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May 15, 2013
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May 15, 2013
Linear and nonlinear analyses of embankment and concrete dams;
Seismic fluid-structure and soil-structure interaction modeling and analyses;
Assessment of ultimate seismic capacity of embankment and concrete dams;
Seismic optimization of new built and seismic strengthening of existing dams;
Probabilistic seismic hazard analyses and microzonation;
Seismic probabilistic safety assessment of large dams
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SPSA of Chaira Dam SPSA of Tsankov Kamak Dam
Kardjali Arch Dam
Tsankov Kamak Double Arch Dam
Seismic Probabilistic Safety Assessment of Vacha Dam SPSA of Kardjali Dam
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Studen Kladenetz Gravity Dam
Seismic Probabilistic Safety Assessment of Iskar Dam
SPSA of Beli Iskar Dam Beli Iskar Gravity Dam
SPSA of Studen Kladenetz Dam
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Vacha Dam
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All types of Gravity dams Arch and Double-arch Dams
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PSA procedure used for critical facilities mainly in nuclear industry
Codes requirements taken into account (ICOLD, USACE, FERC, FEMA)
Realistic assessment of the seismic hazard for the region
Statistically defined material properties
Statistically defined loads
Reliable numerical models
Reliable calculation procedure
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Statistical assessment of the response:
• Maximal and average stresses;
• Depth of cracks;
• Sliding and overturning forces etc.
Definition of damage and failure scenarios:
• Exceedance of the material strength;
• Occurrence of critical cracks;
• Loss of global and local stability;
• Abutments failure (for arch dams);
• Criteria based on various damage and failure parameters: strength, displacements, DI etc.;
• Secondary risk assessment
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Definition of the conditional probability of failure:
Pf= FR(x)fL(x)dx
• FR(x) - distribution function of the resistance
• fL(x) - density function of the loading distribution
Generation of fragility curves;
Definition of the global seismic risk;
Sensitivity analysis 0 0.4 0.8 1.2 1.60.2 0.6 1 1.4
PGA (g)
0
0.2
0.4
0.6
0.8
0.1
0.3
0.5
0.7
Pro
bability o
f F
ailure
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2D and 3D FEM models including foundation rock base and water reservoir
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Rock foundation:
Elastic massless media;
All foundation layers and weak zones included;
Material properties from laboratory and in-situ tests
Size of the model depends on Ef/Ec (foundation/concrete):
• if Ef/Ec ≥ 1 → 1 dam height in the three directions;
• if Ef/Ec = ½ or ¼ → up to 2 dam height in the three directions.
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Springs or contact (interface) elements;
Layer of finite elements representing the real geometry and base joint behavior;
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Якост на срязване по контакта "бетон - скала"
Зависимост между нормални и тангенциални напрежения
y = 0.8283x + 1.7094
R2 = 0.7558
y = 0.7692x + 0.4769
R2 = 0.9356
y = 0.8874x + 2.9419
R2 = 0.9509
0.000
1.000
2.000
3.000
4.000
5.000
6.000
7.000
8.000
0.000 1.000 2.000 3.000 4.000 5.000 6.000
Нормални напрежения σ [MPa]
Тан
ген
ци
ал
ни
нап
реж
ен
ия τ
[MP
a]
"Линейна зависимост" "Доверителен интервал 95%" Series3
Linear ("Линейна зависимост") Linear ("Доверителен интервал 95%") Linear (Series3)
Material properties based on laboratory tests;
Nonlinear material and reduced shear transfer after cracking;
Decreased dynamic tensile strength - up to 30% of the concrete tensile strength;
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Contact (interface) elements;
Coupled springs;
Layer of finite elements with adequate behavior (intact shear stress transfer after cracking);
Decreased dynamic tensile strength – lower than base joint: 0-15% of concrete tensile strength;
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Seismic tomography
Geological and seismic investigations
Laboratory tests
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Concrete dynamic material properties:
• Linear or nonlinear material models;
• E-modulus – 15-25% higher than static;
• Compressive strength – 15-25% higher than static;
• Tensile strength – 40-60% higher than static (Raphael, 1984).
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Максимално Хидродинамично
Налягане 0
10
20
30
40
50
60
70
80
90
0 200 400 600 800 1000
Налягане (kPa)
Дъ
лб
очи
на (
м)
Модел - маси Модел - флуид
Westergaard added masses approach;
Fluid elements based on velocity potential;
Min 3 layers of elements and minimum extend equal to the depth of the reservoir;
F.E.R.C.
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Based on Seismic Hazard Assessment
Input records compatible with the uniform hazard response spectrum
Excitations for various Seismic Levels with different return periods, including OBE and MCE
0.1 1
NATURAL PERIOD (sec.)
0
4
8
12
16
20
SP
EC
TR
AL
AC
CE
LE
RA
TIO
N (
m/s
ec*
*2)
ACCELERATION RESPONSE SPECTRA (damping 0.05)
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Air and Water Temperature curves for the dam site;
Transient thermal analyses based on annual temperature changes;
Displacements and stressed state from temperature loading;
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First mode shape: 1.919 Hz
Second mode shape: 2.772 Hz
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Excess of tensile stress;
Cracks propagated into dam’s body;
Cracks across whole cross section and subsequent detached fragment stability;
Zones with maximum compressive stresses;
Abutment stresses and stability;
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Maximum Contraction Joints Opening (cm)
0.49
R8-R7
AIR SIDE
0.27
0.20
R7-R6
WATER SIDE
0.00
0.44
R6-R5
0.63
0.05
R5-R4
0.63
R4-R3
-0.01
0.29
R3-R2
-0.01
0.26
0.41
R2-R1
-0.01
0.22
R1-M
0.01
M-L1
0.31
0.00
L1-L2
0.72
0.16
L2-L3
0.54
0.01
L3-L4
0.07
0.56
0.40
L4-L5
0.15
L5-L6
0.53
0.55
0.18
L6-L7
0.01 0.10
0.45
L7-L8
Zones with maximum and residual contraction joint opening;
Loss of arch action;
Free cantilever stability in case of opened contraction joints;
Base joint damages and possible water infiltration;
Critical Zones. Damage and Failure Scenarios
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Post-earthquake Safety Assessment
Post-earthquake stability assessment for static loads;
Post-earthquake stability assessment for dynamic loads (aftershock);
Stability of Detached Fragments
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Abutment Sliding Stability
Generation of Fragility Curves for Damage and Failure scenarios
0 0.2 0.4 0.6 0.8 1Amax (g)
0
0.2
0.4
0.6
0.8
1
Pro
ba
bility o
f fa
ilu
re
Damage scenario for Base joint
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№ Damage Scenarios Confidence Level
15% 50% 85%
1. Downstream side cracking damages 4.89E-5 8.96E-5 1.64E-4
2. Base joint cracking damage 4.89E-5 9.25E-5 1.76E-4
3. Compressive Strength Exceedance 1.11 E-5 2.48E-5 5.57E-5
4. Contraction joints opening 9.33E-7 1.85E-6 3.7E-6
Failure Scenarios Confidence Level
1. Global Sliding of the Dam structure 2.54E-7 3.32E-7 4.32E-7
2. Abutment Sliding 2.31E-6 4.64E-6 9.32E-6
3. Global Upstream failure of the Dam Structure 4.43E-7 1.74 E-6 6.83E-6
4. Global Downstream failure of the Dam Structure 9.33E-7 1.85E-6 3.7E-6
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Dam pre-stressing;
Seismic belt;
Vertical reinforced concrete elements;
etc.
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Adaptive Capacity Spectrum Method
Displacement-Based
Seismic Capacity Assessment
Rapid Seismic assessment and Damage prediction;
Better understanding of Classical methods results;
Use of displacement-based procedures;
yu
yir
idd
ddDI
,
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Stability Assessment in case of Static and Dynamic Loads;
Overall Stability Assessment;
Seepage studies;
Slope Stability Investigations;
Stress and Deformation Analyses
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Alerts for expected damages in the dam structure after seismic event;
Based on various Damage Intensity Parameters (DIP);
Multi-stage algorithms;
Implementation in the monitoring system of the dam;
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BELI ISKAR DAM
Type – concrete gravity Height – 50.7 m Crest length – 533 m Crest thickness – 3.4 m Reservoir volume – 15.3 mln. m3
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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Peak ground acceleration (g)
1E-006
1E-005
0.0001
0.001
0.01
0.1
An
nu
al p
rob
abil
ity
of
exce
edan
ce
Mean
Median
15, 85 percentiles
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Period (s)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Sp
ectr
al a
ccel
erat
ion
(g
)
RP=100
RP=475
RP=1000
RP=10 000
RP=100 000
RP=1 000 000
RP - Return period in years
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STUDEN CLADENEC DAM
Type – concrete gravity Height – 67.5 m Crest length – 338 m Crest thickness – 8.8 m Reservoir volume – 380 mln. m3
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Type – arch gravity Height – 103.5 m Crest length – 338 m Crest thickness – 5.0 m Reservoir volume – 530 mln. m3
KARDJALY ARCH DAM
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Completed 2010 Type – arch double curvature Height – 130.0 m Crest length – 468 m Crest thickness – 9.0 m Reservoir volume – 111 mln. m3
Tsankov Kamak HPP under construction
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Type – concrete gravity dam Height – 75.0 m Crest length – 204 m Crest thickness – 7.3 m Reservoir volume – 650 mln. m3
ISKAR DAM