop yield curves appear to reduce intersection angles. Finally, experiments show that these results are reproduced for different sea ice initial conditions. With rheologies that favor smaller intersection angles, sea ice models move a step closer to accurate sea ice dynamics at high-resolution.

Description: Recent high resolution pan-Arctic sea ice simulations show fracture patterns that are typical of granular materials but with intersection (fracture) angles wider than those observed from high-resolution satellite images (with a modal value of θ = 20º). In this work, we investigate the mechanism of formation and parameter dependencies of ice fracture in simple numerical uni-axial test on a 8 km x 25 km ice floe at an unprecedented resolution of 25 m for two different Visco-Plastic (VP) yield curves: an elliptical (standard in sea ice models) and a coulombic yield curve both with normal flow rule. In the standard VP model, the simulated angle of fracture is θ=33.9º. The dependence of the angle of fracture on the ice shear strength is also contrary to that of typical granular materials with larger angle of fracture for higher shear strength. In this model, the divergence along the fracture lines (or LKFs) is entirely dictated by the ice shear strength with high shear strength resulting in convergence along LKFs and low shear strength resulting in divergence along LKFs. This is again contrary to typical granular materials. Moreover, the angle of fracture depends on the confining pressure in the uni-axial test with more convergence as the confining pressure increases, again contrary to granular material. In the Coulombic model, the angle of fracture is smaller (θ=23.5º), but the solution is unstable because of the discontinuity between the straight limbs of the yield curve and the elliptical capping. Our results show that while the VP model gives angles of fracture that are visually correct, the bias in the magnitude of the angle of fracture and the physical dependencies of the angle of fracture on mechanical strength parameters and stress fields couple the sea ice mechanical strength parameters, the sea-ice drift, sea-ice deformation (strain-rate) field in an inconsistent way. We consider this evidence to move away from the elliptical yield curve and associative (normal) flow rule.

Description: Arctic sea ice plays a critical role in the climate system. Therefore it needs to be modeled accurately to make precise climate predictions of the current anthropogenic climate change. Most of today’s climate models simulate sea ice motion using a viscous-plastic (VP) rheology with an elliptical yield curve and a normal flow rule [1]. This rheology gives accurate predictions at low resolution but features discrepancies at high resolution when compared to observations. Observations show that narrow lines of deformation dominate the pattern of sea ice motion. Models using the VP rheology feature these fracture lines but overestimate the intersection angles between them [2]. To understand and solve these differences, we study the creation of fracture angles using idealized compression experiments. We test several yield curves and flow rules and investigate their effect on the angles between fracture lines. The results show that: first, the fracture angle depends on the shape of the yield curve as well as the flow rule, in agreement with Roscoe’s angle [3]; second, the elliptical yield curve with normal flow rule cannot create angles lower than 30° in uniaxial compression; finally, implementing a non-normal flow rule can lead to fracture angles as low as 22°. Results also show that sea ice dynamics in models disagree with sea ice observed granular behavior. With the new knowledge gained from these idealized experiments, we can now define new VP rheologies for more accurate sea ice modeling, e.g., with Mohr-Coulomb or teardrop yield curves. REFERENCES: [1] Hibler III WD: A dynamic thermodynamic sea ice model, Journal of physical oceanography. Jul;9(4):815-46, 1979. [2] Hutter, N. and Losch, M.: Feature-based comparison of sea ice deformation in lead-permitting sea ice simulations, The Cryosphere, 14, 93–113, https://doi.org/10.5194/tc-14-93-2020, 2020. [3] Roscoe, K. H.: The Influence of Strains in Soil Mechanics, Géotechnique, 20, 2, 129-170, 1970.

Description: Sea ice is an essential component of the climate system because it modulates the exchange of energy between the ocean and the atmosphere. Under stress from wind and ocean currents, sea ice deforms constantly. Sea ice deformation takes the shape of narrow lines, the Linear Kinematic Features (LKFs). LKFs influence the heat transfer, mass balance, and sea ice dynamics, so LKFs should be accurately represented in high-resolution climate models. Sea ice is commonly modeled using viscous-plastic (VP) rheologies defined by a yield curve and a flow rule. Recent work showed that VP sea ice models explicitly create LKFs but overestimate their intersection angles. This thesis aims to investigate the link between the angles of fracture in sea ice models and the parametrization of the sea ice internal stresses using idealized compression experiments. Three questions are addressed: Which parameters of the VP rheologies influence the fracture angle? Which theoretical framework explains this influence? Which rheologies should be used to simulate intersection angles at the observed range? With the commonly used standard VP rheology with an elliptical yield curve and a normal flow rule, the fracture angles are linked to the yield curve's elliptical shape. Because of this shape, this rheology cannot create sea ice fracture angles more acute than 30 degrees in uniaxial compression, even by changing the aspect of the ellipse. The classical coulombic theory predicts the angle of fracture accurately when adapted to the context of sea ice modeling. A new rheology with an elliptical yield curve and a non-normal flow rule shows that fracture angles are also sensitive to the orientation of the flow rule. Using this new rheology allows creating fracture angles as low as 22 degrees in uniaxial compression. A theory based on the angle of dilatancy and observations of granular materials predicts precisely the simulated angles. Alternative rheologies can create fracture angles lower than 30 degrees. With Mohr--Coulomb yield curves, fracture angles are well predicted by joining the concepts of coulombic friction and angle of dilatancy. Teardrop and Parabolic lens yield curves create small angles of fracture in uni-axial compression when used with small tensile strength. Using a more realistic sea ice cover with heterogeneity, failure under deformation takes the form of a network of fracture lines. The choice of rheology strongly influences the angle of fracture in this network. Two rheologies are suitable candidates to decrease the fracture angles in sea ice VP models. In conclusion, fracture angles in sea ice models are determined by the properties of the VP rheology and can be accurately predicted using fracture orientation theory. Changing the rheology can reduce the fracture angles in sea ice simulations. With the results presented in this thesis, new rheologies could be inferred from observations to represent sea ice fracture more realistically.

Description: Recent high-resolution pan-Arctic sea ice simulations show fracture patterns (linear kinematic features or LKFs) that are typical of granular materials but with wider fracture angles than those observed in high-resolution satellite images. Motivated by this, ice fracture is investigated in a simple uni-axial loading test using two different viscous–plastic (VP) rheologies: one with an elliptical yield curve and a normal flow rule and one with a Coulombic yield curve and a normal flow rule that applies only to the elliptical cap. With the standard VP rheology, it is not possible to simulate fracture angles smaller than 30∘. Further, the standard VP model is not consistent with the behavior of granular material such as sea ice because (1) the fracture angle increases with ice shear strength; (2) the divergence along the fracture lines (or LKFs) is uniquely defined by the shear strength of the material with divergence for high shear strength and convergent with low shear strength; (3) the angle of fracture depends on the confining pressure with more convergence as the confining pressure increases. This behavior of the VP model is connected to the convexity of the yield curve together with use of a normal flow rule. In the Coulombic model, the angle of fracture is smaller (θ=23∘) and grossly consistent with observations. The solution, however, is unstable when the compressive stress is too large because of non-differentiable corners between the straight limbs of the Coulombic yield curve and the elliptical cap. The results suggest that, although at first sight the large-scale patterns of LKFs simulated with a VP sea ice model appear to be realistic, the elliptical yield curve with a normal flow rule is not consistent with the notion of sea ice as a pressure-sensitive and dilatant granular material.