NUMERICAL MODELING OF A CFRD - ANCOLD · 2015-11-02 · ICOLD Committee on Seismic Aspects of Dam Design . NUMERICAL MODELING OF A CFRD. CAMILO MARULANDA Ph.D. NUMERICAL ANALYSIS

NUMERICAL ANALYSIS OF CFRD

ICOLD Committee on Seismic Aspects of Dam Design

NUMERICAL MODELING OF A CFRD

CAMILO MARULANDA Ph.D


• Dumped Rockfill o Compacted Rockfill

1 Strawberry Creek 2 Salt Springs3 Paradela 4 Quioch5 New Exchequer 6 Cethana7 Anchicaya 8 Areia9 Khao Laem 10 Segredo11 Aguamilpa 12 Yacambu13 Tianshenqiao 14 Campos Novos15 Barra Grande 16 Cajon17 Mohale

A 68 CFRDs completed between 1990 and 2006, height 40 to 120 m

(Cooke, 1997, extended to 2006)

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1900 1925 1930 1940 1950 1960 1970 1980 1990 2000 2010

Hei

ght [

m]

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1415

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Early Period Transition Period Modern Period

TREND IN HEIGHT OF CFRD DAMS WITH TIME


Towards the final years of the last century there was a clear tendency to consider that the concrete face dams could be viable for heights of more than 200 m, basically without mayor changes in the configuration and design procedures commonly used. In some cases it was considered the ideal dam, and therefore, to some people there was no limit to its height.


Sherard & Cooke 1985 CFRD ASCE Symposium:“The CFRD is an appropriate type in the future for the very highest dams. For a 300m high CFRD constructed of most rock types, acceptable performance can be predicted, based on reasonable extrapolation of measurements on existing dams”

Sherard & Cooke 1985 CFRD ASCE Symposium:“For CFRD with compacted rockfill and a compacted upstream faace, the thickness increment was decreased to 0.003H, and even to 0.002H or less. These slabs have given satisfactory performance, an thre is a current general trend toward thinner slabs.”


Sherard , 1985 CFRD ASCE Symposium:“….The writer believes that it is likely that the not distance future evolution of the CFRD could arrive at a constant slab thickness of the order of 8 to 10 inches, even for high dams, with simpler and more economical joint seals.””

Cooke 2000 Beijing Symposium:“There has since been no experience to change that conclusion. There have been leakage incidents, and for the CFRD “acceptable performance” can include a leakage incident.”“Experience with existing dams has not identified areas in design which require significant change in design practice for the next generation of higher dams, 190-230m”


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NUMERICAL MODELING OF A CFRD DAM

Objective of the analyses:- Estimation of stress – strain and deformation behavior of the concrete face- Deformation of the rockfill- Displacements of the joints- Maximum deformations at the crest of the dam- Dynamic behavior of the dam


REQUIREMENTS FOR AN ANALYSIS

KEY ISSUE


DEVELOPMENTS OF STRESSES ON A SLAB



• Development of a three dimensional model• Construction Sequence• Modeling of structural elements• Constitutive models for geomaterials• Incorporation of interface elements between

different elements (rockfill – concrete face)


1. Geometry of the model

* Thickness of lift in the construction sequence = 5 m

CONSTRUCTION SEQUENCE


W1 W1

δw1 δw1

Adequate way of modeling a construction sequence of a dam

Erroneous way of modeling a construction sequence of a dam

Activation of elements in stage 1Activation of self-weight for the elements of stage 1

W1 W1

δw1δw1

δw1

Activation of elements in stage 2

W1

W2

W1

W2

δw1+∆δw2δw1+∆δw2

δw1+δw2δw2

Activation of self-weight for the elements of stage 2

MODELING OF CONSTRUCTION SEQUENCE



Concrete face – Plinth interface

Concrete slabinterfaces

Rockfill - Foundationinterface

Curb - Rockfillinterface

Curb – Concrete face interface

MODEL COMPONENTS



INTERFACES


Finite element mesh including the different elements1. Geometry of the model

Concrete Face Hexahedral mesh

Rockfill and Curb Tetrahedral meshPlinth

Hexahedral mesh


Overall views1. Geometry of the model

CONCRETE FACE AND CURB MATERIALS MODELS

-Elastic Model-Mohr-Coulomb Model-Elasto-Plastic Model- Damage Plasticity Models…


1.5. Mesh of model components


Tetrahedrical elements

Hexahedrical elements

Concrete curb

Concrete face

Rockfill

Tetrahedrical elements

RCC Cofferdam Tetrahedrical elements

Concrete Plinth

Hexahedrical elements


1.4. Distribution of concrete face joints


Horizontal joints

Tension jointsCompressible joint


StructureSoilStructure Soil

StructureSoil

Structure Soil

a) Soil-structure interface using continuum elements

b) Use of continuum elements to model interface

c) Use of Springs to model interface

d) Use of special interface elements

INTERFACES ELEMENTS


J.Gómez - 2000

SHEAR TESTS - INTERFACES


0.0 0.4 0.8 1.2 1.6 2.00.2 0.6 1.0 1.4 1.8Interface displacement, . s (mm)

0

40

80

120

160

200

20

60

100

140

180In

terfa

ce s

hear

stre

ss, τ

(kP

a)

Shear tests on dense Density Sand-to-concrete interfaceInterface Peak Friction Angle = 31°

φ=21.8°φ=24.22°

φ=26.56°φ=28.81° φ=31°

φ=21.80° µ=0.40 φ=24.22° µ=0.45φ=26.55° µ=0.50 φ=28.81° µ=0.55 φ=31.00° µ=0.60 σn=274 kPa

σn=102 kPa

σn=33 kPaφ=21.8°

φ=24.22°φ=26.56°

φ=28.81° φ=31°

φ=21.8°

φ=24.22°

φ=26.56°

φ=28.81°

φ=31°

- Shear TestO Numerical Model

SHEAR TESTS - INTERFACES


ROCKFILL – CONSTITUTIVE MODEL

• Constitutive model that captures nonlinear behavior, inelastic, depedent on stress levels.

• Anisotropic behavior

• Volumetric behavior

• Time dependent behavior “creep” - & particle crushing


2.1. Rockfill Behavior – static analysis

2.1.1. Hyperbolic Model (Duncan, 1980)

2. Constitutive models

a. Strength envelope in p-q system

where:

b. Stress-strain curve adjusted to a hyperbolic curve

where: q* = current shearqult= ultimate shear strength and asyntotic to the σ-ε curveEi = Initial tangent modulus

c. Failure ratio

where: qf = shear at failure

( ) 3321 σσσ ++=p ( ) ( ) ( ) ( )222222 6.2

1zxyzxyxzzyyxq τττσσσσσσ +++−+−+−=

ε

φ

φφsen

csenpq f −+

=3

cos..6..6

ulti qEqεε

+=1

*

ult

ff q

qR =


2.1.1. Hyperbolic Model (Duncan, 1980)


d. Strength envelope in terms of qult

e. Tangent modulus for a given stress q*

f. Tangent and Bulk Modulus for mean normal stress p

where: Pa = reference pressure

( )φ

φφsenR

csenpqf

ult −+

=3

cos..6..6

( )( ) i

ft E

csenpqsenR

E2*

cos..6.3

1

+

−−=

φφφ

n

aai P

PPkE

= ..

m

aabk P

PPkB

= ..

k: Modulus numbern: Modulus exponentkb: Bulk Modulus numberm: Bulk Modulus exponentc: Cohesionφ: friction angle

2.1.2. Parameters involved




2.1.3. Estimation of parameters

2.1.4 Parameters obtained from laboratory tests




K n Rf Kb mPinzandaran sub-redondeada 690 0.45 0.59 170 0.22Grava arenosa (Espaldón presa Mica) Sub-angular 420 0.5 0.78 125 0.46Grava areno limosa (Presa Oroville) redondeada 1300 0.4 0.72 900 0.22Grava anfibolítica (Espaldón presa Oroville) redondeada 1780 0.39 0.67 1300 0.16Grava arenosa (Presa Rowallan) redondeada 2500 0.21 0.75 1400 0Gneiss granítico (Presa Mica) Sub-angular 210 0.51 0.64 100 0.34Diorita (Presa El Infiernillo) angular 340 0.28 0.71 0.52 0.18Basalto angular 450 0.37 0.61 253 0.18Roca basáltica triturada (Presa Round Butte) angular 410 0.21 0.71 195 0Basalto olivino triturado subredondeado 1000 0.22 0.75 390 0.14

Gravas

Enrocado

ParámetrosTipo Material Tipo de partícula

* Strength, stress-strain and Bulk modulus parameters for finite element analyses of stresses and movements of soil masses. J.M.Duncan, P. Byrne, K. Wong & P. Mabry. University of California. Berkeley. 1980

2.1.5. Parameters reported in the literature

2.1.6. Expected modulus at the and of construction and the corresponding parameters

Zona 3A = 187 MPaZona 3B =163 MPaZona 3C = 144 MPa

ArchivoZona 3A 3B 3Cϕ0 [°] 55 45 50

Delta ϕ [°] 8 10 8Rf [-] 0.7 0.6 0.7K [-] 1315 828 1169n [-] 0.4 0.5 0.4

Kb [-] 1120 925 925m [-] 0.2 0.3 0.2

Sgmso-HB-VF-C5-UDA-ICE-SD




2.1.7. Strength parameters (Friction angle for different confinig pressures)

2.1.8. Anisotropic behavior of rockfill

Material Zona 3A Zona 3B Zona 3Cφ [°] (0.1 MPa) 55 45 50φ [°] (5.0 MPa) 41 28 36




2.1.8. Anysotropic behavior of rockfill



Zona 3A = 1.5Zona 3B =2.0Zona 3C = 1.5


2.1.8. Anysotropic behavior of rockfill

Et/Ev:




2.1.9. Stiffness matrix for a transverse anisotropic medium

{ } [ ]{ }εσ .anisK=

where: ( ) ∆−== hvh Ekk .1 2

2211 ν

( ) ∆−= vhh Ek .1 233 ν

( ) ∆−== hvhhh Ekk .22112 νν

( ) ∆+==== vvhhhvh Ekkkk .32233113 ννν

222 221 vhhhvhhh νννν −−−=∆

( )hhhhh EGk ν+== 1244

( )vhvhhv EEGkk ν+=== 126655

vhvhhh EEνν = 1 (h)

2 (h)

3 (v)

=

23

13

12

3

2

1

66

55

44

333231

232221

131211

12

13

23

3

2

1

000000000000000000000000

γγγεεε

τττσσσ

kk

kkkkkkkkkk




2.1.10. Additional considerations

Expected critical deflection of the concrete face measured perpendicular to the upstream slope



XX

X X X X

X

XX X X X

X

X

XX

XX

0.04 0.08 0.120

0

2

4

6

8

10

εaxial

σ 1-σ

3[MPa

]

σ3=0.5 MPa

σ3=1.0 MPa

σ3=2.5 MPa

Triaxial Test – San Francisco Basalt - Marsal 1973

X Numerical Model

Experimental Data



0.04 0.08 0.120

-0.02

-0.04

-0.06

0εaxial

ε vol

umet

ric

X

X

X

X

X

XX

X

X XX

X

X

X

X

X

XXσ3=2.5 MPa

σ3=1.0 MPa

σ3=0.5 MPa


X Numerical Model

Experimental Data



0 0.02 0.04 0.06

-0.12

-0.08

-0.04

0

ε axi

al

εradial

σ3=2.5 MPaσ3=1.0 MPa σ3=0.5 MPa

X

X

X

X

X

X

X

X

X

X

X

XX

X

X

X

X


X Numerical Model

Experimental Data



0.06

0.04

0.02

0

2 4 6 8 100

σaxial [MPa]

ε axi

al

X

X

X

X

X

X

XOdometer test– San Francisco Basalt - Marsal 1973

X Numerical Model

Experimental Data




• Development of a three dimensional model• Construction Sequence• Modeling of structural elements• Constitutive models for geomaterials• Incorporation of interface elements between

different elements (rockfill – concrete face)


• El Cajon Dam • Cethana Dam• Antamina Dam• Campos Novos• Barra Grande Dam• Karahnjúkar Dam• Mohale Dam• Porce III

VALIDATION OF ANALYSIS PROCEDURE

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PORCE III DAM


CONCRETE FACE

Extension Joints

Compressible JointsPerimeterJoint

Horizontal Construction Joint

Plinth

Extension Joints

PerimeterJoint


RMVsSettlements during construction and impoundment

2. Instrumentation along the maximum section of the dam


RMVsSettlements during construction and impounding of the reservoir



RMVsSettlements during construction and impounding of the reservoir



3.1. Analysis under static conditions

Comparison between geotechnical instrumentation and results from the numerical model.

Settlements Cells

CeldaNivel

(msnm)Final de

construcción (cm)Incremento durante

llenado (cm)Total al final de

llenado (cm)CA-1 571 -38.1 -22.4 -60.5CA-2 571 -64.8 -15.9 -80.7CA-3 571 -90.1 -2.7 -92.8CA-4 571 -96.6 -10.7 -107.2CA-5 571 -122.2 -2.9 -125.1CA-6 571 -147.2 -0.8 -147.9CA-7 617 -85.4 -19.5 -104.9CA-8 617 -121.0 -14.3 -135.3CA-9 617 -160.8 -12.5 -173.3

CA-10 617 -199.3 -1.0 -200.3CA-11 617 -117.3 -0.5 -117.8CA-12 652 -64.5 -21.4 -86.0CA-13 652 -119.9 -16.1 -136.0CA-14 652 -120.0 11.1 -108.9CA-33 634 -12.3 -23.7 -36.0CA-34 675 -24.0 -11.0 -34.9

Registro de asentamientos - Instrumentación Geotécnica (Sección Máxima - Abscisa 210)

CeldaNivel

(msnm)Final de

construcción (cm)Incremento durante

llenado (cm)Total al final de

llenado (cm)CA-1 571 -36.0 -25.5 -61.5CA-2 571 -65.0 -18.0 -83.0CA-3 571 -82.0 -9.0 -91.0CA-4 571 -99.0 -13.5 -112.5CA-5 571 -116.0 -5.0 -121.0CA-6 571 -145.5 3.5 -142.0CA-7 617 -74.0 -30.0 -104.0CA-8 617 -120.0 -9.5 -129.5CA-9 617 -158.0 -5.5 -163.5

CA-10 617 -200.0 2.5 -197.5CA-11 617 -116.0 -1.0 -117.0CA-12 652 -65.0 -30.5 -95.5CA-13 652 -124.0 -5.5 -129.5CA-14 652 -120.0 -1.0 -121.0CA-33 634 -57.0 -47.0 -104.0CA-34 675 -48.0 -22.0 -70.0

Registro de asentamientos - Modelación Numérica (Sección Máxima - Abscisa 210)

3. Results from the calibrated model



Comparison between geotechnical instrumentation and the results from the numerical model


At the end of construction



Comparison between geotechnical instrumentation and results from the numerical model

Construction and impoundment



RMV-1. At the end of construction

RMV-1. Construction and impoundment



RMV-2. At the end of construction.




RMV-3. At the end of construction





b. Horizontal displacements of therockfill due to construction and impoundment.

a. Horizontal displacements of the rockfill at theend of construction



3D behavior - Vertical displacements3. Results from the calibrated model


Displacement normal to the face in m


0.56 m


Stresses along the slope [kPa]


Stresses in the horizontal direction (S11) [kPa]

7.0 MPa

12.4 MPa



HOT ISSUES – SEISMIC RESPONSE


2.2. Dynamic analysis

2.2.1. Characteristics of the non linear cyclic model


Masing Rules :

1. For initial loadings, the stress-strain relationship follows the initial curve

2. If a stress reversal occurs in the stress –strain curve, the relationship follows :

(τ- τ r)/2 = Fesq (γ- γr)/2

3. If the loading path of loading orunloading exceeds the previousmaximum or intersects the initial back-bone curve, the stress-strainrelationship will follow the originalcurve until the next stress reversal

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0 0.5 1 1.5 2 2.5 3 3.5 4

t [seg]

γ [-]

DYNAMIC ANALYSIS



2.2.1. Characteristics of the non linear cyclic model

a. Variation of secant shear modulus based on the level of deformation


( )[ ]( )[ ]

( )[ ]{ } 10lnlogexp1logexp1

logexp1 2 ⋅−−+⋅−−+⋅

+−−+

=bcb

bcabc

aG

Ge

e

emáx

t

γγ

γ

b. Variation of tangent shear modulus under monotonic loading

c. Variation of secant shear modulus based on the level of deformation for unloading and loading

( )[ ]{ }( )[ ]{ }

( )[ ]{ }{ }22logexp110ln

2logexp2logexp1 bcb

bcabc

aG

G

refe

refe

refemáx

t

−−−+⋅⋅

−−−⋅+

−−−+=

γγ

γγ

γγ

( )[ ]bca

GG

emáx

s

−−+=

γlogexp1


b. Degradation curves for the shear modulus and damping


2.2.2. Maximum Shear Modulus and degradation curves for shear modulus and dampinga. Maximum Shear Modulus (Gmax)

where: K2 for gravels and rockfill ranges between 15 and 60


( ) 5.00.2max 87.218][ PKkPaG ⋅⋅=



2.2.3. Model verification


Average normal stress vs maximum shear modulus (G max) Average normal stress vs shear wave velocity


1 MPa


2.2.3. Model verification


Shear wave velocity and G max for Po between 20 and 2300 Kpa

K2=55



2.2.4. Response spectrum

a. Spectral horizontal acceleration for designearthquake (Safety Evaluation Earhquake (SEE))

b. Preselected seismic signals (Pacific EarthquakeEngineering Research Center)



Selected signal: Earthquake with PGA of 0.26 g recorded at 32 Km from thesource


2.2.4. Response spectrum




2.2.5. Stresses in the concrete face for cyclic loading (Elastoplastic model)


Plasticity parameters:ψ: Dilatancy angle for high confiningpressurese: Eccentricity of the plastic potentialsurface.fb: Compressive strength under planestress conditionfc: Yielding stress in uniaxialcompression.K: Shape parameter of the yieldingsurface

ψ[°] 30e 0.6

fb/fc 1.1K 0.67


Water Pressure = Hydrostatic Pressure + Westergaard Pressure


2.2.6. Aditional considerations

a. Hydrodynamic Effect (Virtual Mass Method)


Manual de obras civiles. Diseño por sismo. Comisión Federal de electricidad

Pressure Coefficient - faces formed by two planes

Virtual mass by unit area.

where:ρ=density of water(1000kg/m³)Hv=Water heightCp=Pressure coefficient



2.3. Interface behaviorContinuous elements Special elements

Normal rigid behavior Tangential behavior – Friction modelNormal behavior with constant stiffness


SOGAMOSO DAM


160 MPa

180 MPa

140 MPa

Deformation moduli at the end of construction at maximum section (abscissa 170) [kPa]

Zona 3A = 180 MPa, Zona 3B =160 MPa, Zona 3C = 140 MPa

3. Results

3.1. Analysis under static conditions with water level at NAME (El. 320 masl)

3.1.1. Sensitivity analysis on rockfill moduli


Stresses in horizontal direction [kPa]:

3. Results




Stresses in horizontal direction [kPa]:

3. Results





Displacements in perpendicular direction to the concrete face [m]:

3. Results






Displacements in vertical direction [m]:

3. Results




Vertical displacements at the end of construction [m] – Compared to damInstrumentation (vertical movements)

3. Results





3. Results

Vertical displacements at the end of construction [m] – Compared to daminstrumentation (vertical movements)





3.1.7. Joints behavior

Perimetral joint displacement

3. Results



Tension joints displacement


3. Results

Distancia a lo largo del eje de la presa [m]


24

115

145

204

174

Altu

ra m

edid

a en

dire

cció

n de

la c

ara

[m]

53

84


1 2 3 4 5

1 2 3 4 5


Tension joints displacement


3. Results


24

115

145

204

174

Altu

ra m

edid

a en

dire

cció

n de

la c

ara

[m]

53

84



1 2 3 4 5

1 2 3 4 5

6

6


3. Results

3.2. Analysis under dynamic conditions

3.2.1. Earthquake loading normal to dam axis (100%) and vertical (50%)

Horizontal displacements:


3.2.1. Earthquake loading normal to dam axis (100%) and vertical (50%)

Accelerations

3. Results


Amplification: 2.5


3.2.2. Displacements normal to the concrete face [m]

t=2.5seg

Min: -0.37

t=0.0seg

t=5.0segt=7.5seg

3. Results


Min: -0.46

Min: -0.46

Min: -0.51


t=12.5segt=10.0seg

t=15.0seg

3.2.2. Displacements normal to the concrete face [m]

3. Results


Min: -0.49

Min: -0.49

Min: -0.49


t=2.5seg t=5.0seg t=7.5seg

t=10.0seg t=12.5seg t=15.0seg

t=0.0seg

3.2.3. Deformations of the dam [m]

3. Results



t=2.5segt=0.0seg

t=5.0seg t=7.5seg

3.2.4. Stresses on the concrete face in direction of the dam axis (S11 rotated) [kPa]

3. Results



t=12.5segt=10.0seg

t=15.0seg

3. Results

3.2. Analysis under dynamic conditions3.2.4. Stresses on the concrete face in direction of the dam axis (S11 rotated) [kPa]


t=2.5segt=0.0seg

t=5.0seg t=7.5seg

3.2.5. Stresses on the concrete face in direction of the slope (S22 rotated) [kPa]

3. Results



t=12.5segt=10.0seg

t=15.0seg

3. Results

3.2. Analysis under dynamic conditions3.2.5. Stresses on the concrete face in direction of the slope (S22 rotated) [kPa]


KEY ISSUES

• Effect on the foundation and the valley geometry on the propagation of the waves (e.g boundary conditions)

• Sophisticated Concrete models to predict damage of the face at different levels of accelerations

• Effect of alternatives ways to model reservoir loading

• Validation of predictions – available data

Documents

NUMERICAL MODELING OF A CFRD - ANCOLD · 2015-11-02 · ICOLD Committee on Seismic Aspects of Dam Design . NUMERICAL MODELING OF A CFRD. CAMILO MARULANDA Ph.D. NUMERICAL ANALYSIS