Prediction of Response of Reinforced Concrete Slabs Using Finite ...

Olmati P(1), Trasborg P(2), Sgambi L(3), Naito CJ(4), Bontempi F(5)

Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

cjn3@lehigh.edu

(3) Associate Researcher, Ph.D., P.E., Politecnico di Milano, Email: sgambi@stru.polimi.it

(1) Ph.D. Candidate, P.E., Sapienza University of Rome, Email: pierluigi.olmati@uniroma1.it

(4) Associate Professor and Associate Chair, Ph.D., P.E., Lehigh University, Email: cjn3@lehigh.edu (5) Professor, Ph.D., P.E., Sapienza University of Rome, Email: franco.bontempi@uniroma1.it

(2) Ph.D. Candidate, Lehigh University, Email: pat310@lehigh.edu

Finite element and analytical approaches for predicting the structural response of reinforced

concrete slabs under blast loading

Section: Blast Blind Predict of Response of Concrete Slabs Subjected to Blast Loading (Contest Winners) - October 22, 4:00 PM - 6:00 PM, C-212 B

Chair: Prof. Ganesh Thiagarajan

Presentation outline

Introduction 1

Finite Element Model 2

Analytical Model 3

Conclusions 4

Questions/References 5

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Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

cjn3@lehigh.edu

The team - Short bio

3 Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

cjn3@lehigh.edu

Pierluigi Olmati is in the last year of his Ph.D. in

Structural Engineering at the Sapienza

University of Rome (Italy), with advisor Prof.

Franco Bontempi from the same University and

co-advisor Prof. Clay J. Naito from the Lehigh

University (Bethlehem, PA, USA).

The principal research topic of Mr. Olmati is blast engineering, addressed from

the point of view of FE modeling and probabilistic design. Mr. Olmati spent six

months at the Lehigh University in 2012 studying the performance of insulated

panels subjected to close-in detonations. Recently he was visiting Prof. Charis

Gantes and Prof. Dimitrios Vamvatsikos at the Department of Structural

Engineering of the National Technical University of Athens (Greece), performing

research on the probabilistic aspects of the blast design, and in particular,

developing fragility curves and a safety for built-up blast doors.

Pierluigi Olmati, Ph.D. Candidate, P.E. 1

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The team - Short bio 4

Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

cjn3@lehigh.edu

Patrick Trasborg, Ph.D. Candidate

Patrick Trasborg is in his 4th year of his

Ph.D. in Structural Engineering at Lehigh

University (Bethlehem, PA, USA), with

advisor Professor Clay Naito from the

same University.

The principal research topic of Mr. Trasborg is blast engineering, addressed from

the point of view of analytical modeling with experimental validation. Mr.

Trasborg’s dissertation is on the development of a blast and ballistic resistant

insulated precast concrete wall panel. Currently he is characterizing the

performance of insulated panels with various shear ties subjected to uniform

loading.

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The team - Short bio 5

Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

cjn3@lehigh.edu

Luca Sgambi, Associate Researcher,

Ph.D., P.E.

He studied Structural Engineering (1998) and took a 2nd

level Master degree in R.C. Structures (2001) at

Politecnico di Milano. He pursued his studies with a Ph.D.

at “La Sapienza” University of Rome (2005).

At present, he holds the position of Assistant Professor at Politecnico di Milano

and teaches “Structural Analysis” (since 2003) at School of Civil Architecture,

Politecnico di Milano. He is author of 7 papers on international journals and 57

paper on national and international conference proceedings; his research fields

concerning the non linear structural analyses, soft computing techniques,

durability of structural systems.

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The team - Short bio 6

Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

cjn3@lehigh.edu

Clay Naito, Associate Professor and

Associate Chair, Ph.D., P.E.

Clay J. Naito is an associate professor of Structural Engineering and associate chair at Lehigh University Department of Civil and Environmental Engineering. He received his undergraduate degree from the University of Hawaii and his graduate degrees from the University of California Berkeley.

He is a licensed professional engineer in Pennsylvania and California. His research interests include experimental and analytical evaluation of reinforced and prestressed concrete structures subjected to extreme events including earthquakes, intentional blast demands, and tsunamis. Professor Naito is Chair of the PCI Blast Resistance and Structural Integrity Committee and an Associate Editor of the ASCE Bridge Journal.

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The team - Short bio 7

Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

cjn3@lehigh.edu

Franco Bontempi, Professor, Ph.D., P.E.

Prof. Bontempi, born 1963, obtained a Degree in Civil

Engineering in 1988 and a Ph.D. in Structural Engineering in

1993, from the Politecnico di Milano. He is a Professor of

Structural Analysis and Design at the School of Engineering of

the Sapienza University of Rome since 2000.

He spent research periods at the Harbin Institute of Technology, the Univ. of Illinois

Urbana-Champaign, the TU of Karlsruhe and the TU of Munich. He has a wide activity

as a consultant for special structures and as forensic engineering expert.

Prof. Bontempi has a deep research activity on numerous themes related to

Structural Engineering, having developed approximately 250 scientific and technical

publications on the topics: Structural Analysis and Design, System Engineering,

Performance-based Design, Hazard and Risk Analysis, Safety and Reliability

Engineering, Dependability, Structural Integrity, Structural Dynamics and Interaction

Phenomena, Identification, Optimization and Control of Structures, Bridges and

Viaducts, High-rise Buildings, Special Structures, Offshore Wind Turbines.

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Presentation outline

Introduction 1

Finite Element Model 2

Analytical Model 3

Conclusions 4

Questions/References 5

8

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cjn3@lehigh.edu

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Finite element for modeling the concrete part of the slab 9

Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

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Image provided by: Lawrence Software Technology Corporation (LSTC). LS-DYNA theory manual. California (US), Livermore Software Technology Corporation.

Eight-node solid hexahedron element (constant stress solid element) with reduced integration. Default in LS-Dyna®. Other choices were prohibitive because computationally expensive.

Hourglass: Flanagan-Belytschko stiffness form with hourglass coefficient equal to 0,05.

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Finite element for modeling the reinforcements of the slab 10

Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

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The Hughes-Liu beam element with cross section integration. Tubular cross section with internal diameter much smaller than the external diameter.

Image provided by: Lawrence Software Technology Corporation (LSTC). LS-DYNA theory manual. California (US), Livermore Software Technology Corporation.

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The finite element mesh 11

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Upper support

Down support

Solid elements: 270,960 Beam elements: 130 Total nodes: 290,628 1

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3

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5

Demand 12

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0

10

20

30

40

50

60

0 20 40 60 80 100

Pre

ssure

[psi

]

Time [msec]

PH-Set 1a

PH-Set 1b

Load 1

Load 2

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3

4

5

Material model for the concrete – The Continuous Surface Cap Model 13

Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

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U.S. Department of Transportation, Federal Highway Administration. Users Manual for LS-DYNA Concrete, Material Model 159.

The cap retract in function of the equation of state.

Material Model 159 – LS-Dyna®

The dynamic increasing factor affects the failure surface.

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Material model for the concrete – The Continuous Surface Cap Model 14

Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

cjn3@lehigh.edu

U.S. Department of Transportation, Federal Highway Administration. Users Manual for LS-DYNA Concrete, Material Model 159.

Material Model 159 – LS-Dyna®

Density 2.248 lbf/in

4 s

2

2.4*103 kg/m

3

fc 5400 psi

37 N/mm2

Cap

retraction active

Rate

effect active

Erosion none

0

2

4

6

8

0.001 0.1 10 1000D

IF [

-]Strain-rate [1/sec]

CompressiveTensile

1

2

3

4

5

Material model for the rebar– Piecewise Linear Plasticity Model 15

Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

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Material Model 24 – LS-Dyna®

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Material model for the rebar– Piecewise Linear Plasticity Model 16

Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

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Material Model 24 – LS-Dyna®

0

20

40

60

80

100

120

140

0 0.05 0.1 0.15 0.2

Str

ess

[kpsi

]

Plastic strain [-]

True Stress

Stress

εT= ln 1 + ε

σT= σ eεT

εTp= εT −σT

E

ε: engineering strain σ: engineering stress εT: true strain σT: true stress σy: engineering yield stress

σTp= σ eεT − σy

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2

3

4

5

Material model for the rebar– Piecewise Linear Plasticity Model 17

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1

1.2

1.4

1.6

1.8

2

0.001 0.01 0.1 1 10 100

DIF

[-]

Strain-rate [1/sec]

US Army Corps of Engineers, 2008.Methodology Manual for the Single-Degree-of-Freedom Blast Effects Design Spreadsheets (SBEDS).

Cowper and Symonds model for the Material Model 24 – LS-Dyna®

DIF = 1 +ε

C

1q

C= 500 [1/s] q=6 1

2

3

4

5

Boundary conditions 18

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Boundary conditions 19

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Down support

Upper support

Contact surfaces

Contact

surfaces

Shock load

Gap 0.25”

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Boundary conditions 20

Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

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Results – Deflection 21

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Results – Deflection 22

Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

cjn3@lehigh.edu

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Results – Crack patterns 23

Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

cjn3@lehigh.edu

33.75 in. (857 mm)

64

in. (

16

25

mm

)

33.75 in. (857 mm)

64

in. (

16

25

mm

)

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Presentation outline

Introduction 1

Finite Element Model 2

Analytical Model 3

Conclusions 4

Questions/References 5

24

Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

cjn3@lehigh.edu

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Analytical Model – Fiber Analysis 25

Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

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Cross Section of Slab

Fiber Analysis of Section

Cross section approximated by dividing into discrete fibers [Kaba, Mahin 1983]

0 0.05 0.1 0.15 0.2

0

50000

100000

150000

200000

0

1500

3000

4500

6000

0 0.01 0.02 0.03

Steel Strain

Ste

el S

tres

s [p

si]

Co

ncr

ete

Str

ess

[psi

]

Concrete Strain

Conc DataMod PopovicsDIF ConcSteel DataDIF Steel

A =d *bi

dd/i

i number of layers

i

b

• Concrete material model approximated with Popovic’s model

• DIF models same as numerical model • Correct DIF required iterative process Normal Strength Panel Strengths

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Analytical Model – Moment Curvature & Boundary Conditions 26

Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

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-100

0

100

200

300

400

-0.02 -0.01 0 0.01 0.02 0.03

Mo

men

t [k

ip-i

n]

Curvature [1/in]

• Obtained through fiber-analysis • Independent of boundary

conditions

Simple-Simple

KLM=0.78

Fixed-Fixed

KLM=0.77

Hinge @ Center

KLM=0.64Mechanism

KLM=0.66

Boundary conditions change as panel deflects due to support gap and panel yielding

3"

4"

BLAST LOAD0.25"

BLAST LOAD

SEC A-A

SEC A-A

52"

SEC A-A Deformed

Simple-Simple

KLM=0.78

Fixed-Fixed

KLM=0.77

Simple-Simple

KLM=0.78Mechanism

KLM=0.66

Normal Strength Panel

High strength panel:

hinging occurs at ends

before center

Normal Strength Panel

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Analytical Model – SDOF Approach & Results 27

Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

cjn3@lehigh.edu

Normal Strength Panel Resistance Function

Simple-Simple

KLM=0.78

Fixed-Fixed

KLM=0.77

Hinge @ Center

KLM=0.64Mechanism

KLM=0.66

0

5

10

15

20

25

30

35

40

0 0.5 1 1.5 2 2.5 3

Res

ista

nce

[p

si]

Deflection [in]

Simp-Simp

0

5

10

15

20

25

30

35

40

0 0.5 1 1.5 2 2.5 3

Res

ista

nce

[p

si]

Deflection [in]

Simp-Simp

Fixed-Fixed

0

5

10

15

20

25

30

35

40

0 0.5 1 1.5 2 2.5 3

Res

ista

nce

[p

si]

Deflection [in]

Simp-Simp

Fixed-Fixed

0

5

10

15

20

25

30

35

40

0 0.5 1 1.5 2 2.5 3

Res

ista

nce

[p

si]

Deflection [in]

Switches to Fixed

Simp-Simp

Fixed-Fixed

0

5

10

15

20

25

30

35

40

0 0.5 1 1.5 2 2.5 3

Res

ista

nce

[p

si]

Deflection [in]

Switches to Fixed

Hinge @ Center

Simp-Simp

Fixed-Fixed

0

5

10

15

20

25

30

35

40

0 0.5 1 1.5 2 2.5 3

Res

ista

nce

[p

si]

Deflection [in]

Switches to FixedHinge @ CenterHinges @ Ends

Simp-Simp

Fixed-Fixed

0

5

10

15

20

25

30

35

40

0 0.5 1 1.5 2 2.5 3

Res

ista

nce

[p

si]

Deflection [in]

Switches to FixedHinge @ CenterHinges @ Ends

Simp-Simp

Fixed-Fixed

Simple-Simple

KLM=0.78

Fixed-Fixed

KLM=0.77

Hinge @ Center

KLM=0.64Mechanism

KLM=0.66

Simple-Simple

KLM=0.78

Fixed-Fixed

KLM=0.77

Hinge @ Center

KLM=0.64Mechanism

KLM=0.66

Simple-Simple

KLM=0.78

Fixed-Fixed

KLM=0.77

Hinge @ Center

KLM=0.64Mechanism

KLM=0.66

1

2

3

4

5

Analytical Model – SDOF Approach & Results 28

Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

cjn3@lehigh.edu

0

5

10

15

20

25

30

35

40

0 0.5 1 1.5 2 2.5 3

Res

ista

nce

[p

si]

Deflection [in]

Switches to FixedHinge @ CenterHinges @ Ends

Simp-Simp

Fixed-Fixed

Normal Strength Panel High Strength Panel

0

20

40

60

80

100

120

0

1

2

3

4

5

0 25 50 75 100 125 150

Def

lect

ion

[m

m]

Def

lect

ion

[in

]

Time [ms]

Load 1 Avg Residual

Load 2 Avg Residual

0

10

20

30

40

50

60

70

0

0.5

1

1.5

2

2.5

3

0 25 50 75 100 125 150

Def

lect

ion

[m

m]

Def

lect

ion

[in

]

Time [ms]

Load 1 Avg ResidualLoad 2 Avg Residual

Results

0

10

20

30

40

50

60

70

0 0.5 1 1.5 2 2.5 3 3.5 4

Res

ista

nce

[p

si]

Deflection [in]

Switches to FixedHinges @ EndsHinge @ Center

Simp-Simp

Fixed-Fixed

1

2

3

4

5

Analytical versus Experimental 29

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cjn3@lehigh.edu

1

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Presentation outline

Introduction 1

Finite Element Model 2

Analytical Model 3

Conclusions 4

Questions/References 5

30

Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

cjn3@lehigh.edu

1

2

3

4

5

Upper support

Down support

Conclusions (1) 31

Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

cjn3@lehigh.edu

- Use the symmetry when possible in order to reduce the

computational cost and to improve the quality of the mesh.

- The CSCM (mat 159 LS-Dyna®) for concrete is appropriate for

modeling component responding with flexural mechanism.

- The reinforcements should be modeled by beam elements in order

to be able to carry shear stresses; this is crucial for component with

thin cross section.

- In this case the boundary conditions have a crucial importance.

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Conclusions (2) 32

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cjn3@lehigh.edu

Simple-Simple

KLM=0.78

Fixed-Fixed

KLM=0.77

Hinge @ Center

KLM=0.64Mechanism

KLM=0.66

Simple-Simple

KLM=0.78

Fixed-Fixed

KLM=0.77

Simple-Simple

KLM=0.78Mechanism

KLM=0.66

Cross Section of Slab

Fiber Analysis of Section

- Analytical methods proved accurate when

compared to numerical methods

- Increasing the material strengths of the panel

affected the progression of hinge formation

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Conclusions (3) 33

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cjn3@lehigh.edu

0

20

40

60

80

100

120

0

1

2

3

4

5

0 25 50 75 100 125

Def

lect

ion

[m

m]

Def

lect

ion

[in

]

Time [ms]

Analytical Numerical

- Analytical methods provide close results to numerical methods. This

is useful for a quick check of results before performing a detailed

design.

- For more detailed analysis, such as crack patterns, numerical

methods are required 33.75 in. (857 mm)

64

in. (

16

25

mm

)

33.75 in. (857 mm)

64

in. (

16

25

mm

)

1

2

3

4

5

Presentation outline

Introduction 1

Finite Element Model 2

Analytical Model 3

Conclusions 4

Questions/References 5

34

Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

cjn3@lehigh.edu

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5

Questions 35

Olmati, Trasborg, Sgambi, Naito, Bontempi Sapienza University of Rome & Lehigh University

cjn3@lehigh.edu

• Kaba, S., Mahin, S., “Refined Modeling of Reinforced Concrete Columns for Seismic Analysis,” Nisee e-library, UCB/EERC-84/03, 1984, http://nisee.berkeley.edu/elibrary/Text/141375

• Lawrence Software Technology Corporation (LSTC). LS-DYNA theory manual. California (US), Livermore Software Technology Corporation.

• U.S. Department of Transportation, Federal Highway Administration. Users Manual for LS-DYNA Concrete, Material Model 159.

• Olmati P, Trasborg P, Naito CJ, Bontempi F. Blast resistance of reinforced precast concrete walls under uncertainty. International Journal of Critical Infrastructures 2013; accepted

References

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Placement

• Normal Strength – Numerical Prediction (LS-Dyna) – 1st place

• Normal Strength – Analytical Prediction (SDOF) – 2nd place

• High Strength – Analytical Prediction (SDOF) – 3rd place (unofficial)

• High Strength – Numerical Prediction (LS-Dyna) – Not released