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Les modules et leurs applications au dimensionnement
et contrôle de qualité des structures de chaussée et des voies ferrées
António Gomes CorreiaUniversité de Minho, Portugal
CFMS, 08-03-12 A. Gomes Correia ([email protected])University of Minho; Campus de Azurém, Guimarães; Portugal
Journée d'hommage au Professeur Jean BIAREZ, 12 Mars 2008
INTRODUCTIONINTRODUCTION
DESIGN PROCESSDESIGN PROCESSLABORATORY TECHNOLOGIESLABORATORY TECHNOLOGIESMODULI FROM LABORATORYMODULI FROM LABORATORYFIELD TECHNOLOGIESFIELD TECHNOLOGIESMODULI FROM FIELDMODULI FROM FIELDCONCLUSIONCONCLUSION
LECTURE OUTLINE
DESIGN PROCESSDESIGN PROCESS
ROUTINE
ADVANCED
STRUCTURAL MODEL
SEMI-EMPIRICAL
ANALYTICAL
FEM (2D; 3D); DFM
Linear elastic(E, ν); pseudo-elasticVisco-elastic
+
Nonlinearσ’−ε −t
DIFFICULTY: DIFFICULTY: IdentificationIdentification ofof modelmodel parametersparameters
DESIGN SOIL MODEL
RESEARCH + DEMHydro-stress/strain-strength-creep
IN SITU STRAIN MEASUREMENTS IN FLEXIBLE PAVEMENT STRUCTURES
FWD – 65 kNdrainage layerbinder
bitumen macadam 2
granular base
granular sub-base
foundation soil
0.040 m
0.055 m
0.095 m
0.105 m
0.200 m
0.300 m
section 1 section 3section 2
L11 L12T11 T12 L13 L14T13 T14 L16 L17T16 T17
V2 V3 V5 V6 V8
V4 V7V1
5 m 5 m
0.024 m 0.2 m 0.2 m
0.3 m
1.49 m
T5
0.96 m
0.9 m 0.3 m
1.47 m
T2T1
1.2 m
T4
T31.03 m
0.70 m0.40 m
1 m
1
3
5
2
4
6
Li (i = 11 to 17) : horizontal longitudinal strain gauges (in italic : not working gauges)
Ti (i = 11 to 17) : horizontal transversal strain gauges (in italic : not working gauges)
Vi (i = 1 to 9) : vertical strain gauges
Ti (i = 1 to 9) : tensiometers
Wi (i = 1 to 12) : TDR
i (i =1 to 6) : thermal gauges
0.11 m0.35 m
0.01 m
0.01 m
0.4 m
0.4 m0.2 m
bitumen macadam 1
0.9 m
T6
1.2 m
T8
T7
0.64 m0.37 m
STRAINS DUE TO MOVING LOADS
q
εPermanentstrains
Unload-reloadstrains
q
εt = εp + εe
The increment of residual or permanent strain over 1 cycle is much smaller than the elastic strain (unload-reload strain)
CYCLIC LOAD TRIAXIAL TEST FOR UGM
(EN 13286-7)EVALUATION OF QUASI ELASTIC BEHAVIOUR
√ Cyclic conditioning (20 000 cycles)√ Series of short unload-reload cycles(100 cycles/stress level)
EVALUATION OF RESISTANCE TO PERMANENT DEFORMATION
√ Single stage procedure (80 000 cycles)√ Multi-stage procedure (10 000 cycles/stress level)
Ranking materials
Parameters for modelling and design
0
5 0
1 0 0
1 5 0
2 0 0
2 5 0
3 0 0
3 5 0
4 0 0
0 1 0 0 2 0 0 3 0 0 4 0 0
p (k P a )
q(kP
a)
M e t . A
M e t . B
Δ q /Δ p = 0 ,5
Δ q /Δ p = 1 ,0 Δ q /Δ p = 1 ,5
Δ q /Δ p = 2 ,0
C y c lic c o n d i t io n in g LSL
0
100
200
300
400
500
600
700
0 100 200 300 400 500
p(kPa)q(
kPa)
Met. A
Met. B
Δq/Δp=0,75
Δq/Δp=1,5
Δq/Δp=2,0
Δq/Δp=2,5
Cyclic conditioning
Δq/Δp=1,0
HSL
LABORATORY TECHNLOGIESStrains from 0,0001% are necessary
0
50
100
150
200
250
300
0,0001 0,001 0,01 0,1 1 10 100Axial strain[%]
Es [MPa] On sample(local)
Off sample(external)
ON AND OF SAMPLE MEASUREMENTS
CYCLIC TRIAXIAL TEST (UMinho)
CYCLIC TRIAXIAL TESTTypical results of strain measurements
MODULI FROM LABORATORYMODULI FROM LABORATORY
σ
ε
E0 Esec Etg
lg ε
E
E0
Esec
Etg
NON LINEAR BEHAVIOURDEFINITIONS OF MODULI
QUASI-ELASTIC PARAMETERS FOR CONSTITUTIVE LAWS
OF SOILS
Biarez
SMALL STRAIN MODULUS FOR SMALL STRAIN MODULUS FOR CLAYEY SOILSCLAYEY SOILS
((BiarezBiarez et al., 2003)et al., 2003)
0 1 2 3 4 5 6 0
500
1000
1500
2000
SAND Hostun R.f :
D60/D10=1.8
emax=0.99 emin=0.66
[EL HOSRI] 1984 [CHARIF]
1991[RIVERA] 1988
0.17 0.40.51.02.0e
AGGREGATES "La Nouleau" :
D60/D10 =36
emax=0.61 emin=0.25
1 e
0.25
E 0σ' 1/2
(MPa)
(MPa) E σ'1/2
ke
SAND Toyoura :D60/D10 = 1.3emax = 0.982emin = 0.617
Yellow clay P300 WL = 35%White clay WL = 61% [HOMSI]Black clay WL = 70% [EL HOSRI] Bentonite WL = 105% [EL HOSRI]
k = 450 if WL > 50
k = 350 (WL = 70%)
k = 180 (WL = 105%)
k = 525
(WL = 61%)
40 80 1200
400
800 k
WL(%)
White clay
IMPORTANCE OF STRAIN LEVEL IN SECANT MODULUSIMPORTANCE OF STRAIN LEVEL IN SECANT MODULUS(Gomes (Gomes CorreiaCorreia, 2000 (data from Loach, 1987)), 2000 (data from Loach, 1987))
10
100
10 100
E s ( MPa)
σ 0́(kPa)
ε1= 2x10-4
ε 1 = 10-3
QUASI-ELASTIC PARAMETERS FOR CONSTITUTIVE LAWS
OF UGM
NON-LINEAR MODELSk-θ
modelCCP
M kp
pr aa
k
=⎛
⎝⎜
⎞
⎠⎟1
3 2
p
Boyce modelVCP ε βv
aa
n n
Kp p
qp
= −⎛⎝⎜
⎞⎠⎟
⎛
⎝⎜⎜
⎞
⎠⎟⎟
−111
2
εq an np p
qp
=⎛⎝⎜
⎞⎠⎟−1 1
3 Ga
31
1
q3
p 3x2
σσ
σσ
−=
=+
( )31
31v
32
2x
εεε
εεε
−=
+=
q
ν = 0.35
K
pp
K Kqp
a
n
a a
=
⎛
⎝⎜
⎞
⎠⎟
−⎛⎝⎜
⎞⎠⎟
−1
21 βG
pp
G
a
n
a
=
⎛
⎝⎜
⎞
⎠⎟
⎛
⎝⎜
⎞
⎠⎟
−1
1( )β = − ⋅
⋅1 n
Ka6 Ga
TRIAXIAL TEST RESULTS MODELLING
RECENT FINDINGS - UGM
MATERIALS & PRECISE LARGE TRIAXIAL TESTSMATERIALS & PRECISE LARGE TRIAXIAL TESTS
0102030405060708090
100
0,01 0,1 1 10 100
Grain size (mm)
Cum
ulat
ive
% p
assi
ng
0/12.5
0/31.5
Modified Modified ProctorProctorMaterialMaterial
DD5050(mm(mm
))UUcc ww
(%)(%)γγdd(Mg/m(Mg/m33))
0/31.50/31.5 8.58.5 5353 5.95.9 2.3102.310 2.712.71
0/12.50/12.5 3.53.5 2828 6.26.2 2.1252.125 2.712.71
Compaction conditionsCompaction conditionsMaterialMaterial
ww00 (%)(%) γγ d0d0 (Mg/m(Mg/m33)) ee00
0/31.50/31.5 3.93.9 2.1932.193 0.2360.236
0/12.50/12.5 4.14.1 2.216 2.216 0.2230.223
GGss
23X23X57 cm
STRESSSTRESS--DEPENDENCY OF YOUNGDEPENDENCY OF YOUNG’’S MODULUS AT S MODULUS AT SMALL STRAINS, SMALL STRAINS, EEvv: a function of : a function of σσvv onlyonly
(Gomes Correia et al., 2005)
Δp (kPa)
Δq (kPa)
0
100
200
300
400
500
600
0 100 200 300 400
A1 A2 A3 A4 B1B2
B3 B4
C1
C2
C3
C4
D1
D2
D3
D4
E1
E2
E3
E4
F1
F2
TYPICAL RESULTS OFCYCLIC TRIAXIAL TEST- CCP
Un.-Rel. Strains – Poisson ratio
““SS”” SHAPED STRESSSHAPED STRESS--STRAIN CURVE UNDER STRAIN CURVE UNDER TRIAXIAL COMPRESSION AFTER CYCLIC PRETRIAXIAL COMPRESSION AFTER CYCLIC PRE--
STRAINING STRAINING (Gomes Correia et al., 2005)
Stress-strain behaviour under cyclic loading, showing:
- large inelastic strains & a typical degradation of the modulus with strain during the first cycle; and
- S-shaped S-S curve after cyclic prestraining
Peculiar but natural trends of the tangent and secant moduli as a function of strain level for a very dense compacted after pre-straining of 21.000 cycles of a constant cyclic deviator stress of 230 kPa
FIELD TECHNOLOGIES
Spectral-Analysis-of-Surface-Waves (SASW)(Nazarian, 2005)
Source
Receiver AReceiver B
Dispersion Curve
Measured
Range Used for Average Modulus
Interpolated
Measured
Seismic Portable DeviceSeismic Portable Device
((““SpotSpot”” tests) : Stiffness (tests) : Stiffness (LDW)
Dynamic plate loading tests – increase:simpler and faster than static PLT
Different equipments: size, measurement principle, parameters determined, …
Different tests results (Flemming & Rogers, 1995, Gomes Correia et al, 2004)
Soil stiffness gauge (Edil & Sawangsuriya,2005)
CONTINOUS COMPACTION CONTROLCONTINOUS COMPACTION CONTROL((BrandlBrandl, 2001; Adam, 2004), 2001; Adam, 2004)
CCC-systemsCompactometerCMV is based on the evaluation of the acceleration in the frequency domain
TerrameterOMEGA is based on the evaluation of the energy transmitted to the soil in thetime domain
CONTINOUS COMPACTION CONTROLCONTINOUS COMPACTION CONTROL(LPC; (LPC; QuibelQuibel, 1998), 1998)
Wheel 1 m, 200 mm wide equipped with a vibratory loading system and instrumented with accelerometers.
Continuous determination of stiffness (3 km/h)
MODULI FROM FIELDMODULI FROM FIELD
MODULI FROM MODULI FROM FIELD TESTSFIELD TESTS
(Jamiolkowski et al., 1988, 2003)(Jamiolkowski et al., 1988, 2003)
G0, E0 (ε < εl) Gsec, Esec (εsec > εl)
DEPENDANT ON:DEPENDANT ON:Relative densityRelative densityAmbient stressAmbient stressCompressibilityCompressibilityAging & FabricAging & Fabric
INDEPENDANT FROM:INDEPENDANT FROM:Strain levelStrain levelStress historyStress history
DEPENDANT ON:DEPENDANT ON:Strain levelStrain levelStress historyStress historyRelative densityRelative densityAmbient stressAmbient stressCompressibilityCompressibilityAging & FabricAging & FabricStrain rateStrain rate
CORRELATIONS WITH G0, E0 are more reliable than with Gsec, Esec
nna peFpSG ′⋅⋅⋅= − )(1
0
SERVICEABILITY STIFFNESSSERVICEABILITY STIFFNESS
Factoring G0 or E0
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛⋅+
=
7,0
0 1
1
γγa
GGs
G/G00
0
0 .2
0 .4
0 .6
0 .8
1
1 .2
0 .0 0 1 0 .0 1 0 .1 1 1 0 1 0 0
R C te s t re sults Hyp e rb o lic c urve
γ/γ0.7
y = 0.0011x0.4973
R2 = 0.6067
y = 0.0006x0.4498
R2 = 0.70570.001
0.01
0.1
10 100 1000
Lateritic soils
Saprolitic soils
p’o
γ0.7 (%)
where γ is shear strain;γ0,7 is the shear strain for a stiffness degradation factor of G/G0=0.7 anda is a constant (a ≈ 0,385, for the database used)
Gomes Correia et al., 2001
Fahey & Carter, 1993; Mayne, 2001
g
ultqqf
EE
⎟⎟⎠
⎞⎜⎜⎝
⎛−= 1
0
PMT PMT –– PLT PLT -- TXTXSimulationSimulationROUTINE & ADVANCED ANALYSIS (ROUTINE & ADVANCED ANALYSIS (HSM HSM –– PLAXIS)PLAXIS)
(Gomes Correia et al., 2004)(Gomes Correia et al., 2004)
0
10000
20000
30000
40000
50000
60000
70000
80000
Mod
ulus
(kPa
)
1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00log(εv ; δ/D)
E Menard (PMT1) E Menard (PMT2)E ur (PMT1)E ur (PMT2)E ur (PLT)E PLT (settlement/D) - ECP 1 E PLT (settlement/D) - ECP 2E PLT (settlement/D) - simulationE sec (PLT) - simulationEsec P/D=0,1Etan P/D=0,1Esec P/D=0,5Etan P/D=0,5Esec P/D=1Etan P/D=1Esec P/D=2Etan P/D=2Esec "Classical" triaxialEtan "Classical" triaxial
Eur (PLT) =3 X Eur (PMT)
CONCLUSIONCONCLUSION
INTEGRATION SYSTEMINTEGRATION SYSTEM
DesignMaterialsCharacterization
Construction
PerformanceMonitoring
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