UNDAMENTALS OF ONSOLIDATION - Faculty Server...
Transcript of UNDAMENTALS OF ONSOLIDATION - Faculty Server...
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FUNDAMENTALS OF CONSOLIDATION
CLAY
SAND
SAND
DEPTH
(Vertical Stress Increase) CONSOLIDATION:Volume change in saturated soils caused by the expulsion of pore water from loading.
Saturated Soils:
causes u to increase immediately
Sands: Pore pressure increase dissipates rapidly due to high permeability.
Clays: Pore Pressure dissipates slowly due to low permeability.
after Figure 7.1a. Das FGE (2005).
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CLAY
SAND
SAND
DEPTH
(Vertical Stress Increase)
after Figure 7.1a. Das FGE (2005).
At Time of Initial Loading (t = 0)
Pore water takes initial change in vertical loading (u) since
water is incompressible
Soil skeleton does not see initial loading
Variation in Total, Pore water, and Effective Stresses in Clay Layer
Figure 7.1b. Das FGE (2005)
FUNDAMENTALS OF CONSOLIDATION
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CLAY
SAND
SAND
DEPTH
(Vertical Stress Increase)
after Figure 7.1a. Das FGE (2005).
Between time t = 0 to t = ∞
Pore water increase due to initial loading dissipates
Soil skeleton takes loading as pore pressure decreases
Variation in Total, Pore water, and Effective Stresses in Clay Layer
Figure 7.1c. Das FGE (2005)
FUNDAMENTALS OF CONSOLIDATION
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CLAY
SAND
SAND
DEPTH
(Vertical Stress Increase)
after Figure 7.1a. Das FGE (2005).
At time t = ∞
Pore water increase due to initial loading completely dissipated
(u = 0)
Soil skeleton has taken loading. Effective stress increase now equals
vertical stress increase '
Variation in Total, Pore water, and Effective Stresses in Clay Layer
Figure 7.1e. Das FGE (2005)
FUNDAMENTALS OF CONSOLIDATION
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CLAY
SAND
SAND
DEPTH
(Vertical Stress Increase)
after Figure 7.1a. Das FGE (2005).
THE SPRING ANALOGY
(a)Initial
Loading
Water takes load
Soil (i.e. spring) has
no load
(b)Dissipationof Excess
Water Pressure
Water dissipating
Soil starts to t k l d
(c)Final
Loading
Water dissipated
Soil has load
FUNDAMENTALS OF CONSOLIDATION
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ConsolidometerFigure 7.2. Das FGE (2005)
D2435-11 Standard Test Methods for One-Dimensional Consolidation Properties of Soils Using Incremental Loading
ONE DIMENSIONAL (1D) CONSOLIDATION TEST
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Figure E-1 USACE EM1110-1-1904.
ShearTrac II DSS Equipment(Courtesy of Geocomp Corporation)
1D CONSOLIDATION TEST EQUIPMENT
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Figure 7.4. Das FGE (2005).
1D CONSOLIDATION TESTINGLOAD INCREMENT DATA
THREE STAGES
Stage I: Initial CompressionPrimarily caused by preloading.
Stage II: Primary ConsolidationExcess pore water pressuredissipation and correspondingsoil volume change.
Stage III: Secondary ConsolidationOccurs after excess porewater pressure dissipation.Due to plastic deformation/readjustment of soil particles.
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VOID RATIO-PRESSURE PLOTS
Figure 7.5. Das FGE (2005)
s
v
s
v
s
vo H
HAHAH
VVe Initial Void Ratio (eo):
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sHHe 1
1
11
Figure 7.6. Das FGE (2005)
Figure 7.5. Das FGE (2005)
Change in Void Ratio due to 1st
Loading (e1):
New Void Ratio after 1st
Loading:11 eee o
@ End of Load 1
VOID RATIO-PRESSURE PLOTS
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sHHe 2
1
22
Figure 7.6. Das FGE (2005)
Figure 7.5. Das FGE (2005)
Change in Void Ratio due to 2nd
Loading (e2):
New Void Ratio after 2nd Loading:
sHHee 2
12
@ End of Load 2
VOID RATIO-PRESSURE PLOTS
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Figure 7.7. Das FGE (2005).
Final e – log ´ plots consist of results of numerous load & unload
incrementsTwo Definitions of Clays based on Stress History:
Normally Consolidated (NC):The present overburden pressure (a.k.a. effective in-situ stress) is the most the soil has ever seen.
Overconsolidated Clay (OC):The present overburden pressure is less than the soil has experienced in the past. The maximum effective past pressure is called the preconsolidation pressure (´c) or Maximum Past Pressure (´vm)
VOID RATIO-PRESSURE PLOTS
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DETERMINATION OF MAXIMUM PAST PRESSURE(´c or ´vm)
Figure 7.8. Das FGE (2005).
Graphical Method(Casagrande, 1936)
1. Visually identify point of minimum radius of curvature on e-log ´curve (i.e. Point a).
2. Draw horizontal line from Point a(i.e. Line ab).
3. Draw Line ac tangent to Point a.4. Draw Line ad bisecting Angle bac.5. Project the straight line portion of
gh on e-log ´ curve to intersect Line ad. This intersection (Point f) is the maximum past pressure (a.k.a. preconsolidation pressure).
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OVERCONSOLIDAITON RATIO (OCR)
Figure 7.8. Das FGE (2005).
(´c or ´vm)
cOCRWhere:
´c (a.k.a. ´vm) = PreconsolidationPressure (a.k.aMaximum Past Pressure).
´ = Present Effective Vertical StressGeneral Guidelines:
NC Soils: 1 ≤ OCR ≤ 2OC Soils : OCR > 2
Possible Causes of OC Soils:Preloading (thick sediments, glacial ice); fluctuations of GWT, underdraining, lightice/snow loads, desiccation above GWT,secondary compression.
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EFFECTS OF SAMPLE DISTURBANCE
OC Clays - Figure 7.10. Das FGE (2005)
NC and OC soils of low to medium sensitivity will experience disturbance due to remolding. This changes the consolidation characteristics of the 1D consolidation tests.
)(
)(
remoldedu
dundisturbeut q
qS Sensitivity (St) Where qu = Unconfined Compressive Strength
NC Clays - Figure 7.9. Das FGE (2005)
Virgin Compression Curve – Consolidation Curve Insitu (i.e. w/o disturbance)
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Reconstruction of Virgin Consolidation Curves (EM 1110-1-1904)
Figure 3-12. EM 1110-1-1904 Settlement Analysis.
EFFECTS OF SAMPLE DISTURBANCE
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Reconstruction of Virgin Consolidation Curves (EM 1110-1-1904)Table 3-6. EM 1110-1-1904 Settlement Analysis.
EFFECTS OF SAMPLE DISTURBANCE
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Reconstruction of Virgin Consolidation Curves (EM 1110-1-1904)Table 3-6. EM 1110-1-1904 Settlement Analysis.
EFFECTS OF SAMPLE DISTURBANCE
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SETTLEMENT FROM 1D PRIMARY CONSOLIDATION
Figure 7.11. Das FGE (2005)
ASASHHAVVV ppo )(1Where:
V = Volume, Vo = Initial Volume, V1 = Final Volume, Sp = Primary Settlement
At End of Primary Consolidation = ´
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vvvop VVVASV 1
oo
os e
AHe
VV
11Figure 7.11. Das FGE (2005).
Where:Vvo = Initial Void Volume, Vv1 = Final Void Volume
At End of Primary Consolidation = ´
Where:e = Change in Void Ratio
sv eVV
Where:e0 = Initial Void Ratio
SETTLEMENT FROM 1D PRIMARY CONSOLIDATION
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ee
AHeVASVo
sp
1
Figure 7.11. Das FGE (2005).
At End of Primary Consolidation = ´
or
vo
p
op
ee
HS
eeHS
1
1
Therefore:
Where:v = Vertical Strain
SETTLEMENT FROM 1D PRIMARY CONSOLIDAITON
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Where:
Cc = Slope of Field VirginConsolidation Curve
= Compression Index
Cs (or Cr) = Slope of ReboundCurve
= Swell Index
´vm = Maximum Past Pressure
´o = Initial Vertical EffectiveStress
VOID
RAT
IO
´v (Log Scale)
Cc
CsorCr
eo
~0.4eo
Virgin ConsolidationLine
´vm = ´o
NC Clay
SETTLEMENT FROM 1D PRIMARY CONSOLIDATION
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VOID
RAT
IO
´v (Log Scale)
Cc
CsorCr
eo
~0.4eo
´vm= ´o
NC Clay
o
ocp e
HCS
log1 0
Settlement (Sp) using Void Ratio
´
Virgin ConsolidationLine
ef
Where:Sp = SettlementH = Height of Soil Layer´vm = Final Vertical Effective
Stress= o´ - Current Vertical
Effective Stress´ = Change in Vertical
Effective Stressf´ = Final Vertical Effective
Stressef = Final Void Ratio´f
SETTLEMENT FROM 1D PRIMARY CONSOLIDATION
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Where:
Cc = Slope of Field VirginConsolidation Curve
= Compression Index
Cs (or Cr) = Slope ofRebound Curve
= Swell Index
´vm = Maximum PastPressure
´o = Initial Vertical EffectiveStress
VOID
RAT
IO
´v (Log Scale)
Cc
CsorCr
eo
´o
~0.4eo
Same Slope as Cr
´vmor´c
OC ClayVirginConsolidationLines
SETTLEMENT FROM 1D PRIMARY CONSOLIDATION
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VOID
RAT
IO
´v (Log Scale)
Cc
CsorCr
eo
´vmor´c
´o
~0.4eo
Same Slope as Cr
o
oc
o
vmrp e
HCeHCS
log
1log
1 00
Settlement (Sp) using Void Ratio
Where:
Sp = SettlementH = Height of Soil Layer´ = Change in Vertical
Effective Stresso´ = Initial Vertical Effective
Stressf´ = Final Vertical Effective
Stressef = Final Void Ratio
´
ef
´f
OC ClaySETTLEMENT FROM 1D PRIMARY CONSOLIDATION
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nc WC 0115.0
Compression Index (Cc) Estimates from Other Laboratory Tests
)25(006.01.0)1( noc WeC
)10(007.0 LLCc
)10(009.0 LLCc
Soil Cc Equation Reference
Undisturbed ClaysTerzaghi & Peck (1967)
Disturbed ClaysOrganic Soils, Peat
EM 1110-1-1904Clays
Varved ClaysUniform Silts 20.0cC
)13(01.0 LLCc
nc WC 012.0
)35.0(15.1 oc eC
SETTLEMENT FROM 1D PRIMARY CONSOLIDATION
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Compression Index (Cc) Estimates from Other Laboratory Tests
sc GLLC
100
2343.0
Soil Cc Equation Reference
Clays Rendon-Herrero (1983)
Clays Nagaraj & Murty (1985)
38.22.1 1141.0
s
osc G
eGC
Where:
Gs = Specific Gravity of SolidsLL = Liquid Limit (in %)Wn = Natural Water Contenteo = Initial Void Ratio
SETTLEMENT FROM 1D PRIMARY CONSOLIDATION
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Compression Index (Cc) Estimates from Other Laboratory Tests
sc GLLC
100
2343.0
Soil Cc Equation Reference
Clays Rendon-Herrero (1983)
Clays Nagaraj & Murty (1985)
38.22.1 1141.0
s
osc G
eGC
SETTLEMENT FROM 1D PRIMARY CONSOLIDATION
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10002000 3000 4000 5000 6000900800700600500
Vertical Effective Stress 'v (psf)
0.96
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
VOID
RA
TIO
(e)
EXAMPLE: SETTLEMENT FROM VIRGINCONSOLIDATION CURVES
GIVEN:
OC CH layer
o´ = 855 psf
vm´ = 1460 psf
´ = 1005 psf
eo = 1.1
Height of CH Layer = 10 ft
Figure 1. Example of Virgin Consolidation Curves.
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Figure 1. Example of Virgin Consolidation Curves.
Sp H e1 eo
e 1.11.045 0.055eo 1.1
Sp (10 ft) 0.05511.1
Sp 0.262 ft
Sp 3.14in 314
in
10002000 3000 4000 5000 6000900800700600500
Vertical Effective Stress 'v (psf)
0.96
0.98
1
1.02
1.04
1.06
1.08
1.1
1.12
VOID
RA
TIO
(e)
1.1
1.0761.076
1.045Cc
Cs
eo
ef
'o 'vm 'f
'
EXAMPLE: SETTLEMENT FROM VIRGINCONSOLIDATION CURVES
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25
20
15
10
5
0
Dep
th fr
om E
xist
ing
Gro
und
Surf
ace
(ft)
0 2000
TOTAL STRESS()
25
20
15
10
5
0
25
20
15
10
5
0
0 200025
20
15
10
5
00 2000
PORE PRESSURE(u)
0 2000
0 2000
EFFECTIVE STRESS(')
0 200025
20
15
10
5
0
25
20
15
10
5
0
25
20
15
10
5
0
25
20
15
10
5
0
Depth
fromExisting
Ground
Surface (ft)
CLsat = 105 pcf
SMsat = 115 pcf
MHsat = 115 pcf
SC = 105 pcfsat = 110 pcf
B = 6 ft SQ
Q = P = 144 kips
EXAMPLE: SETTLEMENT FROM 1D TEST STRAIN RESULTS
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100 1000200 400 600 800 2000 4000 6000
Vertical Effective Stress 'v (psf)
50
45
40
35
30
25
20
15VE
RTIC
AL S
TRAI
N (%
)
CL LayerSample from 12 ft
EXAMPLE: SETTLEMENT FROM 1D TEST STRAIN RESULTS
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25
20
15
10
5
0
Dep
th fr
om E
xist
ing
Gro
und
Surf
ace
(ft)
0 2000
TOTAL STRESS()
25
20
15
10
5
0
25
20
15
10
5
0
AB
C
D
E
F
G
0
315
525
635
980
1325
1670
2015
2360
2820
0 200025
20
15
10
5
00 2000
PORE PRESSURE(u)
0 2000
0 2000
EFFECTIVE STRESS(')
0 200025
20
15
10
5
0
25
20
15
10
5
0
25
20
15
10
5
0
25
20
15
10
5
0
Depth
fromExisting
Ground
Surface (ft)
0
0
60
250
435
625
810
1000
1250
0
315
525
575
730
890
1045
1205
1360
1570
2525
1455
1250
1185
1240
1345
CLsat = 105 pcf
SMsat = 115 pcf
MHsat = 115 pcf
SC = 105 pcfsat = 110 pcf
B = 6 ft SQ
Q = P = 144 kips
CL Layer 1
CL Layer 2
'o'f
EXAMPLE: SETTLEMENT FROM 1D TEST STRAIN RESULTS
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100 1000200 400 600 800 2000
Vertical Effective Stress 'v (psf)
50
45
40
35
30
25
20
15
VERT
ICAL
STR
AIN
(%)
CL LayerSample from 12 ft
'o1
'f1
v1 = 6.5% = 0.065
CL Layer 1
inS
ftS
ftS
HS
p
p
p
vp
7.4
39.0
)065.0)(6(
1
1
1
111
EXAMPLE: SETTLEMENT FROM 1D TEST STRAIN RESULTS
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CL Layer 2Sp2 H2v2
Sp2 (6 ft)(0.024)Sp2 0.14 ftSp2 1.7in
SPtotal Sp1 Sp2
SPtotal 6.4in
SPtotal 6 12
in100 1000
200 400 600 800 2000
Vertical Effective Stress 'v (psf)
50
45
40
35
30
25
20
15
VERT
ICAL
STR
AIN
(%)
CL LayerSample from 12 ft
'o2
'f2
v2 = 2.4% = 0.024Total Settlement
EXAMPLE: SETTLEMENT FROM 1D TEST STRAIN RESULTS
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12 loglog tteC
SETTLEMENT FROM SECONDARY CONSOLIDATION
Where:
C = Secondary CompressionIndex
e = Change in Void Ratiot = Time
Results of 1D Consolidation Test @ One Load Increment
Figure 7.15. Das FGE (2005).
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Where:
H = Height of Soil Layerep = Void Ratio @ End
of Primary Consolidationt = Time
p
s
eCC
ttHCS
1
log1
2
SETTLEMENT FROM SECONDARY CONSOLIDATION
Results of 1D Consolidation Test @ One Load Increment
Figure 7.15. Das FGE (2005).
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TIME RATE OF CONSOLIDATION
Clay Layer Undergoing Consolidation
Figure 7.17a. Das FGE (2005).
Theory of 1D Consolidation(Terzaghi, 1925)
Assumptions:1. The clay-water system is homogenous.2. Saturation is complete (S = 100%).3. Compressibility of water is negligible.4. Compressibility of soil grains is
negligible (but soil particles rearrange).5. Flow of water is in one direction only.6. Darcy’s Law is Valid.
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Flow of Water @ Point AFigure 7.17b. Das FGE (2005).
Clay Layer Undergoing Consolidation
Figure 7.17a. Das FGE (2005).
TIME RATE OF CONSOLIDATION
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Flow of Water @ Point AFigure 7.17b. Das FGE (2005).
dtVdxdydz
zv
ordtVdxdyvdxdydz
zvv
z
zz
z
(Rate of Water Outflow) –
(Rate of Water Inflow) =
(Rate of Volume Changes)Mathematical Equation:
Where:
V = Volume of Soil Elementvz = Velocity of flow in z direction
TIME RATE OF CONSOLIDATION
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Flow of Water @ Point AFigure 7.17b. Das FGE (2005).
Where:
Vs = Volume of Solidsvv = Volume of Voids
t
VeteV
tV
teVV
tV
tV
tV
dxdydz1
zuk
zuk
zhkkiv
tVdxdydz
zv
ss
sssv
2
2
w
wz
z
Using Darcy’s Law (v = ki)
Where u = excess pore pressure. From algebra:
Rate of change in V = Rate of Change in Vv
TIME RATE OF CONSOLIDATION
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Flow of Water @ Point AFigure 7.17b. Das FGE (2005).
te
e11
zuk
te
e1dxdydz
tV
e1dxdydz
e1VV
0t
V
tVe
teV
tV
teVV
tV
tV
o2
2
w
o
oos
s
ss
sssv
From Previous Slide
Assuming soil solids are incompressible
and
eo = Initial Void Ratio. Substituting:
Combining equations:
TIME RATE OF CONSOLIDATION
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o
vv
vo
v
w
vv
ow
eam
tum
tu
ea
zuk
uaae
te
ezuk
1
1
11
2
2
2
2
From Previous Slide
The change in void ratio is caused by the increase in effective stress.
Assuming linear relationship between the two:
av = Coefficient of Compressibility. Can be considered constant over
narrow pressure increases. Combining equations:
mv = Coefficient of Volume Compressibility.
TIME RATE OF CONSOLIDATION
Flow of Water @ Point AFigure 7.17b. Das FGE (2005).
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vwv
v
o
vv
vo
v
w
mkc
zuc
tu
eam
tum
tu
ea
zuk
2
2
2
2
1
1
From Previous Slide
Rearranging Equations:
av = Coefficient of Compressibility.mv = Coefficient of Volume Compressibility.
Where cv = Coefficient of Consolidation.
TIME RATE OF CONSOLIDATION
Flow of Water @ Point AFigure 7.17b. Das FGE (2005).
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0,00,2
0,0
uutuHz
uz
dr
2
2
zuc
tu
v
Can be solved with the following boundary conditions:
Basic Differential Equation of 1DConsolidation Theory
The solution yields
vTMm
m dr
o eHMz
Muu
2
0
sin2
Clay Layer Undergoing
ConsolidationFigure 7.17a. Das FGE (2005).
TIME RATE OF CONSOLIDATION
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From Previous Slide
dr
vv H
tcT 2
pressure waterpore excess Initial
o
TMm
m dr
o
u
mM
eHMz
Muu v
122
sin2 2
0
Clay Layer Undergoing Consolidation
Figure 7.17a. Das FGE (2005).
Where:
TIME FACTOR
TIME RATE OF CONSOLIDATION
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o
z
o
zoz u
uu
uuU
1
Because consolidation progress by dissipation of excess pore pressure, the degree of consolidation
(Uz) at a distance z at any time t is:
Figure 7.18. Das FGE (2006).
TIME RATE OF CONSOLIDATION
Clay Layer Undergoing Consolidation
Figure 7.17a. Das FGE (2005).
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Figure 7.18. Das FGE (2006).
TIME RATE OF CONSOLIDATION
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vTMm
m
eM
U2
02
21
ionConsolidat Primary from Layer of Settlement time at layer of Settlement
ionConsolidat of degree Average
p
t
StS
U
o
Hz
dr
p
t
u
dzuH
SSU
dr
2
021
1
Average degree of consolidation (U) for the entire depth of the clay layer at any time t is:
Where:
Substituting U for u
%)100log(933.0781.1100
%4
2
UTU
UTU
v
v
60%, For
60%, to 0% For
U can be approximated by thefollowing relationships:
TIME RATE OF CONSOLIDATION
Clay Layer Undergoing Consolidation
Figure 7.17a. Das FGE (2005).
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Variation of Tv with UTable 7.1 Das PGE (2006).
TIME RATE OFCONSOLIDATION
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Difference between Average Degree of Consolidation and MidplaneDegree of Consolidation
Figure 7.28. Das FGE (2006).
TIME RATE OF CONSOLIDATION
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COEFFICIENT OF CONSOLIDATION (cv)• Generally decreases as Liquid Limit (LL) increases.
• Determined from 1D Consolidation Test Lab per Load Increment.
Logarithm of Time Method(Casagrande and Fadum, 1940)
Figure 7.19 Das FGE (2006).
Square Root of Time Method(Taylor, 1942)
Figure 7.20 Das FGE (2006).
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Figure 7.19. Das FGE (2006).
Logarithm of Time Method1. Extend the straight line portion of primary
and secondary consolidations to interest at Point A. Point A represents d100(Deformation at 100% primary consolidation).
2. The initial curved portion of the deformation plot versus log t is approximated to be a parabola on a natural scale. Select times t1and t2 on the curved portion such that t2 = 4t1. Let the difference of the specimen deformation between (t2 – t1) be equal to x.
3. Draw a line horizontal to DE such that the vertical distance BD is equal to x. The deformation corresponding to the line DE is d0 (Deformation at 0% primary consolidation).
COEFFICIENT OF CONSOLIDATION (cv)
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Logarithm of Time Method
50
2
250
50
197.0
197.0
tHc
HtcT
drv
dr
v
4. The ordinate of Point F on the consolidation curve represents the deformation at 50% primary consolidation (d50).
5. For 50% average degree of consolidation (U = 50%), Tv = 0.197 (see Table 7.1, Das FGE 2006).
or
Where:Hdr = Average longest drain path
during consolidation.Figure 7.19. Das FGE (2006).
COEFFICIENT OF CONSOLIDATION (cv)
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Figure 7.20. Das FGE (2006).
Square Root of Time Method1. Draw a line AB trough the early portion
of the curve.
2. Draw a line AC such that OC = 1.15OB. The time value for Point D (i.e. the intersection of line AC and the data) is the square root of time for t90 (i.e. the time to 90% primary consolidation).
3. For 90% consolidation, Tv = 0.848 (see Table 7.1, Das FGE 2006).
90
2
290
90
848.0
848.0
tHc
HtcT
drv
dr
v
or
COEFFICIENT OF CONSOLIDATION (cv)
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SP FILL ( = 115 pcf)
SC ( = 115 pcf)
CL ( = 115 pcf)
SM ( = 115 pcf)
3ft
4ft
6ft
5ft
GIVEN: Soil Profile (NTS).2 way drainage.
REQUIRED: Determine the following:
a. The change in pore pressure in the CL layer immediately after the application of the 3 ftof SP Fill.
b. The degree of consolidation in the middle of the clay layer when the excess pore pressure (ue) is 170 psf.
c. How high would the water in a piezometer located in the middle of the layer rise above the GWT when ue = 170 psf?
d. If cv = 0.000004 ft²/sec, how long would it take to get to 25% average degree of consolidation? To U = 50%? To U = 99%?
COEFFICIENT OF CONSOLIDATION (cv)Example
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PRECOMPRESSION – GENERAL CONSIDERATIONSPRECOMPRESSION: Loading an area prior to placement of the planned structural loading to limit post-construction settlement. Also known as Surcharging.
Settlement caused by structural loading (Sp):
o
ocp e
HCS
log1 0
Settlement caused by structural loading and surcharging (S´p or Sp+f):
o
focfpp e
HCSS
log
1 0
Where:f = Change in vertical stress due to Fill added.
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Figure 7.26. Das FGE (2006).
Where:p) = Change in vertical stress due to
structural load.f) = Change in vertical stress due to
Fill added.
Where:Sp = Settlement due to structural load.Sp+f = Settlement due to structural load
and Fill.
PRECOMPRESSION – GENERAL CONSIDERATIONS
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)(
)()(
)(
)()(
)(
11log
1log
log
log
p
f
o
p
o
p
o
fpo
o
po
p
p
U
U
SS
U
Mathematical Equations
Definition of average Degree of Consolidation U
Substitution
Re-arranging (Eqn 7.56 Das FGE 2006)Place in graphical form
for design use(Figure 7.27 Das FGE 2006)
PRECOMPRESSION – PLANNING
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Figure 7.27. Das FGE (2006).
Where:
f) = Change in vertical stressdue to Fill added.
p) = Change in vertical stressdue to Structural Loading.
´o = Initial vertical effectivestress.
PRECOMPRESSION –PLANNING
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Figure 7.27. Das FGE (2006).
STEPS:1. Calculate primary consolidation
settlement from planned loading (Sp).2. Calculate primary consolidation
settlement from planned loading plus surcharge (Sp+f ).
3. Calculate average degree of consolidation U. Note U = Sp/Sp+f. Can also use Figure 7.27 or Eqn 7.56 (Das FGE 2006).
1. Find Tv from calculated U. To find time to when surcharge loading should be removed (i.e. t2):
v
drv
cHTt
2
2
PRECOMPRESSION –PLANNING
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Difference between Average Degree of Consolidation and MidplaneDegree of Consolidation
Figure 7.28. Das FGE (2006).
Removal of Surcharge may still cause net
settlement(swelling near drainage
layers, settlement @ middle)
Conservative Approach:Assume U is the midplanedegree of consolidation.
TIME RATE OF CONSOLIDATION
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Midplane Degree of Consolidation
Figure 7.29. Das FGE (2006).
TIME RATE OF CONSOLIDATION
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SURCHARGING EXAMPLESP FILL ( = 115 pcf)
SC ( = 115 pcf)
CL ( = 115 pcf)
SM ( = 115 pcf)
3ft
4ft
6ft
5ft
GIVEN: Soil Profile (NTS).2 way drainage.
REQUIRED: Determine the following:
a. If cv = 0.000004 ft²/sec, how long would it take to get to 99% average degree of consolidation?
b. If a surcharge of 4 ft of fill was placed in addition to the 3 ft of fill planned, when would you be able to remove the surcharge? Use the same value for cvgiven in a.
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GROUND MODIFICATION FOR CONSOLIDATIONSAND DRAINS
Section ViewFigure 10.38. Das PGE (2006).
Plan View – Triangular SpacingFigure 10.38. Das PGE (2006)
Reduction Drainage Path =Reduction in Drainage Time
rw = Sand Drain Radiusde = Effective Diameter
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Figure 10.39. Das PGE (2006).
1
23
4
5
STEPS
Sand Drain Installation: Auger Method(Kirmani, 2004)
1. Place auger at drain location.2. Screw auger to selected depth.3. Rotate auger at selected depth to remove soil.4. Inject sand while auger is extracted.5. Complete sand drain to working platform level.
GROUND MODIFICATION FOR CONSOLIDATIONSAND DRAINS
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Conceptual ConceptCourtesy of www.americanwick.com
Figure 7.31. Das FGE (2006).
Courtesy ofwww.americandrainagesystems.com
GROUND MODIFICATION FOR CONSOLIDATIONPREFABRICATED VERTICAL DRAINS (PVD’S) (A.K.A. WICK DRAINS)
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Courtesy of www.nilex.com
Courtesy of www.nilex.com
Courtesy of www.americandrainagesystems.com
GROUND MODIFICATION FOR CONSOLIDATIONPREFABRICATED VERTICAL DRAINS (PVD’S) (A.K.A. WICK DRAINS)
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Plan View – Sand DrainTriangular Spacing
Figure 7.30. Das FGE (2006).
wo
hvr
e
vrr
w
e
rr
eekc
dtcT
rdn
nnn
nnm
mTU
)1(
2
413)ln(
1
8exp1
2
2
2
2
2
Ur = Average Degree of Radial Consolidation
Barron (1948)
de = Effective Diameterrw = Sand Drain Radius
cvr = Coefficient of Radial ConsolidationTr = Time Factor for Radial Consolidation
kh = Coefficient of Horizontal PermeabilityTr = Time Factor for Radial Consolidationeo = Initial Void Ratio
GROUND MODIFICATION FOR CONSOLIDATIONRADIAL CONSOLIDATION
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TIME RATE OF RADIAL CONSOLIDATIONVariation of Tr with U - Table 7.3 Das PGE (2006).
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TIME RATE OF RADIAL CONSOLIDATIONVariation of Tr with U - Table 7.3 Das PGE (2006).
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Sand
Clay
Sand
Dra
in
Vertical and Radial DrainageCourtesy of www.nhi.fhwa.dot.gov
Drainage
)1)(1(1, vrrv UUU Where:
Uv,r = Average Degree of Consolidationdue to Vertical & Radial Drainage
Uv = Average Degree of Consolidationdue to Vertical Drainage
Ur = Average Degree of Consolidationdue to Radial Drainage
GROUND MODIFICATION FOR CONSOLIDATIONAVERAGE DEGREE OF CONSOLIDATION DUE TO VERTICAL & RADIAL DRAINAGE
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CONSOLIDATION MONITORINGSETTLEMENT PLATES
Insitu Soil Layerto be Monitored
Fill Layer SettlementPlate Base(Plywood or Steel)
Rod Protection(Typically PVC Pipe)
Settlement Rod(Steel)
General Concept Standard Plan Detail(Courtesy of Iowa DOT)
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Settlement Platforms
Permanent Fill
Soft Clay Vertical Drain
Surcharge
DrainageBlanket
Piezometers
Firm Soil
Not to Scale
Inclinometers
SURCHARGING INSTRUMENTATION EXAMPLE
Courtesy of www.nhi.fhwa.dot.gov