session 7 – 8 settlement of shallow foundation course: s0484/foundation engineering year: 2007...
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Session 7 – 8 SETTLEMENT OF SHALLOW FOUNDATION
Course : S0484/Foundation Engineering
Year : 2007
Version : 1/0
SHALLOW FOUNDATION
Topic:
• General
• Immediate Settlement
• Consolidation Settlement
GENERAL
The settlement of shallow foundation may be divided into three broad categories:
1. Immediate settlement, which is caused by the elastic deformation of dry soil and of moist and saturated soils without any change in the moisture content. Immediate settlement are generally based on equations derived from the elasticity theory
2. Primary consolidation settlement, which is the result of a volume change in saturated cohesive soils because of expulsion of the water that occupies the void spaces.
3. Secondary consolidation settlement, which is observed in saturated cohesive soils and is the result of the plastic adjustment of soil particles.
This course will focus at immediate and primary consolidation settlement only.
IMMEDIATE SETTLEMENT
IMMEDIATE SETTLEMENT
General Equation (Harr, 1966)• Flexibel Foundation
– At the corner of foundation
– At the center of foundation
– Average
• Rigid Foundation
2
1E
q.BS 2
ss
oe
Es = Modulus of elasticity of soil
B = Foundation width L = Foundation length
2s
s
oe 1
E
q.BS
r2s
s
oe 1
E
q.BS
1m1
1m1ln.m
mm1
mm1ln
12
2
2
2
av2s
s
oe 1
E
q.BS
B
Lm; ; H =
IMMEDIATE SETTLEMENT
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
(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, s 0.3. 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.
2s
s
oe 1
E
q.BS
For L/B = 2/1 = 2 1.53, so
mmmSe 9.200209.0)53.1(3.01000,10
)150)(1( 2
22
122 2111
'.FF
E
qBS ssss
s
oe
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
IMMEDIATE SETTLEMENT
General Equation (Bowles, 1982)
2
B'B
1s
2s
oe F.E
1'.B.qS
1NMM
N11MMln
1NM1M
NM1M1ln.M
1F
22
22
22
222
1
'B
'LM
'B
HN
Es = Modulus of elasticity of soil
H = effective layer thickness, ex. 2 - 4B below foundation
At the center of Foundation 2
L'L and F1 time by 4
B'B At the corner of Foundation L'L and F1 time by 1
IMMEDIATE SETTLEMENT
• For saturated clay soil
s
o21e E
B.qA.AS
IMMEDIATE SETTLEMENT
• For sandy soil
where:– Iz = factor of strain influence
– C1 = correction factor to thickness of embedment foundation = 1 – 0.5x[q/(q-q)]
– C2 = correction factor due to soil creep
= 1+0,2.log(t/0,1)– t = time in years– q = stress caused by external load– q = . Df
2z
0 s
z21e z
E
IqqC.CS
Young Modulus
IMMEDIATE SETTLEMENT
Circle Foundation or L/B =1
z = 0 Iz = 0.1
z = z1 = 0,5 B Iz = 0.5
z = z2 = 2B Iz = 0.0
Foundation with L/B ≥ 10
z = 0 Iz = 0.2
z = z1 = B Iz = 0.5
z = z2 = 4B Iz = 0.0
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
1.55 x 10-4
zE
I
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
t
C
mmS
xxS
zE
IqqCCS
e
e
B
s
ze
8.24
)1055.1)(5.18.17160)(34.1)(9.0(
...
4
2
021
CONSOLIDATION SETTLEMENT
CONSOLIDATION SETTLEMENT
• Normal Consolidation
• Over consolidation
oc pp or 1p
p
o
c o
occ p
pplog.H.
eo1
CcS
oc pp or 1p
p
o
c
po + p < pc
o
occ p
pplog.H.
eo1
CsS
po < pc < po+pc
oc
o
ccc p
pplog.H.
eo1
Cc
p
plog.H.
eo1
CsS
CONSOLIDATION SETTLEMENT
where:– eo = initial void ratio– Cc = compression index– Cs = swelling index– pc = preconsolidation pressure– po = average effective pressure on the clay layer before the construction of
the foundation = ’.z
p = average increase of pressure on the clay layer caused by the foundation construction and other external load, which can be determine using method of 2:1, Boussinesq, Westergaard or Newmark.Alternatively, the average increase of pressure (p) may be approximated by:
bmt pppp 46
1
pt = the pressure increase at the top of the clay layer
pm = the pressure increase at the middle of the clay layer
pb = the pressure increase at the bottom of the clay layer
CONSOLIDATION SETTLEMENT
EXAMPLE
A foundation 1m x 2m in plan is shown in the following figure. Estimate the consolidation settlement of the foundation. Assume the clay is normally consolidated.
EXAMPLE
o
occ p
pplog.H.
eo1
CcS
2/45.13
25.3225.31
2.1.150
..
mkNp
zLzB
LBqp o
po = (2.5)(16.5) + (0.50)(17.5-10) +(1.25)(16-10) = 52.5 kN/m2
2:1 method
mmxSc 445.52
45.135.52log5.2
8.01
32.0
ALLOWABLE SETTLEMENT