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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INTERNAL
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
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INTERNAL
VULNERABILITY OF GRAVITY DAM AGAINSTEARTHQUAKE
• Shih-Kang Dam (Taiwan)
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INTERNAL
VULNERABILITY OF GRAVITY DAM AGAINSTEARTHQUAKE
• Sefi Rud Dam (Iran)
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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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INTERNAL
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
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INTERNAL
FAILURE MECANISM
- Excessive cracking can lead to sliding or overturning of the structure
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WHICH APPROACH AND METHOD TO VERIFY THE DAM STABILITY?
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INTERNAL
FAILURE MECANISM
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2
1
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INTERNAL
WHICH METHOD?
- Pseudo-static method
- Simplified dynamic method or dynamic method – FEA taking intoaccount the dynamic response of the dam
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INTERNAL
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
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INTERNAL
TARDIEU’S DYNAMIC SIMPLIFIED METHOD - GENERAL
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INTERNAL
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.
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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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INTERNAL
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 )
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INTERNAL
TARDIEU’S DYNAMIC SIMPLIFIED METHOD – STAGE 2
• 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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INTERNAL
TARDIEU’S DYNAMIC SIMPLIFIED METHOD – STAGE 2
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Spectral amplificationSpectral amplification
Periode in secondsPeriode in seconds
INTERNAL
TARDIEU’S DYNAMIC SIMPLIFIED METHOD – STAGE 3
• 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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INTERNAL
TARDIEU’S DYNAMIC SIMPLIFIED METHOD – STAGE 3
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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
TARDIEU’S DYNAMIC SIMPLIFIED METHOD – STAGE 4
- 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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INTERNAL
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 ).
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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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INTERNAL
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.
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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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INTERNAL
ASSESSMENT OF IRREVERSIBLE DISPLACEMENT
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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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INTERNAL
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 %
GRAVITY DAM AND EARTHQUAKE - 2014/10/09
Damping
Tardieu versus damping
JCOLD versus PGA
PUBLIC
PUBLIC
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