Sediment responses

The yield strength of a subglacial material, which is determined by effective pressure p′, cohesion с and angle of internal friction ϕ increases with depth (assuming that the material has a relatively high permeability) (Reference Boulton, and Dobbie,Boulton and Dobbie, 1993). With respect to the strength, the basal, simple shear stress

as exerted by the glacier in extensional flow conditions, is assumed to be constant with depth throughout the sediment (Reference Alley,Alley, 1989b).

Shear deformation at high strain rates will occur in a layer immediately beneath the glacier sole, where shear stresses exceed local sediment strength. Deformation will cease at some depth z_a, where the shear stress just equals the yield strength (Reference Boulton,Boulton, 1996):

where p′, is the effective pressure at the glacier sole. At this depth z_a, a time-independent, perfectly plastic type of deformation occurs.

The tectonic “A horizon”, thus defined, in which shear stresses and normal loading pressure tend to be accommodated by a subtle interplay between compaction and dilation (Reference Boulton,, Dent and Morris,Boulton and others, 1974), is underlain by a much denser, consolidated “B horizon”.

Towards the base of the A horizon, deformation does not pervade the material equally but tends to be more discrete, and strain rates are significantly lower than in the top part; failure will concentrate in well-developed zones of shear displacement. Theoretically, these shear zones can be regarded as a combined result of uniaxial shortening (compaction, dilatant behaviour being suppressed), and an actual lateral displacement provided by progressive, simple, basal shear.

In the first deformational increments, the failure behaviour of the sediment under these arbitrary brittle-shearing conditions is described mathematically in the failure envelope of Equation (2).

where σ₁ ^′ and σ₂ ^′ represent the largest and smallest principal effective, stresses, respectively. Note that, in order to understand stress transmission in any Cartesian frame of reference, “field stresses” are often transformed and projected into a rotated frame, in which principal stress components are known.

Initially. riedel shears are generated at angles which are determined by the respective orientations of the principal stresses. In a passive propagation through sets of successive riedel shear stages, strain is “rotated” towards the actual shearing orientation and eventually localizes in discrete sub-parallel displacement shears (Reference Morgenstern, and Tchalenko,Morgenstern and Tcha-tenko, 1967; Reference Morrow, and Byerlee,Morrow and Byerlee, 1989; Reference Rajlich,Rajlich, 1993).

Fracturing of grains

Within diamictons, grain fracturing is to be expected predominantly in zones where dilatant strain behaviour is inhibited by high confining ice pressures (Reference Boulton,, Dent and Morris,Boulton and others, 1974; Reference Van der Meer,van der Meer, 1993). A prerequisite for the fracturing process is direct contact between grains, at which tensile stresses are induced by loading compression and enhanced by shear compaction. Initiation and propagation of fractures are best described in the model of “Hertzian fracture mechanics” (Reference Johnson,Johnson, 1985). A precondition of the process initiation is the existence of flaws on the grain surfaces, inherited from weathering or transport (Reference Whalley, and Krinsley,Whalley and Krinsley, 1974; Reference Mahaney,, Vortisch, and Julig.Mahaney and others, 1988).

Maximum tensile stresses

in a grain loaded diametrically occur at the edge of the “contact circle”. Fracturing will be initiated if pre-existing flaws at this point develop into cracks when σ_T exceeds local cohesive strength of the grain lithology (Reference Brzesowsky,Brzesowsky, 1995). Failure of the grain occurs when the stress intensity factor, K_I, exceeds fracture toughness K_IC, as determined by the initial flaw dimension C_f (Equation (3)):

(e.g. constant a = 1.12 for quartz).

In general, fracturing of grains depends on critical stress balances governed by elastic moduli and surface characteristics of the grain material, and is inversely related to the porosity of the sediment, which determines an inflection point beyond which the process of grain fracturing is accelerated (Reference Zhang,, Wong and Davis,Zhang and others, 1990).

Sample selections

The samples described in this paper were collected at Wijnjewoude, The Netherlands, and Kronsberg, Germany. It has been established (Reference Rappol,, Haldorsen,, Jørgensen,, van der Meer and Steltenberg.Rappol and others, 1989; Reference Höfle,Höfle, 1983) that the thin sections come from Pleistocene diamictons of subglacial origin. Reference Solheim,Solheim (1991) illustrated that cores sampled from the northern Barents Sea (Bråsvellbreen, Svalbard), here referred to as samples from “tide-water” settings, are in fact Holocene diamictons affected by a glacier surge.

For the purpose of this study, information regarding the large-scale characteristics of the respective settings was used to relate observed micromorphological structures to deformation caused by over-riding ice and to rule out other sources of deformation.

Procedures

The samples were impregnated with unsaturated polyester resin and subsequently prepared into thin sections according to techniques described by Reference Murphy,Murphy (1986) and Reference Van der Meer, and Menzies,van der Meer (1996). Observations comprise qualitative analyses using optical transmission microscopy at magnifications ranging from 4 × to 32 ×. The terminology used to describe the observed features is consistent with pedologiecl nomenclature suggested by Reference Brewer,Brewer (1976).

Deformation styles

It is argued that the arrangement is a primary feature and that the location of the voids has been governed by subglacial processes. The structure originates in the lower regions of the deforming layer, towards the transition between the A and B horizons, where discrete shearing is the dominant type of failure. The development of the structure is depicted in Figure 6.

Initially, the subglacial sediment accommodates exerted ice pressures by compression, a situation in which water is expelled. Brittle failure will occur by displacement along well-developed, horizontal or sub-horizontal planes Fig. 6a).

Most of the applied strain is focused in the prevailing sub-parallel-oriented displacement planes, which may merge and link into continuous networks (Reference Ramsay,Ramsay, 1980). The remaining strain is taken up in intersecting, smaller-scale planes (Reference Menzies,, Shilts, and Menzies.Menzies and Shifts, 1996). The latter shear localization is predetermined by sets of rieclel shears, representing defects which are only of secondary significance, but can be n aced in the thin sections after brecciation of the till Fig. 4a) (Reference Morrow, and Byerlee,Morrow and Byerlee, 1989).

In the top of the profile, the voids delineating the aggregates display a curvilinear character, marking a sub-rounded, circular to ellipsoid aggregation Fig. 4b). It seems that the edges and corners have been susceptible to adaptation of shape. The roundness of the aggregates suggests a rotational movement in a compound packing, which resembles movement as in a bed of marbles (Reference Van der Meer, and Menzies,van der Meer, 1996), a situation corresponding to stage (b) in Figure 6. The gradual transition from angular to rounded aggregates (Figs 3 and 4a, b) reflects a change in strain rates in the deforming layer. The authors suggest that the top section of the profile experienced progressively higher shear stresses, tending towards a more pervasive type of deformation, which eventually resulted in the rotational movement.

The brittle character of the deformation in the material is evidenced by the fact that the interior of the aggregates appears rather undeformed. The deficiency of turbates (circular, rotational structures (Reference Van der Meer,, Rappol, and Semeyn,van der Meer, 1993, fig 24)) and the poor development of internal plasmic fabric, denoting the birefringence of the plasma (optical property of zones with a preferred clay orientation (Reference Brewer,Brewer, 1976); both indicate conditions of low ductility in the deforming sediment.

With progressive, simple shearing additional strain cannot be converted by further compression. At this stage, the rheological response of the material is characterized by dilation (Reference Murray, and Dowdeswell,Murray and Dowdeswel1, 1992). Aggregates are forced to slide and roll over each other, consequently increasing the pore volume. As a result of negative pore pressures, water is again drawn back into the sediment. It should be noted that dilation in this case does involve modification of the till structure Fig. 6c) rather than interaction between individual grains (Reference Boulton,, Dent and Morris,Boulton and others, 1974; Reference Hooke, and Iverson,Hooke and Iverson. 1995).

The dilated structure collapses if strain rates are insufficiently high and a situation similar to stage (d) is created. Higher water contents in the compound maierial are reflected in the intergrown nature of some of the aggregates. The latter observation may also establish that fissilities and dilated regions act as major preferential conduits for melt-water (Reference Van der Meer,, Kujansuu, and Saarnisto,van der Meer, 1987).

Persistent shearing of the sediment will again generate compression (stage (a)). A new deformational cycle is initiated with expulsion of water and a process similar to the one described above will evolve.

Towards fracturing

A high correlation between the location of fractured grains and the void pattern is evident throughout the profile (Figs 3 and 4c - e). It can be established visually that nearly all comminutive action occurs along planes where discrete shear displacement and rotational movement are to be expected. The observed downward decrease in number of fractured grains may well be accounted for by the decreasing deformational “impact” towards the base of the “A horizon”.

It is argued that dilation tends to minimize the process of grain fracturing. An increase in pore volume, which is inherent in the dilation mechanism, results in subglacial melt-water entering the fracture planes, thus reducing the yield strength of the compound material. The process thus reduces effective pressures due to relatively high pore-water pressures. Contact between the aggregates is less frequent and friction as a result of grinding is diminished. Collision of grains, situated at the edges of the pebbles, is less likely to happen and, if it does, the resulting contact stresses are generally insufficient to cause the grains to fracture.

Because of the cyclicity in the rheological response to shear stresses, the fracturing process attains an intermittent character. Fracturing observed in the profile is related to conditions following collapse of dilated structures, which causes the material to stiffen (Reference Alley,Alley, 1989b). The compres¬sion results in an optimum in the fracturing process, because additionally induced shear mobilization is accommodated by a rotational “marble bed” movement of the till aggregates, similar to a cataclastic flow on the scale of individual skeleton grains (Reference Menéndez., Zhu and Wong.Menéndez and others, 1996). Aggregates will re-arrange in a closed-packing configuration until they are stabilized and further movement is inhibited by the normal loading, which accounts for the “lock-up” in a meta-slable equilibrium Fig. 6d).

Fig. 6. Cartoon depicting the rheological response to exerted stresses of a texturally homogeneous, fine-grained till. (a) Shear-zone development in response to application of shear stresses after dissipation of water. The displacement has occured along discrete planes. Strain hardening has permitted some grain fracturing to occur, predominantly along the sub-horizontal planes. (b) Brecciation of the dry till accounts for aggregation and progressive shear initiales “marble bed” movement. Rotation of till aggregates in combination with limited pore space results in high effective pressures and optimum conditions for the fracturing process to occur. (c) Additional strain causes the till to dilate; the sediment is forced to expand, subglacial meltwater enters the voids, thus reducing contact stresses. Hardly any grain fracturiug has taken place. (d) Collapse of the dilated configuration when strain in the material is not sufficiently rapid. Expulsion of pore water “stiffens” the material and the aggregates become blocked in a metastable configuration. The shear stress exerted may trigger another stage of shear displacement and a situation as in (b) may be generated.

Fracturing styles

The comminution of skeleton grains in tills involves both “crushing” and attrition, a process commonly known as abrasion. The type of grain failure that occurs in specific subglacial conditions depends on morphology of the grain and its texture. Experiments have shown that particles smaller than coarse silt are mechanically relatively stable (Reference Haldorsen,Haldorsen, 1981) and that the highest intergranular stresses occur when grains of similar diameters are in contact (Reference Sammis,, King, and Biegel,Sammis and others, 1987).

Another factor governing fracture is whether contact loading occurs diametrically or tangentially. When stresses act diametrically, i.e. when the direction of contact loading coincides with the imaginary line connecting the centres of the grains in contact, failure often involves the type of fracturing described by Reference Brzesowsky,Brzesowsky (1995). Determined by positions of pre-existing zones of weakness (surface flaws), and dependent on compression rates, fractures propagate from the initially plastically deformed contact region, either as divergent cone cracks (Figs 5b and 7a) or as radial, penetrative meridional cracks (Figs 5a and 7b).

Fig. 7. Cartoon, after Reference Brzesowsky,Brzesowsky (1995), theoretically outlining the respective types of grain fracturing. Dashed lines conned “centres” of grains in contact. Arrows represent contact forces; shaded areas represent deformed contact regions. (a) Diametrical loading at low-compression rates. Ring cracks situated at the edge of the contact region pass into divergent cone cracks. (b) Diametrical loading at high compression rates. Radial fractures propagate as meridional cracks. (c) Tangential loading at high angles of incidence. Frictional sliding gives rise to occasional “chipping-off” of flakes from a grain surface. (d) Tangential loading at low angles of incidence. The process of attrition is exemplified by crushing of all or part of the grain.

A further type of fracturing results from shear loading, which induces frictional sliding at the grain-contact surface (Reference Menéndez., Zhu and Wong.Menéndez and others, 1996). This “crushing” into small equidimensional angular elements exemplifies the process of attrition, which is enhanced by tangential loading. The tensile-stress concentration at the trailing end of the sliding-contact region accounts for the crushing of part of the grain (Figs 5c and 7d), or for the “chipping-off” of flakes from the grain surface (Figs 5d and 7c). The mode of fracturing in the case of tangential loading is influenced by the “angle of incidence” of the contact stress with respect to the line connecting the centres of the grains.

Stress conditions

In order to quantify subglacial stress conditions during grain fracturing, the authors have attempted to specify a range of critical effective pressures in which the process may be initiated. Estimates are based on a series of laboratory experiments (Reference Morrow, and Byerlee,Morrow and Byerlee, 1989; Reference Zhang,, Wong and Davis,Zhang and others, 1990; Brzcsowsky, 1995; Reference Menéndez., Zhu and Wong.Menéndez and others, 1996), which involved triaxial compression tests, and investigations of hydrostatic compaction behaviour and micro-mechanical failure οf sediments. Although the thin sections examined in our study consisted of samples of unlithified diamictons, rather than lithified, porous materials as used in some of the tests, the results can be used to give an indication of the stress range involved in fracturing.

It should be noted that, when trying to match the sediment properties of the thin-section samples with the experimental variables, the commonest constituent in the investigated tills is quartz, with an average grain radius of about 0.15 mm. Lithified test materials with the same characteristics and a porosity of around 25% yielded a range of effective pressures of 300 – 380 M Pa for the onset of grain fracturing (Reference Zhang,, Wong and Davis,Zhang and others, 1990). These values were in agreement with predicted theoretical values using the “Hertzian fracture model”, where characteristic quartz values for initial flaw dimensions, fracture toughness, Poisson ratio and elastic modulus were used.

Reference Morrow, and Byerlee,Morrow and Byerlee (1989) and Reference Brzesowsky,Brzesowsky (1995) carried out experiments on unimodal, essentially unlithified, granular sediments and found that fracturing was initiated at significantly lower values of effective pressure (15–75 M Pa). Although test materials used in these experiments are much more realistic, “translations” to field situations remain hypothetical, since it may well be that the specific textures (Reference Sammis,, King, and Biegel,Sammis and others, 1987; Reference Zhang,, Wong and Davis,Zhang and others, 1990), packing configurations (Reference Hooke, and Iverson,Hooke and Iverson, 1995) and even pore-fluid compositions (Reference May,May, 1980; Brzesousky, 1995) account for accelerated kinematics regarding grain-fracture initiation.

Grain-size distributions within strained materials are shown to change with progressive shearing (Reference Iverson,, Hooyer, and Hooke.Iverson and others, 1996), so governing the type of comminution. Initially, grains may form “networks” to support exerted siresses. In this situation, the relatively small number of contacts between the grains of similar size favour “meridional” fracturing. As a result of this process, larger grains are surrounded by smaller ones, so distributing stresses over more contacts and homogenizing the stress fields. Comminution in the newly formed packing configuration predominantly involves attrition as a result of frictional sliding of grains. It has been shown that critical stress values needed to initiate fracturing changes according to grain-size evolution.

The specified range of 15–380 M Pa for onset values is rather wide but this possibly reflects the differences in intrinsic transmission of externally applied forces. It seems plausible that locally developed contact stresses are determined by textural heterogeneity. Furthermore, these local intrinsic stresses are likely to exceed average effective stresses, suggesting that relatively “low” field stresses can initiate the fracturing process.