The document discusses soil strength and different methods for measuring it. The Mohr-Coulomb failure criterion describes soil strength in terms of effective stresses. Laboratory tests like shear box and triaxial tests are used to measure soil strength parameters. The triaxial test can measure both drained (effective) and undrained strengths under controlled stress conditions. Interpretation of test results requires using concepts like effective and total stress Mohr circles.

1. Soil Strength

3. Mohr-Coulomb failure criterion The limiting shear stress (soil strength) is given by  = c +  n tan  where c = cohesion (apparent)  = friction angle   n

5. Effective stress failure criterion are known as the effective (or drained) strength parameters. If the soil is at failure the effective stress failure criterion will always be satisfied.

6. Effective stress failure criterion are known as the effective (or drained) strength parameters. Soil behaviour is controlled by effective stresses, and the effective strength parameters are the fundamental strength parameters. But they are not necessarily soil constants. If the soil is at failure the effective stress failure criterion will always be satisfied.

7. Total stress failure criterion If the soil is taken to failure at constant volume (undrained) then the failure criterion can be written in terms of total stress as c u and  u are known as the undrained strength parameters

8. Total stress failure criterion If the soil is taken to failure at constant volume (undrained) then the failure criterion can be written in terms of total stress as c u and  u are known as the undrained strength parameters These parameters are not soil constants, they depend strongly on the moisture content of the soil.

9. Total stress failure criterion If the soil is taken to failure at constant volume (undrained) then the failure criterion can be written in terms of total stress as c u and  u are known as the undrained strength parameters These parameters are not soil constants, they depend strongly on the moisture content of the soil. The undrained strength is only relevant in practice to clayey soils that in the short term remain undrained. Note that as the pore pressures are unknown for undrained loading the effective stress failure criterion cannot be used.

10. Tests to measure soil strength 1. Shear Box Test Motor drive Load cell to measure Shear Force Normal load Rollers Soil Porous plates Top platen Measure relative horizontal displacement, dx vertical displacement of top platen, dy

13. Typical drained shear box results Normal load increasing

14. Typical drained shear box results  = F/A  = N/A Peak Ultimate N 1 N 2

18. Tests to measure soil strength 2. The Triaxial Test Cell pressure Pore pressure and volume change Rubber membrane Cell water O-ring seals Porous filter disc Confining cylinder Deviator load Soil

20. Stresses in triaxial specimens  r  r = Radial stress (cell pressure)  a = Axial stress F = Deviator load  r

21. Stresses in triaxial specimens  r  r = Radial stress (cell pressure)  a = Axial stress F = Deviator load  r From equilibrium we have

22. Stresses in triaxial specimens F/A is known as the deviator stress, and is given the symbol q The axial and radial stresses are principal stresses

26. Strains in triaxial specimens From the measurements of change in height, dh, and change in volume dV we can determine Axial strain Volume strain where h 0 is the initial height and V 0 is the initial volume

27. Strains in triaxial specimens From the measurements of change in height, dh, and change in volume dV we can determine Axial strain Volume strain where h 0 is the initial height and V 0 is the initial volume It is assumed that the specimens deform as right circular cylinders. The cross-sectional area, A, can then be determined from

30. Typical triaxial results q  a Increasing cell pressure

31. Mohr Circles To relate strengths from different tests we need to use some results from the Mohr circle transformation of stress.    1  3

32. Mohr Circles To relate strengths from different tests we need to use some results from the Mohr circle transformation of stress.    1  3 c The Mohr-Coulomb failure locus is tangent to the Mohr circles at failure

33. Mohr Circles    1  3  2  (      From the Mohr Circle geometry

35. Mohr-Coulomb criterion (Principal stresses)     1  3 c c cot  p R Failure occurs if a Mohr circle touches the failure criterion. Then R = sin  ( p + c cot 

36. Mohr-Coulomb criterion (Principal stresses)     1  3 c c cot  p R Failure occurs if a Mohr circle touches the failure criterion. Then R = sin  ( p + c cot 

37. Mohr-Coulomb criterion (Principal stresses)     1  3 c c cot  p R Failure occurs if a Mohr circle touches the failure criterion. Then R = sin  ( p + c cot 

38. Effective stress Mohr-Coulomb criterion As mentioned previously the effective strength parameters are the fundamental parameters. The Mohr-Coulomb criterion must be expressed in terms of effective stresses

39. Effective stress Mohr-Coulomb criterion As mentioned previously the effective strength parameters are the fundamental parameters. The Mohr-Coulomb criterion must be expressed in terms of effective stresses

40. Effective stress Mohr-Coulomb criterion As mentioned previously the effective strength parameters are the fundamental parameters. The Mohr-Coulomb criterion must be expressed in terms of effective stresses where

41.    1  3 u u Effective and total stress Mohr circles For any point in the soil a total and an effective stress Mohr circle can be drawn. These are the same size with The two circles are displaced horizontally by the pore pressure, u.

46. Relation between effective and total stress criteria Three identical saturated soil samples are sheared to failure in UU triaxial tests. Each sample is subjected to a different cell pressure. No water can drain at any stage.

47. Relation between effective and total stress criteria Three identical saturated soil samples are sheared to failure in UU triaxial tests. Each sample is subjected to a different cell pressure. No water can drain at any stage. At failure the Mohr circles are found to be as shown    1  3

48. Relation between effective and total stress criteria Three identical saturated soil samples are sheared to failure in UU triaxial tests. Each sample is subjected to a different cell pressure. No water can drain at any stage. At failure the Mohr circles are found to be as shown    1  3 We find that all the total stress Mohr circles are the same size, and therefore  u = 0 and  = s u = c u = constant

49. Relation between effective and total stress criteria    1  3 Because each sample is at failure, the fundamental effective stress failure condition must also be satisfied. As all the circles have the same size there must be only one effective stress Mohr circle

50. Relation between effective and total stress criteria    1  3 Because each sample is at failure, the fundamental effective stress failure condition must also be satisfied. As all the circles have the same size there must be only one effective stress Mohr circle We have the following relations

53. Example In an unconsolidated undrained triaxial test the undrained strength is measured as 17.5 kPa. Determine the cell pressure used in the test if the effective strength parameters are c’ = 0,  ’ = 26 o and the pore pressure at failure is 43 kPa.

54. Example In an unconsolidated undrained triaxial test the undrained strength is measured as 17.5 kPa. Determine the cell pressure used in the test if the effective strength parameters are c’ = 0,  ’ = 26 o and the pore pressure at failure is 43 kPa. Analytical solution Undrained strength = 17.5 =

55. Example In an unconsolidated undrained triaxial test the undrained strength is measured as 17.5 kPa. Determine the cell pressure used in the test if the effective strength parameters are c’ = 0,  ’ = 26 o and the pore pressure at failure is 43 kPa. Analytical solution Undrained strength = 17.5 = Failure criterion

56. Example In an unconsolidated undrained triaxial test the undrained strength is measured as 17.5 kPa. Determine the cell pressure used in the test if the effective strength parameters are c’ = 0,  ’ = 26 o and the pore pressure at failure is 43 kPa. Analytical solution Undrained strength = 17.5 = Failure criterion Hence   ’ = 57.4 kPa,   ’ = 22.4 kPa and cell pressure (total stress) =   ’ + u = 65.4 kPa

57. Graphical solution   26 17.5

58. Graphical solution   26 17.5

59. Graphical solution    1  3 26 17.5