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Viscous circle

I wonder if Mike Keedwell (letters, Ground Engineering, September) sees evidence of 'viscous behaviour' in the ground in this photo taken in a flight along the Grand Canyon 18 months ago? Below the canyon rim are rocks up to 1,000 million years old, formed when palaegic western North America was often inundated with warm shallow equatorial seas. Deep among these rocks there are ancient desert sands, which show fossil tracks of reptiles earlier than the dinosaurs.

About six million years ago, uplift of North America led to the great event in which this canyon was cut. Rock has tensile strength and it stood with vertical cliffs. Soil formed slopes at an angle of repose. In the desert climate each canyon cliff and scree appears to stand much as it was after the event six million years ago. There has been enough time for creep to level the slopes if that was going to happen. I see no sign of viscous behaviour.

Above the rim the catenary forms of the cross-sections of valleys suggest that the canyon cut through an older landform that was created in a wetter climate. The view is typical of scenes everywhere on the Earth, where mountain and valley landforms seem to change in distinct episodes of uplift, or erosion, or slope failure induced by groundwater flow. The same behaviour is seen on the face of the Moon. Rocks ejected from some planetary impact fallen on ground made up of soil particles from earlier impacts, and have stayed where they fell without significant creep. Rocks dropped into a barrel of viscous bitumen soon sink in; ground behaviour seems more elastic plastic than viscous.

Surely that is why we can learn about the past from inspection of landforms. I think that soil is an aggregate of frictional interlocking particles in which stress relaxation and creep are minor effects, and that ground movement is limited by friction and interlocking. For both Coulomb and Rankine, soil can stand for ever at an angle of repose. For me, a definition of soil 'friction' is that the states of soil in repose at various depths below a drained limiting slope, are critical states with equation q=Mp

Professor Andrew N Schofield

University of Cambridge

Cambridge

Friction factor

The and words are called the angles of shearing resistance because, particularly since the work of Angus Skinner (1969), we know that the coefficient of friction between particles is not the controlling factor. Bowden and Tabor (1945 and 1950) showed that on the microscopic scale apparently smooth surfaces are really very irregular with asperities several microns high. On natural quartz crystals they measured asperities of the order of 100 angstroms high. When two surfaces are put together only the asperities touch and as the normal load increases they are compressed and come more into contact. Shear strains cause plastic flow of the asperities, as Mike Keedwell has implied, but that is only exceeding the yield stress of the teeny asperities. His expression 'contact zone stresses exceed the yield stress of the minerals' made me think of crushing at the points of contact, that used to occur in dumped rockfill, especially when the typical specification called for strong rock from the heart of the quarry (lots carted to waste) passed over sieves to remove all fines (more carted to waste). Dumped rockfill dams suffered large deformations, and it took Terzaghi (1960) to point out that the huge contact forces between these large pieces of rock was causing considerable crushing. Under a given overburden the contact force is proportional to d2, where d represents particle average diameter. The many tonnes in dumped rockfill falls to parts of grammes in silts, causing no contact damage.

Engineers find values of c from the intersection of a failure envelope line with the x axis. Even when it is accepted that the line is curved there is still a reluctance to draw it from the origin. The value attributed to c can have a large effect in the design of slopes for small embankment dams, and there is no doubt that in practical designs c should be taken as zero. But it is deformations that concern us. If they are within acceptable limits, that's fine; if they are excessive it would be called failure. We need more research to develop reliable methods for predicting movements and to look into what really gives soil its strength. Professor Schofield's work is magnificent and his article in August quite fantastic, so we can cross out the c word. Mike Keedwell has a point so we can cross out the word as well. We can concentrate on critical state until we have proven deformation prediction methods.

Arthur Penman, geotechnical engineering consultant

References

Bowden FP and Tabor D (1945). Friction and lubrication. Chem Soc Annual Report, vol XLII, p 20.

Bowden FP and Tabor D (1950). The friction and lubrication of solids. Oxford, Clarendon Press.

Skinner AE (1969). A note on the influence of interparticle friction on the shearing strength of a random assembly of spherical particles. Geotechnique, vol 19, no 1, pp 150-157.

Terzaghi K (1960). Discussion on Salt Springs and Lower Bear River Dams. Trans ASCE vol 125 part 2, pp 139-148.

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