lecture3 foundation settlement -161028163727

INTERNATIONAL UNIVERSITY
FOR SCIENCE & TECHNOLOGY
‫م وا‬
‫ا‬
‫ا و‬
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Civil Engineering and Environmental
Department
Lecture
3
303421: Foundation Engineering
Foundation Settlements
Dr. Abdulmannan Orabi
References
ACI 318M-14 Building Code Requirements for Structural
Concrete ( ACI 318M -14) and Commentary, American
Concrete Institute, ISBN 978-0-87031-283-0.
Bowles , J.,E.,(1996) “Foundation Analysis and Design” -5th
ed. McGraw-Hill, ISBN 0-07-912247-7.
Das, B., M. (2012), “ Principles of Foundation Engineering ”
Eighth Edition, CENGAGE Learning,
ISBN-13: 978-1-305-08155-0.
Syrian Arab Code for Construction 2012
Dr. Abdulmannan Orabi
IUST
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Introduction
Foundation settlements must be estimated with
great care for buildings, bridges, towers, power
plants, and similar high-cost structures.
For structures such as fills, earth dams, levees,
braced sheeting, and retaining walls a greater
margin of error in the settlements can usually
be tolerated.
Dr. Abdulmannan Orabi
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Introduction
The settlement of a shallow foundation can be
divided into two major categories: (a) elastic,
or immediate, settlement and (b) consolidation
settlement. Immediate, or elastic, settlement of
a foundation takes place during or immediately
after the construction of the structure.
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Introduction
Consolidation settlement or those that are timedependent and take months to years to develop.
Pore water is extruded from the void spaces of
saturated clayey soils submerged in water.
The total settlement of a foundation is the sum
of the elastic settlement and the consolidation
settlement.
Dr. Abdulmannan Orabi
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Introduction
Consolidation settlement comprises two phases:
primary and secondary.
Secondary consolidation settlement occurs after
the completion of primary consolidation caused
by slippage and reorientation of soil particles
under a sustained load.
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Introduction
Primary consolidation settlement is more
significant than secondary settlement in
inorganic clays and silty soils. However, in
organic soils, secondary consolidation
settlement is more significant.
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Immediate settlement
Immediate settlement analyses are used for all
fine-grained soils including silts and clays with
a degree of saturation S ≤ 90 percent and for
all coarse-grained soils with a large coefficient
of permeability.
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Immediate settlement
Settlement Based on the Theory of Elasticity
The elastic settlement of a shallow foundation
can be estimated by using the theory of elasticity.
From Hooke’s law we obtain
=
Where:
=
1
∆
−
∆
−
∆
=
= ℎ
!" !
# $
= ! % % !"
# !" !
= &! ! ' $ ! !" ℎ !
∆ ,∆ , ∆ = $
$
% ! the net applied
foundation load in the x, y, and z directions, respectively
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Immediate settlement
Settlement Based on the Theory of Elasticity
The settlement of the corner of a rectangular
base of dimensions B' * L' on the surface of an
elastic half-space can be computed from an
equation from the Theory of Elasticity as
,
follows:
1
−
'
= )* +
Dr. Abdulmannan Orabi
- -.
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Immediate settlement
Settlement Based on the Theory of Elasticity
= )* +'
)* =
# !" !
= G $ F
+' =
$
- = "%
"
,
- -.
%$
%
!"
% % % !" !
! !" ! $ E% ' F E
$
1
!$ , /ℎ ℎ 0
!
, thickness of
'
+
"!%
!
0 ℎ D.
stratum H , Poisson’s ratio .
1−2
- = -H +
-,
1−
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#
0$
1−
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Immediate settlement
Settlement Based on the Theory of Elasticity
The influence factors I1 and I2 can be
computed using equations given by
Steinbrenner as follows:
1
-H = L
K
-, =
where
N
,O
1 + L, + 1
L 1+
PH
1'
L= '
+
Dr. Abdulmannan Orabi
L,
+
L, + M ,
M,
+1
+
L + L, + 1
L + L, + M , + 1
Q
PH
N QR S NR SH
M=
+'
1 + M,
+H '
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1, '
$
+H '
1H '
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Immediate settlement
Settlement Based on the Theory of Elasticity Theory
The influence factor -. is from the Fox
equations, which suggest that the settlement
is reduced when it is placed at some depth in
the ground, depending on Poisson's ratio and
L/B.
D.
-. = 0.66
+
Dr. Abdulmannan Orabi
P .HV
1
+ 0.025 ( + 12
+
IUST
− 4.6)
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Immediate settlement
Settlement Based on the Theory of Elasticity Theory
= )* +'
1−
,
- -.
This equation is strictly applicable to flexible
bases on the half-space.
If your base is "rigid" you should reduce the
Is factor by about 7 percent
(that is, Isr = 0.931 Is).
Dr. Abdulmannan Orabi
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Immediate settlement
Settlement Based on the Theory of Elasticity Theory
Note that the stratum depth actually causing settlement is
not at + =→ ∞ but is at either of the following:
a. Depth z =5B where B = least total lateral dimension of
base.
b. Depth to where a hard stratum is encountered.
]^
Dr. Abdulmannan Orabi
=
a
∑`aH
`
`
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Immediate settlement
Settlement of Sandy Soil: Use of Strain Influence Factor
The settlement of granular soils can also be
evaluated by the use of a semiempirical strain
influence factor proposed by Schmertmann et
al. (1978).
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Immediate settlement
Settlement of Sandy Soil: Use of Strain Influence Factor
According to this method the settlement is
= bH b, )* − ) c
/ℎ $ :
bH = 1 − 0.5
)
)* − )
b, = 1 + 0.2 !F
)* =
$
e
ℎ
) = f D. = ""
- =
$
"%
Dr. Abdulmannan Orabi
G
G
=
!$
#
0.1
$
! "
=
!" "!%
$
"
!$$
G
∆
!$ "!$
! ,
ℎ
-
0 ℎ !" "!%
! "
!$ "!$
=
#
!" "!%
$ 0
!
!
% % % !" !
!
!$
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Immediate settlement
Settlement of Sandy Soil: Use of Strain Influence Factor
The following relations are suggested to
determine the strain influence factor
-
0.1 1
- = 0.1 +
− 1 ≤ 0.2
9 +
i=0
j $
! !" iH "!$ -
j $
! !" i, "!$ - = 0
k
H
,
0.5+ 1
−1 ≤+
9 +
2+ 1
= 2+ +
− 1 ≤ 4+
9 +
= 0.5+ +
The maximum value of Iz can be calculated as
)
H
= ""
G
$
Dr. Abdulmannan Orabi
0 ℎ iH
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-
k
= 0.5 + 0.1
)* − )
)H
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Immediate settlement
Settlement of Sandy Soil: Use of Strain Influence Factor
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Primary Consolidation Settlement
On the basis of the one-dimensional
consolidation settlement equations we write
l(m)
where :
=
∆
=
1+
∆ℎ
*−
=
ℎ
1+
Dr. Abdulmannan Orabi
*
`
*
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Primary Consolidation Settlement
∆H= s
Vvo = eoVs
Voids
Vvi = (e i ) Vs
Vs
Voids
Vs
Solids
Solids
After
Before
V
S
V To
=
1+ eo
V Ti
1+ ei
=
V o
1+ eo
Dr. Abdulmannan Orabi
V
e
i
=e
o
S
=
− (1 + e
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V Ti
1+ e
o
i
∆ h
)
h
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Primary Consolidation Settlement
The consolidation settlement Sc due to this
average stress increase can be calculated as
follows:
n!$ !$
# !
=
n!$ !G $ !
=
Dr. Abdulmannan Orabi
l
1+
!
1+
ℎ
*
ℎ
*
!F
!F
!
'
^*
'
^*
+ ∆
'
^*
#
^
#/ ℎ
+ ∆
'
^*
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'
^*
+ ∆
^
≤ &l'
^
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Primary Consolidation Settlement
n!$ !G $ ! !
'
'
≤
&
^*
l ≤
=
where
1+
ℎ
*
!F
bl = ! 0$
b = /
* =
&l' = 0$ !
'
^*
&l'
+
'
^*
F
G!
!
+ ∆
!
$
o
^
l
1+
ℎ
*
o
!F
! !" ℎ
! 0$
ℎ= ℎ
!" ℎ
'
""
^* = !G $E%$
ℎ
!" ℎ
Dr. Abdulmannan Orabi
#/ ℎ
%$
'
^*
+ ∆
&l'
#
# # $
G 0$ %$
# # $
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^
# $
23
Primary Consolidation Settlement
∆
= G $ F
$
# $ %
E# ℎ !
^
0$ %$ ! ℎ
$% ! !" "!%
!
#
Note that the increase in effective pressure, ∆ ^ , on the clay
layer is not constant with depth: The magnitude of ∆ ^
will decrease with the increase in depth measured from the
bottom of the foundation. However, the average increase in
pressure may be approximated by
1
∆ ^=
p+4 k+
q
6
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Primary Consolidation Settlement
Primary consolidation settlement calculation
where :
p,
k , and
q are,
respectively, the pressure
increases at the top, middle,
and bottom of the clay
layer that are caused by the
construction of the
foundation.
Dr. Abdulmannan Orabi
B
Ground surface
q
Ground water table
p
k
h Clay layer
q
z
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Secondary Consolidation Settlement
At the end of primary consolidation (i.e., after the
complete dissipation of excess pore water pressure) some
settlement is observed that is due to the plastic
adjustment of soil fabrics. This stage of consolidation
is called secondary consolidation.
A plot of deformation
against the logarithm of
time during secondary
consolidation is practically
linear as shown in Figure.
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Secondary Consolidation Settlement
From the figure , the secondary compression index can be
defined as
∆
br =
!F , − !F
where
br =
∆ = ℎ
H
!
,
$# ! 0$
F !" G!
=
Dr. Abdulmannan Orabi
$
!
!
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H
o
27
Secondary Consolidation Settlement
The magnitude of the secondary consolidation can be
calculated as
l
br' ℎ
=
!F , /
H
where
br'
m
br
=
1+
= G!
ℎ= ℎ
m
$
!
Dr. Abdulmannan Orabi
ℎ
!" ℎ
#
!" 0$
# $
IUST
$# !
!
!
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Secondary Consolidation Settlement
Secondary consolidation settlement is more
important in the case of all organic and highly
compressible inorganic soils.
In overconsolidated inorganic clays, the
secondary compression index is very small and
of less practical significance.
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Time Rate of Consolidation
Degree of consolidation
The average degree of consolidation for the
entire depth of the clay layer at any time t can
be expressed as
,
where
t=
t=
=
. = "
"$!
p
.
=1−
G $ F
p
Dr. Abdulmannan Orabi
0$
2
1
F$
uv
!" ℎ
$# !
w
%*
!" !
xy
%
!
# $
!" ℎ
# $
!
!
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!
30
Time Rate of Consolidation
Degree of consolidation
The values of the time factor and their
corresponding average degrees of consolidation
for the case presented in may also be approximated
by the following simple relationship:
K
n!$ t = 0 ! 60%, e^ =
4
t%
100
,
n!$ t > 60%, e^ = 1.781 − 0.933 !F 100 − t%
e^ =
Dr. Abdulmannan Orabi
b^
,
uv
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