1. FE: Geotechnical Engineering

2. Geotechnical Engineering I
Topics
Weight Volume relations
Permeability and flow net
Effective stress
Vertical stresses under foundations
Consolidation
Geology
Index properties and soil classifications
Phase relations (air-water-solid)
Laboratory and field tests
Effective stress (buoyancy)
Stability of retaining walls (e.g., active pressure/passive pressure)
Shear strength
Bearing capacity (cohesive and noncohesive)
Foundation types (e.g., spread footings, deep foundations, wall footings, mats)
Consolidation and differential settlement
Seepage/flow nets
Slope stability (e.g., fills, embankments, cuts, dams)
Soil stabilization (e.g., chemical additives, geosynthetics)
Drainage systems
Erosion control
Prof. Monica Prezzi

3. Weight and volume relations
Question 1:

4. Weight and volume relations

5. Weight and volume relations

6. Permeability and Flow Net

7. Permeability and Flow Net
For the flow net shown, what is the number of incremental head drops Nd? What is the number of flow channels Nf?
Calculate the pore water pressure u at points I, J and K.
What is the total flow rate q (m3/s per meter perpendicular to the figure)? The hydraulic conductivity K of the sand is equal to 10-4m/s.

8. Permeability and Flow Net

9. Permeability and Flow Net
Geotechnical Engineering I
Permeability and Flow Net
Number of incremental head losses = 11
Number of flow tubes = 4
Drop per equipotential line = (39-30)/11
Pore water pressure = (upstream head – drop in head – Elevation head) unit weight of water.
Prof. Monica Prezzi

10. Permeability and Flow Net
Geotechnical Engineering I
Permeability and Flow Net
Number of incremental head losses = 11
Number of flow tubes = 4
I =
J =
K =
Prof. Monica Prezzi

11. Effective Stress
The soil profile shown in the figure consists of two soil layers with different dry densities. The average degree of saturation of soil A is 30%. The water table is at 2m depth. Assume that the specific gravity is equal to 2.7 for both soils. Calculate the following values for both soils:
Total vertical stress at P and O
Pore water pressures u at P and O
Effective stress at P and O
Dry density = 17 kN/m3
Dry density = 18 kN/m3

12. Effective stress Concept
Effective stress controls the deformation of the soil
It is defined as the difference of total stress and pore water pressure
Pore water pressure
Effective stress
Total stress

13. Effective Stress Total stress at P
Wet unit weight of soil × depth of soil layer
Wet unit weight of soil
dry unit weight × (1 + Water content)
Water content can be obtained from:
Unit weight of water (9.81)
Saturation (0.3)
Specific gravity (2.7)
Void ratio (0.56)
Water content (?)
wc =
Dry unit weight of Soil (17)

14. Effective Stress Total stress at P
Wet unit weight of soil × depth of soil layer
Wet unit weight of soil
dry unit weight × (1 + Water content)
17 × ( ) = kN/m3

15. Effective Stress Total stress at P Pore water pressure at P = 0
Wet unit weight of soil × depth of soil layer
18.06 × 2 = kN/m2
Pore water pressure at P = 0
Effective stress at P
Total stress - Pore water pressure
36.12 – 0 = kN/m2
Dry density = 17 kN/m3
Dry density = 18 kN/m3

16. Effective Stress Effective stress at O Total stress from Soil A
Dry density = 17 kN/m3
Dry density = 18 kN/m3
Total stress from Soil A
Total stress from Soil B
Pore water pressure from water table
Pore water pressure
Effective stress
Total stress

17. Effective Stress Total stress at O
Wet unit weight of soil × depth of soil layers (A & B)
Wet unit weight of soil B
dry unit weight × (1 + Water content)
Water content can be obtained from:
Unit weight of water (9.81)
Saturation (1.0)
Specific gravity (2.7)
Void ratio (0.47)
Water content (?)
wc = 0.17
Dry unit weight of Soil (18)

18. Effective Stress Total stress at O due to soil B
Wet unit weight of soil B × depth of soil layer B
Wet unit weight of soil
dry unit weight × (1 + Water content)
18 × (1+0.17) = kN/m3

19. Effective Stress Total stress at O
Wet unit weight of soil × depth of soil layer (A & B)
× 3 = 99.3 kN/m2
Pore water pressure at O = 3 × 9.81 = kN/m2
Effective stress at O
Total stress - Pore water pressure
99.3 – = kN/m2
Dry density = 17 kN/m3
Dry density = 18 kN/m3

20. Vertical Stresses under Foundation
If a 200 kN load is applied on a square foundation with dimension of 2X2 m, located at top of soil surface, what would be the increase in stress at 5 m depth of soil?

21. Vertical Stresses under Foundation
200 kN
0.5
2 m 1
2 m
5 m
5 m
5 m
2.5 m
2.5 m
7 m

22. Vertical Stresses under Foundation
200 kN
2 m
2 m
5 m
7 m
7 m

23. Vertical Stresses under Foundation
Load = 200 kN
Area at depth of 5 m = 7 X 7 m2 = 49 m2
Stress at depth of 5 m:
Load / Area at depth of 7 m = 200/49
Stress = 4.08 kN/m2

24. Geotechnical Engineering I
Consolidation
Estimate the change in thickness of a layer of NC clay shown in the figure (next slide) after application of a uniform surcharge of 150 psf.
Cc=0.4
The specific gravity of clay particles is 2.75
Water content = 28%
Saturation = 100%
If cv= 0.1 ft2/day , then determine the time required for 50% consolidation
Add bossinesque and wesstergaard
Prof. Monica Prezzi

25. Normally consolidated clay
Surcharge = 1000 lb/ft2
Sand sat=110 lb/ft3
Sand
8 ft
Normally consolidated clay
sat=110 lb/ft3
2 ft

26. Consolidation Concepts:
The process by which settlement happens is called consolidation:
Saturated soils are made up of the solid particles and pores filled with water
When load is applied, it is completely taken by the water in the pores
This causes the pore water pressure to rise
Pore water wants to loose this excess pressure so it starts to flow out
As pore water flows out (and pre water pressure decreases), the soil settles

27. Geotechnical Engineering I
Consolidation
Steps of calculation of change in layer thickness:
Calculate initial void ratio of clay layer
Calculate initial effective stress at center of clay layer clay layer before application of load
Calculate final effective stress at center of clay layer after application of load
Use consolidation formula to calculate strain
Calculate change in height from calculated strain
One more question about preconsolidation pressure
Prof. Monica Prezzi

28. Consolidation e = 0.77 Calculate initial void ratio of clay layer
Gs = 2.75
wc= 28%
S (saturation) = 100%
e = 0.77

29. Geotechnical Engineering I
Consolidation
Steps of calculation of change in layer thickness:
Calculate initial void ratio of clay layer
Calculate initial effective stress at center of clay layer clay layer before application of load
Calculate final effective stress at center of clay layer after application of load
Use consolidation formula to calculate strain
Calculate change in height from calculated strain
One more question about preconsolidation pressure
Prof. Monica Prezzi

30. Normally consolidated clay
Consolidation
Calculate initial effective stress at center of clay layer clay layer before application of load
Sand sat=110 lb/ft3
Sand
8 ft
Normally consolidated clay
sat=110 lb/ft3
2 ft
2 ft
6 ft
4 ft

31. Consolidation Effective stress at center of clay layer at start:
Total stress from sand layer = 110  2 = 220 psf
Total stress from clay layer = 110  4 = 440 psf
Stress from pore water (pore water pressure)
u = 62  6 = 372 psf
Pore water pressure
Effective stress
Total stress
Effective stress = ( ) – 372 = 288 psf

32. Geotechnical Engineering I
Consolidation
Steps of calculation of change in layer thickness:
Calculate initial void ratio of clay layer
Calculate initial effective stress at center of clay layer clay layer before application of load
Calculate final effective stress at center of clay layer after application of load
Use consolidation formula to calculate strain
Calculate change in height from calculated strain
One more question about preconsolidation pressure
Prof. Monica Prezzi

33. Normally consolidated clay
Consolidation
Effective stress at center of clay layer after application of load:
Surcharge = 1000 lb/ft2
Sand sat=110 lb/ft3
Sand
8 ft
Normally consolidated clay
sat=110 lb/ft3
2 ft

34. Consolidation
Effective stress at center of clay layer after application of load:
1000 psf (surcharge) + effective stress at start
= 1288 psf

35. Geotechnical Engineering I
Consolidation
Steps of calculation of change in layer thickness:
Calculate initial void ratio of clay layer
Calculate initial effective stress at center of clay layer clay layer before application of load
Calculate final effective stress at center of clay layer after application of load
Use consolidation formula to calculate strain
Calculate change in height from calculated strain
One more question about preconsolidation pressure
Prof. Monica Prezzi

36. Consolidation Consolidation formula
Effective stress at center of clay layer at start (288 psf)
0.4
Effective stress at center of clay layer after application of surcharge (1288 psf)
0.77

37. Geotechnical Engineering I
Consolidation
Steps of calculation of change in layer thickness:
Calculate initial void ratio of clay layer
Calculate initial effective stress at center of clay layer clay layer before application of load
Calculate final effective stress at center of clay layer after application of load
Use consolidation formula to calculate strain
Calculate change in height from calculated strain
One more question about preconsolidation pressure
Prof. Monica Prezzi

38. Geotechnical Engineering I
Consolidation
Change in height
0.17
8 ft
Prof. Monica Prezzi

39. Geotechnical Engineering I
Consolidation
Steps of calculation of change in layer thickness:
Calculate initial void ratio of clay layer
Calculate initial effective stress at center of clay layer clay layer before application of load
Calculate final effective stress at center of clay layer after application of load
Use consolidation formula to calculate strain
Calculate change in height from calculated strain
One more question about preconsolidation pressure
Prof. Monica Prezzi

40. Consolidation
If cv= 0.1 ft2/day , then determine the time required for 50% consolidation
Steps:
Figure out if clay layer has single or double drainage
Use formula to calculate Tv (time factor)
Use proper formula
From Tv calculate t (time)

41. Normally consolidated clay
Consolidation
Single or double drainage
Sand sat=110 lb/ft3
Sand
8 ft
Normally consolidated clay
sat=110 lb/ft3
2 ft
Double drainage

42. Consolidation
Steps:
Figure out if clay layer has single or double drainage
Use formula to calculate Tv (time factor)
Use proper formula
From Tv calculate t (time)

43. Geotechnical Engineering I
Consolidation
Calculation of time factor
% consolidation in decimal (0.5)
U < 0.526
U > 0.526
Tv =
Prof. Monica Prezzi

44. Consolidation
Steps:
Figure out if clay layer has single or double drainage
Use formula to calculate Tv (time factor)
Use proper formula
From Tv calculate t (time)

45. Consolidation t = 31.4 days From Tv calculate t (time)
Drainage height (8ft/2 = 4ft)
Coefficient of consolidation (0.1 ft2/day)
t = 31.4 days

46. Geotechnical Engineering I
Questions ?
Prof. Monica Prezzi