settlement of shallow foundation final
TRANSCRIPT
1
Shallow Foundation Settlement���� ��� � ��
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)________________________________________________________________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
4
5
6
8
Stress Due to a Concentrated Load
9
Stress due to a Circularly Loaded Area
10
Distribution of Stress(from a vertical line load)
11
Stress below a Rectangular Area
12
Stress Influence Chart
13
2:1 method
Approximate methods
14
15
17
18
Elastic Settlement
19
Elastic settlement Based on theTheory of Elasticity
20
Elastic Settlement of Rectangular footings
�� �� ��� � � �� ��
��� ������ ����
�������� ���� ��� �
�������� !"�# ��� �
$%" �&���
'() �&���
Es = ��� !&*�&�+� ,-��
21
IMMEDIATE SETTLEMENT
General Equation (Harr, 1966)• Flexibel Foundation
– At the corner of foundation
– At the center of foundation
– Average
• Rigid Foundation
(((( ))))2
1Eq.B
S 2s
s
oe
ααααµµµµ−−−−====
Es = Modulus of elasticity of soil
B = Foundation width L = Foundation length
(((( ))))ααααµµµµ−−−−==== 2s
s
oe 1
Eq.B
S
(((( )))) r2s
s
oe 1
Eq.B
S ααααµµµµ−−−−====
−−−−++++++++++++++++
−−−−++++++++++++
ππππ====αααα
1m1
1m1ln.m
mm1
mm1ln
12
2
2
2
(((( )))) av2s
s
oe 1
Eq.B
S ααααµµµµ−−−−====
B
Lm =; ; H = ∞∞∞∞
23
IMMEDIATE SETTLEMENT
If Df = 0 and H < ∞, the elastic settlement of foundation can be determined from the following formula:
( ) ( ) ( )[ ]
( ) ( ) ( )[ ]22
122
22
12
2
2111.
2
2111
.
FFE
qBS
FF
E
qBS
sssss
oe
ssss
s
oe
µµµµ
µµµµ
−−+−−=
−−+−−= (corner of rigid foundation)
(corner of flexible foundation)
The variations of F1 and F2 with H/B are given in the graphs of next slide
IMMEDIATE SETTLEMENT
IMMEDIATE SETTLEMENT
EXAMPLE
Problem:A foundation is 1 m x 2 m in plan and carries a net load per unit area, qo = 150 kN/m2. Given, for the soil, Es = 10,000 kN/m2, µs0.3. Assuming the foundation to be flexible, estimate the elastic settlement at the center of the foundation for the following conditions:
a. Df = 0 and H = ∞b. Df = 0 and H = 5 m
EXAMPLE
Solution:Part a.
Part b.
(((( ))))ααααµµµµ−−−−==== 2s
s
oe 1
Eq.B
S
For L/B = 2/1 = 2 � α ≈ 1.53, so
( ) mmmSe 9.200209.0)53.1(3.01000,10
)150)(1( 2 ==−=
( ) ( ) ( )[ ]22
122 2111
'.FF
E
qBS ssss
s
oe µµµµ −−+−−=
For L’/B’ = 2, and H/B’ = 10 � F1 ≈ 0.638 and F2 ≈ 0.033, so
( ) ( ) ( )[ ] mmmxSe 3.160163.04)033.0()3.0(23.01)638.0(3.013.01000,10
)150)(5.0( 222 ==−−+−−=
29
30
Elastic Settlement on Saturated Clay
31
32
Elastic Settlement Using the Strain Influence Factor: [Schmertman & Hartman Method (1978)]
33
34
Elastic Settlement Using the Strain Influence Factor: [Schmertman Method (1978)]
35
36
Procedure for Schmertman Method (1978)
37
Procedure for Schmertman Method (1978)
38
Procedure for Schmertman Method (1978)
39
Procedure for Schmertman Method (1978)
40
Notes on Schmertmann Method
EXAMPLE
A shallow foundation 3 m x 3 m (as shown in the following drawing). The subgrade is sandy soil with Young modulus varies based on N-SPT value (use the following correlation: Es = 766N)
Determine the settlement occur in 5 years (use strain influence method)
EXAMPLE
EXAMPLE
Depth(m)
∆z(m)
Es
(kN/m2)Iz
(average) (m3/kN)
0.0 – 1.0 1.0 8000 0.233 0.291 x 10-4
1.0 – 1.5 0.5 10000 0.433 0.217 x 10-4
1.5 – 4.0 2.5 10000 0.361 0.903 x 10-4
4.0 – 6.0 2.0 16000 0.111 0.139 x 10-4
Σ 1.55 x 10-4
zEI
s
z ∆∆∆∆
( ) 9.05.18.17160
5.18.175.015.011 =
−−=
−−=
x
x
qC 34.1
1.0
5log.2.01
1.0log.2.012 =
+=
+= tC
( )
mmS
xxS
zE
IqqCCS
e
e
B
s
ze
8.24
)1055.1)(5.18.17160)(34.1)(9.0(
...
4
2
021
=−=
∆−=
−
∑