To better constrain meltwater transport and ice viscosity in temperate glaciers, particularly in ice stream shear margins, we use a custom permeameter to study the untested model relationship between the permeability of temperate ice and its liquid water content. The permeability of lab-made ice of two mean grain diameters (1.8 and 4.2 mm) is measured, and water content is controlled with the ice salinity and measured calorimetrically. Fluorescein dye is added to through-flowing, chilled water to highlight flow pathways through the ice after experiments. As predicted by a simple model, permeability increases with approximately the square of the water content and by about three orders of magnitude across water contents of 0.1–4.4%. However, permeability values are less than those of the model by average factors of 2.6 and 4.1 for the finer and coarser ice, respectively. This discrepancy is likely due to tortuous, truncated or air-clogged veins. The order-of-magnitude agreement between measured and modeled values may indicate that reduced permeability from these factors is nearly compensated by preferential flow in oversized veins that are isolated or arborescent. Both kinds of preferred flow pathways are observed but the latter only in fine-grained ice at water contents > 2%.

Sea-level projections depend sensitively on the parameterization used for basal slip in glacier flow models. During slip over rock-beds, ice-bed separation increases with slip velocity and basal water pressure. We present a method for using these variables and measured bed topography to estimate the average bed slope in contact with ice, ${\bar m}$. Three-dimensional numerical modeling of slip over small areas of former beds has shown that changes in ${\bar m}$ with increasing slip velocity and water pressure mimic changes in basal drag. Computed values of ${\bar m}$ can thus provide the form of the slip law that relates drag to velocity and water pressure, avoiding computationally expensive numerical modeling. The method is applied to 618 sections from four former glacier beds. Results generally show an increase in ${\bar m}$, and hence inferred basal drag, with slip velocity up to a limiting value, consistent with a regularized Coulomb slip law.

Results of ice-stream models that treat temperate ice deformation as a two-phase flow are sensitive to the ice permeability. We have constructed and begun using a custom, falling-head permeameter for measuring the permeability of temperate, polycrystalline ice. Chilled water is passed through an ice disk that is kept at the pressure-melting temperature while the rate of head decrease indicates the permeability. Fluorescein dye in the water allows water-vein geometry to be studied using fluorescence microscopy. Water flow over durations of seconds to hours is Darcian, and for grain diameter d increasing from 1.7 to 8.9 mm, average permeability decreases from 2 × 10−12 to 4 × 10−15 m2. In tests with dye on fine (d = 2 mm) and coarse (d = 7 mm) ice, average area-weighted vein radii are nearly equal, 41 and 34 μm, respectively. These average radii, if included in a theory slightly modified from Nye and Frank (1973), yield permeability values within a factor of 2.0 of best-fit values based on regression of the data. Permeability values depend on d−3.4, rather than d−2 as predicted by models if vein radii are considered independent of d. In future experiments, the dependence of permeability on liquid water content will be measured.

Glacier slip is usually described using steady-state sliding laws that relate drag, slip velocity and effective pressure, but where subglacial conditions vary rapidly transient effects may influence slip dynamics. Here we use results from a set of laboratory experiments to examine the transient response of glacier slip over a hard bed to velocity perturbations. The drag and cavity evolution from lab experiments are used to parameterize a rate-and-state drag model that is applied to observations of surface velocity and ice-bed separation from the Greenland ice sheet. The drag model successfully predicts observed lags between changes in ice-bed separation and sliding speed. These lags result from the time (or displacement) required for cavities to evolve from one steady-state condition to another. In comparing drag estimates resulting from applying rate-and-state and steady-state slip laws to transient data, we find the peaks in drag are out of phase. This suggests that in locations where subglacial conditions vary on timescales shorter than those needed for cavity adjustment transient slip processes control basal drag.

Drumlins form at the ice/bed interface through subglacial processes that are not directly observable. The internal stratigraphy of drumlins provides insight into how they developed and associated subglacial processes, but traditional stratigraphic logging techniques are limited to natural exposures and excavations. Using ground-penetrating radar, we imaged the internal stratigraphy of seven drumlins from a recently exposed drumlin field in the forefield of Múlajökull, Iceland. Data were collected with 100 and 200 MHz antennas with maximum resolvable depths of 8 and 4 m, respectively. Longitudinal echograms contained coherent down-ice dipping reflectors over the lengths of the drumlins. Near the drumlin heads (i.e., stoss sides), down-glacier dipping beds lie at high angles to the surface, whereas on the lee sides, the down-glacier dipping beds lie at low angles, or conform, to drumlin surfaces. Transverse echograms exhibited unconformities along the flanks of drumlin heads and conformable bedding across the lee side widths of the drumlins. These observations were ground-truthed with stratigraphic logs from a subset of drumlins and good agreement was found. The stratigraphic patterns support previous conclusions that drumlins at Múlajökull formed on a deformable bed through both depositional and erosional processes which may alternate between its surge and quiescent phases.

Theory and experiments indicate that ice–bed separation during glacier slip over 2-D hard beds causes basal shear stress to reach a maximum at a particular slip velocity and decrease at higher velocities. We use the sliding theory of Lliboutry (1968) to explore how friction between debris particles in sliding ice and a rock bed affects this relationship between shear stress and slip velocity. Particle–bed contact forces and associated debris friction increase with increasing slip velocity, owing to increased rates of ice convergence with up-glacier facing surfaces. However, debris friction on diminished areas of the bed counteracts this effect as cavities grow. Thus, friction from debris alone increases only slightly with slip velocity, and for sediment particles larger than ~60 mm in diameter, debris friction peaks and decreases with increasing slip velocity. The effect on the sliding relationship is to steepen its rising limb and shift its shear stress peak to a slightly higher velocity. These results, which exclude the effect of debris friction on cavity size and debris concentrations above ~15%, indicate that the effect of debris in ice is to increase basal shear stress but not significantly change the form of the sliding relationship.

Where polythermal glaciers have frozen margins that buttress otherwise temperate-based sliding ice, longitudinal compression can strongly influence ice-flow trajectory, and consequently sediment transport paths. Past efforts to model flow in the vicinity of a basal thermal transition (BTT) have generally relied on simplified boundary conditions or rheological idealizations, making these model results difficult to apply to real glacier termini. Herein, we present results of numerical simulations using a power-law rheology and with boundary conditions that better represent the frozen margin. Model results indicate that a transition to a non-sliding frozen margin causes a decline in surface velocity made possible by upward ice flow, implying either enhanced ablation for steady-state simulations or the formation of a surface bulge. Permitting ice loss by ablation combined with numerical smoothing of the basal slip transition subdues basal stress concentrations and thereby inhibits development of structural discontinuities such as thrust faults. Upward ice flow is accommodated by vertical extension up-glacier of the BTT. This strain regime can potentially account for key structural features in polythermal glacier termini without appealing to thrusting.

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’s 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.

The field observations of G.S. Boulton stimulated widespread interest in deformable beds. Shear resistance of till in its critical state is insensitive to strain rate and increases linearly with effective pressure. During unsteady deformation, pseudo-viscous shear resistance can be caused by dilation of consolidated tills and resultant pore-pressure decline. This effect is probably uncommon, however, because susceptible tills of low hydraulic diffusivity are also those least likely to consolidate significantly during effective-pressure transients. Stick-slip motion at Whillans Ice Stream, Antarctica, indicates that its basal till must weaken during rapid slip and strengthen during longer periods of slower slip. Recurrence intervals for rapid-slip episodes there (6-18hours) indicate that till-strength variations, if driven by changes in pore pressure either related or unrelated to basal freezing, are focused in the uppermost several centimeters of the bed. Ploughing of grains at the bed surface and associated excess pore pressures in adjacent till can account for rate-weakening during rapid slip, with pore-pressure decay causing strengthening between slip episodes. By promoting shallow, sluggish subglacial water flow and low effective pressure, soft beds may help sustain themselves by slowing their own transport. Soft-bed shear resistance, kinematics and continuity are problems rooted in subglacial hydrology.

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.

A new ring-shear device allows basal slip and related processes to be studied in laboratory experiments for the cases of hard or soft beds. The device rotates a confined ring of ice (0.9 m outside diameter) across a horizontal bed at a constant velocity or drag, while a vertical stress is applied and basal water pressure is controlled. A bath with circulating fluid regulated to ∼0.01°C surrounds the ice chamber and keeps the ice at its pressure-melting temperature. In a first experiment with a stepped rigid bed and zero basal water pressure, steady lengths of step cavities depended upon slip velocity raised to a power of 0.59, in general agreement with the square-root dependence of some models of sliding and linked-cavity hydraulics. Transient cavity growth after slip velocity increases was not monotonic, with damped volume oscillations that converged to a steady value. Once ice separated from lee surfaces, drag on the bed was constant and independent of slip velocity and cavity size, consistent with a shear-stress upper bound like that indicated by sliding models. Shear strains near the bed exceeded 30 and ice developed multiple-cluster c-axis fabrics similar to those of sheared ice in temperate glaciers.

At Engabreen, Norway, an instrumented panel containing a decimetric obstacle was mounted flush with the bed surface beneath 210 m of ice. Simultaneous measurements of normal and shear stresses, ice velocity and temperature were obtained as dirty basal ice flowed past the obstacle. Our measurements were broadly consistent with ice thickness, flow conditions and bedrock topography near the site of the experiment. Ice speed 0.45 m above the bed was about 130 mm d−1, much less than the surface velocity of 800 mm d−1. Average normal stress on the panel was 1.0–1.6 MPa, smaller than the expected ice overburden pressure. Normal stress was larger and temperature was lower on the stoss side than on the lee side, in accord with flow dynamics and equilibrium thermodynamics. Annual differences in normal stresses were correlated with changes in sliding speed and ice-flow direction. These temporal variations may have been caused by changes in ice rheology associated with changes in sediment concentration, water content or both. Temperature and normal stress were generally correlated, except when clasts presumably collided with the panel. Temperature gradients in the obstacle indicated that regelation was negligible, consistent with the obstacle size. Melt rate was about 10% of the sliding speed. Despite high sliding speed, no significant ice/bed separation was observed in the lee of the obstacle. Frictional forces between sediment particles in the ice and the panel, estimated from Hallet’s (1981) model, indicated that friction accounted for about 5% of the measured bed-parallel force. This value is uncertain, as friction theories are largely untested. Some of these findings agree with sliding theories, others do not.

Rapid flow of the Des Moines lobe of the Laurentide ice sheet may have been related to its unlithified substrate. New reconstructions of the lobe, based on moraine elevations, sediment subsidence during moraine deposition, and flow-direction indicators, indicate that the lobe may have been ∼3 times thicker than in previous reconstructions. Nevertheless, implied basal shear stresses are <15 kPa, so internal ice deformation was not significant. Instead, the lobe likely moved by a combination of sliding, plowing of particles through the bed surface, and bed shear. Consolidation tests on basal till yield preconsolidation stresses of 125–300 kPa, so effective normal stresses on the bed were small. A model of sliding and plowing indicates that at such stresses most particles gripped by the ice may have plowed easily through the till bed, resulting in too small a shear traction on the bed to shear it at depth. Consistent with this prediction, measurements of orientations of clasts in basal till yield a weak fabric, implying pervasive bed shear strain less than ∼2, although some stronger fabrics have been reported by others. We infer, tentatively, that movement was principally at the bed surface by plowing.

The cold-based termini of polythermal glaciers are usually assumed to adhere strongly to an immobile substrate and thereby supply significant resistance to the flow of warm-based ice up-glacier. This compressive environment is commonly thought to uplift basal sediment to the surface of the glacier by folding and thrust faulting. We present model and field evidence from the terminus of Storglaciären, Sweden, showing that the cold margin provides limited resistance to flow from up-glacier. Ice temperatures indicate that basal freezing occurs in this zone at 10−1 −10−2 m a−1, but model results indicate that basal motion at rates greater than 1 m a−1 must, nevertheless, persist there for surface and basal velocities to be consistent with measurements. Estimated longitudinal compressive stresses of 20–25 kPa within the terminus further indicate that basal resistance offered by the cold-based terminus is small. These results indicate that where polythermal glaciers are underlain by unlithified sediments, ice-flow trajectories and sediment transport pathways may be affected by subglacial topography and hydrology more than by the basal thermal regime.

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 ~1.3x 1011 Pas. Newtonian behavior is expected due to small and transient stresses. A model of regelation indicates that it had a negligible (<5%) 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’s 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.

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.

Deep, pervasive shear deformation of the bed to high strains (>100) may have been primarily responsible for flow and sediment transport of the Lake Michigan lobe of the Laurentide ice sheet. To test this hypothesis, we sampled at 0.2 m increments a basal till from one advance of the lobe (Batestown till) along vertical profiles and measured fabrics due to both anisotropy of magnetic susceptibility and sand-grain preferred orientation. Unlike past fabric studies, interpretations were guided by results of laboratory experiments in which this till was deformed in simple shear to high strains. Fabric strengths indicate that more than half of the till sampled has a <5% probability of having been sheared to moderate strains (7–30). Secular changes in fabric azimuth over the thickness of the till, probably due to changing ice-flow direction as the lobe receded, indicate that the bed accreted with time and that the depth of deformation of the bed did not exceed a few decimeters. Orientations of principal magnetic susceptibilities show that the state of strain was commonly complex, deviating from bed-parallel simple shear. Deformation is inferred to have been focused in shallow, temporally variable patches during till deposition from ice.

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.

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.

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.