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
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.
The editor welcomes letters at 151 Rosebery Avenue, London EC1R 4GB; UK fax: +44(0)171 505 6790