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

• Main Authors: D. Ringeisen, M. Losch, L. B. Tremblay, N. Hutter
• Format: Article
• Language: English
• Published: Copernicus Publications 2019-04-01
• Series: The Cryosphere
• Online Access: https://www.the-cryosphere.net/13/1167/2019/tc-13-1167-2019.pdf

<p>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 <span class="inline-formula">30^∘</span>. 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 (<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M2" display="inline" overflow="scroll" dspmath="mathml"><mrow><mi mathvariant="italic">θ</mi><mo>=</mo><mn mathvariant="normal">23</mn><msup><mi/><mo>∘</mo></msup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="38pt" height="11pt" class="svg-formula" dspmath="mathimg" md5hash="4ce44c981e6549817727c7ca362d1318"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="tc-13-1167-2019-ie00001.svg" width="38pt" height="11pt" src="tc-13-1167-2019-ie00001.png"/></svg:svg></span></span>) 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.</p>