Introduction
Glacier erosion of hard rock is a complex process controlled by material properties interacting at what Reference WeertmanWeertman (1979) termed the bed water-ice interface. Bedrock properties determine exclusively the first of these components and hydraulic conductivity influences the second. Although many ice-flow problems have been resolved, rock-mass performance under stress beneath and adjacent to glaciers has received little attention, although the extent to which the close control on 91acier erosion exerted by geological structure has been recognized, especially by geomorphologists. Reference RandallRandall (1961), Reference HoltedahlHo1tedahl (1967), and Reference NilsenNilsen (1973) considered that large-scale fractures or joints of Caledonian age determined fjord and other glacially-eroded valley alignment in Norway; Reference TrainerTrainer (1973) described incipient joints opened by ice flow in a wide range of rock from California, Maine, and New York State, and Reference ZumbergeZumberge(1955) demonstrated structurally-aligned glacier scouring around western Lake Superior. In all cases, structural elements involved are clearly of pre-glacial tectonic origin, where as relaxation of overburden-confining stresses was believed by some authors to cause rock fracture immediately preceding or during glaciation, and hence to facilitate “quarrying”, often enhanced by freeze-thaw loosening (Reference JahnsJahns 1943, Reference LewisLewis 1954, Reference Chapman and RiouxChapman and Rioux 1958, Reference Battey and LewisBattey 1960, Reference WhillansWhi11ans 1978). Although the age, formation, and significance of the resultant sheeting structures(supposedly formed irrespective of any existing anisotropy) are sometimes qualified, preoccupation with “pressure release” demonstratesa simplistic and frequently inaccurate view of rock-mass properties and response to stress, as other authors have indicated (Reference HarlandHarland 1957, Reference TwidaleTwidale 1972, Reference Twidale1973, Reference Brunner and ScheideggerBrunner and Scheidegger 1973). Occasionally, absence of serious attention to rock-mass performance under stress has led to many omissions. The “melt-water hypothesis” of cirque erosion (Reference LewisLewis 1938, Reference Lewis1940) is one clear example, where the effect of water pressure on stability is ignored, often despite sub stantial evidence of its abundant presence in rock mass; another is the notable avoidance of suggested failure mechanisms in studies which otherwise demonstrate intimate structural control over erosion (Reference HaynesHaynes 1968, Reference Sugden, Waters and BrownSugden 1974).
Bedrock performance has been examined in more detail recently. Reference Broster, Oreimanis and WhiteBroster and others (1979) give qualified support to the fracture of in tactrock by glacier ice; this is questioned later in this paper. Although primarily not investigating nor modelling rock properties, Reference Morland and BoultonMorland and Boulton (1975), Reference Morland and MorrisMorland and Morris (1977), and Reference BoultonBoulton (1979) consider that a jointed bed rock model responding to basal ice shear would be more appropriate. up to now, studies of bed rock response to specific stress conditions induced by glacier ice lack an understanding of the principles of rock mechanics and resulting failure mechanisms. Those principles considered by the present author to be important win now be outlined.
Principal geomechanical rock-mass properties
A major problem in assessing the erodibility of rock stems from the gross inequality between the internal shear strength of rock and glacier ice; this, is partially resolved for abrasion by regarding the glacier sole as an ice-rock-debris mix, but large-scale block removal or “ quarrying” is not so effectively explained.
Intact rock-mass strength (IRMS)
The failure criteria for rock is usually defined by a simple linear Mohr-Coulomb equation (Fig. l):
where τ and σ are shear and normal stresses, respectively, c is the value for internal cohesion, and ϕ is the angle of friction along the eventual failure plane (Reference HoekHoek 1970). A distinction is made betweenpeak shear strength, beyond which the rock deforms, and the residual shear strength of the deformed mass. These may be similar for soft rock, whereas residual strength may be as little as half the peak strength for hard igneous rock (Reference Hoek and BrayHoek and Bray 1974). Typical intact rock shear strengths and other properties are shown in Table I.
Fig. 1. Linear Mohr-Coulomb relationships between shear stress and normal stress for intact rock mass (IRM); the progressive reduction in required shear stress is shown for dry discontinuous rock mass (DRMd) where C = 0, and wetted discontinuous rock mass (DRMw), where a given friction angle ϕ is reduced to an effective friction angle ϕ r.
Table 1 Some typical rock-mass properties (after Reference Hoek and BrayHoek and Bray (1974), Reference KulhawyKulhawy (1975), among others)
Discontinuous rock-mass strength (DRMS)
Intact strength offers little scope for low-magnitude shear stress, of the order of 0.lMN m-2 (Reference WeertmanWeertman 1979), at the glacier sole, and a substantial reduction in strength is required to permit large-scale erosion. Discontinuities Footnote * render rock mechanically and hydraulically defective to an extent where this is possible, by altering stress relationships in the rock mass and providing release planes requiring much lower disturbing forces (Reference Hoek and BrayHoek and Bray 1974). IRMS values become less meaningful in discontinuous rock and are replaced by DRMS.
The principal modification to the Mohr-Coulomb criterion lies initially in lower values for the parameters of cohesion c, and friction angle ϕ, and a comparison of typical values is made in Table I. The cohesion is now solely that of the discontinuity plane and is effectively zero, except in the presence of fill. How ever, the failure criteria are for dry rock and a further significant modification afforded by discontinuous rock mass (DRM) is high secondary permeability (Reference Witherspoon and GaleWitherspoon and Gale 1977). A swell as contributing to shear stress, water reduces normal stress σ to effective normal stress ση̃ by a value u (Reference Hoek and BrayHoek and Bray 1974), and for practical purposes the modified Mohr-Coulomb equation may be written as
or, in a simplified form, as
where ϕr is the effective friction angle. Roughness increases the friction angleϕ by an amountϕ f, and the plane possesses, more correctly, bi-linear shear strength, which assumes the lower (residual) value upon shearing of asperities (Reference Witherspoon and GaleWither spoon and Gale 1977).
In practice, all rock mass possesses internal fractures which normally demonstrate a strongly preferred geometry, determined by geological(principally tectonic)history (Reference BartonAttewell and Farmer 1976). Marked planar anisotropy renders DRM liable to simple failure in a coaxial stress field and to complex failure, involving multiple planes, elsewhere. Compound failure along discontinuities and cracks propagated across rock bridges was reported in laboratory tests (Reference BrownBrown 1970). Brown also suggested that discontinuous rock-mass failure (DRMF) only shears through intact rock and ignores discontinuities under very high confining pressures (1400 MN m-2), thus tending to confirm that glacier ice can only “ quarry” DRM and that failure of supposedly intact isotropic rock (Reference Broster, Oreimanis and WhiteBroster and others 1979) may be in error, overlooking pre-existing anistropy (Reference HoekHoek 1964).
Conditions of DRM stability and failure
Practical application of the modified failure criterion permits assessment of stability under gravitational and dynamic loading. Design in engineered slopes is particularly concerned discontinuity geometry (Reference HoekHoek 1973), (ii)individual block size and shape, and (iii)cohesion of any infilling material. Calculation of stability or predicted failure mode is then relatively straightforward. From the Mohr-Coulomb criterion, resistance to gravitational sliding is defined (after Reference Hoek and BrayHoek and Bray 1974) as
where A is the block/slope contact area, W is the block weight and ψd is the discontinuity angle. If shearing and resisting forces are exactly balanced, the block is said to be in limiting equilibrium for dry slopes when
and for wet slopes when
where V is the additional loading due to the weight of water behind the block, and u is the reduction of normal stress due to uplifting pressure of water under the block.
Failure modes
Probable failure modes on unstable slope scan be determined from the relationship between the excavated slope and discontinuity geometry. Three of four principal failure mechanisms recognized in slope engineering are considered here (Fig. 2). (Circular failure is disregarded for DRM with well-defined discontinuities.)
Fig. 2. Failure modes and their related discontinuity stereonet (equatorial equal-area lower hemisphere projection).
Plane failure (of single or multiple slabs)occurs when
and wedge failure occurs when
where ψs and ψd are the slope and discontinuity angles and ψi is the angle of the slope of intersection of two planes defining a wedge. (The excavated slope must permit the potential failure planes to “daylight”.) Failure, particularly in the case of planar slides, requires the presence of other release surfaces provided by other discontinuities.
Toppling failure occurs when the primary plane D1 dips into the slope and is apparently stable, but also when a secondary stable plane D2 is so spaced as to define a block whose centre of gravity overhangs a pivot point (Reference Freitas and Wattersde Freitas and Watters 1973).
It is emphasized that, although actual slope stability may be complex, practical application of theoretical analysis is generally successful (Reference HoekHoek 1973). Also, whilst its primary application is for gravitational loading, an extension of principles to dynamic glacier loading may be appropriate and theoretical modifications to stress relationships induced by glacier ice are now proposed.
Stress modifications by glacier ice
A glacier must activate inherent rock-mass instability for erosion to occur (Reference TerzaghiTerzaghi 1962); this investigation restricts itself to suggested de-stabilizing processes and not to the necessary resultant entrainment or incorporation with the glacier. Two quite different domains are recognized; (i) rock mass confined by ice and under dynamic load, and (ii) rock mass unconfined and primarily loaded by gravity.
Rock mass confined by ice
This is the more difficult to analyse because of the relative inaccessibility of the ice-rock contact, and also because DRM is inherently stable in its primary valley-floor position. Equations (7) and (8) do not apply, and discontinuity-stress relationships show
Although gravitational load does not meet limiting equilibrium requirements, two factors increase shear stress. First, ice flow generates a low-magnitude shear stress of about 0.1 MN m-2 (Reference WeertmanWeertman 1979) enhanced for an ice-rock mix. Second, melt water at the ice-rock mass contact penetrates discontinuities, contributing a force V and reducing normal stress by a value u (Equation 6). However, it is recognized that a complex feedback relationship exists here, where by secondary penne ability afforded by DRM may alter critically the basal pressure-melting balance. Two further qualifications are made to this domain. Once begun, block removal permitting low-angled planes to “ daylight”, and also removing the restraining presence of the block, may reduce sliding resistance sufficiently under dynamic load, where ψd, j< ϕ. More significantly, the primary sub glacial loading mode assumes alow-angled bedrock floor; in practice this is probably unnecessarily conservative, since steep slopes occur frequently beneath ice for short distances, and DRMF may approach more closely that of the unconfined domain discussed below.
Rock mass unconfined by ice
Glacier erosion in this domain is in two parts: (i) an initial amount of vertical or horizontal excavation in the confined domain, cutting the slope beyond the limiting equilibrium, followed by (ii) unconfined DRMF of a mode determined by slope-discontinuity geometries. Equations (7) or (8) must apply. The amount of confined excavation need not be large, as will be shown later. Progressive failure in one mode may destabilize other blocks unmoved by initial disturbance, and very large volumes ofrock mass may be involved in such compound translation failures; this is also shown infield examples presented later.
Water derived from ice-melt and also precipitation beyond the glacier margin assumes a considerable significance in destabilizing unconfined rock. Reference BartonBarton (1973) states that water may reduce the friction angleϕ by as much as 30°, and therefore the presence of water throughout the back-wall zone of cirque glaciers must be considered to make a major contribution to DRMF without recourse to freeze-thaw mechanisms.
Again, further qualifications may be made with respect to the destabilizing mechanism. (i) Unconfined failure can only apply to glaciers confined within bedrock channels, limiting the mechanism almost entirely to valley and cirque glaciers, and thus accounting in part for their significantly greater erosive power. (ii) Once initiated, progressive failure is controlled primarily by the DRM geometry; unlike engineering applications, where the required slope and discontinuity geometries mayor may not coincide favourably, it is suggested that glacier erosion will always show close conformation. Principal applied stress will seek out the most closely related potential failure planes, and hence structure controls glacier erosion.
Geo mechanical principles, modified for the glacier environment, are now investigated for application to glacier-eroded rock mass in Snowdonia, North Wales, after reviewing the general structural geology of the region.
Structural geology of snowdonia, north wales
Clastic marine sediments, progresssively interstratified with ignimbrites and later intruded by dolerites, rhyolites, and microgranites, form almost all of the 1200 k m2 study area, and represent a complex Lower Palaeozoic (late Cambrian to late Ordovician) synclinal accumulation whose axis forms the mountain core above 1000 m.
The pile was subjected to pronounced polyphase deformation of Caledonian tectonic origin(late Silurian-early Devonian (Reference ShackletonShackleton 1954)), and four distinct structural components are recognized, represented by four fold axes (F1-4) and associated syngenetic axial-planar cleavage (S1-4) (Reference Helm, Roberts and SimpsonHelm and others 1963, Reference LynasLynas 1970). The regional structure is dominated by F2, S2, with their typical Caledonoid NNE-SSW strike, mainly dipping steeply north-west.
A primary fracture geometry of steep vertical discontinuities, which confirms the Caledonoid tectonic stress field, has been described (Reference AddisonAddison, unpublished). Over 2900 km of principal fractures were recorded. The systematic regional (“ master”) fracture pattern(Fig. 3) corresponds to expected tectonic configuration (Reference BadgleyBadgley 1965, Reference Fookes and WilsonFookes and Wilson 1966, Reference PricePrice 1966, Reference Causay Causay 1977); in the field, the three-dimensional discontinuity geometry measured in bedrock outcrops replicates the established regional pattern, and continues within rock slabs with close facsimile planar anistropy. Strengthand spacing depend on lithology at the smaller scales, but otherwise the fracture network disregards lithological boundaries.
Previous research on glacier erosion in Snowdonia concentrated on the significance of the orientation and elevation of nearly 50 cirques in reconstructing Pleistocene glacio-climatology (Reference SeddonSeddon 1957, Reference UnwinUnwin, unpublished), and, whilst distribution conforms to a north-west European pattern, it also corresponds intimately to the fracture geometry (Reference AddisonAddison 1977). Moreover, arecently reconstructed Pleistocene “Merioneth ” ice cap, centred to the south-east of Snowdonia(Reference AddisonAddison, unpublished, Reference FosterFoster unpublished, Rowlands, unpublished), was shown to have been the source of radial outlet glaciers which breached the mountain axis with transfluent troughs up to 600 m deep. As with the cirques, they too show a marked conformity to the regional fracture geometry (Fig. 4). In both cases, structurally controlled DRMF beneath and adjacent to the glacier bed is believed to have been the principal mechanism of excavation.
Fig. 3. Frequency orientation diagrams of regional fracture systems for each of the six mountain groups of Snowdonia, mapped from stereo graphic air photograph cover. Circular scale shows 5 k m. Inset outline shows location of Figure 4.
Fig. 4. Primary fractures in the Snowdon (SW) and Glyder (NE) groups and principal glacier-eroded cirques and troughs. Fractures are shown by broken lines, cliffs by toothed shading, and lakes by stippling.
Field evidence of glacier-induced discontinuousrock-mass failure
A combination of inferred and calculated conditions identifies failure in a previously glaciated environment. The difficulties of observing rock-mass failure and erosion around existing glaciers, especially under the ice, justify the study of failure at previously glaciated sites (where a comprehensive survey of the fracture systems is possible), provided that the evidence for a glacial origin of failure is convincing. Location and mode of failure is easily recognized by residual rock-wall elements representing the release surfaces, block debris where present, and visual comparisons of the slope and discontinuity geometries (Reference Freitas and Wattersde Freit as and Watters 1973, Reference AddisonAddison, unpublished, Reference CausayCausay and Farrar, in preparationFootnote * ). Detailed confirmation may be calculated from measurement of the discontinuity geometry (Reference Silveira, Rodrigues, Grossmann and MendesSilveira and others 1966, Reference Young and FowellYoung and Fowell 1978) with typical values of geo mechanical properties, or specific values obtained from in situ and laboratory tests, and expressed as a factor of safety F where F =1 represents limiting equilibrium (Reference HoekHoek 1970, Reference Hoek1973).
Aglacial origin for DRMF is inferred from the glacial history of the site, contemporary stability in the absence of glacier-related disturbing forces, and, in particular, absence of the failed mass at the toe of the slope. Site examples from Snowdonia are now presented.
Confined failure
Slope-failure criteria do not apply so readily here as stated earlier. At the three chosen sites, DRMF was compound, being induced dynamically in otherwise stable rock mass by basal shear, and then, once block separation began, local small-scale slab, wedge, and toppling failures occurred along destabilized discontinuities.
(i) Cwm Stwlan
Excavation for the upper dam foundations of the Ffestiniog pumped-storage hydro-electric scheme, constructed on the bedrock threshold of a glacial cirque, revealed considerably disturbed, hard, un weathered rhyolite dislocated along pre existing discontinuities to a depth of 13 m across a front 150 m wide, which necessitated design modifications. Reference AndersonAnderson (1969:193) considered the dislocation to have been caused by glacier drag across the threshold: “ ... facilitated by the presence of five faults in the part most affected and by joints almost at right angles to the rock-lip ... The affected zone does not tail off but ends abruptly on both sides. The limits may be partly related to the faults. but they may also mark the width within which the glacier was thick enough to exert drag ”.
(ii) Ogwen
Bedrock floor in a major glacier-breached watershed is shown in Figure 5. Ice flowing from left to right first abraded the rock, followed by “ quarrying” (displaced blocks show striation son one surface only) which removed some blocks altogether and displaced others; there after, gravitationally loaded secondary failure further dislocated the rock mass, at least in part sub-glacially since many blocks are missing. Failure surfaces were entirely controlled by the discontinuity geometry, and primary and modified confined failure is indicated by the displacement of debris down-glacier and down-slope.
Fig. 5 Ogwen valley floor. Sub-glacier confined DRMF, with secondary failure evident in excavated sections. Slab failure occurred along two planar sets (a, b) and toppling failure away from (c).
(iii)Nant Peris
Figure 6 shows an example of toppling failure towards the valley floor generated by the removal of adjacent rock mass under glacier confinement close to the valley floor. Cliff elements such as these are common, with at least the greater part of the failed rock mass absent from the toe; by comparison, the few remaining instable blocks which have recently toppled from the now unconfined face are all present at the toe, and exhibit less-weathered contact planes.
Fig. 6 Toppling failure in Nant Peris; destabilization caused the parting of blocks along arrowed discontinuities.
Unconfined failure
CWm Graianog
This cirque basin affords one of the finestsite concentrations of all modes of rock-massfailure in Snowdonia. It is excavated inFfestiniog grit, and failure modes are discussedwith reference to a standard structural presentation (Reference Hoek and BrayHoek and Bray 1974) shown in Figure 7.
Fig. 7. Bedrock map and discontinuity stereonet for Cwm Graianog.
The north sidewall consists almost entirely of a spectacular series of D1 surfaces (Fig.8) and the slope angle is effectively the same as the discontinuity dip of 38-40° to the south-east. Slab failure down D1 was released along D2, which frequently possesses an injected quartz fill, and D3 and the vertical extent of individual slabs is limited by D4 with the same strike, but opposite dip, as D1. slab towards the western end of the basin may have failed to the full height of the rock wall(200 m) and across a width averaging 60 m. The remaining rock wall is clean, being devoid of residual blocks, overhanging elements below which rock mass have been released, and stable laterally confining units. With a principal D1 spacing of 3 01, this would have yielded a single failure of 36 000 m3 of the side wall, all of which was removed by the glacier. D1 planes in the wall at this point are marked uniquely by large-scale bedding-plane ripples (Fig. 9), and the only debris blocks so marked are found several hundred metres away in, and resting upon, cirque moraines in positions where they could have been deposited only by glacier ice.
Fig. 8. Cwm Graianog (Ffestiniog grit). North side wall (right) with D1 planar surfaces; head wall (1eft) with D1- D2 wedging and D2 planar surfaces.
Fig. 9. Cwm Graianog. Single D1 major planar slide release surface, (showing ripple marks).
The irregular strength and spacing of D5 renders it less apparent as a control, but D2 and D4 become more important as the back wall is approached. The “curved” transition is effected by D1- D2 wedge failure (ψi=39°, orientated at 130°) producing a series of buttresses, and the extent to which the geometry predetermined failure on excavated slopes is completed by the superimposition of topp1ing failure released from D1 and low-angled D4 (itself below tile assumed friction angle) on more complex slab and wedge failure in the south wall. A rapid assessment of current stability (after Reference HoekHoek 1970) suggests that D1 has a factor of safety F≥ 1 for typical assumed mechanical values, which has two important implications. (i) Excavation at the toe would rapidly cause D1 to “ daylight” and generate further slab failure; this is considered to be typical of the effect of glacier erosion. (ii) Other modifications to Mohr-Coulomb parameters would result in failure; locally small contemporary slides are evident, considered to be the smoothing effect of weathering on rough nesses along the D1 planes.
There is a dramatic decline in side-wall height at the Ll an virn slates-granophyre contact; it is suggested that the lower ORMS of slates permitted greater excavation of the side wall, and it is further noted here and elsewhere that cleavage planes do not appear to have provided significant failure surfaces during glacier erosion.
Conclusion
Geo mechanical rock-mass' properties have been neglected in examining processes of glacier erosion, and it is proposed that alteration of stress relationships in discontinuous rock mass directly or indirectly by glacier ice provides a realistic principal mechanism for the study of bedrock excavation by glaciers. Theoretical failure criteria applied to specific rock-mass properties are sustained by field evidence, and support the following conclusions.
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Failure of rock slabs occurs along pre existing discontinuities, and the relative disposition and strength of the discontinuity geometry provides an exclusive framework for excavation and is manifest in structurally controlled erosional landforms at all scales.
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Failure in confined rock is due primarily to the dynamic loading potential of the conditions at the ice-rock mass contact, and in unconfined rock to the activation of gravitational loading on otherwise stable slopes.
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ORMF re-defines in more appropriate mechanical terms conditions which in certain circumstances have been identified as erosion processes involving “ pressure release” and “ melt-water sapping”. It is contended that many quoted instances of pressure release in fact describe parallel slope facets determined by pre-existing discontinuity geometry, where forms of glacial erosion have been controlled by structure rather than vice versa.
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Stress conditions in discontinuous rock mass can be incorporated usefully into theoretical and practical examination of ice flow patterns and behaviour at the rock-ice interface.
Acknowledgements
The author wishes to thank M.V. Barr, British Petroleum Research Centre, Sunbury, for commenting on the draft; Peter Masters and Jack Landon, School of Geography, University of Oxford, for photographic work; Brenda Cartwright, The Polytechnic, Wolverhampton, for typing the manuscript; and The Polytechnic, Wolverhampton, for financial support in presenting the paper.
