Glacier geometry and flow speed determine how Arctic marine-terminating glaciers respond to lubricated beds

Basal conditions directly control the glacier sliding rate and the dynamic discharge of ice flow. Recent glacier destabilization events indicate that some marine-terminating glaciers quickly respond to lubricated beds with increased flow speed, but the underlying physics, especially how this vulnerability relates to glacier geometry and flow characteristics, remains unclear. This paper presents a 1-D physical framework for glacier dynamic vulnerability assuming sudden basal lubrication as an initial perturbation. In this new model, two quantities determine the scale and the areal extent of the subsequent thinning and acceleration after the bed is lubricated: Péclet number (Pe) and the product of glacier speed and thickness gradient (dubbed J0 in this study). To validate the model, this paper calculates Pe and J0 using multi-sourced data from 1996–1998 for outlet glaciers in Greenland and Austfonna Ice Cap, Svalbard, and compares the results with the glacier speed change during 1996/1998–2018. Glaciers with lower Pe and J0 are more likely to accelerate during this 20-year span than those with higher Pe and J0, which matches the model prediction. A combined factor of ice thickness, surface slope, and initial speed for ice flow physically determines how much and how fast glaciers respond to lubricated beds, as forms of speed, elevation, and terminus change.

Brief communication: Estimating the ice thickness of the Müller Ice Cap using an inversion of the shallow ice approximation

The Müller Ice Cap will soon set the scene for a new drilling project. Therefore, ice thickness estimates are necessary for planning since thickness measurements of the ice cap are sparse. Here, two models are presented and compared, i) a simple inversion of the shallow ice approximation (SIA inversion) by the use of a single radar line in combination with the glacier outline, surface slope, and elevation, and ii) an iterative inverse method using the Parallel Ice Sheet Model (PISM). The two methods mostly agree about a good drill site candidate. However, the new semi-empirical SIA inversion is insensitive to mass balance, computationally fast, and provides better fits.

Topology Optimization of Self-Supported Enclosed Voids for Additive Manufacturing

The paper proposes a heat-flux based topology optimization approach to design self-supported enclosed voids for additive manufacturing. The enclosed overhangs that require supports in additive manufacturing are removed from the optimized design by constraining the maximum temperature of a pseudo heat conduction problem. In the pseudo problem, heat flux is applied on the non-self-supported open and enclosed surfaces. Since the density-based topology optimization involves no explicit boundary representation, we impose such surface slope dependent heat flux through a domain integral of a Heaviside projected density gradient. In addition, the solid materials and the void materials in the pseudo problem are assumed to be thermally insulating and conductive, respectively. As such, heat flux on the open surfaces can be successfully conducted to external heat sink through the void (or conductive) materials. However, heat flux on the non-self-supported enclosed surfaces is isolated by the solid (or insulating) materials and thus leads to locally high temperature. Hence, by limiting the maximum temperature of the pseudo problem, self-supported enclosed voids can be achieved, and the slope of the open surfaces would not be affected. Numerical examples are presented to demonstrate the validity and effectiveness of the proposed approach in the design of self-supported enclosed voids.

Theoretical Study on Relaxed Surrounding Rock Pressure on Shallow Bias Neighborhood Tunnels under Seismic Load

To study the distribution of relaxed surrounding rock pressure on the shallow bias neighborhood tunnels under the combined action of horizontal and vertical earthquake force, finite element software was used for failure mode analysis. Moreover, with the pseudo-static method, the calculation formula for the relaxed pressure on the shallow bias neighborhood tunnels was derived and used to analyze the variation of the rupture angle of these tunnels under the action of the seismic force. The study shows that: shallow bias neighborhood tunnels basically follow a “W” failure pattern under the combined action of horizontal and vertical seismic force, and the failure scope of the surrounding rock is controlled by four rupture angles. Rupture angles β2 and β3 between the deep and shallow tunnels of the shallow bias neighborhood tunnels are not affected by the surface slope. For tunnels with the same grade of the surrounding rock, the greater the seismic intensity, the smaller the value of β2, and the greater the value of β3. While at the same seismic intensity, the higher the grade of the surrounding rock, the smaller the β2 and β3. Ruptures angles β1 and β4 are influenced by the surface slope, seismic intensity and surrounding rock grades. A steeper surface slope leads to a smaller β1 and a greater β4; β1 increase and β4 decrease with increasing seismic intensity; while, β1 and β4 both show a decreasing trend with an increasing rock grade.