This note was published in Geotechnical News Vol 17 No 4 December 1999.
A note on Taylor's interlocking and Terzaghi’s "true cohesion" error.
Andrew N. Schofield, Cambridge University Engineering Department.
A section in the new biography of Terzaghi (Goodman 1999 page 212) explains that, directly after publication of Terzaghi "Theoretical Soil Mechanics" (1943), Terzaghi and Peck began to write a new book as an "Introduction" to it. On page 213 Goodman reports that the writers were frustrated by the "unfinished state of soil mechanics" and that progress with this book was delayed. The process of rewrite, review, and alteration dragged on year after year until 1946, when a very different book, Terzaghi and Peck (1948), neared completion. At that stage ‘The authors, now mutually trusting and united, ganged up on what they perceived as an increasingly theoretical and esoteric portrayal of soils in university education, as depicted in Ralph Peck’s review of the book manuscript from Professor Donald Taylor of MIT "Blind application of theory can directly lead to disaster" he wrote: "this is the idea which nearly ruined soil mechanics and against which the best efforts of Terzaghi and a few others have only recently been able to make headway."’
All three textbooks proved useful. For example, in Cambridge University, Roscoe’s lectures to 3rd year undergraduates in 1950 were based on Terzaghi (1943). In 1954 Roscoe’s research students studied Taylor (1948), as well as the internationally recognised work of Terzaghi’s research student Hvorslev (1937). In 1958 I introduced a 2nd year course on soil mechanics based on Terzaghi and Peck (1948). All our undergraduate soil mechanics teaching followed Terzaghi closely, but the great influences on our research were Hvorslev’s thesis and Taylor’s work on interlocking. They led directly to "Critical State Soil Mechanics", Schofield and Wroth (1968).
When the Concise Oxford Dictionary applies "esoteric" to philosophical doctrines etc. it means "only for the initiated", and critical state theories are esoteric in the sense that many geotechnical engineers were initiated into these theories after graduation. However, only a few initiates in North America will have read about Terzaghi’s "true cohesion" error in the August 1998 issue of "Ground Engineering", Schofield (1998), and this note aims to link that issue to a section of Goodman’s book between pp 63-83. Terzaghi's book Erdbaumechanik, about his system of effectively stressed soil mechanics, was based on his own research work from 1917 to 1923 while he was a university lecturer. He published Theoretical Soil Mechanics 20 years later after much experience of successful application of his system in practice. Both these books contained an error that he had made and needed to detect, and his chance came with a new insight on interlocking in a new book by Taylor, one of the next generation of young lecturers who in their turn undertook research on their own as university lecturers. Taylor’s qualities led Terzaghi to select him to become Secretary General for the ISSMFE Conference in Zurich, but Taylor died of cancer and his chance to correct Terzaghi’s error was gone. Taylor did not live to continue work in the MIT laboratory and the error eluded "the observational method" in the field.
Terzaghi’s error can be explained as follows. Figure 14.2 in Taylor’s book shows data of shear box tests of dense sand during shear. Interlocking causes dense sand to dilate in the initial strain increments. Taylor calculates (pp 346, 347) the rate at which work must be done to increase soil volume at peak shear strength of sand. He shows that the peak is due to addition of an interlocking strength component to the shearing friction component. Taylor did not question the Mohr Coulomb equation, but the idea he proposed for sand also applies to the clay tested by Hvorslev. When Terzaghi and Hvorslev plotted their peak strength data to give a straight line and interpreted the values of the slope and intercept of this line as "true" friction and cohesion components they had no interlocking component of peak strength. Terzaghi’s error in adopting the Mohr Coulomb equation and in proposing that soils have ‘true cohesion’ was to ignore the effects of interlocking that are clearly observed in the field and in the laboratory.
Over consolidation of clay soil forms a dense interlocked aggregate of fine soil grains. Dilation of this aggregate is unstable and is localised in loosened and softened "gouge" material on thin planes of progressive failure. Dilation during distortion of the aggregate of grains requires increase of water content and of volume in gouge material. A volume increase requires work to push back external pressures. The shear box test gave no data of the rate of dilation on the slip planes at the time of failure. Terzaghi and Hvorslev thought of only two components of peak strength of clay; cohesion and friction. They and Taylor knew that gouge material in stiff over consolidated clay becomes "slick" as water is sucked in to it, but they did not appreciate that it is the work done to suck water slowly into that slick soil paste that also causes the peak strength. Stiff clay and dense sand are both dense aggregates of soil grains, deriving strength from mechanical interlock. This strength involves the strain factor that Terzaghi knew must be introduced in earth pressure calculations. He discussed it in the 1936 ISSMFE conference but did not see that interlocking must be present whenever softening and water content increase are observed in the field. Interlocking strength components can be present in undisturbed soil, acting in addition to any strength components due to cementing, ageing and creep.
If any idea "nearly ruined soil mechanics" it is Mohr’s idea of circles of stress at rupture having an envelope that can be defined by a function of stress, unrelated to strain. In 1936 Terzaghi called this Mohr’s "hypothesis"; he saw that it involved a bold approximation, but did not see why it is untrue. If plane failure of soil could be defined by any function of the three components of plane stress then that function plus the two equations of equilibrium would form a hyperbolic system of three equations in three unknown stress components. For given stress boundary conditions the solution is a plane limiting stress field independent of strains. He observed earth pressures that depended on strain, but what was the error in the system of equations? It had to be an error in Mohr’s hypothesis. It is not a simple matter of a curved envelope rather than the straight line Mohr Coulomb equation. The rupture of dense soil is an instability phenomenon, like buckling, that depends on strain boundary conditions. There is no unique envelope to Mohr’s circles. A failure criterion can not be defined in stress space.
Rather than introduce an apparent cohesion of soil that is itself a function of strain, it is better to characterise peak strength as the sum of the critical state angle of repose plus a dilation angle; this interlocking strain rate depends on effective pressure and relative density. On the dry side of critical states the dilation angle is positive. The opposite effect is observed if the soil is initially on the wet side of critical states. Roscoe, Schofield, and Wroth (1958) used test paths to critical states to explain water content changes in drained triaxial tests and pore-pressure changes in undrained tests. The rate at which work is done in general triaxial tests was analysed by Roscoe, Schofield and Thurairajah (1963). Volumes tend to decrease as loose soil yields. There are rates at which external effective pressure does work in volume reduction, and rates of change of elastic energy stored in the aggregate of grains, and rates at which work is input in shear distortion. Together these must equal the rate at which work is dissipated in critical state friction in shear distortion under the mean effective pressure. This analysis was the basis of a stable yield function (Roscoe and Schofield 1963) for an ideal fine-grained soil at first called wet clay and later called Cam clay (Schofield and Togrol 1966). Schofield and Wroth (1968) wrote a textbook on this body of knowledge, and taught that the strength of soil on a drained or an undrained path at and near critical states is simple. In the first case the strength is defined by a drained friction anglejd based on the critical state friction coefficient M. In the second case the rapid undrained shear strength of soil is cu=Mp˘ where p˘ is the constant critical state effective pressure for that soil at the constant water content at which undrained shearing takes place.
Modelling clay is used in experiments of classical plasticity. Plastic limiting stress equations are valid for un-drained large strain plastic flow of soil in critical states. However there is a difference between metal and soft soil. In a ductile metal, as atoms slip past each other, they are held together by shared bonding electrons. In disturbed saturated fine-grained soil the effective stress holds fine grains together. Disturbed clay strength does not derive from clay grains adhering to each other with chemical bonds. All effects caused by clay mineral and pore fluid chemistry are seen in the pore pressure. In the absence of external total stress (for example in the fall cone test) the pore water suction is equal to the mean normal effective stress in the soil. Un-drained cohesion cu in ductile plastic soil is the product of critical state friction and this effective stress. No grain to grain adhesion is present in newly disturbed clay. In addition to this simple interpretation of large strain flow of soil, critical state soil mechanics interpreted triaxial test data of stable yielding and hardening by the Cam clay model, which has interlocking and friction but no cohesive strength component. The good fit of the Cam clay prediction to newly disturbed clay test data on the wet side of critical states confirms the assumed lack of cohesion. Cohesive bonds can form in soil only after a period of ageing and creep, and observations in undisturbed soils with unknown creep histories in the field are hard to interpret. Bonds are destroyed by disturbance, so geotechnical centrifuge tests use models made of disturbed soil and their interpretation avoids the problems of undisturbed soil.
The idea that newly disturbed soil has no cohesion is not new. Coulomb’s (1773) paper quoted the idea of Musschenbroek (1729) that for construction materials, tensile strength (adhesion) is about equal to shear strength (cohesion). Coulomb reports tension and shear tests on two square inch cross section specimens of limestone. The tensile failure load was 430 lbs. and the shear failure load was 440 lbs. These, and other tests on brick and wood, confirmed Musschenbroek’s idea. Hence for Coulomb, if adhesion is known to be small or negligible for some material, then the cohesion of that material must also be taken to be zero. For Coulomb the fracture of intact bodies of undisturbed soil and rock does involve both friction and cohesion; the flow of ground that has been broken up and is newly disturbed does not involve cohesion. Placing of fill behind a wall involves breaking up ground with picks, shovelling soil or broken rock into barrows, wheeling it to the site, and tipping it behind the wall. Coulomb states three times in his design calculations for such fill that there is no adhesion in newly disturbed soil.
For Coulomb and for Rankine (1874), the difference between soft rock and soil is that rock stands up with a vertical face while soil "tends to assume an uniform slope". For Rankine some shear strength in soil arises from temporary adhesion between grains, which "is useful in the execution of earthwork", but this adhesion is not permanent so "friction is the only force which can be relied upon to produce permanent stability". Rankine saw friction in natural slopes, "whose inclination to the horizontal is the angle of repose, or angle whose tangent is the coefficient of friction". In one example where Coulomb calculates earth pressure on a retaining wall, he assumes that "the coefficient of friction is unity, as for soils which take a slope of 45 degrees when left to themselves, and that the cohesion is zero, as for newly turned soils". A difficulty with Coulomb’s 1773 approach is that angles of repose are hard to measure with accuracy. Terzaghi and Hvorslev did not deliberately contradict Coulomb’s statement that disturbed soil has no cohesion, but probably thought Mohr’s ideas advanced soil mechanics and c' andj' could be got more accurately in laboratory tests than angles of repose could be estimated in the field. Designers who rely on Mohr’s component of cohesion in soil differ from Coulomb who designed with a factor of safety of 1.25 and only relied on critical state friction. Rankine taught students to rely only on friction in soil. This still is safe teaching today.
Some of my recent papers can be found on the CUED Soil Mechanics Group web site at (www2.eng.cam.ac.uk/~ans/ans1.htm).
Andrew N Schofield, email@example.com, October 1999.
Coulomb (1773); see Heyman, (1997), Imperial College Press.
Goodman (1999), ASCE Press.
Hvorslev (1937); see Schofield and Wroth, (1968).
Musschenbroek (1729); see Heyman, (1997), Imperial College Press.
Rankine (1874), A Manual of Civil Engineering; 10th edition; London.
Roscoe and Schofield (1963); see Schofield and Wroth (1968).
Roscoe, Schofield and Thurairajah (1963); see Schofield and Wroth, (1968).
Roscoe, Schofield, and Wroth (1958); see Schofield and Wroth, (1968).
Schofield, (1998); Ground Engineering, August issue.
Schofield and Togrol (1966); see Schofield and Wroth, (1968).
Schofield and Wroth (1968); ‘Critical State Soil Mechanics’, McGraw Hill, Maidenhead.
Taylor (1948); ‘Fundamentals of Soil Mechanics’, Wiley, New York.
Terzaghi (1943); ‘Theoretical Soil Mechanics’, Wiley, New York.
Terzaghi and Peck (1948); ‘Soil Mechanics in Engineering Practice’, Wiley, New York.