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 (agc@civil.uminho.pt)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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