Settlement Analysis
STABILITY
DURING CONSTRUCTION
STAGED CONSTRUCTION:
TYPICALLY IN TWO TO THREE STAGES AND
COMPLETED IN ONE OR TWO CONSTRUCTION
SEASONS (REMEMBER THAT WE CANNOT INSTALL
WICK DRAINS IF THE GROUND IS FROZEN AND WE
USUALLY DO NOT PLACE FILL DURING THE WINTER)
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STABILITY
DURING CONSTRUCTION
STAGED CONSTRUCTION:
TYPICAL STAGES IN CENTRAL AND NORTHERN
ONTARIO:
•STAGE 1: 0 TO 8m, WAIT FOR 3 MONTHS
•STAGE 2: 8 TO 12m, WAIT FOR 3 MONTHS
•STAGE 3: 12 TO 14m, WAIT FOR 3 MONTHS
BEFORE REMOVING SURCHARGE
Loaded Soil will Compress Due to:
1.
Deformation of soil grains (elastic)
Degree water saturation <1
2.
3.
4.
Compression of air and water in voids
Squeezing out of water and air out of
voids
Plastic flow (creep)
Degree water saturation =1
5.
6.
7.
Compression of water (very small)
Squeezing out of water out of voids
Plastic flow (creep)
2
For Load Problems Need to Answer
‡
How much settlement will occur due to an
applied load?
„
‡
Magnitude of consolidations
How long will it take for settlement to
occur?
„
Time rate of consolidation
EMBANKMENT SETTLEMENT
IMMEDIATE (“ELASTIC”)
PRIMARY CONSOLIDATION (ASSOCIATED WITH
DISSIPATION OF EXCESS PORE PRESSURES)
SECONDARY CONSOLIDATION (ASSOCIATED WITH
REARRANGEMENT OF PARTICLES)
CREEP (ASSOCIATED WITH SHEAR STRESS-STRAIN)
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EMBANKMENT SETTLEMENT
IT IS IMPORTANT TO RECOGNIZE THE IMPACT OF
DIFFERENT TYPES OF SETTLEMENTS ON THE
PROJECT:
SETTLEMENTS THAT OCCUR DURING
CONSTRUCTION (PRIOR TO DRIVING PILES AT THE
BRIDGE ABUTMENTS AND PRIOR TO CONSTRUCTION
OF THE BRIDGE)
POST CONSTRUCTION SETTLEMENTS (HAVE
SERIOUS COST IMPLICATIONS: BRIDGE AND
PAVEMENT PERFORMANCE)
EMBANKMENT SETTLEMENT
WE USUALLY DESIGN THE EMBANKMENT SO THAT:
IMMEDIATE SETTLEMENTS AND SETTLEMENTS DUE
TO PRIMARY CONSOLIDATION OCCUR DURING
CONSTRUCTION
AND SETTLEMENTS DUE TO SECONDARY
CONSOLIDATION AND CREEP OCCUR AFTER THE
END OF CONSTRUCTION
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EMBANKMENT SETTLEMENT
IMMEDIATE SETTLEMENTS
USUALLY NOT A KEY ISSUE:
USE CLOSED FORM SOLUTIONS BASED ON THE
THEORY OF ELASTICITY WITH CONSERVATIVE
UNDRAINED SOILS PROPERTIES
ALTERNATIVELY, CARRY OUT NUMERICAL
SIMULATION USING TOTAL STRESS ANALYSIS WITH
UNDRAINED SOIL PROPERTIES
EMBANKMENT SETTLEMENT
PRIMARY CONSOLIDATION
TERZAGHI’S 1D THEORY OF CONSOLIDATION
KEY ASSUMPTIONS:
•CONSTANT VERTICAL TOTAL STRESS AND
ELASTIC PROPERTIES DURING CONSOLIDATION
•VERTICAL DRAINAGE ONLY
•NO LATERAL STRAINING OF THE SOIL
(OEDOMETER TESTING)
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EMBANKMENT SETTLEMENT
PRIMARY CONSOLIDATION
THE THEORY IS COMMONLY USED BECAUSE:
•IT IS SIMPLE (IT CAN EASILY BE INCORPORATED IN
A FINITE DIFFERENCE FORMULATION)
•IT PROVIDES REASONABLE PREDICION OF
SETTLEMENT OF WIDE EMBANKMENTS FOUNDED
ON RELATIVELY THIN CLAY LAYER
OEDOMETRIC CONDITIONS
Spring Analogy to Soil Consolidation
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q=P/A
Δσv’
Soil Vertical Stress
P
z
σ v’
z
σ v’
Δσv’
z
Spring Analogy to Soil Consolidation
Immediate settlement
Note: porewater pressure
increased by Δu = ue
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Spring Analogy
Smax occurs when Δu = 0
Change in volume in container =
volume of water removed if Srw=1
Oedometer Test
t=1, ue=100%
t=2, ue=50%
Δσ=P/A
hw = Δσ/γw
t=0, ue=0%, t=∞
Record for each stress
increment (Δσ):
Change in height of
specimen with time
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Typical
Stress
Increment
Test Data
Casagrande Log Time Method
U = degree of pore water pressure dissipated
ue=100%, U = 0%
R=0
ue=50%, U = 50%
R=50
R=100
ue=0%, U=100%
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Casagrande Log Time Method
Root
Time
Method
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Settlement Calculations
ΔH=s
Δe
H0
water
&
solids
e0
voids
ef
voids
Hf
1
solids
1
Initial
solids
Final
Consolidation Settlement Calculations
εv = ΔH/H0 = s/H0= Δe/1+e0
s = εv H0= (Δe/1+e0) H0
Note: Want settlement @ U=100%
100% dissipation of excess porewater pressure
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U100 Data for Stress Increments
av= -Δe/Δσv’
mv= Δεv/Δσv’
Coef. Volume change (mv)
Coef. Of compressibility (av)
U100 Data for Stress Increments
Compression Index (Cc)
e1
cc= Δe/(logσ2’- logσ1’)
cc =(e1-e2)/log (σ2’/σ1’)
If σ2’ = σ1’+Δσ
cc =Δe/log
[(σ1’+Δσ)/σ1’]
e2
Δσ
σ’1
σ’2
e1 =2.4, e2=1.4 Δe = 1.0
σ’1=7.1, σ’2=49
cc = 1.0/(log49-log7.1) = 1.19
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Settlement Equation in Terms of mv
S = εvHo
mv =
Δε v
Δσ '
(1/kPa = m 2 /kN)
H
S = ∫ m v Δσ ' dz
0
if m v and Δσ ' are assumed constant with depth then
S = m v Δσ ' H
Settlement Equation in Terms of av
S = εvHo =
Δe
H
1 + eo
Δe
(1/kPa = m 2 /kN)
Δσ '
H
a
S = ∫ v Δ σ ' dz
1 + eo
0
av =
if a v and Δ σ ' are assumed constant w ith depth then
S=
av
Δσ ' H = m v Δσ ' H
1 + eo
therefore m v =
av
1 + eo
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Settlement Equation in Terms of cc
S = εvHo =
cc =
Δe
log
S=
Δe
H
1 + eo
σ2'
σ1'
Note: cc = 0.009(LL-10)
⎛ σ '+ Δσ
cc
c
σ '
H log 2 = c H log⎜⎜ 1
σ 1 ' 1 + eo
1 + eo
⎝ σ1'
⎞
⎟⎟
⎠
Settlement due to Δσ
Stotal = S r + S c
S r = S rebound =
σ'
Cr
C
σ'
H 0 log( 2 ) = r H 0 log( c )
σ '1 1 + e0
σ '1
1 + e0
note : for this case σ '1 = 0
Sc =
Cc
C
σ ' + Δσ
σ'
)
H 0 log( 2 ) = c H 0 log( c
σ '1 1 + e0
σ 'c
1 + e0
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Over Consolidation Ratio (OCR)
OCR =
σ 'c
σ'
where :
OCR = Over Consolidation Ratio
σ 'c = preconsolidation pressure of a specimen
σ ' = present (field) effective overburben pressure
Over Consolidation Ratio (OCR)
σ’
efield =e0
σ’c
Log σ’
OCR =
σ 'c
σ'
e
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Determination of σc’
See Das for procedure
Note σc’ is not a distinct point
Over Consolidation Ratio (OCR)
‡
If OCR ≤ 1.2 σ’c ~ σ’ then soil is normally
consolidated
‡
If OCR ≥ 1.2 then soil over consolidated
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EMBANKMENT SETTLEMENT
PRIMARY CONSOLIDATION
1D THEORY OF CONSOLIDATION TIME-INDEPENDENT ANALYSIS
COMPRESSION INDEX
1
VOID RATIO
Cr
ΔH =
H*C
1 + eo
Log (
σf’
σi’
)
LOG EFFECTIVE STRESS
PRECONSOLIDATION
PRESSURE( pc)
1
Cc
EMBANKMENT SETTLEMENT
PRIMARY CONSOLIDATION
1D THEORY OF CONSOLIDATION TIME-INDEPENDENT ANALYSIS
INITIAL STRESS
LOG TOTAL STRESS
VOID RATIO
FINAL STRESS
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EMBANKMENT SETTLEMENT
PRIMARY CONSOLIDATION
1D THEORY OF CONSOLIDATION TIME-DEPENDENT ANALYSIS
INITIAL STRESS
LOG TOTAL STRESS
VOID RATIO
FINAL STRESS
UNDRAINED LOADING:
•PORE PRESSURE GENERATION
•NO CHANGE IN EFFECTIVE STRESSES
•NO SETTLEMENT
EMBANKMENT SETTLEMENT
PRIMARY CONSOLIDATION
1D THEORY OF CONSOLIDATION TIME-DEPENDENT ANALYSIS
INITIAL STRESS
LOG TOTAL STRESS
VOID RATIO
FINAL STRESS
DRAINED LOADING:
•PORE PRESSURE DISSIPATION
•INCREASE IN EFFECTIVE STRESSES
•SETTLEMENT
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