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Frost heave occurs when the ground swells during freezing conditions due to the growth of ice lenses in the subsurface. The mechanics of ice-infiltrated sediment, or frozen fringe, influences the formation and evolution of ice lenses. As the frozen fringe thickens during freezing, progressive unloading can result in dilation of the pore space and the formation of new ice lenses. Compaction can also occur as water is expelled from the pore space and freezes onto the ice lenses. We introduce a mathematical model for compaction within frozen fringe to explore how internal variability influences the fundamental characteristics of frost heave cycles. At faster freezing rates, compaction below ice lenses can generate complex dynamics and chaos when the frozen fringe follows a consolidation law based solely on the sediment yield stress. The complex oscillations arise because a downward water flux below the compacting zone generates a distributed zone of weakening. We introduce viscous effects into the compaction law through a bulk viscosity to determine how the cycles could be influenced by the creep of ice through the pore space. Localized zones of decompaction in the viscoplastic model can prevent the feedback mechanisms that cause complex oscillations in the perfectly plastic model. 

Abstract Glacier-erosion rates range across orders of magnitude, and much of this variation cannot be attributed to basal sliding rates. Subglacial till acts as lubricating ‘fault gouge’ or ‘sawdust’, and must be removed for rapid subglacial bedrock erosion. Such erosion occurs especially where and when moulin-fed streams access the bed and are unconstrained by supercooling or other processes. Streams also may directly erode bedrock, likely with strong time-evolution. Erosion is primarily by quarrying, aided by strong fluctuations in the water system driven by variable surface melt and by subglacial earthquakes. Debris-bed friction significantly affects abrasion, quarrying and general glacier flow. Frost heave drives cirque headwall erosion as winter cold air enters bergschrunds, creating temperature gradients to drive water flow along premelted films to growing ice lenses that fracture rock, and the glacier removes the resulting blocks. Recent subglacial bedrock erosion and sediment flux are in many cases much higher than long-term averages. Over glacial cycles, evolution of glacial-valley form feeds back strongly on erosion and deposition. Most of this is poorly quantified, with parts open to argument. Glacial erosion and interactions are important to tectonic and volcanic processes as well as climate and biogeochemical fluxes, motivating vigorous research. 

Abstract Quarrying and abrasion are the two principal processes responsible for glacial erosion of bedrock. The morphologies of glacier hard beds depend on the relative effectiveness of these two processes, as abrasion tends to smooth bedrock surfaces and quarrying tends to roughen them. Here we analyze concentrations of bedrock discontinuities in the Tsanfleuron forefield, Switzerland, to help determine the geologic conditions that favor glacial quarrying over abrasion. Aerial discontinuity concentrations are measured from scaled drone-based photos where fractures and bedding planes in the bedrock are manually mapped. A Tukey honest significant difference test indicates that aerial concentration of bed-normal bedrock discontinuities is not significantly different between quarried and non-quarried areas of the forefield. Thus, an alternative explanation is needed to account for the spatial variability of quarried areas. To investigate the role that bed-parallel discontinuities might play in quarrying, we use a finite element model to simulate bed-normal fracture propagation within a stepped bed with different step heights. Results indicate that higher steps (larger spacing of bed-parallel discontinuities) propagate bed-normal fractures more readily than smaller steps. Thus, the spacing of bed-parallel discontinuities could exert strong control on quarrying by determining the rate that blocks can be loosened from the host rock. 

Abstract Glacier sliding has major environmental consequences, but friction caused by debris in the basal ice of glaciers is seldom considered in sliding models. To include such friction, divergent hypotheses for clast‐bed contact forces require testing. In experiments we rotate an ice ring (outside diameter = 0.9 m), with and without isolated till clasts, over a smooth rock bed. Ice is kept at its pressure‐melting temperature, and meltwater drains along a film at the bed to atmospheric pressure at its edges. The ice pressure or bed‐normal component of ice velocity is controlled, while bed shear stress is measured. Results with debris‐free ice indicate friction coefficients < 0.01. Shear stresses caused by clasts in ice are independent of ice pressure. This independence indicates that with increases in ice pressure the water pressure in cavities observed beneath clasts increases commensurately to allow drainage of cavities into the melt film, leaving clast‐bed contact forces unaffected. Shear stresses, instead, are proportional to bed‐normal ice velocity. Cavities and the absence of regelation ice indicate that, unlike model formulations, regelation past clasts does not control contact forces. Alternatively, heat from the bed melts ice above clasts, creating pressure gradients in adjacent meltwater films that cause contact forces to depend on bed‐normal ice velocity. This model can account for observations if rock friction predicated on Hertzian clast‐bed contacts is assumed. Including debris‐bed friction in glacier sliding models will require coupling the ice velocity field near the bed to contact forces rather than imposing a pressure‐based friction rule. 

Abstract The morphology of glacier beds is a first‐order control on their slip speeds and consequent rates of subglacial erosion. As such, constraining the range of bed shapes expected beneath glaciers will improve estimates of glacier slip speeds. To estimate the variability of subglacial bed morphology, we construct 10 high‐resolution (10 cm) digital elevation models of proglacial areas near current glacier margins from point clouds produced through a combination of terrestrial laser scanning and photogrammetry techniques. The proglacial areas are located in the Swiss Alps and the Canadian Rockies and consist of predominantly debris‐free bedrock of variable lithology (igneous, sedimentary, and metamorphic). We measure eight different spatial parameters intended to describe bed morphologies generated beneath glaciers. Using probability density functions, Bhattacharyya coefficients, principal component analysis, and Bayesian statistical models we investigate the significance of these spatial parameters. We find that the parameters span similar ranges, but the means and standard deviations of the parameter probability density functions are commonly distinct. These results indicate that glacier flow over bedrock may lead to a convergence toward a common bed morphology. However, distinct properties associated with each location prevent morphologies from being uniform.