Settlement of Foundation

1. CVLE451
1
Lecture 6: Settlement of
Foundations

2. Settlement
• Immediate Settlement: Occurs immediately after the construction. This is
computed using elasticity theory (Important for Granular soil)
• Primary Consolidation: Due to gradual dissipation of pore pressure induced
by external loading and consequently expulsion of water from the soil mass,
hence volume change. (Important for Inorganic clays)
• Secondary Consolidation: Occurs at constant effective stress with volume
change due to rearrangement of particles. (Important for Organic soils)
2
Settlement
S = Se + Sc + Ss
Immediate
Settlement
Se
Primary
Consolidation
Sc
Secondary
Consolidation
Ss
For any of the above mentioned settlement calculations, we first need vertical
stress increase in soil mass due to net load applied on the foundation

3. Stress Distribution: Concentrated load
3
Boussinesq Analysis
Where
,

4. Vertical Stress: Concentrated load
4
Influence Factor for
General solution of vertical stress
2
z B
P
I
z
 
0.0
0.1
0.2
0.3
0.4
0.5
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
B
I
r z

5. Vertical Stress: Uniformly Distributed
Circular Load
5

6. Vertical Stress: Uniformly Distributed Circular Load
6
Rigid Plate on half Space

7. Vertical Stress: Rectangular Area
7

8. Vertical Stress: Rectangular Area
8

9. 9
Pressure Bulb
Square Footing Strip Footing

10. Pressure
Bulb for
Square
Foundation
10

11. 11
Pressure
Bulb for
Circular
Foundation

12. Newmark’s Chart
12
Influence Value
This Model is good for normally-consolidated, lightly
overconsolidated clays, and variable deposits

13. Newmark’s Chart
• Determine the depth, z, where you wish to
calculate the stress increase
• Adopt a scale as shown in the figure
• Draw the footing to scale and place the
point of interest over the center of the
chart
• Count the number of elements that fall
inside the footing, N
• Calculate the stress increase as:
13
Point of
stress
calculation
Depth = z1
Depth = z2

14. Westergaard’s Method
• Provided solution for layered soils
• Point Loads
• Assumption:
Elastic soil mass is laterally reinforced by numerous, closely
spaced, horizontal sheets of negligible thickness but infinite
rigidity, that allow only vertical movement , preventing the
mass as a whole from undergoing any lateral strain.
14
 
3
2
2
2 2
1
2
z
P
z C r z


 
  

 
 
 
1 2
2 1
C





This Model is specially good for pre-compressed or
overconsolidated clays

15. 15
Westergaard’s influence Chart

16. Fröhlich Chart with
concentration factor m‘ = 4
16
 
0.005 .
z n q

 
This Model is especially good
for Sands

17. Simplified Methods (Poulos and Davis, 1974)
17
1.5
2
1 1 ( )
2
z zD
B
q
z
 

 
 
 
  
    
 
 
 
 
 
 
 
Circular Foundation:
Square Foundation:
1.76
2
1 1 ( )
2
z zD
f
B
q
z
 

 
 
 
 
  
    
 
 
 
 
 
 
 
 

18. Simplified Methods (Poulos and Davis, 1974)
18
Strip Foundation:
Rectangular Foundation:
2.60
2
1 1 ( )
2
z zD
f
B
q
z
 

 
 
 
 
  
    
 
 
 
 
 
 
 
 
 
2.60 0.84 /
1.38 0.62 /
1 1 ( )
2
B L
B L
z zD
f
B
q
z
 
 

 
 
 
 
  
    
 
 
 
 
 
 
 
 

19. Approximate
Methods
19
   
.
.
z
B L
q
B z L z

 
 
 
2
2
z
B
q
B z

 

 
z
B
q
B z

 

Rectangular Foundation:
Square/Circular Foundation:
Strip Foundation:

20. Contact Pressure and Settlement Distribution
20
Cohesive Soil - Flexible Footing
Cohesive Soil - Rigid Footing
Granular Soil Flexible Footing
Granular Soil - Rigid Footing

21. Elastic Settlement of Foundation
21
 
0 0
1
H H
e z z s x s y
s
S dz dz
E
     
      
 
s
E  Modulus of elasticity
H  Thickness of soil layer
s
  Poisson’s ratio of soil
Elastic settlement:
Elastic settlement for Flexible Foundation:
 
2
1
e s f
s
qB
S I
E

 
f
I = influence factor: depends on the rigidity and shape of the foundation
s
E = Avg elasticity modulus of the soil for (4B) depth below foundn level

22. Elastic Settlement of Foundation
22
E in kPa

23. Elastic Settlement of Foundations
23

24. Elastic Settlement of Foundations
24
Soil Strata with
Semi-infinite depth

25. Steinbrenner’s Influence Factors for Settlement of the Corners of
loaded Area LxB on Compressible Stratus of  = 0.5, and Thickness Ht
25

26. Strain Influence Factor Method for Sandy Soil:
Schmertmann and Hartman (1978)
26
 
2
1 2
0
z
z
e f
s
I
S C C q D z
E

  

1
C  Correction factor for foundation depth
 
 
1 0.5 f f
D q D
 
 
 
 
2
C  Correction factor for creep effects
q For square and circular foundation:
For foundation with L/B >10:
Interpolate the values for 1 < L/B < 10
 
1 0.2log time in years 0.1
 

 

27. Example
27
 
2
1 2
0
z
z
e f
s
I
S C C q D z
E

  

3.5
s c
E q

2
31.39
f
D kN m
 
2.5
s c
E q

For square and
circular foundations
For rectangular
foundations
800 in kPa
s
E N

Correlation with SPT data:

28. Burland and Burbidge’s Method for Sandy Soils
Depth of Stress Influence (z'):
28
 
0.75
1.04 ,where B is in meters
z B
 
If N60 is constant or increasing with depth, then
If N60 is decreasing with depth, use smaller of
 
 
2
1 2 3
1.25
0.25
e
L B
S Bq
L B
  
 

  

 
 
Elastic Settlement (Se):
where B is in meters
and is in kPa
q
1
  0.0047 for NC sand
0.0016 for OC sand with qna ≤ po‘
0.0047 for OC sand with qna ≤ po‘
 
 
1.4
2
1.4
1.71
0.57
N
N
 



Compressibility Index: for NC sand
for OC sand
3 2 1
z z
z z

 
 
  
 
 
 
for NC sand and for OC sand with qna ≤ po‘
for OC sand with qna ≤ po‘
0.67
na o
q q p
 
 
na
q q
 
2 and Thickness of soft layer below foundation
z B z z
  
  

29. Settlement due to Primary Consolidation
29
log log
1 1
s c c c c o av
c
o o o c
C H C H
S
e e
  
 
   
  
 
 
   
 
 
   
log
1
s c o av
c
o o
C H
S
e
 

 
 
 
  

  
log
1
c c o av
c
o o
C H
S
e
 

 
 
 
  

  
For NC clay
For OC clay  
o av c
  
  
  
For OC clay  
o c o av
   
   
   
 
c o o av
   
   
   
o
  Average effective vertical stress before construction
av

  Average increase in effective vertical stress
c
  Effective pre-consolidation pressure
o
e  Initial void ratio of the clay layer
c
C  Compression Index
s
C  Swelling Index
c
H  Thickness of the clay layer
 
1
4
6
av t m b
   
   
      
t


b


m



30. Settlement Correction for Effect of 3-D Consolidation
30
   
3 1
c c
D D
S S



31. Fox’s Depth Correction Factor
for Rectangular Footings of
L x B at Depth D
31
 
 
Depth factor
c Embedded
c Surface
S
S

Rigidity Factor
Total settlement of
rigid foundation
Total settlement at the center
of flexible foundation
Rigidity factor 0.8


32. Settlement Due to Secondary
Compression
32
2
1
log
1
c
s
p
C H t
S
e t

 
  
  
p
e 
C  Secondary Compression Index
 
2 1
log
e
t t


Time, t (Log scale)
Void
Ratio,
e
p
e
1
t 2
t
e

Void ratio at the end of primary consolidation
c
H  Thickness of Clay Layer
Secondary compression settlement is more important in the
case of organic and highly-compressible inorganic clays

33. Total Settlement
from SPT Data for
Cohesionless soils
33
Multiply the settlement
by factor W'

34. Total Settlement from CPT Data for
Cohesionless Soils
• Depth profile of cone resistance
can be divided in several segments
of average cone resistance
• Average cone resistance can be
used to calculate constant of
compressibility.
• Settlement of each layer is
calculated separately due to
foundation loading and then
added together
34
3
2
c
o
q
C

 
  
 
ln
t o
t
o
H
S
C
 

 
 
  
 

35. Plate Load Test
35

36. Plate Load Test
• Rough mild steel bearing plate in circular or square shape
• Dimension: 30 cm, 45 cm, 60 cm, or 75 cm.
Thickness > 25 mm
• Smaller size for stiff or dense soil. Larger size for soft or loose soil
• Bottom of the plate is grooved for increased roughness.
• Concrete blocks may be used to replace bearing plates.
36
Bearing Plate:

37. Plate Load Test
• Usually to the depth of foundation level.
• Width equal to five times the test plate
• Carefully leveled and cleaned bottom.
• Protected against disturbance or change in natural formation
37
Section
Plan
Test Pit:

38. Plate Load Test
• Selection of Location
– Based on the exploratory boring.
– Test is carried out at the level of proposed foundation. If water table is
below the foundation level but the depth is less than width of plate then
the test is carried out at the level of water table. If the water table is above
the foundation level then the water level is reduced to proposed foundation
level by pumping out the water during the test; however, in case of high
permeability material perform the test at the level of water table.
– In case the soil is expected to have significant capillary action and the water
table is within 1 m below the foundation, it becomes necessary to perform
the test at the level of water table in order to avoid the effect of higher
effective stresses due to capillary action resulting in lower values of
interpreted settlements.
• Reaction supports should be at least (3.5 x width of plate) away from the test
plate location, and loading arrangement should provide sufficient working
space.
• Test plate should be placed over a 5 mm thick sand layer and it should be
centered with the loading arrangement.
38
Procedure:

39. Plate Load Test
• A seating pressure of 7 kPa is applied and then released after some time before
the test.
• Loads are applied in the increments of approximately 1/5th of the estimated
ultimate safe load. (Or, one may choose to increase the load at an increment of
0.5 kN.)
• At each load settlement is recorded at time intervals of 1, 2, 4, 6, 9, 16, 25 min
and thereafter at intervals of one hour.
• For clayey soil, the load is increased when time settlement curve shows that the
settlement has exceeded 70-80% of the probable ultimate settlement or a
duration of 24 Hrs.
• For the other soils, the load is increased when the settlement rate drops below
0.02 mm/min.
• The minimum duration for any load should, however, be at least 60 min.
• Dial gauges used for testing should have at least 25 mm travel and 0.01 mm
accuracy.
• The load settlement curve can then be platted from settlement data.
39
Procedure: (Contd.)

40. Plate Load Test – Load-Settlement Curve
40
Zero Correction:

41. Plate Load Test – Load-Settlement Curve
41
Terzaghi and Peck (1948):
 
 
2
30
30
f p
f
p p f
B B
S
S B B
 

 


 
 
f
S  Settlement of a foundation of
width Bf (cm)
p
S  Settlement of the test plate of
width Bp (cm) at the same load
intensity as on the foundation
Bond (1961):
n
f f
p p
S B
S B
 
  
 
 
Soil Index - n
Clay 1.03 to 1.05
Sandy clay 1.08 to 1.10
Loose sand 1.20 to 1.25
Medium sand 1.25 to 1.35
Dense sand 1.40 to 1.50

42. Plate Load Test: Some Considerations
• The width of test plate should not be less than
30 cm. It is experimentally shown that the load
settlement behavior of soil is qualitatively
different for smaller widths.
• The settlement influence zone is much larger
for the real foundation sizes than that for test
plate, which may lead to gross
misinterpretation of expected settlement for
proposed foundation.
42
Soft soil
layer
• The foundation settlements in loose sands are usually much larger than what is
predicted by plate load test.
• Plate load test is relatively short duration test and gives mostly the immediate
settlements.
• In case of granular soils the immediate settlement is close to total settlements.
• However, due to considerable consolidation settlement in case of cohesive soils, the
plate load test becomes irrelevant in such case. Although the following relationship is
suggested for interpreting the settlements in cohesive soils, it can not be used
seriously for design.
f f
p p
S B
S B


43. Plate Load Test: Bearing Capacity
• In case of dense cohesionless soil and highly cohesive soils ultimate bearing capacity
may be estimated from the peak load in load-settlement curve.
• In case of partially cohesive soils and loose to medium dense soils the ultimate
bearing capacity load may be estimated by assuming the load settlement curve so as
to be a bilinear relationship.
43

44. Plate Load Test: Bearing Capacity
• A more precise determination of
bearing capacity load is possible if
the load-settlement curve is plotted
in log-log scale and the relationship
is assumed to be bilinear. The
intersection point is taken as the
yield point or the bearing capacity
load.
44
uf f
up p
q B
q B

For cohesioless soil 
uf up
q q

For cohesive soil 

45. Modulus of
Sub-grade
Reaction
45

46. Differential Settlement
46
Terzaghi’s recommendation:
Differential settlement should not exceed 50% of the total settlement calculated for the foundation.
Considering the sizes of different footing, the following criteria is suggested for buildings:
For raft foundation the requirements shall be more stringent and they may be designed for the
following criteria
Differential settlement of footing 75% of max calculated settlement of footing

Differential settlement of raft footing 37% of max calculated settlement of raft footing

d


L
= maximum settlement
d= differential settlement
d/ = angular distortion
Allowable maximum and differential settlements are given on the next slide

47. 47

48. Rotation of Footings Subjected to
Moment
• Footings subjected to moment will have the tendency to rotate and the
amount of rotation can be estimated by assuming that the footing is
supported on a bed of springs and using the modulus of sub-grade
reaction theory.
48
Modulus of sub-grade reaction:
 
2
1
s
E
k
B 


L
M
Q
Moment about the base due to
soil reaction:
 
3
2
0
2 . .
12
B LB k
M L k dx


 


49. Rotation of Footings Subjected to
Moment
49
   
2 2
3 2 2
12 1 1
12
s s
M
M M
I
LB k LB E E LB

 

 
  
Influence factor
to compute
rotation of
footing
I values

50. Allowable Bearing Pressure
• Maximum bearing pressure that can be applied on the soil
satisfying two fundamental requirements
– Bearing capacity with adequate factor of safety
– net safe bearing capacity
– Settlement within permissible limits (critical in most cases)
– net safe bearing pressure
50

51. Allowable Bearing
Pressure
51
Terzaghi and Peck (1967):
 
2
1
0.3
1.37 3
2
n w D a
B
q N R R S
B


 
 
   
 

0.5 1 1
w f
w w
f
D D
R R
D
 

 
  
 
 
 
1 depth correction factor
1 0.2 1.2
D
f
R
D
B

  
a
S  Permissible settlement in mm.
(25 mm)
Sa in mm and all other
dimensions in meter.
2
kN m

52. Allowable Bearing Pressure
52
Peck, Hanson, and Thornburn (1974):
N-values are corrected for dilatancy and overburden
Initial straight line  safe bearing capacity with FS =2
Later horizontal portion  permissible settlement of 25 mm.
0.44
a net w a
q C N S



Allowable bearing pressure from settlement consideration:
a
S  Permissible settlement in mm. (25 mm)
water table correction 0.5 0.5 w
w
f
D
C
D B
 
    
 

 
2
kN m

53. Allowable Bearing Pressure
53
Teng’s (1962) Correlation:
depth correction factor 1 2
f
D
D
C
B
   
Sa in mm and all other
dimensions in meter.
.
cor N
N C N

 
1.75
for 0 1.05
0.7
N o a
o a
C P
P


 

  
 
 
 
 
3.5
for 1.05 2.8
0.7
N o a
o a
C P
P


 

  
 
 
 
o
  Effective Overburden stress
 
2
0.3
1.4 3
2
n cor w D a
B
q N R C S
B


 

   
 
Net safe bearing pressure
2
kN m

54. Allowable Bearing Pressure
54
Meyerhof’s (1974) Correlation:
2
1
0.49 for 1.2 m
n D a
q N R S kN m B


 
1 depth correction factor
1 0.2 1.2
D
f
R
D
B

  
2
2
2
0.3
0.32 for 1.2 m
n D a
B
q N R S kN m B
B


 

 
 
 
Net safe bearing pressure
2 depth correction factor
1 0.33 1.33
D
f
R
D
B

  
Bowel’s (1982) Correlation:
2
1
0.73 for 1.2 m
n D a
q N R S kN m B


 
2
2
2
0.3
0.48 for 1.2 m
n D a
B
q N R S kN m B
B


 

 
 
 
N-value corrected for overburden using bazaraa’s equation, but
the N-value must not exceed field value

55. Allowable Bearing Pressure
55
Recommendation: Use total settlement correlations with SPT
data to determine safe bearing pressure.
Correlations for raft foundations:
Rafts are mostly safe in bearing capacity and they do not show much
differential settlements as compared to isolated foundations.
  2
0.7 3
n w D a
q N R C S kN m

 
 
Teng’s Correlation:
Peck, Hanson, and Thornburn (1974):
2
0.88
a net w a
q C N S kN m



Correlations using CPT data:
Meyerhof’s correlations may be used by substituting qc/2 for N,
where qc is in kg/cm2.