lecture 3 foundation settlement
TRANSCRIPT
Lecture
3
INTERNATIONAL UNIVERSITY FOR SCIENCE & TECHNOLOGY
�م وا����������� ا������ ا��و��� ا����� �
Dr. Abdulmannan Orabi
Civil Engineering and Environmental Department
303421: Foundation Engineering
Foundation Settlements
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
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Introduction
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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.
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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 time-dependent 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.
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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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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
Immediate settlement
�� = � ���� = 1�
�
� ∆�� − ��∆�� − ��∆�� ��
�
Where: �� = ����������������� � = �ℎ�� ����!"�!����#�$� = �!�%�%�!"���������#!"�!���� = &!���!�'�$���!!"�ℎ��!��∆��, ∆��, ∆��= ��$������$�����%��! the net applied
foundation load in the x, y, and z directions, respectively
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Immediate settlement
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:
Settlement Based on the Theory of Elasticity
�� = )*+' 1 − �,� -�-.
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-� = ��"�%����"���!$, /ℎ��ℎ��0���!� 1'
+' ,thicknessofstratumH,Poisson’sratio�. ���"!%�����!���0�ℎD.
)* = �������#!"�!�����0$���%$���%����!"�
+' = ���������$���������!�!"�!��$�E%���FE����$��� = �G�$�F����������#�%�%�%�!"�!��
Immediate settlement
Settlement Based on the Theory of Elasticity
�� = )*+' 1 − �,� -�-.
-� = -H +1 − 2�1 − � -,
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Immediate settlement
Settlement Based on the Theory of Elasticity
-H = 1K L�� 1 + L, + 1 L, + M,
L 1 + L, + M, + 1 + �� L + L, + 1 1 + M,L + L, + M, + 1
-, = N,O ���PH
QN QRSNRSH
The influence factors I1 and I2 can be computed using equations given by Steinbrenner as follows:
���PH��$������where L = 1'
+' M = �+'
1,'+H'
+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.
-.
-. = 0.66 D.+
P .HV+ 0.025(1+ + 12� − 4.6)
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This equation is strictly applicable to flexible bases on the half-space.
Immediate settlement
Settlement Based on the Theory of Elasticity Theory
�� = )*+' 1 − �,� -�-.
If your base is "rigid" you should reduce the Is factor by about 7 percent (that is, Isr = 0.931 Is).
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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.
�+ =→ ∞
�]^ = ∑ �`�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
� = bHb, )* − ) c -�� ∆�
� = ���������#�%�%�%�!"�!��
/ℎ�$�:bH = 1 − 0.5 )
)* − ) = ��!$����!�"���!$"!$���0�ℎ!""!%�����!�
b, = 1 + 0.2�!F e�����#��$�0.1 = ��!$$����!�"���!$"!$��$��0���!��
)* = ��$������ℎ���G��!""!%�����!�,
) = fD. = �""����G���$������ℎ���G��!""!%�����!�-� = ��$�����"�%����"���!$
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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 + 0.19
1+ − 1 ≤ 0.2
�H = 0.5+ + 0.5+9
1+ − 1 ≤ +
�, = 2+ + 2+9
1+ − 1 ≤ 4+
-���i = 0
j�$����!�!"iH"!$-�kj�$����!�!"i,"!$-� = 0
The maximum value of Iz can be calculated as -�k = 0.5 + 0.1 )* − ))�H)�H = �""����G���$��������0�ℎiH
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Immediate settlement
Settlement of Sandy Soil: Use of Strain Influence Factor
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On the basis of the one-dimensional consolidation settlement equations we write
�l(m) = � �����
Primary Consolidation Settlement
�� = ∆�1 +�*
where :
∆ℎℎ = �* − �`
1 +�*Dr. Abdulmannan Orabi IUST 20
VoidsVoids
Solids
Vvo = eoVs
Vs
∆ H = s
Vvi = (e i ) Vs
Vs Solids
Before After
1
T o
S
o
VV
e=
+ 1
T i
S
i
VV
e=
+
1
1
T i i
o o
V e
V e
+=
+( 1 )
i o o
he e e
h
∆= − +
Primary Consolidation Settlement
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Primary Consolidation Settlement
� = �l ℎ1 + �* �!F
�^*' +∆�^�^*'
� = ��ℎ1 + �* �!F
�^*' +∆�^�^*'
n!$�!$����#�!��!����������#
n!$!G�$�!��!����������#/��ℎ�^*' +∆�^ ≤ &l'
The consolidation settlement Sc due to this average stress increase can be calculated as follows:
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� = ��ℎ1 + �* �!F
&l'�^*' + �l ℎ
1 + �* �!F�^*' +∆�^
&l'
&l' = 0$��!��!������!�0$���%$�
bl = �!�0$����!�����ob� = �/�����F����o�* = �������G!��$���!!"�ℎ����#��#�$
ℎ = �ℎ�� ����!"�ℎ����#��#�$�^*' = !G�$E%$����""����G�0$���%$�
���ℎ�������!"�ℎ����#��#�$
n!$!G�$�!��!����������#/��ℎ�^*' ≤ &l' ≤�^*' +∆�^
Primary Consolidation Settlement
where
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∆�^ = �G�$�F����$������0$���%$�!��ℎ����#��#�$��%���E#�ℎ��!���$%���!�!""!%�����!�
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
∆�^ = 16 ��p + 4��k + ��q
Primary Consolidation Settlement
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Primary consolidation settlement calculation
Clay layer h
��p
��k��q
Ground water table
Ground surface
q
B
Primary Consolidation Settlement
z
����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.
where :
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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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From the figure , the secondary compression index can be defined as
Secondary Consolidation Settlement
br = ∆��!F�, − �!F�Hwhere
br = ���!���$#�!�0$����!�����o∆� = �ℎ��F�!"G!��$���!�H����, = ����
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where
The magnitude of the secondary consolidation can be calculated as
�l� = br' ℎ�!F �,/�H
br' = br1 + �m
�m = G!��$���!���ℎ����!"0$���$#�!��!������!�ℎ = �ℎ�� ����!"�ℎ����#��#�$
Secondary Consolidation Settlement
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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.
Secondary Consolidation Settlement
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where
Degree of consolidation
Time Rate of Consolidation
The average degree of consolidation for the entire depth of the clay layer at any time t can be expressed as
t = �p�. = 1 −1
2�uv w %���,�xy %*
t = �G�$�F���F$��!"�!��!������!��p = ����������!"�ℎ���#�$��������. = "��������������!"�ℎ���#�$
"$!�0$���$#�!��!������!�Dr. Abdulmannan Orabi IUST 30
The values of the time factor and their corresponding average degrees of consolidation for the case presented in may also be approximated by the following simple relationship:
Time Rate of Consolidation
Degree of consolidation
n!$t = 0�!60%,e = K4
t%100
,
n!$t > 60%,e = 1.781 − 0.933�!F 100 − t%e = b^�
�uv,
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