Settlement of shallow foundation

1
Shallow Foundation
Settlement

2
Total Settlement
Total settlement
scet SSSS ++=
Se = immediate settlement (elastic deformation)
Sc = primary consolidation settlement (due to
dissipation of excess pore water pressure)
Ss = secondary consolidation settlement (due to
adjustment of soil fabric)

3
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)
________________________________________________
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

7
Stress Due to a Concentrated Load

8
Stress due to a Circularly Loaded
Area

9
Distribution of Stress
(from a vertical line load)

10
Stress below a Rectangular Area

12
2:1 method
Approximate methods

14
Types of elastic settlement in foundation

16
Elastic settlement Based on the
Theory of Elasticity

17
If the foundation is perfectly flexible then,
the elastic settlement (Se) may be
If = depth factor (Fox, 1948)
α = factor that depends upon the location of foundation where
settlement is being calculated

22
F1 and F2 versus H/B ( After Steinbrenner, 1934)

23
If = depth factor (Fox, 1948)

24
α = factor that depends upon the location of
foundation where settlement is being
calculated
α = 4, settlement at the center of foundation
α = 1, settlement at the corner of foundation

26
A rigid foundation 1 mX 2m is shown in Fig. Calculate the elastic settlement at the
center of the foundation.

27
(a) Initial condition (b) At the moment of load
Consolidation Process
Valve closed
S=0
∆σ∆σ∆σ∆σ’=0
∆∆∆∆u=0
Valve closed
S=0
∆σ∆σ∆σ∆σ’=0
∆∆∆∆u=P/A
PA

28
Valve opened
Consolidation Process (Continued)
(c) At a time, t
S=δδδδ(t)
∆σ∆σ∆σ∆σ’=kδδδδ(t)
∆∆∆∆u=P/A-kδδδδ(t)
P
δδδδ(t)
Valve opened
S=δδδδp
∆σ∆σ∆σ∆σ’=kδδδδp=P/A
∆∆∆∆u=0
P
δδδδp
(d) At completion of
consolidation

29
Load
Dial gauge
Oedometer
Consolidation Test

30
Consolidation Curve
Time (log scale)
Deformation
Stage I: Initial compression
Stage II: Primary
consolidation
Stage III: Secondary
consolidation
tp

31
Over-Consolidation Ratio
A
Current ground surface
Highest ground surface
in the past
γγγγ z
h
Preconsolidation stress (pressure) - the maximum effective
stress the soil has experienced in the past
pc (or σσσσp’) = γγγγ(h+z)
OCR = pc/σσσσz’
OCR > 1 Overconsolidated soil
OCR = 1 Normally-consolidated soil
OCR < 1 Under-consolidated soil

32
Pressure, p (log scale)
VoidRatio,e
pc
a b
c
d
e
f
g
αααα
αααα
Determination of Preconsolidation
Stress from Lab Results

33
VoidRatio,e
e0
Field consolidation curve
Lab consolidation curve
Remolded specimen
Consolidation curveDisturbance
increases
0.42e0
Effect of Soil Disturbance

34
VoidRatio,e
e0
Virgin consolidation curve
0.42e0
Cc
pc=σσσσz’
e - logp Curve for Normally
Consolidated Soil
Cc = Compression index

35
VoidRatio,e
e0
Virgin consolidation curve
0.42e0
Cc
pcσσσσz’
Cr
Lab rebound curve
e - logp Curve for
Overconsolidated Soil
Cr = Recompression index

36
VoidRatio,e
ep
∆∆∆∆e
Time, t (log scale)
t1 t2
Cαααα=∆∆∆∆e/log(t2/t1)
e - logt Curve for
Secondary Consolidation

37
Typical Compression Indices
Cc = 0.1 to 0.8 and Cc = 0.009(LL-10)
Cr = Cc/5 to Cc/10
Cαααα/Cc = 0.01 to 0.07
For soils

38
Stress, σσσσ’ (log scale)
VoidRatio,e
pc = σσσσz’
∆σ∆σ∆σ∆σ
Primary Consolidation Settlement
of Normally Consolidated Soil








σ
σ∆+σ
+
= '
z
'
z
o
c
c log
e
HC
S
1 H = Thickness of soil layer

39
Primary Consolidation Settlement
of Overconsolidated Soil
VoidRatio,e
σσσσz’
∆σ∆σ∆σ∆σ pc
σσσσ
Cr
1
VoidRatio,e
σσσσz’
∆σ∆σ∆σ∆σ
pc
Cr
1
Cc
1








σ
σ∆+σ
+
= '
z
'
z
o
r
c log
e
HC
S
1 






 σ∆+σ
+
+
+
=
c
'
zc
o
r
c
p
log
e
HC
)OCRlog(
e
HC
S
011

40
Rate of Consolidation
For U<60%
2
v
100
U
4
T 




π
=
( )U10093307811Tv −−= log.. For U>60%
2
dr
v
v
H
tC
T =
Clay
Sand
H
Hdr

43
Elastic settlement Based on the
Theory of Elasticity

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Elastic Settlement of Rectangular
footings

45
Elastic Settlement on Saturated
Clay

54
Elastic Settlement Using the Strain Influence
Factor: [Schmertman Method (1978)]

55

56
Elastic Settlement Using the Strain Influence Factor:
[Schmertman Method (1978)]

57
[Schmertman Method (1978)]

58
[Schmertman & Hartman Method (1978)]

60
Procedure for Schmertman Method (1978)

61

62

63

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Notes on Schmertmann Method

67

76
Primary Consolidation
• Expulsion of water from soils accompanied by
increase in effective stress and strength
• Amount can be reasonably estimated based
on lab data, but rate is often poorly estimated

77
Consolidation Settlement
• This method makes use of the results of the conventional
oedometer test where the consolidation parameters of the soil
are measured.
• To compute the stress changes within the soil mass. The
stress changes are computed using a Boussinesqtype
approach assuming elasticity.
• The important parameter for consolidation settlement
calculation is the net effective stress change in the soil.
• Usually the settlements are calculated for the soil divided into
a number of sub-layers and the final total settlement is the
sum of individual sub-layer settlements

85
Average Vertical Stress Increases
Due to a Rectangularly Loaded Area

86

87
in a given layer

88
Secondary Consolidation
• At the end of primary settlement, settlement
may continue to develop due to the plastic
deformation (creep) of the soil.
• The stage of consolidation is called secondary
consolidation.

89
Secondary Compression Index

90
Field Load Test
• Ultimate load, allowable
load, and settlement can
be determined from a
field load test (ASTM D-
1194-72).
• The test plates are either
square (12”or 18”) or
circular (12” to 30”)

91
Allowable Bearing Capacity for
Sandy Soil based on Settlement

92
Allowable Bearing Capacity for
Sandy Soil based on Settlement

93
Reliability of Settlement
Computations
• The predication is quite satisfactorily in
general.
• The predication is better for inorganic,
insensitive clays than for others.
• The time rate of consolidation settlement
is not well-predicted.

95

96

97
in a given layer

Settlement of shallow foundation

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