1. ECGD 4122 – Foundation Engineering
Faculty of Applied Engineering and Urban Planning
Civil Engineering Department
2nd Semester 2008/2009
ECGD 4122 – Foundation Engineering
Lecture 4

2. Content
Shear Strength
Subsoil Exploration

3. Mohr-Coulomb Failure Criterion
Total Stresses:
Coulomb approximation for shear stress on the failure plane:

4. Mohr-Coulomb Failure Criterion

5. Shear Strength Measurement
Based on Mohr’s circle criteria, two ways are possible to cause failure:

6. Shear Strength Measurement
First:
Increase the normal stress in one direction

7. Shear Strength Measurement
Second:
Apply shear directly

8. Shear Strength Measurement
3=0 1
Direct Shear
Uniaxial Compression

9. Shear Strength Measurement1
Unconfined compression test is used when  = 0 assumption is valid
Triaxial compression is a more generalized version
The soil sample is first compressed isotropically and then sheared by axial loading 3
Triaxial Compression

10. Direct Shear Test

11. Direct Shear Test

12. Direct Shear Test

13. Direct Shear Test

14. Direct Shear Test

15. Direct Shear Test

16. Direct Shear Test

17. Unconfined Compression Test
3 = 0 1
For clay soils
Cylindrical specimen
No confining stresses
(i.e. 3 = 0)
Axial stress = 1
Uniaxial Compression

18. Unconfined Compression Test
3=0 1
Uniaxial Compression

19. Unconfined Compression Test Data

20. Unconfined Compression Test Data

21. Unconfined Compression Test Data

22. Unconfined Compression Test
3=0 1
Uniaxial Compression 
Max. shear plane
Horiz. plane  1

23. Unconfined Compression Test

24. Triaxial Compression Test

25. Triaxial Compression Test

26. Triaxial Compression Tests
Unconsolidated Undrained (UU-Test); Also called “Undrained” Test
Consolidated Undrained Test (CU- Test)
Consolidated Drained (CD-Test); Also called “Drained Test”

27. Consolidated Undrained Triaxial Test for Undisturbed Soils

28. Shear Strength in terms of Total Stress
Shear Strength in terms of effective stress
Shear strength in terms of total stress
hydrostatic pore pressure

29. Shear Strength Total Stress -  = 0 condition
Shear strength in terms of total stress
For cohesive soils under saturated conditions,  = 0.

30. Mohr-Coulomb Failure Criterion
Shear Strength,S
 = 0 C
Normal Stress, 

31. Subsoil Exploration Boring Sampling Standard Penetration Test (SPT)
Vane Shear Test
Cone Penetration Test (CPT)
Observation of Water Table

32. Boring
Boring Spacing

33. Boring
ASTM Method

34. ASTM Method for Calculating Depth of Boring

35. Boring Methods
Auger
3-5 m deep
Hand-driven

36. Boring Methods
Flight Auger
1-3 steps
Tractor
mounted

37. Boring Methods
Rotary drilling
Wash boring

38. Common Sampling Methods
Standard Split Spoon
The sampler is driven into the soil at the bottom of the borehole by means of hammer blows.

39. Sampling

40. Sampling

41. Sampling

42. Common Sampling Methods
Standard Split Spoon
The number of blows required for driving the sampler through three mm (6”) intervals is recorded. The sum of the number of blows required for driving the last two mm (6 in.) intervals is defined as the standard penetration number (N).

43. Standard Penetration Number

44. Standard Penetration Number

45. Vane Shear Test

46. Vane Shear Test

47. Vane Shear Test

48. Cone Penetration Test Measures: The Cone Resistance
The Frictional Resistance

49. Cone Penetration Test

50. Cone Penetration Test

51. Cone Penetration Test

52. Assignment # 1
Determine the effective stress at point X for the two cases shown below. The drawing is not to scale. Take sat = 19 kN/m3.

53. Assignment # 1 Static condition: s = (9.81)(0.6) + (19)(1) = 24.89 kPa
u = ( )(9.81) = kPa
s’ = s – u = 9.19 kPa
Flow-down condition:
i = h/L = 0.6/3.0 = 0.2
u = ( )(9.81) - (0.2)(1.0)(9.81) = kPa
s’ = s – u = kPa

54. Assignment # 2
A soil deposit is composed of clay with Sat = 20 kN/m3. The GWT is at the ground surface. Calculate the shear strength on a horizontal plane at a depth of 10m, if c’ = 5 kPa and ’ = 30º.

55. Assignment # 2 t = c’ + s’tanf’ s’ = (20)(10) – (9.81)(10) = 101.9 kPa
t = 5 + (101.9)(tan30º) = kPa

56. Assignment # 2
A drained direct shear test is performed on a normally consolidated silty soil. The soil sample is 75 mm in diameter and 25 mm in height. The vertical load is 883 N and the shear force at failure is 618 N. Calculate c and .

57. Assignment # 2 Drained test  t = c + stanf
Normally consolidated soil  c = 0
t = c + stanf  t = stanf  f = tan-1(t/s)
t = S/A = 618/[(37.510-3)2]
t = kPa
s = N/A = 883/[(37.510-3)2]
s = kPa
 f = tan-1(139.89/199.87)  35º

58. Quiz # 1
Determine the height of water level (H) above the surface of gravel, given that the flow rate (q) is to be maintained at 40 liters per second.

59. Quiz # 1
q1 = q2 = q = 4010-3 m3/s
a1 = a2 = a = r2 = (0.75)2 = m2
v1 = v2 = v = q/a = 2.26410-2 m/s
i1 = v1/k1 = 2.26410-2/1010-2 =
i2 = v2/k2 = 2.26410-2/110-2 = 2.264
i1 = = h1/L1 = (H + 1 – z)/(1.0)
i2 = = h2/L2 = (z + 1)/(1.0)
Solving the equations for z and H 
z = m
H = m

60. Quiz # 1

61. Quiz # 2
For a clay deposit: Cc = 0.4 and Cr = 0.05, determine the final void ratio for each of the following loading conditions:
a) Initially s¢ = 50 kPa, e = 1.2, Finally s¢ = 90 kPa, and given that s¢pc = 100 kPa
b) Initially s¢ = 50 kPa, e = 1.2, Finally s¢ = 190 kPa, and given that s¢pc = 100 kPa

62. Quiz # 2 C = slope = e/logs’ = (ei – ef)/log(s’f/s’i)
(a) = (1.2 – ef)/log(90/50)
 ef = 1.187
(b) Two stages:
0.05 = (1.2 – efi)/log(100/50)
 efi = 1.185
0.4 = (1.185 – ef)/log(190/100)
 ef = 1.073