Simulating intersection angles between conjugate faults in sea ice with different viscous–plastic rheologies

Abstract

Abstract. 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.

The material properties of ice bridges in the Maxwell Elasto-Brittle rheology

“…8c). Again, this angle deviates from the theoretical fracture orientation in a granular material with φ = 45 • , at 22.5 • from the second principal stress orientation (Ringeisen et al, 2019).…”

“…8c). This differs from the expected angle of fracture in a coulombic material, at θ = ±(π/4−φ/2) from the second principal stress orientation (Ringeisen et al, 2019). This deviation results from the absence of a flow rule in the MEB model.…”

“…That is, the orientation of the failure surface is determined by the point at which the Mohr circle reaches the yield criterion in the Mohr circle space. This point of failure is aligned at angle θ = ±(π/4 − φ/2) from the first principal stress direction (Ringeisen et al, 2019). In the MEB model, the angle of fracture does not follow the theory (see Fig .16b).…”

“…In theory, the angle of internal friction governs the intersection angle between lines of fracture (Marko and Thomson, 1977;Pritchard, 1988;Wang, 2007;Ringeisen et al, 2019). That is, the orientation of the failure surface is determined by the point at which the Mohr circle reaches the yield criterion in the Mohr circle space.…”

Feature-based comparison of sea-ice deformation in lead-resolving sea-ice simulations

“…9 to sea ice fields with a different amount of LKFs. Ringeisen et al (2019) derived for idealized compression experiments that it is impossible to obtain intersection angels smaller than 60 • with an elliptical yield curve. This explains the deficit of small intersection angles in our simulations.…”