LEC-1 CL 601 Historical Developement of Constitutive Modelling of Soil.pptx

Constitutive Modelling;
Historical Development;
Karl Terzaghi;
D W taylor;
Taylor;
Roscoe, Schofield, and Wroth;
Critical state flow;
Plastic design;
Thurairajah (1961);
Original Cam-clay (1963);
M Tech Geotechnical Engineering;

1. Constitutive Modelling of Geomaterials Prof. Samirsinh P Parmar Mail: [email protected] Asst. Prof. Department of Civil Engineering, Faculty of Technology, Dharmasinh Desai University, Nadiad , Gujarat, INDIA Lecture:1: Constitutive Modelling – Historical Development

2. Re-appraisal of Terzaghi’s soil mechanics Andrew Schofield, Emeritus Professor, Cambridge University “Terzaghi and Peck” versus “Taylor” (Goodman p 213) Civil engineering plastic design Continuum of grains at repose ( i ) Coulomb’s and (ii) Rankine’s errors Yielding of a saturated soil paste Conclusion Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 2

3. D. W. Taylor (1900-55) Associate Professor, MIT K. H. Roscoe taught hıs students to respect D. W. Taylor The x- y =x in “Fundamentals of soil mechanics” led us to an understanding of the mechanics of soil as a n elastıc- plastic continuum Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 3

4. “Terzaghi and Peck” versus “Taylor” (1948) Taylor's “interlocking” theory (1948) Review of Taylor’s manuscript John Wiley & Sons reply to Terzaghi Critical state flow of grains without damage Roscoe, Schofield, and Wroth (1958) Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 4

5. Taylor's “interlocking” theory (1948) i Workis x=x+y so strength is (friction) plus (interlocking) /=+y/x. x sand in y shear box y / y/x  x x x Increase of water content on slıck slıp planes shows that thıs applıes to“true” cohesıon of over-consolıdated clay Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 5

6. Peck’s review of Taylor’s manuscript “ I am convınced that the theorıes of soıl mechanıcs and the results of laboratory tests serve only to guıde the engıneer toward a recognıtıon of the factors whıch may affect the desıgn and constructıon of a real project ” from review sent to Wiley by R B Peck July 31, 1944 quoted from page 213 “Karl Terzaghi; the Engineer as Artist” R E Goodman (1999) Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 6

7. ... (Taylor’s book) will be published by one of our competitors if we do not take it. Under the circumstances, we see nothing to do but publish it. However, as I said in the first paragraph of this letter, we believe that each book will be judged on its own merits, and certainly we have no fears for the success of (Terzaghi & Peck). E P Hamilton (President) December 17, 1946 John Wiley & Sons reply to Terzaghi Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 7

8. Roscoe, Schofield, and Wroth (1958) Triaxial test paths approach steady flow in critical states with aggregates of grains at constant v specific volume As strain increases v and p are constant at a Critical-state ( v p ) v  = { v+  lnp } =  q= p  wet dry Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 8

9. Critical state flow of grains without damage Competent aggregate of selected sand grains flows in critical states v  = v +  ln p  =  with no dust or damage Soıl p aste is unchanged in mixing or yielding on the “wet” side, v  >  Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 9

10. Plastic design in civil engineering Construction without plastic ductility Plastic design of a steel frame, Baker (1948) Plastic design of structures Ductility and continuity in soil mechanics Strains by the associated plastic flow rule Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 10

11. Construction without plastic ductility Ductility can save life. The 1995 bomb at the Oklahoma Federal Centre, and similar damage in the 1999 Turkish earthquake, show the risk of brittle behaviour Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 11

12. Plastic design of a steel frame, Baker (1948) Cambridge text book example plastic design of shelter to resist floor load 20 lb / sq.ft falling 9 ft in bombed house; Mother and 3 children survived WW II 250kg bomb in Falmouth, UK Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 12

13. Plastic design of structures Small imperfections causes big local stress concentrations in elastic analysis of steel frames In practice plastic yield of steel relieves high stress Ductility of steel gives safety, rather than high yield strength Claddıng breaks up but framework survıves Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 13

14. Ductility and continuity in soil mechanics A paste of soil saturated with water is plastic, (from the Greek word  plassein to mould, as in moulding pottery from clay). A n aggregate of separate hard grains ın a crıtıcal state behaves as a duc tile plastic continuum . Plastic design guıdes us to select construction materials and methods; soil is not plastic and ductile if over compacted to high peak strength Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 14

15. Strains by the associated plastic flow rule For stability the product of any stress increment vector ( i  j ) and the plastic strain rate flow vector may not be negative;  i  i p +  j  j p > 0. In plastic flow, as a body yields under combined stresses  i  j with strain increments  i p  j p , the flow vector is normal to the yield locus at ( i  j ) .  i p  j p  i  i  j ( i  j )  j Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 15

16. Calladine’s associated plastic flow (1963) Yield loci for paste with v  = ( const ) on wet side of Critical-states, satisfy the associated flow rule dp  dv+dqd  =0 The Original Cam-clay locus was based on this plus Thurairajah’s dissipation function Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 16

17. A continuum of grains Some historical dates Belidor and Navier Coulomb ’s error Rankine Active slope at angle-of-repose Drained angle-of-repose slope Flow of grains with elastic energy dissipation Elastic-plastic strains of aggregates of grains Undrained and drained ultimate strength Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 17

18. Some historical dates Coulomb , at school in Mezieres , learned friction theory from a text book written by Belidor in 1737 (reprinted with notes by Navier in 1819) and a Dutch concept of (cohesion) = (adhesion). I n his 1773 paper he reported new rock strength data Terzaghi (1936), in “A fundamental fallacy in earth pressure computation”, rejected Rankine’s theory of limiting statics of granular media, ( Sokolovski ), for lacking consideration of strains Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 18

19. Belidor’s friction hypothesis (1737) Belidor attributed sliding friction coefficients of 1/3 to the hemispherical geometry of roughness Navier (1819) called Belidor’s theory très-fautive but he offered no alternative to it. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 19

20. Navier (1819); a footnote in his edition of Belidor Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 20

21. Coulomb’s soil (1773) Friction Coulomb defined soil internal friction as the angle of repose  d of drained slopes Grand rock face Canyon soil slope Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 21

22. Coulomb’s soil (1773) Cohesion In Coulomb’s rock tests, cohesion in shear was slightly greater than adhesion in tension, so he considered it safe to design with tension data His wall design assumed that newly compacted soil has zero cohesion error Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 22

23. Terzaghi interprets Hvorslev’s (1937) shear box tests Terzaghi fitted “true” cohesion and friction to peak strengths found by Hvorslev in shear box tests , normalısıng them by equıvalent pressure . wet sıde of crıtıcal states Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 23

24. A point Terzaghi missed in interpreting test data cs wet side Hvorslev’s data ended at a critical state point. Terzaghi should have asked Hvorslev why he put equations in space where there were no peak strengths. Filling the space meant that he asked no questions about the wet side of critical states v  = { v+  lnp } >  Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 24

25. Alternative strength components in soil paste For Belidor (and Navier ) the 2 soil strength components were ( cohesion ) + ( interlocking = friction ) For Terzaghi (and Mohr) the 2 soil strength components were ( true cohesion) + ( true friction) Critical State Soil Mechanics has only 2 strength components ( interlocking = cohesion ) + ( friction ); it is a theory for dust with ( true cohesion) = (zero) Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 25

26. Rankine Active slope at angle-of-repose i Stress on a sloping plane  z   d  z cos  d Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 26

27. Rankine Active slope at angle-of-repose ii Stresses on sloping planes and on vertical planes are conjugate. Rankine hypothesised  that  d is a limiting angle z  for both vectors of  d stress, and also that both these planes slip. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 27

28. Rankine Active slope at angle-of-repose iii Slip lines are lines of constant length. If vertical lines had constant  length, all slope material z  would move forward  d horizontally. If we accept Belidor’s error, (friction) = (dilation), no work is done or dissipated . Rankine (1851) should have deduced that slip planes are not p lanes of limiting stress. Terzaghi called Rankine’s earth pressures “fallacy”. Let us replace Rankine’s “loose earth” by an elastic-plastic continuum. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 28

29. Drained angle-of-repose slope i Stresses on sloping planes and on vertical planes remain conjugate in a plastic  continuum. Instead of z  d  two sets of slip planes  d in a Rankine Active zone  r  a let us have many ‘triaxial test’ cylinders in constant volume shear, giving plastic flow at all depths z Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 29

30. Drained angle-of-repose slope ii  z  d   d  r  a For q= (  a - r ) and p= (  a +2 r )/ 3 in triaxial tests, and q/p=3 (  a  r )/ (  a +2 r ) =6sin  d /(3– sin  d )=  =( const ), a continuum with ( a / r )=(1+ sin  d ) /(1- sin  d )=( const ) , has constant slope angle  d as q and p increase, without the assumption of slip in two directions . Cırcle dıameters ıncrease wıth depth z. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 30

31. Flow of grains with elastic energy dissipation Elastic energy is lost on wood surfaces as fibre brushes spring free; Coulomb (1785) Frameworks of soil grains carry load (after Allersma ). Elastic energy is stored and lost as frameworks buckle Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 31

32. Elastic-plastic strains of aggregates of grains Elastic compression and swelling states with specific volume v, spherical pressure p , fit v  = {v +  lnp } Plastic compression fits v  = {v +  lnp } ,  are constants Elastic slope  Plastic slope  Taylor (1948) data Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 32

33. Elastic-plastic strains of aggregates of grains Elastic compression of aggregate fits v  ={v+  lnp } A yield locus defines how elastically compressed grains yield when sheared  line shift v  = v p gives plastic volume change (hardening) v  =v p plastic volume change Roscoe and Schofield (1963) loci Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 33

34. Plastic compression is explained by  lines Elastic compression  lines in plot of v  =v+  lnp against lnp  go past t he cs line v  = v  +( -) lnp = and yield at a  line. Plastic compression in tests is observed to fit predicted stable yielding in ( -) gap of v  >  lines v   line cs  line ( -) lnp Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 34

35. Undrained and drained ultimate strength Crıtıcal States Undrained strength c=c u with v=const., c u = /2exp{(-v)/ } Drained strength in p=const. tests = = d =sin -1 3/ (1+ 6/  ) See Schofield and Wroth (1968) CSSM q= p Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 35

36. Fall cone tests of mixtures of clay and silt Fall cone tests with 80 and 240gm cones give v= lnp =ln3 If p  PL = 100 p  LL then I P = 1.71  (from CSSM) Plasticity index I P is loss of water content for strength increase by factor of 100 (triaxial test data; Lawrence MPhil 1980) 80gm 240gm v v ln (penetration) Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 36

37. Yielding of a saturated-soil paste Taylor / Thurairajah (1961) dissipation function Paste mechanics Original Cam-clay (1963) Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 37

38. Taylor / Thurairajah (1961) dissipation function Taylor’s dissipation x- y =x (note ,x are orthogonal) Undrained and drained triaxial test data, including data of change of elastic energy, fit a function p  dv p + qd  =  p  d  ( p , d  are orthogonal) Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 38

39. Original Cam-clay (1963) q/ p =1-ln(p/p c ) p  c p  dp dv + dqd = 0 associated flow p dv + qd =  p  d dissipation function cs dv/d = -(dq/ dp )= -(q/ p ). Introduce =q/p so d/dp=1/p(dq/dp-q/p)= -/p. Hence ln p  d= -dp/p. When integrated this gives /=1-ln(p/p c ). q cs (dv,d ) v q =  p  Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 39

40. Original Cam-clay (figure from my 1980 Rankine Lecture) Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 40

41. Original Cam-clay (1963) +(-) 1 ln (p  /p  c ) S (-) q/  p =1 v    q/  p  =0  Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 41

42. Interım c onclusion s Coulomb’s zero cohesion “Law” is confirmed by data on the wet sıde of crıtıcal states T erzaghı’s Mohr-Coulomb error ıs clear Map of soil behaviour (Schofield 1980) Centrifuge work of TC2 up to 1998 Choice between two liquefaction hypotheses Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 42

43. Coulomb’s zero cohesion “Law” is confirmed Cam-clay model fits test data on the wet side of critical, which confirms Coulomb’s “law” that newly disturbed soil paste has zero cohesion (CSSM figure; paste data (kaolin-clay)+(rock-flour) (Lawrence1980)) Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 43

44. T erzaghı’s Mohr-Coulomb error Terzaghi and Hvorslev wrongly claimed that true cohesion and true friction in the Mohr-Coulomb model fits disturbed soil behaviour. Geotechnical practice using Mohr-Coulomb to fit undisturbed test data has no basis in applied mechanics. Critical State Soil Mechanics offers geotechnical engineers a basis on which to continue working. The original Cam-clay model requires modification to fit effects of anisotropy and cyclic loading. Good centrifuge tests of soil-paste models achieves this. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 44

45. Map of soil behaviour (Schofield 1980) Regimes of soil behaviour 1 1 ductile plastic 2 2 dilatant rupture 3 3 cracking 3 2 1 (fracture with high hydraulic gradient causes clastic liquefaction) A centrifuge test of a model made of soil paste will display integrated effects in behaviour mechanisms Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 45

46. Choice between two liquefaction hypotheses A CVR A Casagrande Boston There is a unique critical void ratio and a risk of liquefaction in any embankment built with higher void ratio Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 46

47. Choice between two liquefaction hypotheses B B Casagrande Buenos Aires Even a dense sand if heavily loaded can liquefy . Reject both A and B . Sand yields, it is stable, on the wet side of critical states Figure: from Schofield and Togrol 1966 Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 47

48. Centrifuge work of TC2 up to 1998 We should claim a fundamental significance for centrifuge tests of models made of reconstituted soil, and explain how our tests can correct some errors that were made in Harvard. If it led to serious discussions in Istanbul, it would be good for Terzaghi’s Society. A concluding comment on the Report of TC2 to the Istanbul Conference, Schofield (1998) Lecture in “Centrifuge 98 Vol 2 ”- IS Tokyo Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 48

49. Terzaghi’s low expectation for applied mechanics was in error when he said at Harvard (1936) ...(the) possibilities for successful mathematical treatment of problems involving soils are very low When I asked Bjerrum “What should Universities teach in soil mechanics?” he replied “Universities should not teach soil mechanics; they should teach mechanics” ( teaching in the spirit of K. H. Roscoe) ISSMGE should correct error. We all should teach Plasticity and Critical State Soil Mechanics and promote ce ntrifuge m odel tests with soil paste. Prof. Samirsinh P Parmar, CL-DDU, Gujarat, India 49

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