I propose two questions for discussion in the pages of Géotechnique as follows.
The soil property called cohesion is given a different meaning on either side of critical states (CS). Schofield (2005) explains how Hvorslev, a Danish research engineer in Terzaghi's Vienna laboratory, tested drained specimens of Danish Little Belt clay and of Viennese clay on the ‘dry’ side of C S in a shear box. His seminal study in 1937 interpreted the peak strength data (for specimens with the same water content at failure) as the sum of ‘true’ cohesion c and 'true' friction on the line BC (Fig. 1(a)). Terzaghi and Hvorslev extended this interpretation to the right without limit in Fig. 1(a), but their actual peak strength data went only to the CS point C on line BC in Fig. 2. They thought the cause of true cohesion to be the close approach of clay mineral grains with surface chemistry, and did not realise that apparent cohesion could result from a change of volume as water content changes. On the ‘dry’ side of CS, slip−surface deformation is localised in a thin layer of gouge material that dilates in shearing and becomes a slick paste with high water content that is hard to measure with accuracy. Actual slip surface failures are unstable, with a peak strength that is higher (and less safe) than the ultimate C S frictional strength.
When Taylor (1948) tested dry sand at the Massachusetts Institute of Technology he found that shear distortion, de, of a dense aggregate of soil grains could cause a volume increment, dv, of the soil. He gave the name 'interlocking' to the rate of dilation (dv/dε). He calculated the peak load on his shear box test specimens on the 'dry' side of CS by adding an interlocking work increment (p′dv) to the work dissipated by internal friction in shear distortion of soil (Fig. 1(b)). His shear stress rose to a peak and fell back to a constant CS value through continuing drained shearing. In Fig. 2 this is shown by dashed arrows that rise up to the line BC of peak strengths and fall back to the CS line AC. As effective pressure rose on the ‘dry’ side of C, Taylor's (dv/dε) interlocking fell. It became zero at C, after which the aggregate on the ‘wet’ side of CS became contractive and the difference between a yield point on the curve CD and ultimate C S friction is provided by work done by effective stress during contraction. On the dry side of CS, the disruption of the interlocked aggregate is localised in a small volume of gouge material. On the wet side of CS the effective pressure on the contractive aggregate delivers a flow of work that provides part of the frictional work needed in extensive shear deformation of the aggregate of grains. The yield points on the undrained test path CD lie below the CS stress points on the extension of line AC. The work done on the contractive aggregate by the effective pressure assists yielding of the aggregate in a ductile plastic mechanism, dissipating energy in a stable manner.
The path of an undrained test in Fig. 2 will follow curve DC with rising pore water pressures and falling effective pressure σ' as the test approaches the CS. In CS soil mechanics (Schofield and Wroth, 1968) the ultimate shear strength su in Fig. 2 is the soil property often called cohesion on the wet side of CS. It is the constant strength of soil paste at C flowing in undrained plastic deformation, with work being dissipated by CS internal friction and not by cohesive or adhesive bonds between disturbed soil grains. In contrast, in a drained test at constant σ' on the wet side of C S the soil yields at a point on CD and then strength increases until it reaches a CS frictional value on the extension of line AC. If there were true cohesion on the dry side there would be the same cohesion on the wet side as shown in Fig. 1(a). In CS theory the soil properties of a fine-grained soil depend on interlocking of a compacted fine grain aggregate and not on surface chemistry of bonds between clay grains (Schofield, 2005).
Tests of soil behaviour on the ‘wet’ side of CS are made with much better control of ultimate water content than on the ‘dry’ side. The original Cam-clay model on the ‘wet’ side was generated using Taylor's calculation for dissipation of work in stable yielding. It predicted the points on the curve CD as soil paste yielded and hardened in an undrained test path. This model (based only on the sum of friction and interlocking) made novel but correct predictions of soil behaviour (including the form of the curve CD). Schofield (2005) concluded that Coulomb was correct to state in his original work that disturbed soil has no cohesion at all, and that proposition (a)(ii) above is right and (a)(i) is wrong.
This leads to the second question for discussion. Plastic design requires one to ensure (by choice of construction materials and construction methods) that work done by loads that cause plastic flow is dissipated in failure mechanisms. The total work dissipated in the deforming soil when a CS is reached will approximate to the total displacement multiplied by the CS ultimate load. Interlocking work is not automatically dissipated; it can be stored or transmitted from a region of interlocking to some other part of a structure, as can be seen when joints in masonry open and close. So, strength due to interlocking on the dry side of CS cannot be included in plastic design calculations. The failures on the dry and wet side of the CS are very different, but in both cases dissipation is frictional so plasticity calculations may only use the C S frictional strength.
CS concepts provide clear answers to these questions. Schofield (2005) explains that Hvorslev's data of disturbed soil behavior did not show Terzaghi's ‘true’ cohesion and friction (his soil had CS internal friction and no cohesion), and that Rankine taught his students that ‘friction is the only force that can be relied upon to produce permanent stability’. Coulomb's design practice of using CS friction and zero cohesion in limiting equilibrium design methods with a safety factor of 1·25 is safe over all regions of soil behaviour (Fig. 2), and not over-conservative. In contrast, Fig. 2 shows that an analysis in terms of the cohesion and friction of Fig. 1(a) is risky in the region of B where peak strength is relied upon and the soil is brittle and liable to crack.
