Gravity dam and earthquake - ANCOLD · 2015. 11. 25. · 31/07/2015 2 INTERNAL VULNERABILITY OF...

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Gravity dam and earthquake

Château des Comtes de Challes9 octobre 2014

Tardieu’s Dynamic simplified method

Patrick LIGNIER, Tractebel Engineering –Coyne et Bellier

INTERNAL

• Vulnerability of gravity dam against earthquake

• Which approach and method to verify the dam stability?

• Tardieu’s dynamic simplified method

GRAVITY DAM AND EARTHQUAKE - 2014/10/092

CONTENTS

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VULNERABILITY OF GRAVITY DAMS TO EARTHQUAKES

• No actual dam failures except for Shih-Kang Dam (Taiwan) built on an active fault

• Local failure (cracks in the upper part of the dam, opening or displacement at vertical construction joints) for PGA up to 0.6 g

3GRAVITY DAM AND EARTHQUAKE - 2014/10/09

INTERNAL

VULNERABILITY OF GRAVITY DAM AGAINSTEARTHQUAKE

• Shih-Kang Dam (Taiwan)


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VULNERABILITY OF GRAVITY DAM AGAINSTEARTHQUAKE

• Sefi Rud Dam (Iran)


INTERNAL

VULNERABILITY OF GRAVITY DAM AGAINST EARTHQUAKE

• Main conclusions

- Generally satisfactory behaviour of gravity dams (no failure but damage) up to PGA of 0.6 g

- Amplification of the acceleration (PGA) due to the dynamicresponse of the dam can lead to excessive stresses in the upperpart of the dam

- We do not know the actual safety margin of gravity dams underseismic loading (dynamic resistance, increase of damping withhigher oscillations)


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WHICH APPROACH AND METHOD TO VERIFYTHE DAM STABILITY?- Imagine a failure scenario

- Demonstrate that for this scenario the dam is stable during and after the earthquake


INTERNAL

FAILURE MECANISM

- Excessive cracking can lead to sliding or overturning of the structure


WHICH APPROACH AND METHOD TO VERIFY THE DAM STABILITY?

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INTERNAL

FAILURE MECANISM

9

2

1


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WHICH METHOD?

- Pseudo-static method

- Simplified dynamic method or dynamic method – FEA taking intoaccount the dynamic response of the dam


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TARDIEU’S DYNAMIC SIMPLIFIED METHOD - GENERAL

- This method estimates the maximum acceleration at each point of the dam then the maximum stresses.

- This method is based on two assumptions: - 1) the acceleration depends on the seismic spectrum and on the shape of the dam

- 2) Gravity dams always have the same triangular shape


INTERNAL

TARDIEU’S DYNAMIC SIMPLIFIED METHOD - GENERAL


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TARDIEU’S DYNAMIC SIMPLIFIED METHOD - HYPOTHESES

• The dam is founded on sound rock

• The effect of the bank to bank acceleration is negligible

• The dam behaves as a triangle where the height is equivalent to the upstream water height for a reservoir at Full Supply Level.

• The maximum acceleration is supposed to be reached for the most critical fundamental frequency of the dam

• The hydrodynamic effect is taken into account by Westergaardanalysis.


INTERNAL

TARDIEU’S DYNAMIC SIMPLIFIED METHOD IN 4 STAGES

• 1) Determine the first, and most critical natural frequency of the gravity dam

• 2) Compare with spectrum to know the spectral amplification of the dam

• 3) Evaluate the shape of the envelope of the maximum accelerationin the dam

• 4) Assess the maximum stresses at the u/s and d/s faces


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TARDIEU’S DYNAMIC SIMPLIFIED METHOD – STAGE 1

• N=0,23 S/H for empty reservoir

• N=0,17 S/H for full reservoir

where S=(G/ )0,5 (Shear wave velocity) with G=E/2(1+ )

For example, an RCC dam 110 m meters high (Case 1)

N =2,9 Hz (E = 20 GPa, 2400kg/m3 , v=0,2)

A masonry dam 40 meters high (Case 2) N = 7,2 Hz (E= 15 GPa , 2200 kg/m3 , v=0,2 )


INTERNAL


• This frequency is compared with the spectrum of the site to know the spectral acceleration of the dam for a certain level of damping which increase when the oscillation increases.

• For example, for NF EN 1998-1 spectrum and Case 1 Concrete dam or Case 2 Masonry Dam the spectral amplification is 1,5 or 2,0


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Spectral amplificationSpectral amplification

Periode in secondsPeriode in seconds

INTERNAL


• Maximum acceleration in all part of the dam can also be calculated with regards to the relative height of the dam according to a diagram presenting the following characteristics.

• At the bottom, the PGA

• At level corresponding to 0.6 H, the spectral acceleration multiplied by 1 for concrete dams and 0.9 for masonry dams

• At the crest, the spectral acceleration multiplied by 2.5 for concrete dams and 1.9 for masonry dams

• For example, the maximum amplification for Case 1 is 3,75 and 2,85 for Case 2


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Rel

ativ

e el

evat

ion

(tot

al d

am h

eigh

t)R

elat

ive

elev

atio

n(t

otal

dam

hei

ght)

Acceleration amplificationAcceleration amplification

INTERNAL


- Maximum stresses can be calculated at each level with regards to the forces and moments by assuming a linear distribution between the u/s and d/s face of the dam.


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ANALYSIS OF THE RESULTS

- To evaluate of the risk of cracking, the maximum tensile stress shall be compared with the maximum dynamic tensile resistance of the material.

- If cracking does occur, check the stability post-earthquake taking into account the pressure inside the cracks.

- Another approach is to compare the maximum acceleration to the critical acceleration at any level on an horizontal joint (g . tan ).


INTERNAL

ANALYSIS OF THE CRITICAL ACCELERATION TO CHECK THE STABILITY OF THE UPPER PART OF THE DAM

- For a concrete dam, we can assume the friction angle at the beginning of the movement to be as high as 50°; tan = 1,19

- For a masonry dam, we can assume the friction angle at the beginning of the movement to be as high as 45°; tan = 1


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ANALYSIS OF THE CRITICAL ACCELERATION TO CHECK THE STABILITY OF THE UPPER PART OF THE DAM

- At the upper part of the dam, above the full supply level, there is no water effect.

- For a concrete dam , we can assume an amplification equal to 6,25 x PGA. Risk of irreversible displacement is unlikely to occur for PGA below 0,2 g

- For a masonry dam, we can assume an amplification equal to 3,8 x PGA. Risk of irreversible displacement is unlikely to occur for PGA below 0,25 g.


INTERNAL

ASSESSMENT OF IRREVERSIBLE DISPLACEMENT

- Irreversible displacement can be assessed by integrating twice the part of the accelerogram which overpass the critical acceleration.

- Assuming that the curve of the accelerogram is a sinusoid with a period T, the irrevesible displacement is equal to

- Dirr = A.T² / 4 x (1-2/ . Asin(g.tan / A) with T period and A maximum acceleration of the accelogramm at the upper part of the dam.


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ASSESSMENT OF IRREVERSIBLE DISPLACEMENT


0

20

40

60

80

100

120

140

160

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Dam

hei

ght

m

PGA (g)

Irreversible displacement

5 cm

1 cm

2 mm

INTERNAL

COMPARISON WITH DATA GIVEN BY THE JCOLD

- JCOLD provides data showing amplification versus PGA.

- These data are compared with the amplification calculated with Tardieu’s method versus damping.


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COMPARISON WITH DATA GIVEN BY THE JCOLD

27

5

10

0,1g

15

0,2g 0,3g 0,4g 0,5g

P.G.A

Ampl

ifica

tion

5 % 10 %2 %


Damping

Tardieu versus damping

JCOLD versus PGA

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Gravity dam and earthquake - ANCOLD · 2015. 11. 25. · 31/07/2015 2 INTERNAL VULNERABILITY OF...

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