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NUMERICS IN GEOTECHNICS AND STRUCTURES, ZSoil Day, 30 August 2010, Lausanne

Seismic safety of a buttress dam and appurtenant structures

- 3D static and dynamic analyses -

Dr Aïssa Mellal, Civil Engineer

STUCKY SA, Switzerland

A. MellalNumerics in Geotechnics and Structures - ZSoil Day, 30-31 August 2010, Lausanne, SwitzerlandSeismic safety of a buttress dam - 3D static and dynamic analyses

Outline

1. Introduction: General context – Description

2. Numerical model2.1 Model assumptions2.2 Geometry and FE mesh2.3 Geomechanical parameters

3. Model calibration and validation3.1 Methodology3.2 Temperatures3.3 Water level3.4 Comparison model vs. measurements

4. Eigen modes and frequencies

5. Seismic safety assessment5.1 Initial static conditions5.2 Seismic load5.3 Dynamic stress analyses5.4 Verification of concrete strength (stresses)5.5 Verification of global stability (sliding, overturning)5.6 Verification of hydromechanical equipments (gates)

6. Conclusions and comments

A. MellalNumerics in Geotechnics and Structures - ZSoil Day, 30-31 August 2010, Lausanne, SwitzerlandSeismic safety of a buttress dam - 3D static and dynamic analyses 1. Introduction

Rossinière Dam


Rossinière

Swiss Seismic Hazard Map (10’000 years return period)


1.1 Main characteristics of the dam

• Type: gravity-buttress dam

• Construction period: 1969-1972

• Height: 30 m

• Crest elevation: 862.50 m

• Volume of reservoir: 2.9 millions m3

• Volume of concrete: 10’000 m3

• Crest length: 35 m

• Flap gates (2): 2.5 m x 5.0 m

• Outlet gates (2): 2.5 m x 5.0 m


1.2 Context of the study

• The seismic safety assessment of Rossinière Dam is carried out following the requirements andrecommendations of the Swiss Federal Office of Energy

• Dam category: classe I (H = 30 m, V = 2.9 millions m3)

1. Introduction

Classement des barrages suisses selon l’OSOA

0

10

20

30

40

50

60

0 250'000 500'000 750'000 1'000'000 1'250'000Capacité de la retenue (m3)

Hau

teur

de

la re

tenu

e (m

)

Classe I

Classe II

Classe IIIBassins de rétention

Rossinière Dam


2.1 Model assumptions

• Linear isotropic elastic materials (concrete and rock)

• Monolithe structure: joints not modeled explicitly

• Perfect bonding at rock-concrete interface

• One-phase calculations: no fluid flow, uplift pressure not considered for stress analysis

2. Numerical model


2.2 Model geometry and FE mesh

• Geometry of the dam (3D), appurtenanant structures and foundation, reconstructed on the basis of existing drawings and topographic maps.

• Finite element analyses performed using Z_Soil 3D v2009 (dynamic) and v2010_beta (eigen modes)

• Finite element model: 80’279 nodes

• Dam and adjoining structures: 37’259 volumetric 8-node elements (hexaedrons)• Foundation : 28’074 volumetric 8-node elements (hexaedrons)• Gates: 3’658 shell elements, 354 beams and 4 truss elements (jacks)

2. Numerical model

A. MellalNumerics in Geotechnics and Structures - ZSoil Day, 30-31 August 2010, Lausanne, SwitzerlandSeismic safety of a buttress dam - 3D static and dynamic analyses 2. Numerical model


Geometry FE mesh

X

Y

Z X

Y

Z

86 m

Downstream 3D view


X

YZ

X

YZ

Geometry FE mesh

Upstream 3D view


X

Y

Z X

Y

Z

Geometry FE mesh


Geometry

FE mesh

Right wing Left wing Central buttress Lateral buttress


Geometry FE mesh


Flap gate

Outlet gate

Flap gate

Outlet gate

Geometry FE mesh


2.3 Numerical model: geomechanical parameters

• Mechanical properties:Rocher Béton Béton armé et

de masse parties massivesStat/Dyn Stat/Dyn Stat/Dyn

Specific weight, γ [kN/m3] : 24/0 25 25Elastic modulus, E [GPa] : 15/18.75 20/25 30/37.5Poisson coefficient, ν [-] : 0.25 0.2 0.2Compressive strength, fc : - 27/40 40/60Tensile strength, ft : - 2.9/4.3 3.8/5.6

• Thermal properties:

Thermal expansion coefficient, α [1/°C] : 6.66 x 10-6

Thermal conductivity, K [kJ/m/h°C] : 8Heat capacity, C* [kJ/m3/°C] : 2’200Diffusivity, µ [m2/h] : 36.36 x 10-4

2. Numerical model


3.1 Methodology

• Calibration on displacements measurements for a static load (hydrostatic pressure +temperature) case over 1997-2008 period.

• Analysis procedure:

1. Initial state: dam’s self-weight

2. Application of measured ambient temperatures during the considered period => determination of temperature fields within the dam

3. Evaluation of displacements induced by temperatures evolution and water levelvariations during the considered period.

4. Comparison of calculated displacements with measurements over the considered period

3. Model calibration and validation


3.1 Methodology: location of instruments



3.2 Thermal load

• Thermal boundary conditions• T(dry) = T(air) + ∆T(solar radiation)• T(wet) = T(water) + ∆T(surface)


Solar radiation: winter: +3°, summer: +3°C∆Twater (surface, 0-3m) : winter: 0°, summer: +2°C

-20

-15

-10

-5

0

5

10

15

20

25

30

Tem

péra

ture

[°C]

Barrage de Rossinière - Température de l'air

Mesures journalières Mesures mensuelles

0

2

4

6

8

10

12

14

16

18

Tem

péra

ture

[°C]

Température de l'eau

Teau en profondeur (> 3m) Teau en surface (< 3m)

Assumption on water temperature: Sinusoidal variation between 5°C and17°C at depth 0-3m and between 5° and 15° at depth >3m(consistent assumption with measurements of the closest-to-water thermometer (T2)).

A. MellalNumerics in Geotechnics and Structures - ZSoil Day, 30-31 August 2010, Lausanne, SwitzerlandSeismic safety of a buttress dam - 3D static and dynamic analyses 3. Model calibration and validation

3.2 Calculated temperature fields in the dam

04.01.2001 01.02.2001

08.08.2001

05.09.2001 09.10.2001 08.11.2001 05.12.2001

26.02.2001 04.04.2001

04.05.2001 01.06.2001 05.07.2001

A. MellalNumerics in Geotechnics and Structures - ZSoil Day, 30-31 August 2010, Lausanne, SwitzerlandSeismic safety of a buttress dam - 3D static and dynamic analyses 3. Model calibration and validation

3.2 Comparaison calculated vs. measured temperatures (thermometers)

-10-505

1015202530

Tem

péra

ture

[°C]

Mesure T1 Calcul

-10-505

1015202530

Tem

péra

ture

[°C]

Mesure T2 Calcul

-10-505

1015202530

Tem

péra

ture

[°C]

Mesure T3 Calcul

-10-505

1015202530

Tem

péra

ture

[°C]

Mesure T4 Calcul


3.3 Hydrostatic load

• Applied loads on upstream face of the dam correspond to water level variation


854

855

856

857

858

859

860

861

862N

ivea

u du

lac [

m]

Barrage de Rossinière - Niveau du lac


3.4 Comparison calculated vs. measured displacements


Upstream-Downstream Left-Right

Vertical

-3

-2

-1

0

1

2

3

Dépl

. [m

m] -

Aval

/ +

Am

ont

Mesure R Calcul

-3

-2

-1

0

1

2

3

Dépl

. [m

m] -

Haut

/ +

Bas

Mesure Invar Calcul

-3

-2

-1

0

1

2

3

Dépl

. [m

m] -

Droi

te /

+ G

auch

e

Mesure T Calcul

A. MellalNumerics in Geotechnics and Structures - ZSoil Day, 30-31 August 2010, Lausanne, SwitzerlandSeismic safety of a buttress dam - 3D static and dynamic analyses 4. Eigen modes and frequencies

Mode Frequency(Hz)

Mass contribution (%)

X Y Z

1 19.28 0.00 0.74 47.98

X

Y

Z

X

Y

Z

X

Y

Z

Dam – Full reservoir


Mode Frequency(Hz)


X Y Z

2 25.95 0.36 0.07 0.11

X

Y

Z

X

Y

Z

X

Y

Z



Mode Frequency(Hz)


X Y Z

3 28.84 5.42 27.08 12.69

X

Y

Z

X

Y

Z

X

Y

Z



Mode Frequency(Hz)


X Y Z

4 28.94 10.91 8.24 8.58

X

Y

Z

X

Y

Z

X

Y

Z



Mode Frequency(Hz)


X Y Z

5 29.73 0.02 22.19 16.77

X

Y

Z

X

Y

Z

X

Y

Z



Mode Frequency(Hz)


X Y Z

6 31.34 14.44 0.12 0.03

X

Y

Z

X

Y

Z

X

Y

Z



Mode 1 : f = 12.99 Hz Mode 2 : f = 13.33 Hz Mode 3 : f = 13.94 Hz


Flap gate – Full reservoir




Outlet gate – Full reservoir


5.1 Initial static conditions

• Self-weight

• Hydrostatic pressure: full reservoir (860 msm upstream, 842.30 msm downstream)

• Silt load: 850 msm (constant), buoyant density 0.36 t/m3

•Temperature load:• Reference : annual average (daily measurements 1997-2008)• Summer: thermal gradient T(summer)-T(reference)• Winter: thermal gradient T(winter)- T(reference)

Température [°C] Gradient [°C]

moyenne Eté (21.06 - 20.09)

Hiver (21.12 - 20.03)

Max (été)

Min (hiver)

Rocher 8 8 8 0 0 Eau (< 3 m) 10 15 5 +5 -5 Eau (> 3 m) 11 17 5 +6 -6 Air 8.1 16.5 -0.3 +8.4 -8.4 Surface barrage (air + ensoleillement)

11.1 19.5 2.7 +8.4 -8.4

5. Seismic safety assessment


842.30 msm

842.30 msm

860 msm

850 msm

Normal water level

Silt

Tailwater

Downstream view Upstream view

850 msm

860 msm




5.1 Initial static conditions : reference temperature field

Longitudinal section

Downstream 3D view

Upstream 3D view




Downstream 3D view

Upstream 3D view

5.1 Initial static conditions : summer temperature field




Downstream 3D view

Upstream 3D view

5.1 Initial static conditions : winter temperature field



Selected zones for the assessment of static and dynamic stresses




• Extreme static stresses

• Extreme static displacements

s1 max (tractio s3 min (comp s1 max (tractio s3 min (comp s1 max (tractio s3 min (comp s1 max (tractio s3 min (compr Aile rive droite 0.3 -0.4 0.2 -0.5 0.5 -2.5 2.6 -1.4Aile rive gauche 0.3 -0.4 0.3 -0.6 0.5 -2.0 2.3 -1.2Contrefort1 rive gauche 0.2 -0.5 0.3 -0.7 0.8 -2.3 1.4 -0.7Contrefort2 central 0.1 -0.5 0.1 -0.7 0.8 -2.2 1.8 -1.1Contrefort3 rive droite 0.2 -0.5 0.3 -0.8 0.8 -2.8 1.6 -0.7Corps central 0.1 -0.4 0.4 -1.0 0.2 -2.4 2.1 -1.0Passerelle amont 0.0 -0.8 0.0 -0.8 0.0 -3.0 1.6 0.0Passerelle aval 0.0 -0.8 0.0 -0.6 0.1 -3.2 2.6 -0.1Fondation niveau 838 0.0 -0.3 0.0 -0.4 0.0 -1.0 0.5 -0.3

Poids propre Printemps, lac plein Eté, Lac plein Hiver, Lac plein

Gauche-DroiteVertical Amont-Aval Absolu[mm] [mm] [mm] [mm]

Poids propre 0.00 0.00 0.00 0.00Poids propre + lac plein 0.00 0.06 0.34 0.35Eté lac plein -0.06 0.86 -0.86 1.22Hiver lac plein 0.06 -0.74 1.55 1.72



5.2 Seismic load: MSK intensity map (10’000 years return period)

log ah = 0.26 IMSK + 0.19 ah = 0.27 g

RossinièreIMSK = 8.6



5.2 Seismic load: accelerograms and correspondant spectra

ah = 0.27 g

av = 0.18 g

0.01 0.1 1 100

1

2

3

4

5

6

7

8

9

10

Période [s]

Accé

léra

tion

spec

trale

[m/s

2 ]

série 1 - composante horizontale amont-aval

0.01 0.1 1 100

1

2

3

4

5

6

7

8

9

10

Période [s]

Accé

léra

tion

spec

trale

[m/s

2 ]

série 1 - composante verticale

0.01 0.1 1 100

1

2

3

4

5

6

7

8

9

10

Période [s]Ac

célé

ratio

n sp

ectra

le [m

/s2 ]

série 1 - composante horizontale rive-rive

-3

-2

-1

0

1

2

3

0 5 10 15 20 25 30Ac

célé

ratio

n [m

/s2 ]

Temps [s]

série 1 - composante horizontale amont-aval

-3

-2

-1

0

1

2

3

0 5 10 15 20 25 30

Accé

léra

tion

[m/s

2 ]

Temps [s]

série 1 - composante verticale

-3

-2

-1

0

1

2

3

0 5 10 15 20 25 30

Accé

léra

tion

[m/s

2 ]

Temps [s]

série 1 - composante horizontale rive-rive



Upstream – DownstreamOscillating water : Westergaard

5.2 Seismic load

Left – RightOscillating water : total quantity between walls

VerticalOscillating water : water column height


• Hydrodynamic pressure: oscillating added masses

• Rayleigh damping (global): <5% between 10 Hz and 50 Hz

• HHT integration scheme (α = -0.3)


5.3 Dynamic stress analyses: ENVELOPE OF DYNAMIC PRINCIPAL STRESSES

Stress (MPa)

Time (s)

Compression (-) -3.78 13.00

Tension (+) 0.97 18.68

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

0 5 10 15 20 25 30

Cont

rain

te (k

Pa)

Temps (s)

Enveloppe des contraintes principales - Eté, Lac plein, Séisme 1

S3min S1max



Stress (MPa)

Time (s)

Compression (-) -1.74 20.84

Tension (+) 3.35 10.84

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

0 5 10 15 20 25 30

Cont

rain

te (k

Pa)

Temps (s)

Enveloppe des contraintes principales - Hiver, Lac plein, Séisme 1

S3min S1max


5.3 Dynamic stress analyses: ENVELOPE OF DYNAMIC PRINCIPAL STRESSES


(Winter, full reservoir, earthquake 1)


5.3 Dynamic stress analyses: Extreme dynamic displacements

A. MellalNumerics in Geotechnics and Structures - ZSoil Day, 30-31 August 2010, Lausanne, SwitzerlandSeismic safety of a buttress dam - 3D static and dynamic analyses 5. Seismic safety assessment

5.3 Dynamic stress analyses: Extreme dynamic stresses

(Winter, full reservoir, earthquake 1)


• Extreme dynamic stresses

• Extreme dynamic displacements and accelerations

Eté, Lac plein Hiver, Lac plein

Séisme 1 Séisme 1 Séisme 2 Séisme 3

σt max [MPa]

σc min [MPa]

σt max [MPa]

σc min [MPa]

σt max [MPa]

σc min [MPa]

σt max [MPa]

σc min [MPa]

Aile droite 0.8 -3.0 3.2 -1.7 3.3 -1.7 3.2 -1.7

Aile gauche 1.0 -2.3 2.5 -1.7 2.5 -1.8 2.5 -1.7

Contrefort 1 (gauche) 1.0 -3.1 1.7 -1.1 1.7 -1.1 1.7 -1.1

Contrefort 2 (central) 0.8 -3.1 2.4 -1.3 2.6 -1.4 2.5 -1.4

Contrefort 3 ( droite) 0.9 -3.7 2.3 -1.0 2.4 -1.0 2.3 -1.0

Corps central 0.8 -2.7 2.4 -1.7 2.4 -1.8 2.4 -1.8

Passerelle amont 0.0 -3.5 2.1 -0.8 2.4 -0.8 2.1 -0.8

Passerelle aval 0.3 -3.8 3.4 -0.8 3.3 -0.8 3.2 -0.8

Fondation niveau 838 0.0 -1.1 0.5 -0.3 0.5 -0.3 0.5 -0.3

Absolute displacement

Value (mm) Time (s)

Summer Earthquake 1 1.70 18.68

Winter

Earthquake 1 2.42 10.84



Absolue acceleration

Value (m/s2) Time (s)

Summer Earthquake 1 7.67 10.82

Winter





5.3 Dynamic stress analyses: summary


• Compressive stresses• estimated dynamic strength: 60 MPa• maximum stress: 3.8 MPa (footbridge downstrem, in summer)

=> Compressive strength criterion satisfied

• Tensile stresses:• estimated dynamic strength : 5.6 MPa• maximum stress : 3.4 MPa (footbridge downstrem, in winter)

=> Tensile strength criterion satisfied


5.4 Verification of concrete strength (stresses)


• Assumptions:

• Analysis of 3 buttresses with two half-openings• self-weight• Hydrostatic pressure (full reservoir)• Silt load (850 msm)• Uplift pressure (100% of total pressure, evolution according to average measurements)• No thermal load• Resisting lateral forces (3D) neglected• Earthquake: horizontal and vertical components• Evaluation of stresses at time of maximal US-DS crest displacement


5.5 Verification of global stability (sliding, overturning)


5.5 Dam stability

Mass concrete

Buttress

Basin

Rock

Potential sliding surface (838 msm)Potential pivot-point for overturning



t (uA-A= max) Normal and shear stresses on potential sliding surface

Efforts N, T and M

5.5 Dam stability



5.5 Dam stability

Sliding stability Overturning stability

• Foundation bearing capacity

=> Both local and global stability of the dam is satisfied

φ = 55° ; c = 0 kPa

FHSPNSG

φtan)( −=

)()(

SéismeSPPSPEMPPM

MMS

R

SR +++

==

Pied amont Pied avalS1 max [MPa]

S3 min [MPa]

S1 max [MPa]

S3 min [MPa]

Contrefort rive droite 0.0 -0.3 0.1 -0.3Contrefort rive gauche 0.0 -0.5 0.0 -0.3Contrefort central 0.0 -0.5 0.0 -0.3

Sous-pression [MPa] 0.22 0.05

SG [-]sans séisme avec séisme

Contrefort rive droite 1.97 1.47

Contrefort rive gauche 2.78 1.50

Contrefort central 3.96 2.19

Ensemble contreforts 2.99 1.77

SR [-]sans séisme avec séisme

Contrefort rive droite 1.20 1.03

Contrefort rive gauche 1.29 1.18

Contrefort central 1.47 1.28Ensemble contreforts 1.33 1.17



5.6 Verification of gates: stresses

vanne-clapet

Déplacement Amont-Aval max (mm) temps (s)

Contrainte de compression max (MPa)

Contrainte de traction max (MPa)

Eté Séisme 1 4.35 20.84 -35.2 56.4

Hiver Séisme 1 5.11 20.84 -35.3 58.7

Séisme 2 5.32 13.28 -36.1 64.4

Séisme 3 5.16 7.94 -37.1 59.8

vanne-secteur Déplacement

Amont-Aval max (mm) temps (s)


Contrainte de traction max (MPa)

4.81 15.52 -217.4 126.0

4.91 15.52 -209.2 126.7 5.04 23.22 -221.0 134.9 5.70 19.42 -220.5 133.1

S1 (traction) S3 (compression)S1 (traction) S3 (compression)

Flap gate Outlet gate

=> Strength criterion of metallic gates is satisfied



00.05

0.10.15

0.20.25

0.30.35

0 5 10 15 20 25 30

Dépl

acem

entr

elat

ifde

s con

tref

orts

[m]

-éca

rtem

ent/

+ ra

ppro

chem

ent

x 0.0

01

Temps (s)

Vanne clapet

Dépl. relatif haut Dépl. relatif bas

-0.010

0.010.020.030.040.050.06

0 5 10 15 20 25 30

Dépl

acem

entr

elat

ifde

s con

tref

orts

[m]

-éca

rtem

ent/

+ ra

ppro

chem

ent

x 0.0

01

Temps (s)

Vanne secteur


Déplacement relatif latéral des contreforts

0.31 mm @ 11.00 s

0.12 mm @ 11.00 s

0.05 mm @ 18.62 s

0.01 mm @ 17.88 s

Vanne clapet

Vanne secteur

5.6 Verification of gates: blocking hazard

Summer

Flap gate Outlet gapOpening width 4.90 5.00Gate width 4.82 4.92Wall-gate gap (mm) 40 40

=> No risk of blocking of gates (earthquake in summer)5. Seismic safety assessment


Winter

Déplacement relatif latéral des contreforts

0 mm @ 0.00 s

0 mm @ 0.00 s

-0.1

-0.08

-0.06

-0.04

-0.02

0

0 5 10 15 20 25 30

Dépl

acem

entr

elat

ifde

s con

tref

orts

[m]

-éca

rtem

ent/

+ ra

ppro

chem

ent

x 0.0

01

Temps (s)

Vanne secteur


Vanne clapet

Vanne secteur

-0.4-0.35

-0.3-0.25

-0.2-0.15

-0.1-0.05

0

0 5 10 15 20 25 30

Dépl

acem

entr

elat

ifde

s con

tref

orts

[m]

-éca

rtem

ent/

+ ra

ppro

chem

ent

x 0.0

01

Temps (s)

Vanne clapet


Flap gate Outlet gapOpening width 4.90 5.00Gate width 4.82 4.92Wall-gate gap (mm) 40 40

=> No risk of blocking of gates (earthquake in winter)5. Seismic safety assessment

5.6 Verification of gates: blocking hazard


Flap gate jack Outlet gate jackBar diameter (mm) 150 100Area (mm2) 17671.5 7854.0Length (m) 6.35 5.27Critical Effort N (kN) 1277.3 366.3

5.6 Verification of jacks

Vérin vanne-clapet Vérin vanne-secteur

Compression N max (kN)

temps (s)


Compression N max (kN)

temps (s)


Eté, Lac plein Séisme 1 -418.9 20.84 -23.7 -123.4 0.01 -15.7

Hiver, Lac plein Séisme 1 -419.8 20.84 -23.8 -199.8 0.01 -25.4

Séisme 2 -432.0 13.28 -24.4 -199.8 0.01 -25.4

Séisme 3 -437.2 7.94 -24.7 -199.8 0.01 -25.4

Vérin vanne-clapet Vérin vanne-secteur

Eté, Lac plein Séisme 1 3.05 2.97

Hiver, Lac plein Séisme 1 3.04 1.83

Séisme 2 2.96 1.83

Séisme 3 2.92 1.83

Buckling safety afctors:

Maximal compression (dynamic) of jacks:

20

2

lEINcritique

π=

=> No risk of buckling of jacks’ bars

N

N

N

N




• 3D numerical (FE) model of Rossinière dam including wing buildings, hydromechanical equipment(gates) and foundation was developed to evaluate seismic safety of the dam

• Model preparation and analyses were carried out using FE software Z_Soil 3D (versions 9 and 10beta)

• Large number of the program’s features were successfully used

• Calibration and validation of the model showed very good agreement with measurements over several years (temperatures and displacements)

• Dynamic stress analyses show that compressive and tensile stresses remain below concrete strength

• Stability analyses of the dam indicate that neither sliding nor overturning may occur under the considered loads

• Assessment of the metallic gates stresses and deformations during earthquake indicates that:

• stresses fulfill strength criteria both in tension and in compression

• no risk of gate blocking between buttresses was identified

• no risk of jack bars buckling was identified

• Therefore, the seismic safety of Rossinière dam is fulfilled


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