1. Stress-strain behaviour
Tuesday, 5th December , 2006— 1a
Stress-strain behaviour

2. Actual test data on four types of tests on normally consolidated clay and overconsolidated clay will be presented here.

3. The tests on the normally consolidated clay are
i. Isotropic and anisotropic consolidation 
ii. Undrained tests 
iii. Constant p drained tests 
iv. Fully drained tests with constant consolidation pressure

4. Isotropic and anisotropic consolidation

5. Altogether five anisotropic consolidation tests were carried out in this series. These tests correspond to stress ratio h of 0.0, 0.2, 0.4, 0.6, and 0.8. All specimens were isotropically
consolidated to kN/m2 and were then sheared under fully drained condition with constant cell pressure until the relevant stress ratio was reached.

6. During anisotropic consolidation the stress ratio q/p was maintained
constant. Fig. 3.1 shows the stress paths followed in the tests. The state paths followed are shown in Fig In Fig. 3.2 the dotted path correspond to the state boundary surface as obtained from undrained tests.

7. Figure 3.1: Stress path followed during isotropic and anisotropic consolidation

8. Figure 3.2: State path followed during anisotropic consolidation

9. Note that the state paths during anisotropic consolidation do lie close to the state path obtained from undrained tests.Ideally, the data from each anisotropic consolidation test should plot as a single point on the undrained state path.

10. Fig. 3.3 shows the strain paths followed by each specimen during anisotropic consolidation. Note that the strain paths followed are linear in the ev (in Fig.3.3 v is used for volumetric strain) , es plot.

11. Figure 3.3: Strain paths followed during anisotropic consolidation

12. It is therefore apparent that the strain increment ratio
is a constant for each stress ratio value during the anisotropic consolidation.

13. Fig. 3.4 shows the variation of with h. The values of
for the four tests are 2.03, 1.37,
0.99, and 0.67.
The variation of voids ratio
with logarithm of mean
normal stress is shown in Fig. 3.4

15. The voids ratio is found to vary linearly with the logarithm of the mean normal stress. The value of l for the stress ratio, 0.0, 0.2, 0.4, 0.6, and 0.8 were 0.51, 0.51, 0.515, 0.51
and 0.53 respectively. The slope k during isotropic swelling is found
to be 0.07.

16. Undrained behaviour

17. In this series the results of five undrained tests at pre-shear
consolidation pressures of 138, 207, 276, 345 and 414 kN/m2 will be presented. Fig. 3.5 shows the effective stress paths followed
by the specimens in the (q,p) plot.

18. Figure 3.5: Effective stress paths under undrained tests

19. The dashed lines in this figure corresponds to the constant shear
strain contours and will be discussed shortly. The effective
stress paths are similar and are normalized and presented in Fig In this figure the state paths followed by the specimens are approximately the same.

20. Figure 3.6: Normalized undrained stress paths

21. Figure 3.7 contains the data related to shear strain and excess pore pressures. The pore pressure coefficient A is computed and is plotted in Fig. 3.8.
The stress ratio strain relationship in Fig. 3.7 is approximately the same for
all the specimens. The normalized deviator stress and the pore pressures are presented in Fig. 3.9 and are found to be normalizable.

22. Figure 3.7 Pore pressure, shear strain and deviator stress stress
ratio shear strain relationships in undrained shear

23. Figure 3.8: Pore pressure parameter A

24. Figure 3.9: Normalized deviator stress and pore pressure relationships

25. The projections of the critical state line in the (q,p ) plot and the (e, ln p) plots are shown in Figs and 3.11.

26. Figure 3.10: Critical state line in (q,p) plot from undrained test data

27. Figure 3.11: Critical state line in (e, ln p) plot

28. Drained behaviour under constant p
In this series four specimens were sheared under constant p drained conditions from pre-shear consolidation pressures of 138, 207, 276, and 414 kN/m2. During these tests the axial stress was increased and the cell pressure was reduced so that p remains a constant. The effective stress paths for a fully drained test lie in between the effective stress path for an undrained test and a fully drained test.

30. The volumetric strain experienced by
these specimens will be less than those
experienced by the specimens sheared
under fully drained condition with
constant cell pressure. The state paths
followed by the specimens are shown
in Fig The stress strain behavior
of the specimens is shown in Fig

31. Figure 3.13: State paths followed by constant p test specimens

32. The volumetric strain shear strain plot of the specimens is shown in Fig and the stress ratio strain relations in Fig

33. Figure 3.14: Stress strain behaviour of constant p test specimens

34. Figure 3.15: Volumetric strain- shear strain plot

35. Figure 3.16: Stress ratio strain relationship

36. Fully drained behavior

37. Five fully drained tests were carried out from consolidation pressures of 138, 207, 275, 345, and 414 kN/m2. The state paths followed by the specimens are shown in Fig The stress strain behaviour of the fully rained specimens is shown in Fig The volumetric strain shear strain relationship is shown in Fig.3.19.

38. Figure 3.17: State path followed by full drained test specimens

39. Figure 3.18: Stress strain behavior of full drained test specimens

40. Figure 3.19: Volumetric strain shear strain plot of drained test specimens

41. The stress ratio strain relationships are shown in Fig. 3. 20
The stress ratio strain relationships are shown in Fig The peak stress conditions and the water content log stress
relationships are shown in Fig and They support the
critical state concept.

42. Figure 3.20: Stress ratio strain relationship for fully drained tests

43. Figure 3.21: Critical state line from constant p and fully drained tests in (q,p) plot

44. Figure 3.22: Water content Stress projection of critical
state line from constant p and fully drained tests

45. Overconsolidated clay behaviour

46. The behaviour of overconsolidated clays will only be discussed briefly in this chapter even though all clay deposits are either lightly over consolidated or heavily over consolidated. Extensive experimental work had been done
on the overcosolidated behaviour of clays.

47. It is good to compare the behaviour of overconsolidated clays with those of the corresponding normally consolidated clay.
In the study of the normally consolidated clay we particularly
concentrated on the behaviour with various degrees of drainage.

48. We noted that for any one type of drainage and corresponding
stress path, the behaviour is normalizable with respect to the
pre-shear consolidation pressure and we also saw the role of the
mean equivalent pressure in transforming the 3D state boundary surface to a 2-D one.

49. In the case of normally consolidated clays various stress
strain theories were developed based on elasto-plastic behaviour and also from a thermodynamics point of view.
Also theories based on contact stresses were developed.

50. However to date such theories are not there for overconsolidated clays as the overconsolidated behaviour depend on the overconsolidation ratio of the sample.

51. So for each overconsolidation ratio, the shape of the undrained stress path is different and distinct. Thus in the case of undrained behaviour a series of samples with the same OCR have normalizable behaviour. Thus attempts be made to incorporate the OCR values in our theories in some fundamental form.

52. Undrained behaviour of overconsolidated samples
Typical undrained stress paths obtained with over consolidated samples is shown in Fig

53. Figure 3.23: Undrained stress paths and constant shear strain contours

54. In Fig. 3. 23 the maximum OCR reached is only 4
In Fig the maximum OCR reached is only 4.If we increase the OCR, further then in in the heavily over consolidated states negative pore pressures will develop and the stress path becomes concave on the side of the origin of the stress plot.

55. In the normally consolidated clay, the shear strain contours were found to pass through the origin and thus the undrained shear strain only depended on the stress ratio. However in the case of the overconsolidated clay, the undrained shear strain contours
are sub-parallel to the p-axis when the OCR is less than 2 or so.

56. As the OCR increase
the contours converge to a
point on the negative p-axis.
This behaviour makes
the undrained shear strain
in heavily overconsolidated
clay to be some what
similar to the
normally consolidated clay
but with a shifted origin.

57. Dilatancy ratio in overconsolidated clays
In the case of normally consolidated clays we noted that the dilatancy ratio
is depended only on the
stress ratio for radial type of stress paths. However for non-radial types, the dilatancy ratio is also dependent on the
stress increment ratio,

58. This will be further discussed in the next chapter when the modelling of clay behaviour is discussed. The dilatancy ratio for overconsolidated clay for limited directions of stress increment ratio is shown in Fig

60. In Fig. 3.24, the gradient of the reduction in dilatancy ratio
from that of the normally consolidated value is plotted wth respect to the stress ratio. The gradient is plotted with respect to
the value of

61. Failure envelope of overconsolidated clay
The failure envelope of overconsolidated clay was of the Hvorslev failure type indicating a curved failure envelope which locates above the critical state line as shown in Fig

62. Figure 3.25: Failure envelope of overconsolidated samples

63. Comments and concluding remarks
In this chapter the essential features of the stress strain behaviour
of soft clays is described with a view to introduce the modelling concepts
in the next chapter.

64. The choice of the material is rather deliberate to concentrate more on the modelling concepts and in formalizing the behaviour in a form that it will be easy for students and practitioners to have a clear view of the demands in modelling to fulfill the actual behaviour of clayey soils.

65. For the normally consolidated states we noted
1. the undrained stress paths
are similar and develop
the maximum pore pressure due to suppressed dilatancy.
  2. the undrained shear
strains only depend on
the stress ratio. 

66. 3. there is a unique (p,q,e)
surface which enables
the volumetric strains to
be computed using undrained
stress paths.

67. 4. during anisotropic and
isotropic consolidation, the strain
increment ratio is only
dependent on the stress ratio.
5. the stress stain behaviour
is normalizable for any one type of
effective stress path using the
pre-shear consolidation pressure.

68. For over consolidated clays
 the stress -strain behaviour
is normalizable for any one
OCR value and for any one type of effective stress path. 
2. the shear strain contours under undrained conditions are
sub- parallel to the p-axis in the lightly overconsolidated state
and converge to a point on the negative side of the p-axis.

69. 3. the dilatancy ratio decreases
from the value corresponding to
the normally consolidated state
for radial stress paths as a function
of for any one stress ratio.
4. the strength envelope is of
the Hvorslev type and curved as well
as locate itself above the critical
state line.