Publications

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Increasing Arctic coastal erosion rates have put critical infrastructure and native communities at risk while also mobilizing ancient organic carbon into modern carbon cycles. Although the Arctic comprises one-third of the global coastline and has some of the fastest eroding coasts, current tools for quantifying permafrost erosion are unable to explain the episodic, storm-driven erosion events. Our approach, mechanistically coupling oceanographic predictions with a terrestrial model to capture the thermo-mechanical dynamics of erosion, enables this much needed treatment of transient erosion events. The Arctic Coastal Erosion Model consists of oceanographic and atmospheric boundary conditions that force a coastal terrestrial permafrost environment in Albany (a multi-physics based finite element model). An oceanographic modeling suite (consisting of WAVEWATCH III, Delft3D-FLOW, and Delft3D-WAVE) produced time-dependent surge and run-up boundary conditions for the terrestrial model. In the terrestrial model, a coupling framework unites the mechanical and thermal aspects of erosion. 3D stress/strain fields develop in response to a plasticity model of the permafrost that is controlled by the frozen water content determined by modeling 3D heat conduction and solid-liquid phase change. This modeling approach enables failure from any allowable deformation (block failure, slumping, etc.). Extensive experimental work has underpinned the ACE Model development including field campaigns to measure in situ ocean and erosion processes, strength properties derived from thermally driven geomechanical experiments, as well as extensive physical composition and geochemical analyses. Combined, this work offers the most comprehensive and physically grounded treatment of Arctic coastal erosion available in the literature. The ACE model and experimental results can be used to inform scientific understanding of coastal erosion processes, contribute to estimates of geochemical and sediment land-to-ocean fluxes, and facilitate infrastructure susceptibility assessments.

Recent developments at Sandia in meshfree methods have delivered improved robustness in solid mechanics problems that prove difficult for traditional Lagrangian, mesh-based finite elements. Nevertheless, there remains a limitation in accurately predicting very large material deformations. It seems robust meshfree discretizations and integration schemes are necessary, but not sufficient, to close this capability gap. This state of affairs directly impacts current and future LEPs, whose simulation needs are not well met for extremely large deformation problems. We propose to use a new numerical framework, the Optimal Transportation Meshfree (OTM) method enhanced by meshfree adaptivity, as we believe that a combination of both will provide a novel way to close this capability gap.

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Scientific knowledge and engineering tools for predicting coastal erosion are largely confined to temperate climate zones that are dominated by non-cohesive sediments. The pattern of erosion exhibited by the ice-bonded permafrost bluffs in Arctic Alaska, however, is not well-explained by these tools. Investigation of the oceanographic, thermal, and mechanical processes that are relevant to permafrost bluff failure along Arctic coastlines is needed. We conducted physics-based numerical simulations of mechanical response that focus on the impact of geometric and material variability on permafrost bluff stress states for a coastal setting in Arctic Alaska that is prone to toppling mode block failure. Our three-dimensional geomechanical boundary-value problems output static realizations of compressive and tensile stresses. We use these results to quantify variability in the loci of potential instability. We observe that niche dimension affects the location and magnitude of the simulated maximum tensile stress more strongly than the bluff height, ice wedge polygon size, ice wedge geometry, bulk density, Young's Modulus, and Poisson's Ratio. Our simulations indicate that variations in niche dimension can produce radically different potential failure areas and that even relatively shallow vertical cracks can concentrate displacement within ice-bonded permafrost bluffs. These findings suggest that stability assessment approaches, for which the geometry of the failure plane is delineated a priori, may not be ideal for coastlines similar to our study area and could hamper predictions of erosion rates and nearshore sediment/biogeochemical loading.

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Tetrahedral finite element workflows have the potential to drastically reduce time to solution for computational solid mechanics simulations when compared to traditional hexahedral finite element analogues. A recently developed, higher-order composite tetrahedral element has shown promise in the space of incompressible computational plasticity. Mesh adaptivity has the potential to increase solution accuracy and increase solution robustness. In this work, we demonstrate an initial strategy to perform conformal mesh adaptivity for this higher-order composite tetrahedral element using well-established mesh modification operations for linear tetrahedra. We propose potential extensions to improve this initial strategy in terms of robustness and accuracy.

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This corrigendum clarifies the conditions under which the proof of convergence of Theorem 1 from the original article is valid. We erroneously stated as one of the conditions for the Schwarz alternating method to converge that the energy functional be strictly convex for the solid mechanics problem. We have relaxed that assumption and changed the corresponding parts of the text. None of the results or other parts of the original article are affected.

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