1. Ch. 12
Shear strengths of soil

2. 12.7 Triaxial Shear Test - General

3. 12.7 Triaxial Shear Test - General
※ in this test, a soil specimen about 1.4 in.(35.6mm) in diameter and 3 in. (76.2mm) in length is generally used.
※ confining pressure (구속압, 구속응력)
※ axial stress (sometimes called deviator stress, 축차응력)

4. 12.7 Triaxial Shear Test - General
This can be done in one of two ways :
Application of dead weights or hydraulic pressure in equal increments until the specimen fails.– Stress controlled test
Application of axial deformation at a constant rate by means of a geared or hydraulic loading press This a strain – controlled test
Three standard types of triaxial tests :
Consolidated – drained test or drained test(CD test)
Consolidated – undrained test (CU test)
Unconsolidated – undrained test or undrained test (UU test)

5. 12.8 Consolidated – Drained Triaxial Test

6. 12.8 Consolidated – Drained Triaxial Test
Confining pressure σ3
where B = Skempton’s pore pressure parameter
(Skempton, 1954)
※ For saturated soft soils, B is approximately equal to 1
(12.18)

7. 12.8 Consolidated – Drained Triaxial Test
If drainage is opened, with time, 𝑢 𝑐 will become equal to 0.
In saturated soil, the change in the volume of the Specimen (ΔVc) that takes place during consolidation can be obtained from the volume of pore water drained (Figure 12.21a)

8. 12.8 Consolidated – Drained Triaxial Test
Next, the deviator stress, Δσd, on the specimen is increased at a very slowly(Figure 12.20b) (Δud = 0)
※ A typical plot of the variation of deviator stress against strain in loose sand and normally consolidated clay is shown in Figure 12.21b
※ Figure 12.21c show a similar plot for dense sand and overconsolidated clay
※ The volume change, ΔVd , of specimens that occurs because of the application of deviator stress in various soils is also shown in Figure 12.21d and e.

9. 12.8 Consolidated – Drained Triaxial Test

10. 12.8 Consolidated – Drained Triaxial Test
Fig 12.21(d) volume change in loose sand and normally consolidated clay during deviator stress application;
Fig.12.22(e) volume change in dense sand and overconsolidated clay during deviator stress application
total and effective confining stress =σ3 = σ3’
total and effective axial stress at failure

11. For NC clay

12. 12.8 Consolidated – Drained Triaxial Test
※ Overconsolidation results when a clay is initially consolidated under an all – around chamber pressure of σc(=σc’ ) and is allowed to swell by reducing the chamber pressure to σ3(=σ3’ ).
OC clay shows 2 distinct branches of failure envelope (Fig ).
※ A consolidated-drained triaxial test on a clayey soil may take several days to complete.
※ For that reason, the CD type of triaxial test is not common.

13. 12.8 Consolidated – Drained Triaxial Test

14. 12.9 Consolidated – Undrained Triaxial Test
※ CU test is the most common type of triaxial test.
In this test, the saturated soil specimen is first consolidated by all-round chamber fluid pressure.
After the pore water pressure generated by the application of confining pressure is completely dissipated (that is, uc = Bσ3 = 0), the deviator stress, Δσd, on the specimen is increased to cause shear failure.
During the test, simultaneous measurements of Δσd and Δud are made.

15. 12.9 Consolidated – Undrained Triaxial Test

16. 12.9 Consolidated – Undrained Triaxial Test
Pore water pressure parameter 𝐴
(12.25)

17. 12.9 Consolidated – Undrained Triaxial Test
※ The general pattern of variation of Δσd and Δud with axial strain for sand and clay soils are shown in Figure 12.26d, e, f and g.
In loose sand and normally consolidated clay, the pore water pressure increases with strain.
In dense sand and overconsolidated clay, the pore water pressure increases with strain to a certain limit, beyond which it decreases and become negative(with respect to the atmospheric pressure).
This decrease is because of a tendency of the soil to dilate.

18. 12.9 Consolidated – Undrained Triaxial Test
Major principal stress at failure(total) :
Major principal stress at failure(effective) :
Minor principal stress at failure(total) :
Minor principal stress at failure(effective) :
※ → Fig 12.27

19. 12.9 Consolidated – Undrained Triaxial Test

20. 12.9 Consolidated – Undrained Triaxial Test
For sand and NC clay
For OC clay
Consolidated-drained tests on clay soils take considerable time For this reason, consolidated – undrained tests can be conducted on such soils with pore pressure measurements to obtain the drained shear strength parameters.
(12.26)
(12.29)

21. 12.9 Consolidated – Undrained Triaxial Test

22. 12.9 Consolidated – Undrained Triaxial Test
Skempton’s pore water pressure parameter at failure
(12.18)
The general range of vaules in most clay soils
Normally consolidated clays : 0.5 to 1
Overconsolidated clays : -0.5 to 0

23. 12.9 Consolidated – Undrained Triaxial Test

24. 12.9 Consolidated – Undrained Triaxial Test

25. 12.10 Unconsolidated – Undrained Triaxial Test
In unconsolidated–undrained tests, drainage from the soil specimen is not permitted during the application of chamber pressure, Δσ3
The test specimen is sheared to failure by the application of deviator stress, Δσd, and drainage is prevented.
- This test is usually conducted on clay specimens and depends on a very important strength concept for saturated cohesive soils.
(12.32)

26. 12.10 Unconsolidated – Undrained Triaxial Test

27. 12.10 Unconsolidated – Undrained Triaxial Test

28. 12.10 Unconsolidated – Undrained Triaxial Test
Ф = 0 condition,
Explanation of Ф = 0 concept
Specimen no.1
consolidated at 𝜎 3 and then sheared to failure without drainage
Total Mohr’s circle : P
Pore pressure at failure =
∴ At Failure
Effective Mohr’s circle : Q
(12.33)

29. 12.10 Unconsolidated – Undrained Triaxial Test
Specimen no.2
consolidated to σ3 and increase by Δσ3 without drainage
Total Mohr’s circle : R
Δuc = Δσ3
Effective Confining Pressure
Then Shear → should fail at the same deviator stress(Δσd)f and pore water pressure(Δud)f
∴ At failure

30. 12.10 Unconsolidated – Undrained Triaxial Test
And the major principal effective stress :
The effective stress Mohr’s circle : Q

31. 12.11 Unconfined Compression Test on Saturated Clay
A special type of unconsolidated-undrained test that is commonly used for clay specimens.
𝜏 𝑓 = 𝜎 1 2 = 𝑞 𝑢 2 = 𝑐 𝑢
(12.34)
qu = unconfined compression strength(일축압축강도)

32. 12.11 Unconfined Compression Test on Saturated Clay

33. 12.11 Unconfined Compression Test on Saturated Clay

34. 12.11 Unconfined Compression Test on Saturated Clay

35. 12.12 Empirical Relationships Between Undrained Cohesion (cu) and Effective Overburden Pressure ( 𝝈 𝑶 ′ )
Skempton(1957), for NC clay
𝑐 𝑢(𝑉𝑆𝑇) 𝜎 𝑜 ′ = (𝑃𝐼)
Ladd(1977), for OC clay
𝑐 𝑢 𝜎 𝑜 ′ 𝑜𝑣𝑒𝑟𝑐𝑜𝑛𝑠𝑜𝑙𝑖𝑑𝑎𝑡𝑒𝑑 𝑐 𝑢 𝜎 𝑜 ′ 𝑛𝑜𝑟𝑚𝑎𝑙𝑙𝑦 𝑐𝑜𝑛𝑠𝑜𝑙𝑖𝑑𝑎𝑡𝑒𝑑 = 𝑂𝐶𝑅 0.8
Where OCR = overconsolidation ratio.
(12.35)
(12.36)

36. 𝑠 𝑡 = 𝑞 𝑢(𝑢𝑛𝑑𝑖𝑠𝑡𝑢𝑟𝑏𝑒𝑑) 𝑞 𝑢(𝑟𝑒𝑚𝑜𝑙𝑑𝑒𝑑) ; Sensitivity (예민비)
12.13 Sensitivity and Thixotropy of Clay
𝑠 𝑡 = 𝑞 𝑢(𝑢𝑛𝑑𝑖𝑠𝑡𝑢𝑟𝑏𝑒𝑑) 𝑞 𝑢(𝑟𝑒𝑚𝑜𝑙𝑑𝑒𝑑) ; Sensitivity (예민비) .
(12.37)

37. 12.13 Sensitivity and Thixotropy of Clay
The sensitivity ratio of most clays changes from about 1 to 8; however, highly flocculent marine clay deposits may have sensitivity ratios ranging from about 10 to 80
There are some clays that turn to viscous fluids upon remodeling. →”quick” clays
The loss of strength of clay soils from remolding is primarily caused by the destruction of the clay particle structure that was developed during the original process of sedimentatioin
Thixotropy : If, however, after remolding, a soil specimen is kept in an undisturbed state (that is, without any change in the moisture content), it will continue to gain strength with time.

38. 12.13 Sensitivity and Thixotropy of Clay

39. 12.13 Sensitivity and Thixotropy of Clay
𝑇ℎ𝑖𝑥𝑜𝑡𝑟𝑜𝑝𝑖𝑐 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ 𝑟𝑎𝑡𝑖𝑜= 𝑐 𝑢(𝑎𝑡 𝑡𝑖𝑚𝑒 𝑡 𝑎𝑓𝑡𝑒𝑟 𝑐𝑜𝑚𝑝𝑎𝑐𝑡𝑖𝑜𝑛) 𝑐 𝑢(𝑎𝑡 𝑡𝑖𝑚𝑒 𝑡=0 𝑎𝑓𝑡𝑒𝑟 𝑐𝑜𝑚𝑝𝑎𝑐𝑡𝑖𝑜𝑛)
(12.38)

40. 𝜏 𝑓 = 𝑐 ′ + 𝜎− 𝑢 𝑎 −𝜒 𝑢 𝑎 − 𝑢 𝑤 𝑡𝑎𝑛𝜙 𝜏 𝑓 =𝑐+𝜎𝑡𝑎𝑛𝜙
12.17 Shear Strength of Unsaturated Cohesive Soils
𝜎 ′ =𝜎− 𝑢 𝑎 −𝜒 𝑢 𝑎 − 𝑢 𝑤
𝜏 𝑓 = 𝑐 ′ + 𝜎− 𝑢 𝑎 −𝜒 𝑢 𝑎 − 𝑢 𝑤 𝑡𝑎𝑛𝜙
𝜏 𝑓 =𝑐+𝜎𝑡𝑎𝑛𝜙
(12.48)
(12.49)
(12.50)

41. 12.17 Shear Strength of Unsaturated Cohesive Soils
Figure shows the variation of the total stress envelopes with change of the initial degree of saturation obtained from undrained tests on an in organic clay.
For design purpose the unsaturated soil specimens collected from the field must be saturated in the laboratory and the undrained strength determined.
→ Rainfall Effect

42. 12.17 Shear Strength of Unsaturated Cohesive Soils

43. 12.18 Stress Path
Lambe (1964)
𝑝 ′ = 𝜎 1 ′ + 𝜎 3 ′ 2
𝑞 ′ = 𝜎 1 ′ − 𝜎 3 ′ 2
(12.51)
(12.52)

44. 12.17 Shear Strength of Unsaturated Cohesive Soils

45. 12.18 Stress Path
At the beginning of the application of deviator stress
𝜎 1 ′ = 𝜎 3 ′ = 𝜎 3 , so
𝑝 ′ = 𝜎 3 ′ + 𝜎 3 ′ 2 = 𝜎 3 ′ = 𝜎 3
𝑞 ′ = 𝜎 3 ′ − 𝜎 3 ′ 2 =0
(12.53)
(12.54)
At some other time during deviator stress application
𝜎 1 ′ = 𝜎 3 ′ +∆ 𝜎 𝑑 = 𝜎 3 +∆ 𝜎 𝑑 , 𝜎 3 ′ = 𝜎 3

46. 12.18 Stress Path
𝑝 ′ = 𝜎 1 ′ + 𝜎 3 ′ 2 = 𝜎 3 ′ +∆ 𝜎 𝑑 + 𝜎 3 ′ 2 = 𝜎 3 ′ + ∆ 𝜎 𝑑 2
𝑞 ′ = 𝜎 3 ′ +∆ 𝜎 𝑑 − 𝜎 3 ′ 2 = ∆ 𝜎 𝑑 2
(12.55)
(12.56)
The straight line ID is referred to as the stress path in a q’-p’ plot for a consolidated – drained triaxial failure stress condition
It may be seen that Mohr’s circle B represents the failure stress condition.
𝜏 𝑓 = 𝜎 ′ 𝑡𝑎𝑛𝜙
𝑞 ′ = 𝑝 ′ 𝑡𝑎𝑛𝜙
(12.57)

47. 12.18 Stress Path

48. tanα= 𝜎 1 ′ − 𝜎 3 ′ 2 𝜎 1 ′ + 𝜎 3 ′ 2 = 𝜎 1 ′ − 𝜎 3 ′ 𝜎 1 ′ + 𝜎 3 ′
12.18 Stress Path
DO′ OO′ =tanα
tanα= 𝜎 1 ′ − 𝜎 3 ′ 𝜎 1 ′ + 𝜎 3 ′ 2 = 𝜎 1 ′ − 𝜎 3 ′ 𝜎 1 ′ + 𝜎 3 ′
(12.58)
CO′ OO′ =sinϕ
sinϕ= 𝜎 1 ′ − 𝜎 3 ′ 𝜎 1 ′ + 𝜎 3 ′ 2 = 𝜎 1 ′ − 𝜎 3 ′ 𝜎 1 ′ + 𝜎 3 ′
(12.59)

49. 12.18 Stress Path
sinϕ=tanα
(12.60)
ϕ= sin −1 tanα
(12.61)

50. 12.18 Stress Path