1. YULVI ZAIKA JURUSAN TEKNIK SIPIL FAK.TEKNIK UNIV.BRAWIJAYA
SHEAR STRENGTH II
YULVI ZAIKA
JURUSAN TEKNIK SIPIL
FAK.TEKNIK UNIV.BRAWIJAYA

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

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

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

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

6. 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
Components of the shear box
Preparation of a sand specimen
Porous plates

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

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

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

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

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

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

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

14. Direct shear tests on sands
Some important facts on strength parameters c and f of sand
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

15. 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
Shear stress at failure, tf
Normal force, s f’
Normally consolidated clay (c’ = 0)
Overconsolidated clay (c’ ≠ 0)

16. 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)
Where,
ca = adhesion,
d = angle of internal friction

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

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

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

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

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

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

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

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

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

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

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

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

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

30. CD tests fd s or s’ Failure envelopes For sand and NC Clay, cd = 0
Shear stress, t
s or s’ fd
Mohr – Coulomb failure envelope
s3a
s1a
(Dsd)fa
Therefore, one CD test would be sufficient to determine fd of sand or NC clay

31. t CD tests f c s or s’ Failure envelopes For OC Clay, cd ≠ 0 OC NC s3
(Dsd)f c sc OC NC

32. Some practical applications of CD analysis for clays
1. Embankment constructed very slowly, in layers over a soft clay deposit
Soft clay t
t = in situ drained shear strength

33. Some practical applications of CD analysis for clays
t = drained shear strength of clay core t
Core
2. Earth dam with steady state seepage

34. Some practical applications of CD analysis for clays
3. Excavation or natural slope in clay t
t = In situ drained shear strength
Note: CD test simulates the long term condition in the field. Thus, cd and fd should be used to evaluate the long term behavior of soils

35. Consolidated- Undrained test (CU Test)
Total, s =
Neutral, u
Effective, s’ +
Step 1: At the end of consolidation
sVC
shC
s’VC = sVC
s’hC = shC
Drainage
Step 2: During axial stress increase
sVC + Ds
shC
s’V = sVC + Ds ± Du = s’1
s’h = shC ± Du = s’3
No drainage
±Du
Step 3: At failure
sVC + Dsf
shC
s’Vf = sVC + Dsf ± Duf = s’1f
s’hf = shC ± Duf = s’3f
No drainage
±Duf

36. Consolidated- Undrained test (CU Test)
Volume change of sample during consolidation
Volume change of the sample
Expansion
Compression
Time

37. Consolidated- Undrained test (CU Test)
Stress-strain relationship during shearing
Deviator stress, Dsd
Axial strain
Dense sand or OC clay
(Dsd)f
Loose sand or NC Clay
(Dsd)f Du + -
Axial strain
Loose sand /NC Clay
Dense sand or OC clay

38. CU tests fcu s or s’ s3 Shear stress, t s3b s1b s3a s1a (Dsd)fa
How to determine strength parameters c and f
Deviator stress, Dsd
Axial strain
(Dsd)fb
Confining stress = s3b
s1 = s3 + (Dsd)f s3
Total stresses at failure
(Dsd)fa
Confining stress = s3a
Shear stress, t
s or s’
fcu
Mohr – Coulomb failure envelope in terms of total stresses
ccu
s3b
s1b
s3a
s1a
(Dsd)fa

39. CU tests f’ fcu s or s’ s’3 = s3 - uf Shear stress, t (Dsd)fa s3b s1b
How to determine strength parameters c and f
s’1 = s3 + (Dsd)f - uf
s’3 = s3 - uf uf
Mohr – Coulomb failure envelope in terms of effective stresses f’ C’
Effective stresses at failure
Shear stress, t
s or s’
Mohr – Coulomb failure envelope in terms of total stresses
fcu
(Dsd)fa
s3b
s1b
ufb
ufa
ccu
s’3b
s’1b
s3a
s1a
s’3a
s’1a
(Dsd)fa

40. CU tests Strength parameters c and f obtained from CU tests
Shear strength parameters in terms of effective stresses are c’ and f’
Shear strength parameters in terms of total stresses are ccu and fcu
c’ = cd and f’ = fd

41. CU tests f’ fcu s or s’ Failure envelopes
For sand and NC Clay, ccu and c’ = 0
Shear stress, t
s or s’
fcu
Mohr – Coulomb failure envelope in terms of total stresses
s3a
s1a
(Dsd)fa f’
Mohr – Coulomb failure envelope in terms of effective stresses
Therefore, one CU test would be sufficient to determine fcu and f’(= fd) of sand or NC clay

42. Some practical applications of CU analysis for clays
1. Embankment constructed rapidly over a soft clay deposit
Soft clay t
t = in situ undrained shear strength

43. Some practical applications of CU analysis for clays
2. Rapid drawdown behind an earth dam t
Core
t = Undrained shear strength of clay core

44. Some practical applications of CU analysis for clays
3. Rapid construction of an embankment on a natural slope
t = In situ undrained shear strength t
Note: Total stress parameters from CU test (ccu and fcu) can be used for stability problems where,
Soil have become fully consolidated and are at equilibrium with the existing stress state; Then for some reason additional stresses are applied quickly with no drainage occurring

45. Unconsolidated- Undrained test (UU Test)
Data analysis
s3 + Dsd s3
No drainage
Specimen condition during shearing
sC = s3
No drainage
Initial specimen condition
Initial volume of the sample = A0 × H0
Volume of the sample during shearing = A × H
Since the test is conducted under undrained condition,
A × H = A0 × H0
A ×(H0 – DH) = A0 × H0
A ×(1 – DH/H0) = A0

46. Unconsolidated- Undrained test (UU Test)
Step 1: Immediately after sampling
Step 2: After application of hydrostatic cell pressure
s’3 = s3 - Duc
sC = s3
No drainage
Duc = +
Increase of pwp due to increase of cell pressure
Duc = B Ds3
Increase of cell pressure
Skempton’s pore water pressure parameter, B
Note: If soil is fully saturated, then B = 1 (hence, Duc = Ds3)

47. Unconsolidated- Undrained test (UU Test)
Step 3: During application of axial load
s’1 = s3 + Dsd - Duc  Dud
s’3 = s3 - Duc  Dud
s3 + Dsd s3
No drainage =
Duc ± Dud +
Increase of pwp due to increase of deviator stress
Dud = ABDsd
Increase of deviator stress
Skempton’s pore water pressure parameter, A

48. Unconsolidated- Undrained test (UU Test)
Combining steps 2 and 3,
Duc = B Ds3
Dud = ABDsd
Total pore water pressure increment at any stage, Du
Du = Duc + Dud
Du = B [Ds3 + ADsd]
Skempton’s pore water pressure equation
Du = B [Ds3 + A(Ds1 – Ds3]

49. Unconsolidated- Undrained test (UU Test)
Total, s =
Neutral, u
Effective, s’ +
Step 1: Immediately after sampling
s’V0 = ur
s’h0 = ur
-ur
Step 2: After application of hydrostatic cell pressure
s’VC = sC + ur - sC = ur
s’h = ur sC
No drainage
-ur + Duc = -ur + sc
(Sr = 100% ; B = 1)
Step 3: During application of axial load
s’V = sC + Ds + ur - sc  Du
s’h = sC + ur - sc  Du
sC + Ds sC
No drainage
-ur + sc ± Du
Step 3: At failure
s’hf = sC + ur - sc Duf = s’3f
s’Vf = sC + Dsf + ur - sc  Duf = s’1f sC
sC + Dsf
No drainage
-ur + sc ± Duf

50. Unconsolidated- Undrained test (UU Test)
Total, s =
Neutral, u
Effective, s’ +
Step 3: At failure
s’hf = sC + ur - sc Duf = s’3f
s’Vf = sC + Dsf + ur - sc  Duf = s’1f
-ur + sc ± Duf sC
sC + Dsf
No drainage
Mohr circle in terms of effective stresses do not depend on the cell pressure.
Therefore, we get only one Mohr circle in terms of effective stress for different cell pressures
s’3
s’1
Dsf t s’

51. Unconsolidated- Undrained test (UU Test)
Total, s =
Neutral, u
Effective, s’ +
Step 3: At failure
s’hf = sC + ur - sc Duf = s’3f
s’Vf = sC + Dsf + ur - sc Duf = s’1f
-ur + sc ± Duf sC
sC + Dsf
No drainage
Mohr circles in terms of total stresses
Failure envelope, fu = 0 t
s or s’ cu
s’3
s’1
s3a
s1a
Dsf
s3b
s1b ub ua

52. Unconsolidated- Undrained test (UU Test)
Effect of degree of saturation on failure envelope t
s or s’
S < 100%
S = 100%
s3a
s1a
s3b
s1b
s3c
s1c

53. Some practical applications of UU analysis for clays
1. Embankment constructed rapidly over a soft clay deposit
Soft clay t
t = in situ undrained shear strength

54. Some practical applications of UU analysis for clays
2. Large earth dam constructed rapidly with no change in water content of soft clay
t = Undrained shear strength of clay core t
Core

55. Some practical applications of UU analysis for clays
3. Footing placed rapidly on clay deposit
t = In situ undrained shear strength
Note: UU test simulates the short term condition in the field. Thus, cu can be used to analyze the short term behavior of soils

56. s1 = sVC + Ds s3 = 0 Unconfined Compression Test (UC Test)
Confining pressure is zero in the UC test

57. Unconfined Compression Test (UC Test)
s1 = sVC + Dsf
s3 = 0
Shear stress, t
Normal stress, s qu
τf = σ1/2 = qu/2 = cu

58. Various correlations for shear strength
For NC clays, the undrained shear strength (cu) increases with the effective overburden pressure, s’0
Skempton (1957)
Plasticity Index as a %
For OC clays, the following relationship is approximately true
Ladd (1977)
For NC clays, the effective friction angle (f’) is related to PI as follows
Kenny (1959)

59. Shear strength of partially saturated soils
In the previous sections, we were discussing the shear strength of saturated soils. However, in most of the cases, we will encounter unsaturated soils
Solid
Unsaturated soils
Pore water pressure, uw
Effective stress, s’
Water
Air
Pore air pressure, ua
Solid
Water
Saturated soils
Pore water pressure, u
Effective stress, s’
Pore water pressure can be negative in unsaturated soils

60. Shear strength of partially saturated soils
Bishop (1959) proposed shear strength equation for unsaturated soils as follows
Where,
sn – ua = Net normal stress
ua – uw = Matric suction
= a parameter depending on the degree of saturation
(c = 1 for fully saturated soils and 0 for dry soils)
Fredlund et al (1978) modified the above relationship as follows
Where,
tanfb = Rate of increase of shear strength with matric suction

61. t s - ua Shear strength of partially saturated soils f’
Same as saturated soils
Apparent cohesion due to matric suction
Therefore, strength of unsaturated soils is much higher than the strength of saturated soils due to matric suction t
s - ua
(ua – uw)2 > (ua – uw)1
(ua – uw)1 > 0 f’
ua – uw = 0

62. t s - ua f’ How it become possible build a sand castle
Same as saturated soils
Apparent cohesion due to matric suction t
s - ua
(ua – uw) > 0
Failure envelope for unsaturated sand
Apparent cohesion f’
ua – uw = 0
Failure envelope for saturated sand (c’ = 0)