Shear Strength of Soils

1. Shear Strength of Soils CEL 610 – Foundation Engineering

2. Steel Concrete Soil Compressive strength Shear strength Tensile strength Presence of pore water Complex behavior Strength of different materials

3. Embankment Strip footing Failure surface Mobilized shear resistance Shear failure of soils Soils generally fail in shear At failure, shear stress along the failure surface (mobilized shear resistance) reaches the shear strength.

4. Retaining wall Shear failure of soils Soils generally fail in shear

5. Mobilized shear resistance Failure surface Shear failure of soils Soils generally fail in shear Retaining wall At failure, shear stress along the failure surface (mobilized shear resistance) reaches the shear strength.

6. failure surface Shear failure mechanism The soil grains slide over each other along the failure surface. No crushing of individual grains.

7.       Shear failure mechanism At failure, shear stress along the failure surface () reaches the shear strength (f).

8.  failure envelope Friction angle Cohesion f c   Mohr-Coulomb Failure Criterion(in terms of total stresses)  f is the maximum shear stress the soil can take without failure, under normal stress of .

9.  ’ failure envelope Effective cohesion Effective friction angle f c’ ’ ’ Mohr-Coulomb Failure Criterion(in terms of effective stresses) u = pore water pressure f is the maximum shear stress the soil can take without failure, under normal effective stress of ’.

10.  f ’f tan ’ frictional component ’ cohesive component c’ c’ ’f ' Mohr-Coulomb Failure Criterion Shear strength consists of two components: cohesive and frictional.

11. c and  are measures of shear strength. Higher the values, higher the shear strength.

12. s’1 s’ s’3 s’3 t q s’1 Soil element Mohr Circle of stress Resolving forces insandtdirections,

13. t s’ Mohr Circle of stress

14. t (s’, t) q s’ PD = Pole w.r.t. plane Mohr Circle of stress

15. Failure surface Y Y X X Soil elements at different locations X ~ failure Y ~ stable Mohr Circles & Failure Envelope  ’

16.  c c Y c+  Initially, Mohr circle is a point Mohr Circles & Failure Envelope The soil element does not fail if the Mohr circle is contained within the envelope GL c

17. As loading progresses, Mohr circle becomes larger…  c c .. and finally failure occurs when Mohr circle touches the envelope Mohr Circles & Failure Envelope GL Y c

18. (s’, tf) (90 – q) q Therefore, 90 – q + f’ = q q = 45 + f’/2 PD = Pole w.r.t. plane Orientation of Failure Plane Failure envelope f’ s’

19. v v’ u h h’ + u X X X t effective stresses total stresses s or s’ h’ v’ h v u Mohr circles in terms of total & effective stresses =

20. v v’ u h h’ + u X X X Failure envelope in terms of effective stresses Failure envelope in terms of total stresses t f’ f effective stresses total stresses c’ c s or s’ h’ v’ h v u Failure envelopes in terms of total & effective stresses = If X is on failure

21. t ’v = s’1 Failure envelope in terms of effective stresses ’h = s’3 effective stresses (s’1 - s’3)/2 X c’ f’ X is on failure ’3 ’1 s’ (s’1+ s’3)/2 c’ Cotf’ Therefore, Mohr Coulomb failure criterion with Mohr circle of stress

22. Mohr Coulomb failure criterion with Mohr circle of stress

23. Laboratory tests on specimens taken from representative undisturbed samples Field tests • Most common laboratory tests to determine the shear strength parameters are, • Direct shear test • Triaxial shear test • Vane shear test • Torvane • Pocket penetrometer • Fall cone • Pressuremeter • Static cone penetrometer • Standard penetration test Determination of shear strength parameters of soils (c, forc’, f’) Other laboratory tests include, Direct simple shear test, torsional ring shear test, plane strain triaxial test, laboratory vane shear test, laboratory fall cone test

24. A representative soil sample z z svc + Ds svc shc shc shc shc svc svc + Ds After and during construction Before construction Laboratory tests Field conditions

25. svc + Ds shc shc Traxial test 0 svc svc + Ds svc shc shc 0 0 t Direct shear test svc 0 t svc Representative soil sample taken from the site Step 1 Set the specimen in the apparatus and apply the initial stress condition Laboratory tests Simulating field conditions in the laboratory Step 2 Apply the corresponding field stress conditions

26. Direct shear test Schematic diagram of the direct shear apparatus

27. Porous plates Components of the shear box Preparation of a sand specimen Direct shear test Direct shear test is most suitable for consolidated drained tests specially on granular soils (e.g.: sand) or stiff clays Preparation of a sand specimen

28. Pressure plate Leveling the top surface of specimen Specimen preparation completed Direct shear test Preparation of a sand specimen

29. Steel ball P Pressure plate Porous plates S Proving ring to measure shear force Step 1: Apply a vertical load to the specimen and wait for consolidation Direct shear test Test procedure

30. Steel ball P Test procedure Pressure plate Porous plates S Proving ring to measure shear force Step 1: Apply a vertical load to the specimen and wait for consolidation Direct shear test Step 2: Lower box is subjected to a horizontal displacement at a constant rate

31. Dial gauge to measure vertical displacement Shear box Proving ring to measure shear force Loading frame to apply vertical load Dial gauge to measure horizontal displacement Direct shear test

32. Direct shear test Analysis of test results Note: Cross-sectional area of the sample changes with the horizontal displacement

33. Shear stress, t Dense sand/ OC clay tf Loose sand/ NC clay tf Shear displacement Expansion Dense sand/OC Clay Change in height of the sample Shear displacement Loose sand/NC Clay Compression Direct shear tests on sands Stress-strain relationship

34. Shear stress, t Normal stress = s3 Normal stress = s2 Shear displacement Normal stress = s1 tf2 tf1 tf3 Shear stress at failure, tf Mohr – Coulomb failure envelope f Normal stress, s Direct shear tests on sands How to determine strength parameters c and f

35. Some important facts on strength parameters c and f of sand Direct shear tests on sands Direct shear tests are drained and pore water pressures are dissipated, hence u = 0 Sand is cohesionless hence c = 0 Therefore, f’ = f and c’ = c = 0

36. Overconsolidated clay (c’ ≠ 0) Shear stress at failure, tf Normally consolidated clay (c’ = 0) f’ Normal force, s Direct shear tests on clays In case of clay, horizontal displacement should be applied at a very slow rate to allow dissipation of pore water pressure (therefore, one test would take several days to finish) Failure envelopes for clay from drained direct shear tests

37. Where, ca = adhesion, d = angle of internal friction Interface tests on direct shear apparatus In many foundation design problems and retaining wall problems, it is required to determine the angle of internal friction between soil and the structural material (concrete, steel or wood)

38. Piston (to apply deviatoric stress) Failure plane O-ring impervious membrane Soil sample Soil sample at failure Porous stone Perspex cell Water Cell pressure Pore pressure or volume change Back pressure pedestal Triaxial Shear Test

39. Sampling tubes Sample extruder Triaxial Shear Test Specimen preparation (undisturbed sample)

40. Setting up the sample in the triaxial cell Edges of the sample are carefully trimmed Triaxial Shear Test Specimen preparation (undisturbed sample)

41. Sample is covered with a rubber membrane and sealed Cell is completely filled with water Triaxial Shear Test Specimen preparation (undisturbed sample)

42. Proving ring to measure the deviator load Dial gauge to measure vertical displacement Triaxial Shear Test Specimen preparation (undisturbed sample)

43. deviatoric stress ( = q) c Step 2 Step 1 c c c c c+ q c Under all-around cell pressure c Shearing (loading) yes no yes no Consolidated sample Undrained loading Drained loading Unconsolidated sample Types of Triaxial Tests Is the drainage valve open? Is the drainage valve open?

44. Step 2 Step 1 Under all-around cell pressure c Shearing (loading) Is the drainage valve open? Is the drainage valve open? CD test UU test yes no yes no Consolidated sample Undrained loading Drained loading Unconsolidated sample CU test Types of Triaxial Tests

45. = + Total, s Effective, s’ Neutral, u sVC s’VC =sVC shC s’hC =shC 0 Drainage Drainage Drainage sVC + Ds sVC + Dsf s’V =sVC +Ds = s’1 shC shC s’h =shC = s’3 0 0 s’Vf =sVC +Dsf= s’1f s’hf =shC = s’3f Consolidated- drained test (CD Test) Step 1: At the end of consolidation Step 2: During axial stress increase Step 3: At failure

46. s1 = sVC + Ds s3 = shC Consolidated- drained test (CD Test) Deviator stress (q or Dsd) = s1 – s3

47. Time Expansion Volume change of the sample Compression Consolidated- drained test (CD Test) Volume change of sample during consolidation

48. Deviator stress, Dsd Dense sand or OC clay (Dsd)f Loose sand or NC Clay (Dsd)f Axial strain Expansion Dense sand or OC clay Volume change of the sample Axial strain Compression Loose sand or NC clay Consolidated- drained test (CD Test) Stress-strain relationship during shearing

49. Deviator stress, Dsd s1 = s3 + (Dsd)f (Dsd)fc Confining stress = s3c s3 Confining stress = s3b Confining stress = s3a (Dsd)fb Axial strain (Dsd)fa Shear stress, t f Mohr – Coulomb failure envelope s or s’ s3c s3a s3b s1a s1b s1c (Dsd)fa (Dsd)fb CD tests How to determine strength parameters c and f

50. Strength parameters c and f obtained from CD tests CD tests Therefore, c = c’ and f = f’ Since u = 0 in CD tests, s = s’ cd and fd are used to denote them