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TOPIC 4
DEFORMATION AND SETTLEMENT OF SOIL
Course : S0705 – Soil Mechanic
Year : 2008
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CONTENT
• SETTLEMENT
• CONSOLIDATION
• TIME RATE OF CONSOLIDATION
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SETTLEMENT
• Definition
The total vertical deformation at the surface resulting from :
– External Load
– Dewatering
• Settlement Components
– Immediate Settlement ; Se
– Primary Consolidation Settlement ; Sc
– Secondary Settlement (Creep) ; Ss
sce SSSS ++++++++====
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SETTLEMENT
• Purpose – Study the settlement behavior
– Determine the settlement value and time
– Study the settlement influence to the structure stability
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SETTLEMENT INFLUENCE
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IMMEDIATE SETTLEMENT
• Defined as settlement which occurred directly after the application of a load, without a change in the moisture content.
• Caused by soil elasticity behavior
• The magnitude of the contact settlement will depend on the flexibility of the foundation and the type of material on which it is resting.
• For clay, the immediate settlement generally very small comparing to the consolidation settlement, therefore this immediate settlement mostly ignored.
• Usually considered at sand or sandy soil.
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IMMEDIATE SETTLEMENT
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IMMEDIATE SETTLEMENT
General Equation (Harr, 1966)
• Flexible Foundation
– At corner
– At center
– Average
• Rigid Foundation
(((( ))))2
1E
q.BS
2
s
s
o
e
ααααµµµµ−−−−====
Es = Elasticity modulus of soil
B = Foundation width L = Foundation Length
(((( ))))ααααµµµµ−−−−==== 2
s
s
o
e1
E
q.BS
(((( )))) r
2
s
s
oe 1
E
q.BS ααααµµµµ−−−−====
−−−−++++
++++++++++++
−−−−++++
++++++++ππππ
====αααα1m1
1m1ln.m
mm1
mm1ln
1
2
2
2
2
(((( )))) av
2
s
s
o
e1
E
q.BS ααααµµµµ−−−−====
L
Bm ====; ; H = ∞∞∞∞
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IMMEDIATE SETTLEMENT
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IMMEDIATE SETTLEMENT
General Equation (Bowles, 1982)
2
B'B ====
1
s
2
soe F.
E
1'.B.qS
µµµµ−−−−====
(((( ))))(((( ))))
(((( ))))
++++++++++++
++++++++++++++++
++++++++++++
++++++++++++ππππ
====1NMM
N11MMln
1NM1M
NM1M1ln.M
1F
22
22
22
222
1
'B
'LM ====
'B
HN ====
Es = Elasticity modulus of soil
H = Effective thickness of soil layer, e.g. 2 to 4B under foundation
At the center 2
L'L ==== and F1 is multiplied by 4
B'B ====At the corner L'L ==== and F1 is multiplied by 1
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IMMEDIATE SETTLEMENT
• Saturated Clay
s
o21eE
B.qA.AS ====
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IMMEDIATE SETTLEMENT
• Sandy soil
where :
– Iz = strain influence factor
– C1 = correction factor of foundation embedded thickness
= 1 – 0.5.[q/(q-q)]
– C2 = correction factor for soil creep = 1 + 0.2 . log(t/0,1)
– t = time in year
– q = the stress at foundation base caused by external load
– q = γ . Df
( )∑ ∆−=z
s
ze z
E
IqqCCS
021.
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Modulus Young
IMMEDIATE SETTLEMENT
Circular 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
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EXAMPLE
A shallow foundation on a deposit of sandy soil that is 3m x 3m in plan. The actual variation of the values of Young’s Modulus with depth determined by using the Standard Penetration numbers
(correlation : Es = 766N) are also shown in the following figure.
Estimate the immediate settlement of the foundation five years after construction by using the strain influence
factor method.
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EXAMPLE
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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
zE
I
s
z ∆∆∆∆
( )9.0
5.18.17160
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
=
−=
∆−=
−
∑
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CONSOLIDATION
• When the stress on a saturated clay layer in the field is increased, the pore water pressure in the clay will increase.
Because the coefficients of permeability of clays are very low, it will take some time for the excess pore water pressure to dissipate and the stress increase to be transferred to the soil skeleton gradually.
• Consolidation is the process of dissipation of excess pore water pressure in a row of time.
Note:
Dissipation of pore water pressure occurs simultaneously with the squeezing out of the pore water. Therefore the consolidation time depend on:
The distance of pore water to be squeezed out
The coefficient of permeability of soft soil
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CONSOLIDATION
SECONDARYSETTLEMENT (Ss)
HYDROSTATICPRESSURE
IMMEDIATE
SETTLEMENT (Si)
PRIMARY OR
CONSOLIDATIONSETTLEMENT (Sc)
LOG TIME
SETTLEMENT
SETTLEMENT CURVE
IDEALISASI
Spring(so il particles)
Valve(so il’s permeability)
Water filled c hamber
(water satura ted soil’s pores)
ao
Ho
ai
ao
UNDRAINED
(Ho - Si)
Si
Pressure is borne by pore water
La tera l defo rmation
(Ho - Si - Sc)
Sc
ai
ac
Spring compressed
Water p ressure reduced
CONSOLIDATION
Water is expelled
LOAD
DRAINED CREEP
No water flow
ac a
s
Ss
(Ho - Si - Sc - Ss)
All load is borne by spring
Hydrostatic p ressure(zero exc ess pore water p ressure)
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CONSOLIDATION
First time, suggested by Terzaghi (1920-1924) with several assumption :
– 1 dimensional
– Saturation is complete
– Compressibility of water is negligible
– Compressibility of soil grains is negligible (but soil grains rearrange)
– Darcy’s Law is valid
– Soil deformation is small
– Soil permeability is constant
– Soil skeleton of each layer is homogeneous, so isotropic linier elastic constitutive law is valid
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CONSOLIDATION
• Consolidation Type
– Normal consolidation
Preconsolidation pressure (Pc) just equals the
existing effective vertical overburden pressure (Po)
– Over consolidation
If the soil whose preconsolidation pressure (Pc) is
greater than the existing overburden pressure
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CONSOLIDATION
• Normal Consolidation
• Over consolidation
oc pp ≈≈≈≈ OR 1p
p
o
c ≈≈≈≈o
occ
p
pplog.H.
eo1
CcS
∆∆∆∆++++
++++====
ocpp >>>> OR 1
p
p
o
c >>>>
po + ∆∆∆∆p < pc
o
o
ccp
pplog.H.
eo1
CsS
∆∆∆∆++++++++
====
po < pc < po+∆∆∆∆p c
oc
o
ccc
p
pplog.H.
eo1
Cc
p
plog.H.
eo1
CsS
∆∆∆∆++++++++
++++++++
====
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CONSOLIDATION
Where :
– eo = initial void ratio which getting from index test
– Cc = compression index from consolidation test
– Cs = swelling index from consolidation test
– pc = preconsolidation pressure from consolidation test
– po = Σ γ’.z – ∆p = the total stress at any depth of the clay layer caused by external load, which can be determined by using method of Boussinesq, Westergaard or Newmark
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DETERMINATION OF CONSOLIDATION PROPERTIES
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DETERMINATION OF CONSOLIDATION PROPERTIES
Procedures :
1. Determine the point O on the e-
lop p curve that has the sharpest
curvature (that is, the smallest radius of curvature)
2. Draw a horizontal line OA
3. Draw a line OB that is tangent to
the e-log p curve at O
4. Draw a line OC that bisects the
angle AOB
5. Produce the straight line portion
of the e-log p curve backward to intersect OC. This is point D. The
pressure that corresponds to the
point p is the preconsolidation
pressure, pc.
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DETERMINATION OF CONSOLIDATION PROPERTIES
−−−−====
1
2
21
p
plog
eeCc
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DETERMINATION OF CONSOLIDATION PROPERTIES
−−−−====
3
4
43
p
plog
eeCs
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DETERMINATION OF COMPRESSIVE PARAMETER
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CONSOLIDATION SETTLEMENT
• Other equation
p.H.mS cvc ∆∆∆∆====
Where :
mv = Compression Index
Hc = Thickness of soft soil layer
∆p = The stress increment due to the external
load
o
vv
'
1
'
2
21v
e1
am
pp
eea
++++====
−−−−
−−−−====
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CONSOLIDATION TIME
Cv
H.Tt
2
v====
(((( ))))%U100log.933,0781,1Tv −−−−−−−−====
%100xS
SU
c
i,c====
Where : t = consolidation time
Tv = consolidation factor depended on consolidation degree (U)
U = consolidation degree in percent, descript as ratio of design settlement to total settlement
Cv = coefficient of consolidation, get from consolidation test
2
v100
%U
4T
ππππ====U = 0 – 60%
U > 60%
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Hc
Porous Layer
Porous Layer
Hc
Porous Layer
Impermeable
layer
CONSOLIDATION TIME
Cv
H.Tt
2
v====
Where : H = length of water path
H = Hc H = 0.5Hc
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CONSOLIDATION TIME OF LAYERED SOIL
Hc,1
Hc,2
Hc,3
Cv1
Cv2
Cv3
(((( ))))1
2
1,cv
1Cv
2H.Tt ====
(((( ))))2
2
2,cv
2Cv
2H.Tt ====
(((( ))))3
2
3,cv
3Cv
H.Tt ====
Take the longest time
= 5.2 years
= 3.4 years
= 6.1 years
t = 6.1 tahun
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CONSOLIDATION TIME OF LAYERED SOIL
Hc,1
Hc,2
Hc,3
Cv1
Cv2
Cv3
-Determine the equivalent of Hc of each layer
ref
iicicCv
CvHH ,
', =
-Determine the sump of equivalent Hc
(((( ))))ek
2
c
Cv
H.Tvt
∑∑∑∑====
-Determine the consolidation time
( )( )2
2'
.∑∑=
c
crefek
H
HCvCv
-Determine the equivalent of Cv
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EXAMPLE
Determine the total consolidation time of 3 layer of clay, which have different value of coefficient of consolidation and thickness for 90% degree of consolidation. 1st Layer : thickness 5 m, Cv = 5 x 10-3 cm2/s 2nd Layer : thickness 3 m, Cv = 6 x 10-3 cm2/s 3rd Layer : thickness 8 m, Cv = 7 x 10-3 cm2/s
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SOLUTION
Layer Thickness
(Hc)
Cv
(m2/s)
Equivalent Thickness
(Hc’)
Cvek
(m2/s)
T
(years)
1 5 m 5 x 10-7 5.00 m
6.16 x 10-7 11.18
2 3 m 6 x 10-7 3.29 m
3 8 m 7 x 10-7 9.47 m
Total 17.76 m
Cvref is Cv1
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EXAMPLE
A laboratory consolidation test on a normally clay showed the following result :
Load, p (kN/m2) Void ratio at the end of consolidation, e
140 0.92
212 0.86
The specimen thickness was 25.4 mm and drained on both sides. The time required for the specimen to reach 50% consolidation was 4.5 min.
A similar clay layer in the field, 2.8 m thick and drained on both sides, is subjected to similar average pressure increase that is po = 140 kN/m
2 and po+∆p = 212 kN/m2. Determine the following :
1. The expected maximum consolidation settlement in the field
2. The length of time it will take for the total settlement in the field to reach 40 mm
3. Repeated no.2 problem in case of drained on one side
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EXAMPLE
• Question no.1
−=
1
2
21
logp
p
eeCc 333.0
140
212log
86.092.0=
−
=Cc
o
occ
p
pplog.H.
eo1
CcS
∆∆∆∆++++
++++====
mmSc 5.87140
212log.8.2.
92,01
333.0=
+=
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EXAMPLE
• Question no.2
– Determine the coefficient of consolidation (Cv)
t
HTCv
2
v====
From laboratory testing
where :
Tv = π/4 (U2) = 0.197 (U = 50%)
H = Hc/2 = 12.7 mm
t = 4.5 min
We got
061.75.4
7.12197.0
2
==Cv mm2/min
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EXAMPLE
• Question no.2
– Determine field consolidation coefficient
– Calculate consolidation time
Cv
H.Tt
2
v====
Where :
U = 45.7%
Tv = π/4 (U2) = 0.164 (U = 45.7%)
H = Hc/2 = 1.4 m = 1400 mm
Cv = 7.061 mm2/min
We got 061.7
1400164.02
xt = = 45523 min = 31.6 days
%7,45%100x5,87
40%100x
S
SU
c
i,c ============
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EXAMPLE
• Question no.3
– Calculate consolidation time
Cv
H.Tt
2
v====
Dimana :
U = 45.7%
Tv = π/4 (U2) = 0.164 (U = 45.7%)
H = Hc = 2.8 m = 2800 mm
Cv = 7.061 mm2/menit
Diperoleh 061.7
2800164.02
xt = = 182093 min = 126.5 days
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THE INFLUENCE OF PORE WATER PRESSURE
Two influences of pore water pressure to the settlement
are :
– Initial average overburden pressure (po) � should be in effective
condition (po’)
– External Load
the uplift of water pressure will reduce the increase of vertical
pressure by external load
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SECONDARY CONSOLIDATION (CREEP)
• Occur after primary consolidation process finished
• Defined as an adjustment of soil skeleton after the excess pore water dissipated.
• Depend on time and will be occurred in a long time
• Difficult to be evaluated
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SECONDARY CONSOLIDATION (CREEP)
p
p
c
p
st
ttlog.H.
e1
CS
∆∆∆∆++++
++++αααα
====
Where :
ep = void ratio at the end of primary consolidation
tp = time at the end of primary consolidation
∆t = time increment t2 = tp +∆t
p
2
t
tlog
eC
∆∆∆∆====αααα See the graph
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SECONDARY CONSOLIDATION (CREEP)
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EXAMPLE
A laboratory testing of consolidation for specimen thickness 25.4 mm is carried out to determine the secondary settlement, with the result as shown in the following table :
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EXAMPLE
Assume the thickness of the compressible layer is 10 m and the
consolidation settlement is 30 cm which occurs after 25 years. The
initial void ratio eo is 2.855, and the initial dial reading is 12.700
mm
Required :
Compute the amount of secondary compression that would occur
from 25 to 50 years after construction. Assume the time rate of
deformation for the load range in the test approximates that occur in the field.
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EXAMPLE
ep = 2,372
Cαααα = 0.052
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EXAMPLE
p
p
c
p
st
ttlog.H.
e1
CS
∆∆∆∆++++
++++αααα
====
+
=25
50log.10.
372.21
052.0sS
Ss = 4.6 cm
