standard problem exercise no. 3 phase twostandard problem exercise no. 3 model 4 – case 1 and 2...

Standard Problem Exercise No. 3

Phase Two

March 27, 2012

Herman Graves

Madhumita Sircar

Lili Akin

Robert Dameron

Christopher Jones

Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation,

a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s

National Nuclear Security Administration under contract DE-AC04-94AL85000.

Agenda

2

Tuesday, March 27, 2012

Time Topic Speaker

8:30 Meet at Building Lobby for

Badging and Security

9:30 Opening Remarks / Welcome

Address NRC / AERB

9:45 Overview of Model 4 – Case 1

and 2

NRC / SNL /

M&N

10:00 Model 4 Case 1 Presentations All Participants

12:00 Group Photo

12:15 Lunch – NRC Cafeteria

1:00 Case 1 – Comparison of Results

NRC / SNL /

M&N

1:30 Case 1 – Panel Discussion All Participants

2:30 Break All Participants

2:45 Model 4 Case 2 Presentations All Participants

4:45 Adjourn

Wednesday, March 28, 2012

Time Topic Speaker

8:30 Meet at Building Lobby for Badging

and Security

9:00 Model 4 Case 2 Comparisons

NRC / SNL /

M&N

9:30 Model 4 Case 2 Panel Discussion All Participants

10:30 Break

10:45 Leakage Rate Problem Definition

NRC / SNL /

M&N / AERB

11:00 Leakage Rate Presentations By

Participants All Participants

12:00 Lunch – NRC Cafeteria

1:00 Leakage Rate Presentations By

Participants (continued) All Participants

2:00 Leakage Rate Panel Discussion All Participants

3:30 Discussion of Transition to

Probabilistic Space

NRC / SNL /

M&N

4:00 Probabilistic Space Presentations All Participants

4:45 Adjourn

Agenda

3

Thursday, March 29, 2012

Time Topic Speaker

8:30 Meet at Building Lobby for Badging and

Security

9:00 Probabilistic Space Presentations

(Continued) All Participants

10:30 Probabilistic Space Panel Discussion Participants

11:30 Discussion of In-Situ Vs Design (If

Applicable) Participants

12:00 Projects of Interest to Panel NRC / SNL

12:15 Discussion of Future Work (Publications,

Results sent in, Next Workshop) All Participants

12:45 Adjourn


Phase One Overview

March 27, 2012

Herman Graves

Madhumita Sircar

Lili Akin

Robert Dameron

Christopher Jones

Model 1 Summary

• Model 1: Tendon Behavior

Model

– Investigate Tendon Forces

as a Function of

Containment Dilation

– Use Friction Models to

Represent Slippage of

Prestressing Cables

– Pressure and

Pressure/Temperature

Analyses Completed

5

Model 1 Results

• Milestones:

1. Concrete Hoops

Stress Equals 0

2. Concrete Hoop

Cracking Occurs

3. Tendon A

Reaches 1% Strain

4. Tendon B

Reaches 1% Strain

5. Tendon A

Reaches 2% Strain

6. Tendon B

Reaches 2% Strain

6

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1 2 3 4 5 6

Pre

ssure

(M

Pa)

Milestone

Comparison of Pressure Milestones at 135o Azimuth

NRC

SCANSCOT

FORTUM

EDF/NECS

GRS

Model 1 Results

• Example of Tendon Stress Distribution

7

0

200

400

600

800

1000

1200

1400

1600

1800

2000

-270 -240 -210 -180 -150 -120 -90 -60 -30 0 30 60 90

Str

ess

(M

Pa)

Azimuth (Deg)

Tendon Stress Distribution at 2.5 x Pd

NRC - 2.5 x Pd

SCANSCOT - 2.5 x Pd

FORTUM - 2.5 x Pd

EDF/NECS - 2.5 x Pd

GRS - 2.5 x Pd

Model 2 Summary

8

• Model 2: Equipment Hatch

Model

– Effects of Containment

Dilation on Prestressing

Force

– Slippage of Prestressing

Cables

– Steel-Concrete Interface

– Fracture Mechanics Behavior

– Ovalization of Concrete vs

Steel

– Pressure Only Analysis

Model 2 Results

Pressure Milestones:

1. Concrete Hoop

Cracking Occurs

2. Tendon Reaches

1% Strain

9

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 1 2 3

Pre

ssu

re (

MP

a)

MIlestone #

Comparison of Pressure Milestones

NRC

GRS

AERB

SCANSCOT

Model 2 Results

10

-0.001

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.010

.00

0

0.2

00

0.4

00

0.6

00

0.8

00

1.0

00

1.2

00

1.4

00

Str

ain

Pressure (MPa)

Liner Strain Magnitude vs Pressure - Location 1

NRC - Model 2a - Location 1

SCANSCOT - Model 2a - Location 1

GRS - Model 2a - Location 1

AERB - Model 2a - Location 1

Model 3 Summary

11

• Model 3: Detailed Global 3D

Model

– Effects of Containment

Dilation on Prestressing

Force

– Slippage of Prestressing

Cables

– Steel-Concrete Interface

– Fracture Mechanics Behavior

– Ovalization of Concrete vs

Steel

– Pressure Only Anlaysis

Model 3 Results

12

-5

0

5

10

15

20

25

30

35

40

0 0.4 0.8 1.2 1.6

Dis

pla

cem

en

ts (

mm

)

Pressure (MPa)

Displacements - SOL 4

NRC

SCANSCOT

FORTUM

AERB

LST - SOL4

SFMT - SOL 4

Model 3 Results

13

-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

0 0.4 0.8 1.2 1.6

Str

ain

Pressure (MPa)

Liner Strains - SOL 39 -h,6.2m

NRC

SCANSCOT

FORTUM

AERB

LST


Model 4 – Case 1 and 2

March 27, 2012

Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation,

a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s

National Nuclear Security Administration under contract DE-AC04-94AL85000.

Phase Two Overview

• Examine differences in behavior brought on by

temperature

• Estimate Leak Rates as a Function of Pressure

• Estimate Leak Rates as a Function of Pressure

and Temperature

• Transition to Probabilistic Space

15

Model 4 Overview

• Use Model 3 as a Starting Point

• Modify Model 3 as Needed

• Apply Two New Load Cases To Model 4: Cases 1 and 2

16

Case 1 – Saturated Steam

17

0.00

50.00

100.00

150.00

200.00

250.00

0.00 10.00 20.00 30.00 40.00 50.00

Time (m)

Tempe

ratu

re (C)

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

Press

ure (M

Pa)

Temperature Pressure

Case 1: Pressure-Temperature Relationship

18

80

100

120

140

160

180

200

220

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Pressure (MPa)

Tempe

ratu

re [C]

Case 2 – Station Blackout

19

Thermal Analysis – Temp distr. From ISP48

• Model: Full-scale Axisymmetric with additional nodes throughout cylinder and dome - 12 through-thickness

• Material Properties: based on typical data

• Thermal Gradient calculation locations:

– See figure

• Boundary Conditions:

– Liner: Uniformly applied temperature; quasi-static, but transient

– Dome & Cylinder: convection to air

– Basemat/soil: conduction

• Reference:

Dameron, et. al., “Analysis of Axisymmetric Presstressed Concrete Containment Vessel (PCCV) Including Thermal Effects”, May, 2004

1

2

3

4

5

6 7 8

Case 1 Thermal Time Histories @ Section 2

0.00

50.00

100.00

150.00

200.00

250.00

0.00 10.00 20.00 30.00 40.00 50.00

Time (m)

Tempe

ratu

re (C)

0%

5%

10%

18%

25%

35%

52%

75%

100%

d/T

Case 1 Gradients @ Section 2

0.00

50.00

100.00

150.00

200.00

250.00

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

d/T (%)

Tempe

ratu

re (C)

0.00

2.83

7.57

15.01

26.16

42.23

Time (m)

Case 1 Contours

VALUE, °C

-19

-1

16

32

49

66

82

99

116

132

149

166

182

200

Case 2 Thermal Time Histories @ Section 2

0.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

0.00 600.00 1200.00 1800.00 2400.00 3000.00 3600.00

Time (m)

Tempe

ratu

re (C)

0%

5%

10%

18%

25%

35%

52%

75%

100%

d/T

Case 2 Gradients @ Section 2

0.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

d/T (%)

Tempe

ratu

re (C)

0.02

104.08

260.18

260.60

261.02

268.72

284.12

299.52

959.62

1619.72

1839.83

2279.83

2940.00

3600.00

Time (m)

Case 2 Contours

VALUE, °C

-18

32

82

132

182

232

282

332

382

432

482

532

582

616

Concrete Degradation Properties at Elevated

Temperatures per Eurocode

27

Steel Degradation Properties at Elevated

Temperatures per Eurocode

28

Analysis Results

Required Output/Results for Model 4:

1. Description of Failure Prediction Model or Criteria Selected

2. Assumptions Made In Geometric Modeling / Model Description

3. Subset of response information defined by “55 standard output

locations” of 1:4 Scale PCCV round-robin;

4. Contour Plot of Peak Strains in Liner During LST at pressure

milestones: P = 0 (prestress applied); 1 x Pd; 1.5 Pd; 2 Pd; 2.5 Pd;

3 Pd; 3.3 Pd; 3.4 Pd; Ultimate Pressure

29

For direct comparison amongst participants,

also requested to plot (Using Excel)

• Liner Strain Magnitudes (Hoop Direction) at Locations Indicated in

Figure 11 (of SPE problem statement), versus pressure

• Tendon stress distribution at P = 0 (prestress applied); 1 x Pd; 1.5

Pd; 2 Pd; 2.5 Pd; 3 Pd; 3.3 Pd; 3.4 Pd; Ultimate Pressure for

– Hoop Tendons # H35, H53, H68

– Vertical Tendon # V37 and V46

– Plots of response versus pressure for Standard Output

Locations:

• 1-15 (displacements)

• 22-29 (rebar strains)

• 36-42 (liner strains)

• 48-55 (tendon strains and stresses)

(see Table 4-1 in NUREG/CR-6809 for locations of SOL’s)

30


Leak Rate Problem Definition

March 28, 2012

Failure Criteria for PCCV

• From SPE Phase 1, the relevant failure criterion

for Model 1 was Tendon failure. The rebar

generally has higher ductility than the tendons,

so it is not the controlling criteria. For Models 2,

3, and 4, Tendon Failure criteria remains at 3.8%

strain as for Model 1. But for Models 3 and 4, liner

tearing is the predominate failure mode

• For SPE Phase 2, a key objective of the work is to

estimate crack size and leak area

• Based on the existing research of behavior of

steel-lined concrete containments, liner-tearing

with associated leakage is the failure mode for

slow pressurization of the containment 32

Calculate Leak Rate

• Participants are asked to develop a prediction of

leak rate as a function of pressure.

– Liner Strains

– Crack Size

– Leak Rate

• Participants shall use the functions provided by

AERB to calculate leak rate based on crack area if

they so desire

33

Liner Tears and Acoustic Events

180° 270°90°0° 62°

E/HM/S, F/WA/L

12

3

4

5

6

7

8

9

10

11

1213

B CA D E F G H I J K L A

16.125

15.716

14.551

12.807

10.750

9.230

7.730

6.200

4.680

2.630

1.430

0.2500.000

Top of

Basemat

Springline

Top of Dome

Tendon Gallery

Bottom of

Basemat

-1.175

-2.000

-3.500

Z

Free-FieldButtress Buttress

30° 60° 120° 135° 150° 210° 240° 300° 324° 330° 360°

Elevation

(meters)

(El.

ID)

Azimuth

(Az. ID)

Instr Frame Platforms

1

3

4

6

2

5

7

#14

#8

#1

#9

#2

#16

#10

#3

#4

#5 #6

#11

#15

#13

#12

#7

#17

Acoustic Events:

1: 2.4 Pd 5: 2.8 Pd

2: 2.6 Pd 6: 2.8 Pd

3: 2.7Pd 7: 3.0 Pd

4: 2.8 Pd

Liner Strain Map (see results presentation)

35

PCCV LST - Calculated Leak Rate

0.482%

0.003%

1.628%

-2.0%

-1.0%

0.0%

1.0%

2.0%

3.0%

4.0%

09

/26

/20

00

16

:00

09

/26

/20

00

20

:00

09

/27

/20

00

0:0

0

09

/27

/20

00

4:0

0

09

/27

/20

00

8:0

0

09

/27

/20

00

12

:00

Time (day/hour)

Leak R

ate

(% m

ass

/day)

Total Time (1.5 Pd) Point-to-Point (1.5 Pd)Total Time (2.0 Pd) Point-to-Point (2.0 Pd)Total Time (2.5 Pd) Point-to-Point (2.5Pd)

PCCV LST - Estimated Leak Rates (2.5-3.1 Pd)

0.0%

50.0%

100.0%

150.0%

200.0%

250.0%

300.0%

350.0%

10:0

0

11:0

0

12:0

0

13:0

0

14:0

0

15:0

0

16:0

0

Time (hour)

Leak R

ate

(% m

ass

/day)

Total Time Point-to-Point

2.5 Pd

2.55 Pd 2.6 2.65

2.7 2.752.8

2.852.90

2.95

3.0

3.1 Pd

PCCV LST - Calculated Leak Rate

56.7%

391.1%

585.4%

27.3%

851.83%

0.0%

100.0%

200.0%

300.0%

400.0%

500.0%

600.0%

700.0%

800.0%

900.0%

09

/27

/20

00

12

:00

09

/27

/20

00

16

:00

09

/27

/20

00

20

:00

09

/28

/20

00

0:0

0

09

/28

/20

00

4:0

0

09

/28

/20

00

8:0

0

09

/28

/20

00

12

:00

09

/28

/20

00

16

:00

09

/28

/20

00

20

:00

09

/29

/20

00

0:0

0

09

/29

/20

00

4:0

0

09

/29

/20

00

8:0

0

Time (day/hour)

Leak R

ate

(% m

ass

/day)

Total Time Point-Point

Leak Rate @ 170 psig

Terminal Leak Rate @ 180 psig

Leak Rate as a Function of Crack Size

• See Presentation by AERB

39


Transition to Probabilistic Space

Problem Definition

March 28, 2012

Probabilistic Space

41


42

Projects of Interest

March 29, 2012


NRC / SNL Projects:

43

Degraded containment research

• Detailed submodeling – Global boundary conditions

– Refined mesh

– Additional detail

– XFEM

• Plant specific investigation – Forensic analysis

– Computational reconstruction

Grouted Tendon Study • Behavior

• Monitoring

• Corrosion


• Insert Slides from NRC here

44


Future Work

March 29, 2012

45

Future Work

• NUREG Publication of Phase One and Phase Two

Reports

• Follow Up Workshop?

• Additional Publications?

46

standard problem exercise no. 3 phase twostandard problem exercise no. 3 model 4 – case 1 and 2...

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