May 15, 2013

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

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

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

Vacha Dam

All types of Gravity dams Arch and Double-arch Dams

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

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

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

2D and 3D FEM models including foundation rock base and water reservoir

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.

Springs or contact (interface) elements;

Layer of finite elements representing the real geometry and base joint behavior;

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;

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;

Seismic tomography

Geological and seismic investigations

Laboratory tests

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).

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.

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)

Air and Water Temperature curves for the dam site;

Transient thermal analyses based on annual temperature changes;

Displacements and stressed state from temperature loading;

First mode shape: 1.919 Hz

Second mode shape: 2.772 Hz

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;

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

Post-earthquake Safety Assessment

Post-earthquake stability assessment for static loads;

Post-earthquake stability assessment for dynamic loads (aftershock);

Stability of Detached Fragments

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

№ 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

Dam pre-stressing;

Seismic belt;

Vertical reinforced concrete elements;

etc.

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

,

Stability Assessment in case of Static and Dynamic Loads;

Overall Stability Assessment;

Seepage studies;

Slope Stability Investigations;

Stress and Deformation Analyses

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;

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

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

STUDEN CLADENEC DAM

Type – concrete gravity Height – 67.5 m Crest length – 338 m Crest thickness – 8.8 m Reservoir volume – 380 mln. m3

Type – arch gravity Height – 103.5 m Crest length – 338 m Crest thickness – 5.0 m Reservoir volume – 530 mln. m3

KARDJALY ARCH DAM

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

Type – concrete gravity dam Height – 75.0 m Crest length – 204 m Crest thickness – 7.3 m Reservoir volume – 650 mln. m3

ISKAR DAM