Most theories of glacier movement and subglacial erosion have assumed that glaciers rest on rigid bedrock surfaces. Whilst this is probably correct for much of the bed area of most modern glaciers, deformable sediments do occur beneath them and formed a substantial area of the beds of large ice sheets during glacial periods. Observations and theories are presented and reviewed about the processes of glacier erosion of rock and unlithified sediment beds both when they are frozen and unfrozen.

Erosional bedrock landforms, such as roches moutonnées, indicate two principal subglacial erosional processes, plucking and abrasion. Where supraglacially derived debris is unimportant, plucking provides the tools which abrade the bed, and must be a quantitatively more important process than abrasion, though more localized. Where plucking is suppressed, erosion rates must be slow. Subglacial measurements of abrasion rates beneath a temperate glacier are used to test an earlier abrasional theory (Boulton, [C1974]). The form of the predicted abrasion-rate curve for changing ice velocity and pressure is verified. This theory successfully simulates two-dimensional erosional bedforms. Subglacial observations demonstrate how flow basal ice around the flanks of bedrock obstacles causes streaming of debris to occur. It is suggested that this streaming process is primarily responsible for the longitudinally lineated form of large-scale surfaces typical of glacially eroded bedrock.

Plucking and abrasion also occur beneath cold ice, though at slow rates, and are probably restricted to places where the ice thickness is small.

Where the glacier bed is composed of unlithified sediment, subglacial measurements show that deformation can produce very large discharges of subglacial material, which makes this a potential agent of very rapid subglacial landform production. The heterogeneity of subglacial sediment leads to spatially variable rates of deformation, and it is suggested that relatively stronger parts of the sediment body may form the nuclei for drumlin and mega-flute formation.

Whereas unlithified unfrozen sediment deforms beneath the glacier rather than being incorporated within it, ice-cemented subglacial sediments can behave like bedrock, because of their relative rigidity, and are readily plucked and incorporated englacially. They may also deform beneath the glacier.

Preliminary results of a quantitative model of glacial abrasion are presented. The analysis, which is constructed within a framework of modern glaciological views of processes near to the bed, is aimed at modeling abrasion under a temperate glacier whose basal layers contain only occasional rock fragments. It does not simulate abrasion by debris-rich ice or by subglacial drift. Calculations of abrasion-rates reduce to evaluations of the forces pressing rock fragments against the glacier bed and of the rates at which they are moved along the bed. The estimated viscous drag induced by ice flow toward the bed due to basal melting is generally the dominant contribution to this contact force. Although the analysis shares several important elements with the pioneering study of Boulton ([c1974]), sufficient fundamental differences in the modeling lead to distinctly different conclusions. Several new results are noteworthy: (1) other parameters being equal, abrasion will tend to be fastest where basal melting is most rapid, (2) glacier thickness does not affect abrasion through its influence on basal pressures, and (3) lodgement of rock fragments is only possible if the sliding velocity is very low, equivalent to the rate of basal melting.

Glacial abrasion has been simulated by turning a grindstone made of ice and crushed quartz between two stone plates within a domestic deep-freeze. Within limits, the speed of rotation, the normal loading, and the temperature of operation can be controlled. The tangential force exerted on one of the stone plates can be measured. The ratio of tangential to normal force, the effective coefficient of friction, is found to vary with the “roughness” of the grindstone, to increase gradually as abrasion proceeds, and to increase with decreasing velocity. Even at very low temperatures (to −26°C), abrasion products accumulated in a pad of ice frozen to the tablet “down-stream” from the grindstone, indicating that a water phase at least momentarily exists. The abraded surface of a fine-grained limestone displays grain-from-grain plucking dominating over abrasion of individual crystals. The abraded surface of a granite, by contrast, shows striations of crystals and rupture of cleavage along individual striae.

Longitudinal profiles of roches moutonnées have been measured once every centimetre over a total length of more than 100 m. Only wavelengths in the range 3.6 cm < λ < 40 cm have been kept and analysed. Levels and their slopes have a symmetrical, non-Gaussian distribution. The spectral power density varies roughly as γ0ν–n (ν ═ wavenumber ═ 1/λ); n being the same for all the profiles (n ═ 2.36) and γ0 being dependent on the studied area. No significant difference has been found for the shadowing function of the different studied areas. It differs consistently from Smith’s theoretical function.

“Sliding velocity” and “friction law” are precisely defined. Different scales for tackling glacier dynamics are introduced. The energy balance in the melting-refreezing process is clarified. The validity of a Glen body as a model for ice rheology is discussed. The assumed model for subglacial water is a very slightly pervious ice, and a not absolutely watertight ice-bedrock interface, owing to glacial striae and rock joints. Then autonomous hydraulic regimes and cavities at water vapour pressure have a negligible influence on the drag, and only the interconnected regime has to be considered.

A more rigorous treatment of Weertman’s model (independent knobs) gives quite different numerical factors. In general a term increasing with Terzaghi’s effective pressure N has to be added to the drag. The double-valued friction law found by Weertman is shown to have been an error.

Kamb’s relations for the model with a vanishing microrelief are considerably simplified. His conjectural solution cannot be extended to slopes actually found in the microrelief.

The author’s (Lliboutry, 1968) treatment is unsatisfactory and includes an error. With a model consisting of irregular bumps of similar length, a new friction law is given. The pertinent measure of the bedrock roughness is then the shadowing function, not the spectral power density.

The status of the theory of glacier sliding is reviewed in this paper. The theory of Nye and Kamb essentially solves the problem of glacier sliding when the basal ice is in intimate contact with a non-deformable bed. But experimental work is needed on cyclic creep and the regelation process in order to put better numbers into the theory. The outstanding problem that remains to be solved, called in this paper the general glacier sliding problem, is the case of sliding when basal ice is not in intimate contact with a non-deformable bed because of the presence of cavities and a water film of finite thickness. This problem involves solving an intricately coupled basal water-flow problem. A new field of research is the study of the motion of glaciers over deformable beds.

This paper describes an analytical solution of the equations of motion and heat conduction for ice flowing around a cylindrical solid inclusion and over a solid plane boundary. This is intended to be a simplified representation of the flow of clean glacier ice around a stone and over a rigid rock bed. The ice is treated as a Newtonian viscous liquid and the equations are solved in two dimensions. Regelation boundary conditions are applied at both ice–rock interfaces. It is found that finite solutions for the temperature and stream function only exist for the special cases in which two dimensionless critical wavelengths are zero. That is, unless the stone is very far from the glacial bed, the classical regelation boundary conditions cannot be obeyed over the whole of its surface.

Previous theories of glacier sliding are subject to the criticism that they are not properly formulated. Here we describe how the basal ice flow may be related to the bulk ice flow by means of the formal mathematical method of matched asymptotic expansions. A complete model of the basal sliding (involving coupled problems in ice, water film, and bedrock) may be rationally reduced by a dimensional analysis to a consideration of the ice flow only, and regelation may be neglected provided roughness is absent on the finest scales (< c. 1 mm). If the viscosity is supposed to be independent of the moisture content, then complementary variational principles exist which allow bounds on the drag to be obtained. In particular, these determine the magnitude of the basal velocity in terms of two crucial dimensionless parameters. Arguments are presented as to why realistic sliding laws should be taken as continuous functions of the temperature, and a (major) consequence of this assumption is mentioned. Finally the effect of cavitation is discussed, via an (exact) leading-order solution of the ice flow in the particular case of a Newtonian fluid and a “small” bedrock slope.

The sliding of temperate ice over two obstacles with sine-wave profiles (wavelength, 0.53 m; maximum slope, 0.22) and low thermal conductivity has been reproduced at full scale within a steel chamber. As expected, large cavities form between the ice and the obstacles so that the drag is limited. However, the delayed elasticity of bubbly ice modifies the expected behaviour. At the base of the ice a fine-grained, bubble-free blue ice layer develops. The shear strain concentrates on the up-stream side of bumps and in the blue ice layer. Tap-water ions enhance tertiary creep-rates.

An experimental programme has been carried out for studying temperate-ice sliding over rock surfaces with a wide range of roughnesses, for normal and shear stresses comparable to those expected under real ice masses. The limiting static shear stress for acceleration has been found to be directly proportional to the normal load giving a constant limiting coefficient of static friction characteristic of the surface. For a constant applied normal stress N and shear stress τb, well below the limiting static shear, a steady velocity Vb results which increases approximately proportionally to τb and decreases with increasing N and the roughness of the surface. For high normal stress the velocity becomes approximately proportional to the shear stress cubed and inversely proportional to the normal stress. As the shear stress increases acceleration sets in, which, for different roughness and normal loads, tends to occur for a constant value of the product τbVb. For some surfaces at high normal loads this acceleration was retarded by erosion. For constant-applied-velocity tests a steady shear stress resulted, which tended to become constant with high velocities, and which increased with increasing normal stress but with a reduced coefficient of sliding friction. The relevance of the results to the sliding of real ice masses is discussed with particular reference to the importance of the effect of the relative normal stress, above basal water pressure, to the sliding rate.

Seismic monitoring on three Cascade volcanoes in Washington State, U.S.A., has shown that small seismic events are generated by the active glaciers found on each mountain. Detailed seismic experiments have been conducted to investigate the sources for these icequakes. Considerable evidence indicates that the events are the result of a stick–slip type of motion taking place at the bed of the glaciers. The few events we have been able to locate had depths comparable with the glaciers’ thickness. The similarity of wave form from an explosion at the bottom of a glacier and natural icequakes suggests that the complexity of the seismic wave form is due to the path and not the source. The events exhibit an annual trend with more events being recorded in the summer than during the winter. A ten-fold increase in the number of events preceded a large ice avalanche that involved the entire glacier thickness, suggesting that seismic monitoring may be useful in predicting catastrophic ice movements.

Cores from the bottom 4.83 m of the Antarctic ice sheet at Byrd Station contain abundant stratified debris ranging from silt-sized particles to cobbles. The nature and disposition of the debris, together with measurements of the physical properties of the inclosing ice, indicate that this zone of dirt-laden ice originated by “freezing-in” at the base of the ice sheet. The transition from air-rich glacial ice to ice practically devoid of air coincided precisely with the first appearance of debris in the ice at 4.83 m above the bed. Stable-isotope studies made in conjunction with gas-content measurements also confirm the idea of incorporation of basal debris by adfreezing of melt water at the ice―rock interface. It is suggested that the absence of air from basal ice may well constitute the most diagnostic test for discriminating between debris incorporated in a melt―refreeze process and debris entrapped by purely mechanical means, e.g. shearing. We conclude from our observations on bottom cores from Byrd Station that “freezing-in” of basal debris is the major mechanism by which sediment is incorporated into polar ice sheets.

The Camp Century, Greenland, ice core was recovered from a bore hole which extended 1 375 m from the surface of the Greenland ice sheet to the ice/sub-ice interface. The bottom 15.7 m of the core contain over 300 alternating bands of clear and debris-laden ice. The size of the included debris ranges from particles less than 2 μm in diameter to particle aggregates which are a maximum of 3 cm in diameter: the average debris concentration is 0.24ºº by weight. The debris size, concentration, and composition indicate that the debris originates from the till-like material directly below the debris-laden ice. The total gas concentration averages 51 ml/kg ice compared to the average of 101 ml/kg ice for the top 1 340 m. The gas composition of debris-bearing ice has apparently been modified by the oxidation of methane as reflected by traces of methane, high CO2 levels, and low O2 levels with respect to atmospheric air. Argon, which is not affected by the oxidation, shows an enrichment in samples with lower gas concentrations. Both the low gas concentrations in the debris-laden zone and the argon enrichment may be explained by the downward diffusion of gases from bubbly glacier ice into an originally bubble-free zone of refrozen debris-laden ice. Ice texture and ice-fabric analyses reveal extremely fine-grained ice and highly preferred crystal orientation in the lowermost 10 m of the core, indicating a zone of high deformation.

Surface-to-bedrock cores obtained with a CRREL thermal drill were taken in 1972 and 1973 from the top of the Devon Island ice cap. There are very pronounced variations in oxygen isotope, micro-particle concentration, and ice texture in the lowermost 5 m of the core. There is a section of isotopically cold, very fine bubbly ice with high micro-particle concentrations between 2.6 and 4.4 m above the bed, considered to represent the Last Ice Age. There is coarse, isotopically warm, clean ice above and below this. For 1.2 m above the bed, the ice is finer again with high micro-particle concentrations but it shows very low bubble concentration and is isotopically the warmest in the core. While the broad variations are common to both cores, in detail there are significant variations despite the fact that the cores were taken only 27 m apart. The variations, when analysed statistically, show that at least 25–30% of the originally continuous profile is missing from each core. Faulting within the near-bedrock ice may be responsible for some of the effect but bubble fabric also gives evidence for irregular non-laminar flow. Because of the strong relationship between crystal size and micro-particle concentrations in the Devon Island cores, it is suggested that the fine-grained nature of dirty layers in the Antarctic and Greenland ice sheets is due to the effect of the dirt inclusions and not of shearing. Steep isotopic gradients in the Devon Island cores are shown to be evidence for possible shearing, which does not effect any change in the crystal texture. Clear ice near the bed is considered a tectonic feature, but the lack of effect on its bed by the ice cap confirms the non-erosional nature of an ice cap frozen to its bed.

In terms of paleoclimatic history, it means that, because of bedrock effects, ice caps of intermediate depth (i.e. <400 m) can give continuous information only over the last approximate 5 000 years. Between 5 000 and 10 000 B.P. the time series becomes slightly discontinuous and beyond 10 000 B.P. so discontinuous as to allow only broad climatic inferences to be drawn.

Polar ice is now thought to be marginally birefringent at radio echo-sounding frequencies. An experiment on the polarization behaviour of 60 MHz radio echoes from the bed of both ice shelf and land ice in Antarctica showed a marked difference in the returned polarization. It appears that differences in electrical properties or roughness of the reflecting boundary cannot explain our results. We suggest that there is a large change in the birefringence of the ice sheet at the hinge zone, caused by the effect of tidal strain on crystal orientation. This would imply a minimum value of the radio-frequency anisotropy in permittivity for the single crystal of (0.52±0.8)%. Therefore polarization changes could allow floating and grounded ice to be distinguished.

This study examines the effect of subglacial abrasion on the basal sliding term of the gravitational energy balance of the dynamic, temperate Nisqually Glacier on Mount Rainier, Washington, U.S.A. Subglacial water flux is estimated as 3 × 107 m3 a–1 and suspended sediment flux as 3 × 107 kg a–1. Suspended-sediment flux is assumed to represent, within an order of magnitude, the annual mass eroded by subglacial abrasion.

Subglacial abrasion involves both brittle fracture and plastic deformation. Field observations of bas-relief and grooved depression striations appear to have exact counterparts in rock mechanics experiments approximating subglacial velocities and normal stresses. Boulton's ([Cl974]) abrasion model and a new attritivity model proposed herein are shown to predict subglacial abrasion-rates within the limits of natural variability and the error range of measurements. The first crude gravitational energy balance for lower Nisqually Glacier (1.96 km2) is attempted and probably has only order-of-magnitude accuracy. The importance of subglacial abrasion in dissipating basal sliding energy at Nisqually Glacier is confirmed.

Suspended-sediment concentrations in melt waters from the Gornera, Gornergletscher, Switzerland, were determined at hourly intervals for periods during the ablation seasons of 1974 and 1975. Rapid erratic fluctuations of suspended-sediment concentration produced peaks which occurred both before and after highest daily flows. Clockwise daily hysteresis rating loops between sediment concentration and discharge included many involutions. Suspended-sediment-concentration-discharge rating curves were different for rising and falling limbs of individual diurnal hydrographs and varied from day to day. Close-interval measurements of sediment concentration and discharge records allow interpretation of the nature of ice–water–sediment interactions at the bed of an Alpine glacier. At Gornergletscher, subglacial sediment is delivered to melt waters flowing in the smaller basal conduits, which often change course suddenly, entraining unworked sediment stored at the bed. During diurnal discharge maxima, sediment concentration in the Gornera is reduced because the rate of increase of water volume outstrips the rate of supply of sediment. The drainage of the ice-dammed lake Gornersee, producing exceptionally high flows, extended the drainage network over large areas of the glacier bed, and evacuated much sediment.