Distributed shear of subglacial till due to Coulomb slip

In most models of the flow of glaciers on till beds, it has been assumed that till behaves as a viscoplastic fluid, despite contradictory evidence from laboratory studies. In accord with this assumption, displacement profiles measured in subglacial till have been fitted with viscoplastic models by estimating the stress distribution. Here we present a model that illustrates how observed displacement profiles can result from till deformation resisted solely by Coulomb friction. Motion in the till bed is assumed to be driven by brief departures from static equilibrium caused by fluctuations in effective normal stress. These fluctuations result from chains of particles that support intergranular forces that are higher than average and that form and fail at various depths in the bed during shearing. Newton\u27s second law is used to calculate displacements along slip planes and the depth to which deformation extends in the bed. Consequent displacement profiles are convex upward, similar to those measured by Boulton and colleagues at Breidamerkurjökull, Iceland. The model results, when considered together with the long-term and widespread empirical support for Coulomb models in soils engineering, indicate that efforts to fit viscoplastic flow models to till displacement profiles may be misguided

Coupling between a glacier and a soft bed: II Model results

The relation between the local effective pressure and shear stress on till beneath Storglaciären, Sweden, discussed in Iverson and others (1999), provides an empirical basis for studying the processes that control the strength of the ice/bed coupling. Particles in the bed that protrude into the glacier sole support shear stresses that are limited by either ploughing or the traditional sliding mechanisms. Model calculations, based on studies of cone penetration through fine-grained sediment and sliding theory, agree with the observed relation between shear stress and effective pressure if the water layer at the ice/bed interface is assumed to thicken rapidly as the effective pressure approaches zero. Studies of the hydraulics of linked cavities provide support for this assumption, if the mean thickness of the water layer reflects the extent of microcavity development at the interface. Comparison of the calculated shear stress with the ultimate strength of till suggests that bed deformation limits the shear stress on till beneath Storglaciären only at intermediate effective pressures; at very low effective pressures, like those inferred at the site of the tiltmeter discussed in Iverson and others (1999), and at sufficiently high effective pressures, ploughing and sliding should focus motion near the glacier sole. A calculation using parameter values appropriate for Ice Stream B, West Antarctica, suggests that ploughing may occur there at shear stresses not sufficient to deform the bed at depth. This conclusion is reinforced by the likelihood that pore pressures in excess of hydrostatic should develop down-glacier from ploughing particles, thereby weakening the bed near the glacier sole. However, given the apparent sensitivity of the ice/bed coupling to basal conditions that may be highly variable, any blanket assumption regarding the flow mechanism of ice masses on soft beds should probably be viewed with skepticism

A laboratory study of particle ploughing and pore-pressure feedback: a velocity-weakening mechanism for soft glacier beds

If basal-water discharge and pressure are sufficiently high, a soft-bedded glacier will slip over its bed by ploughing, the process in which particles that span the ice–bed interface are dragged across the bed surface. Results of laboratory experiments indicate that resistance to ploughing can decrease with increasing ploughing velocity (velocity weakening). During ploughing at various velocities (15–400 m a−1), till was compacted in front of idealized particles, causing pore pressures there that were orders of magnitude higher than the ambient value. This excess pore pressure locally weakened the till in shear, thereby decreasing ploughing resistance by a factor of 3.0–6.6 with a six-fold increase in ploughing velocity. Characteristic timescales of pore-pressure diffusion and compaction down-glacier from ploughing particles depend on till diffusivity, ploughing velocity and sizes of ploughing particles. These timescales accurately predict the ranges of these variables over which excess pore pressure and velocity weakening occurred. Existing ploughing models do not account for velocity weakening. A new ploughing model with no adjustable parameters predicts ploughing resistance to no worse than 38% but requires that excess pore pressures be measured. Velocity weakening by this mechanism may affect fast glacier flow, sediment transport by bed deformation and basal seismicity

Diffusive mixing between shearing granular materials: constraints on bed deformation from till contacts

Shearing of subglacial till has been invoked widely as a mechanism of glacier motion and sediment transport, but standard indicators for determining shear strain from the geologic record are not adequate for estimating the very high strains required of the bed-deformation model. Here we describe a laboratory study of mixing between shearing granular layers that allows an upper limit to be placed on bed shear strain in the vicinity of till contacts. Owing to random vertical motions of particles induced by shearing, mixing can be modeled as a linearly diffusive process, and so can be characterized with a single mixing coefficient, D. Ring-shear experiments with equigranular beads and lithologically distinct tills provide the value of D, although in experiments with till D decreases systematically with strain to a minimum value of 0.0045 mm2. Kinetic gas theory provides an estimate of the dimensionless mixing coefficient which is within an order of magnitude of laboratory values. Knowing the minimum value of D, the distribution of index lithologies measured across till contacts in the geologic record can be used to estimate the maximum shear strain that has occurred across till contacts. Application of this technique to the contact between the Des Moines and Superior Lobe tills in east-central Minnesota, U. S. A., indicates that shear strain did not exceed 15 000 at the depth of the contact

Experimental determination of a double-valued drag relationship for glacier sliding

The contribution of glaciers to sea-level rise and their effects on landscape evolution depend on the poorly known relationship between sliding speed and drag at the ice/bed interface. Results from experiments with a new rotary laboratory device demonstrate empirically for the first time a double-valued drag relationship like that suggested by some sliding theories: steady drag on a rigid, sinusoidal bed increases, peaks and declines at progressively higher sliding speeds due to growth of cavities in the lee sides of bed undulations. Drag decreases with increased sliding speed if cavities extend beyond the inflection points of up-glacier facing surfaces, so that adverse bed slopes in contact with ice diminish with further cavity growth. These results indicate that shear tractions on glacier beds can potentially decrease due to increases in sliding speed driven by weather or climate variability, promoting even more rapid glacier motion by requiring greater strain rates to produce resistive stresses. Although a double-valued drag relationship has not yet been demonstrated for the complicated geometries of real glacier beds, both its potential major implications and the characteristically convex stoss surfaces of bumps on real glacier beds provide stimulus for exploring the effects of this relationship in ice-sheet models

Rate-weakening drag during glacier sliding

Accurately specifying the relationship between basal drag on a hard, rough glacier bed and sliding speed is a long-standing and central challenge in glaciology. Drag on a rigid bed consisting of steps with linear treads inclined upglacier—a good idealization for the bedrock morphology of some hard-bedded glaciers—has been considered in sliding theories but never studied empirically. Balancing forces parallel to step treads indicates that drag should be independent of sliding speed and cavity size and set by the limit-equilibrium condition sometimes called Iken\u27s bound. In this study we used a large ring-shear device to slide ice at its pressure melting temperature across a stepped bed, over a range of steady sliding speeds (29–348 m yr−1), and under a steady effective pressure (500 kPa). Contrary to expectation, drag decreased 42% with increasing sliding speed and cavity size. Experimental deviations from theory cannot explain this decrease in drag with increasing sliding speed (i.e., rate weakening). We suggest that stress bridging in ice between ice-bed contact zones and cavities causes stress gradients that require viscous deformation of ice to sustain stress equilibrium, so that contact zones can be at shear stresses below limit-equilibrium values. A parameter—linearly dependent on sliding speed—that scales the extent of ice deformation to areas of ice-bed contact allows the experimental drag relationship to be fitted with a simple sliding model. Rate-weakening drag has now been observed for two contrasting bed morphologies, stepped and sinusoidal, highlighting the need to consider such behavior in glacier flow models

Ring-shear studies of till deformation: Coulomb-plastic behavior and distributed strain in glacier beds

A ring-shear device was used to study the factors that control the ultimate(steady) strength of till at high shear strains.Tests at a steady strain rate and at different stresses normal to the shearing direction yielded ultimate friction angles of 26.3° and 18.6° for tills containing 4% and 30% clay-sized particles, respectively Other tests at steady normal stresses and variable shear-strain rates indicated a tendency for both tills to weaken slightly with increasing strain rate. This weakening may be due to small increases in till porosity.These results provide no evidence of viscous behavior and suggest that a Coulomb-plastic idealization is reasonable for till deformation. However, viscous behavior has often been suggested on the basis of distributed shear strain observed in subglacial till. We hypothesize that deformation may become distributed in till that is deformed cyclically in response to fluctuations in basal water pressure. During a deformation event, transient dilation of discrete shear zones should cause a reduction in internal pore-water pressure that should strengthen these zones relative to the surrounding till, a process called dilatant hardening. Consequent changes in shear-zone position, when integrated over time, may yield the observed distributed strain

Glacial landscape evolution by subglacial quarrying: A multiscale computational approach

Quarrying of bedrock is a primary agent of subglacial erosion. Although the mechanical theory behind the process has been studied for decades, it has proven difficult to formulate the governing principles so that large-scale landscape evolution models can be used to integrate erosion over time. The existing mechanical theory thus stands largely untested in its ability to explain postglacial topography. In this study we relate the physics of quarrying to long-term landscape evolution with a multiscale approach that connects meter-scale cavities to kilometer-scale glacial landscapes. By averaging the quarrying rate across many small-scale bedrock steps, we quantify how regional trends in basal sliding speed, effective pressure, and bed slope affect the rate of erosion. A sensitivity test indicates that a power law formulated in terms of these three variables provides an acceptable basis for quantifying regional-scale rates of quarrying. Our results highlight the strong influence of effective pressure, which intensifies quarrying by increasing the volume of the bed that is stressed by the ice and thereby the probability of rock failure. The resulting pressure dependency points to subglacial hydrology as a primary factor for influencing rates of quarrying and hence for shaping the bedrock topography under warm-based glaciers. When applied in a landscape evolution model, the erosion law for quarrying produces recognizable large-scale glacial landforms: U-shaped valleys, hanging valleys, and overdeepenings. The landforms produced are very similar to those predicted by more standard sliding-based erosion laws, but overall quarrying is more focused in valleys, and less effective at higher elevations

Subglacial clast/bed contact forces

A laboratory device was built to measure the forces that ice exerts on a 0.05 m diameter rigid plastic sphere in two different configurations: in contact with a flat bed or isolated from the bed. Measurements indicated that bed-normal contact forces were 1.8 times larger than drag forces due to creeping flow past a slippery sphere isolated from the bed. Measurements of forces as a function of the bed-normal ice velocity, estimations of the ice viscosity parameter and observations of markers in the ice indicate ice is Newtonian with a viscosity of ∼1.3 × 1011 Pa s. Newtonian behavior is expected due to small and transient stresses. A model of regelation indicates that it had a negligible (\u3c5%) influence on forces. Water pressure in the cavity beneath the sphere in contact with the bed had a likewise negligible influence on contact forces. When no cavity is present, drag forces can be correctly estimated using Stokes\u27s law (Newtonian viscosity) for a slippery sphere. The same law with a bed-enhancement factor of 1.8 is appropriate for estimating bed-normal contact forces. These results reinforce previous laboratory measurements and theories but provide no support for explanations of high debris/bed friction or rates of abrasion that depend on high contact forces

Preexisting fractures and the formation of an iconic American landscape: Tuolumne Meadows, Yosemite National Park, USA

Tuolumne Meadows, in Yosemite National Park (USA), is a large sub-alpine meadow in the Sierra Nevada Mountains. Immediately adjacent to Tuolumne Meadows—and underlain by the same bedrock lithology (Cathedral Peak Granodiorite)—are vertical rock faces that provide exceptional opportunities to climbers. While the presence of a broad meadow suggests bedrock erodibility, the vertical rock walls indicate bedrock durability. We propose that the Tuolumne Meadows’s landscape is the result of variable glacial erosion due to the presence or absence of pre-existing bedrock fractures. The meadows and valleys formed because of concentrated tabular fracture clusters—a distinctive and locally pervasive type of fracturing—that were particularly susceptible to glacial erosion. In contrast, the vertical rock walls consist of sparsely fractured bedrock that was originally bounded by zones of pervasive tabular fracture clusters. Glacial erosion preferentially removed the highly fractured rock, forming prominent ridges in the upland surrounding Tuolumne Meadows. The orientation and spacing of the tabular fracture clusters, relative to ice flow, has exerted a fundamental control on the geomorphology of the area. The erosional variability exhibited by a single lithology indicates that the degree of fracturing can be more important than the host lithology in controlling landscape evolution