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FINITE ELEMENT ANALYSIS AND EXPERIMENTAL COMPARISON OF
DOUBLY REINFORCED CONCRETE SLABS SUBJECTED TO BLAST LOADS
A THESIS IN Civil Engineering
Submitted to the Faculty of the University of Missouri-Kansas City in partial fulfillment of
the requirements for the degree of
MASTER OF SCIENCE
by
Anirudha Kadambi Vasudevan
Bachelor of Engineering Civil Engineering
University Visveswaraya College of Engineering India
University of Missouri-Kansas City
2012-13
Copyright © by Anirudha Kadambi Vasudevan
2011-12
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FINITE ELEMENT ANALYSIS AND EXPERIMENTAL COMPARISON OF
DOUBLY REINFORCED CONCRETE SLABS SUBJECTED TO BLAST LOADS.
Anirudha Kadambi Vasudevan, Candidate for the Master of Science Degree
University of Missouri-Kansas City
ABSTRACT
In the design of concrete structures, it has become important to understand the
response of concrete as a structural material when subjected to large stresses and strain rates
through explosive loadings. In order to do that, any researcher has to study the dynamic
nonlinear responses of individual structural components like beams, slabs, and columns of an
entire building system. Also, advances in finite element modeling and analysis have further
enhanced interest in studying the behavior and response of these individual components
towards dynamic loadings and arrive at certain answers that can make them stronger and
consequently serve the primary purpose of saving lives of people.
The primary objective of this research is to study numerically, the response of both
high strength concrete and normal strength concrete panels reinforced with double mat high
strength low alloy vanadium (HSLA-V) reinforcement. A numerical validation by comparing
with experimental data , using two pre-defined concrete material models namely, Winfrith
Concrete Model and Concrete Damage Model Release 3 in LSDYNA is performed in order
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to study the model capabilities and limitations of the models so that these material models
may be used as an alternative to expensive field testing for blast protection in structures.
From the study it was concluded that, both the models gave deflection values that
compared well with the experimental results in the normal strength (4 ksi) concrete category.
However, the Winfrith Concrete Model provided a better response in terms of deflection and
crack propagation than the Concrete Damage Model Release 3 in the high strength concrete
(15.5 ksi) category.
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APPROVAL PAGE
The faculty listed below, appointed by the Dean of the School of Computing and
Engineering, have examined a thesis titled “Finite Element Analysis And Experimental
Comparison of Doubly Reinforced Concrete Slabs Subjected To Blast Loads.” presented by
Anirudha Kadambi Vasudevan , candidate for the Master of Science degree, and certify that
in their opinion it is worthy of acceptance.
Supervisory Committee
Ganesh Thiagarajan, Ph. D., P.E., Committee Chair Department of Civil and Mechanical Engineering
Ceki Halmen, Ph.D. Department of Civil and Mechanical Engineering
ZhiQiang Chen, Ph.D. Department of Civil and Mechanical Engineering
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TABLE OF CONTENTS
ABSTRACT………................................................................................................................iii
LIST OF ILLUSTRATIONS…………………………………………………………………ix
LIST OFTABLES…………………………………………………………………………..xiii
ACKNOWLEDGEMENTS…………………………………………………………….......xiv
Chapter 1: INTRODUCTION
1.1 Literature Survey ...............................................................................................2
1.2 Objective ............................................................................................................6
1.3 Scope ..................................................................................................................7
1.4 Thesis Organization.................................................................................…...10
Chapter 2: EXPERIMENTAL PROGRAM
2.2 Rationale behind Using HSLA-V Rebar .........................................................11
2.3 Experimental Data ...........................................................................................13
Chapter 3: NUMERICAL MODELING
3.1 Model Boundary Conditions.............................................................................20
3.2 LSDYNA Material Models.......................................................................…...21
3.3 Blast Load Application ....................................................................................23
3.4 Constrained Lagrange in Solid Formulation .....................................................25
3.5 Damage and Crack Analysis .............................................................................26
Chapter 4: NUMERICAL RESULTS AND EXPERIMENTAL COMPARISONS
4.1 Normal Strength Concrete with HSLA-V Rebar (NSC-VR) ...........................28
4.1.1 With Constrained Lagrange in Solid……………………… .........…29
4.1.2 Without Constrained Lagrange in Solid ...........................................31
4.1.3 Overall Observations .........................................................................33
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4.1.3.1 Mesh Size Study .................................................................34
4.1.3.2 Concrete Material Model Study………………………...…34
4.1.3.3 Constrained Lagrange in Solid Study .................................35
4.1.3.4 Crack propagation Study ....................................................35
4.2 Normal Strength Concrete with Conventional Rebar (NSC-NR) .....................39
4.2.1 Deformation Results………………………………… ..................…39
4.2.2 Overall Observations .........................................................................41
4.2.2.1 Mesh Size Study .................................................................42
4.2.2.2 Concrete Material Model Study………………………..…42
4.2.2.3Crack propagation Study .....................................................42
4.3 High Strength Concrete with Conventional Rebar (HSC-NR) .........................44
4.3.1 Deformation Results………………………………… ..................…45
4.3.2 Overall Observations .........................................................................46
4.3.2.1 Mesh Size Study .................................................................47
4.3.2.2 Concrete Material Model Study………………………..…47
4.3.2.3 Crack propagation Study ....................................................47
4.4 High Strength Concrete with HSLA-V Rebar (HSC-VR) ................................49
4.4.1 Deformation Results………………………………… ..................…50
4.4.2 Overall Observations .........................................................................51
4. 4.2.1 Mesh Size Study ................................................................53
4.4.2.2 Concrete Material Model Study………………………..…53
4.4.2.3 Crack propagation Study ....................................................53
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Chapter 5: ANALYSIS OF RESULTS
5.1 Behavior of High Strength Materials Compared with Conventional.................55
5.2 Effect of Mesh Sizes..........................................................................................56
5.3 Material Model Comparison..............................................................................56
5.4 Comparison of Damage and Crack Patterns......................................................57
Chapter 6: CONCLUSIONS
6.1 Conclusions.......................................................................................................59
6.2 Future Work......................................................................................................61
Appendix A: Summary of Tables............................................................................................62
Appendix B: Input File Descriptions.......................................................................................68
REFERENCES........................................................................................................................72
VITA........................................................................................................................................74
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LIST OF ILLUSTRATIONS
Figure Page
2.1: BLS shock tube used for experimental studies (Courtesy: US Army ERDC)..................11
2.2: Stress vs. Strain behavior of conventional reinforcement and vanadium reinforcement
(Courtesy: US Army ERDC)...................................................................................................12
2.3: Pressure and impulse histories for slab HSC-NR (Courtesy: US Army ERDC)..............14
2.4: Pressure and impulse histories for slab HSC-VR (Courtesy: US Army ERDC)..............14
2.5: Pressure and impulse histories for slab NSC-NR (Courtesy: US Army ERDC)..............15
2.6: Pressure and impulse histories for slab NSC-VR (Courtesy: US Army ERDC)..............15
2.7: Concrete slab in plan and its dimensions (Courtesy: US Army ERDC)..........................16
2.8: Concrete slab at section A-A with double-mat reinforcement.........................................16
3.1: Reinforced Concrete Slab Model with Solid Elements....................................................19
3.2: Double layer Steel Reinforcement Modeled as Hughes-Liu beam Elements..................19
3.3: Boundary conditions on the top and bottom faces...........................................................20
3.4: Boundary conditions on the back face..............................................................................24
3.5: Boundary conditions at the front face of the slab.............................................................24
3.6: Blast Load Applied Uniformly on the Slab..................................................................... 24
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4.1: Deflection Comparison for 1 in. (25.4) Mesh Size with Constrained Lagrange in
Solid........................................................................................................................................ 29
4.2: Deflection Comparison for 0.5 in.(12.7 mm) mesh size with Constrained Lagrange in
Solid.........................................................................................................................................30
4.3: Deflection Comparison for 1 in.(25.4 mm) Mesh Size without Constrained Lagrange in
Solid.........................................................................................................................................32
4.4: Deflection Comparison for 0.5 in. (12.7 mm) Mesh Size without Constrained Lagrange
in Solid.....................................................................................................................................33
4.5: Cracks obtained during the experiment............................................................................36
4.6: Cracks from Winfrith Concrete Model with 1 in.(25.4mm) mesh size........................... 36
4.7: Cracks obtained during the experiment............................................................................37
4.8: Cracks obtained from Concrete Damage Model Release 3 with 1 in.(25.4 mm )mesh
size...........................................................................................................................................37
4.9: Cracks obtained from Concrete Damage Model Release 3 with ½ in.(12.7 mm) mesh
size...........................................................................................................................................38
4.10: Cracks obtained from Concrete Damage Model Release 3 with ¼ in.(6.35mm) mesh
size...........................................................................................................................................38
4.11: Deflection Comparison for 1 in. (25.4 mm) Mesh Size with Constrained Lagrange in
Solid.........................................................................................................................................40
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4.12: Deflection Comparison for 0.5 in. (12.7 mm) Mesh Size with Constrained Lagrange in
Solid........................................................................................................................................ 41
4.13: Cracks obtained during the experiment..........................................................................43
4.14: Cracks from Winfrith Concrete Model with 1 in.(25.4 mm) mesh size........................ 43
4.15: Cracks obtained from Concrete Damage Model Release 3 with ¼ (6.35 mm)in. mesh
size...........................................................................................................................................44
4.16: Deflection Comparison for 1 in. (25.4 mm) Mesh Size with Constrained Lagrange in
Solid.........................................................................................................................................45
4.17: Deflection Comparison for 0.5 in. (12.7 mm) Mesh Size with Constrained Lagrange in
Solid.........................................................................................................................................46
4.18: Cracks obtained during the experiment..........................................................................48
4.19: Cracks from Winfrith Concrete Model with 1 in.(25.4 mm) mesh size.........................48
4.20: Cracks obtained from Concrete Damage Model Release 3 with 1/4 in.(6.35 mm) mesh
size...........................................................................................................................................49
4.21: Deflection Comparison for 1 in.(25.4 mm) Mesh Size with Constrained Lagrange in
Solid.........................................................................................................................................50
4.22: Deflection Comparison for 0.5 in. (12.7 mm) Mesh Size with Constrained Lagrange in
Solid.........................................................................................................................................51
4.23: Cracks obtained during the experiment..........................................................................53
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4.24: Cracks from Winfrith Concrete Model with 1 in.(25.4 mm) mesh size.........................53
4.25: Cracks obtained from Concrete Damage Model Release 3 with 1/4 in.(6.35 mm) mesh
size...........................................................................................................................................54
B1: Input and Output Control Parameters...............................................................................68
B2: Input parameters for Concrete Damage Model Release 3................................................69
B3: Input parameters generated by Concrete Damage Model Release 3...............................69
B4: Input Parameters for Winfrith Concrete Model for 4 ksi Concrete..................................70
B5: Input Parameters for Plastic Kinematic Model.................................................................70
B6: Input parameters for Constrained Lagrange in Solid Formulation...................................70
B7: Input parameters for Mat Add Erosion Material Model...................................................71
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LIST OF TABLES
Table Page
A1: Input Parameters for Concrete Damage Model Release 3................................................62
A2: Input Parameters for Winfrith Concrete Mode.................................................................63
A3: Input Parameters for Volume Compaction Curve in the Winfrith Concrete Model for
15.5 ksi and 4 ksi Concretes....................................................................................................64
A4: Input Parameters for Plastic Kinematic Model for Steel Rebar.......................................65
A5: Analytical and Experimental Deflection Summary..........................................................66
A6: Percentage comparison of deflections with experimental value.......................................66
A7: Percentage change in deflection when the mesh size was reduced from 1 in. (25.4 mm)
to 1/2 in. (12.7 mm).................................................................................................................67
xiv
ACKNOWLEDGEMENTS
This is a great opportunity to express my deep and sincere gratitude to my advisor,
Dr. Ganesh Thiagarajan, for his continuous guidance, support, and motivation during the last
two years. I would also like to thank Dr. Ceki Halmen and Dr. Zhiqiang Chen for serving on
the graduate committee.
I would like to mention my lab colleagues Dr. Yun Kai Lu, Sheetal Ajgaonkar,
Meenakshi Mishra, Vivek Reddy, Sampath Bhashyam, Rasekh Rahimzadeh, Jitesh
Nalagotla, and Gunjan Shetye for the fun and memorable moments that we cherished
together at the Computational Mechanics lab.
I owe my loving thanks to my parents and family members for their encouragement,
patience, and understanding throughout my studies abroad. I would also like to thank my
family members and friends for their loving support.
I gratefully acknowledge the financial support provided by the National Science
Foundation through award Number 0748085.
1
CHAPTER 1
INTRODUCTION
Recent aggressor attacks such as the Oklahoma City bombing on April 19th, 1995 and
the September 11, 2001 attacks, on structures has led researchers to probe into the aspects of
making buildings and other socio economically vital structures strong enough to withstand
extreme loadings, and in this context, explosions. Furthermore, it becomes important to
understand the response of concrete as a structural material when subjected to large stresses
and strain rates through explosive loadings. In order to do that, any researcher has to study
the dynamic nonlinear responses of individual structural components like beams, slabs, and
columns of an entire building system. Also, advances in finite element modeling and analysis
have further enhanced interest in studying the behavior and response of these individual
components towards dynamic loadings and arrive at certain answers that can make them
stronger and consequently serve the primary purpose of saving lives of people. Researchers
studying the numerical response often tend to use finite element codes which vary from
advanced hydrodynamic codes often used by army researchers to commercially available
codes such as ABAQUS® and LSDYNA® amongst others.
Experimental and numerical analysis can be performed on steel reinforced concrete
elements. However, experimental analysis requires a lot of equipment, man power, and has
security issues too. Numerical analysis of the dynamic behavior of steel reinforced concrete
when subjected to the extreme loadings can be studied using the non-linear finite element
software such as ABAQUS® and LS-DYNA®. LS-DYNA® has number of features that
makes it suitable for blast loading type simulations and has been used in this study.
2
The numerical modeling effort focused on using LS-DYNA® and attempting the
simulation using two commercially available material models. Results from the numerical
simulation are compared with the experimental values in order to determine the accuracy of
the models. The concrete material models considered were Winfrith Concrete Model[12] and
Concrete Damage Model Release 3[7].
The experimental work was performed by Torres Alamo, J O. under the guidance of
Robert, S at the U.S Army Engineering and Research and Development Center, Vicksburg ,
MS. The experimental effort involved the fabrication and testing of four types of reinforced
concrete panels namely High Strength Concrete with HSLA-V Steel Reinforcing bars (HSC-
VR), High Strength Concrete with Conventional Steel Reinforcing bars (HSC-NR), Normal
Strength Concrete with HSLA-V Steel Reinforcing bars (NSC-VR), and Normal Strength
Concrete with Conventional Steel Reinforcing bars (NSC-NR). The panels were subjected to
blast loadings using the Blast Loading Simulator (shock tube) at the U.S. Army Engineering
Research and Development Center, Vicksburg; MS. Data recorded included pressures at
various locations, mid-span displacements from accelerometers and laser devices, concrete
surface stresses and observed damage patterns.
1.1 Literature Survey
Several numerical blast analyses work with an explicit non-linear dynamic finite
element code LS-DYNA has been reported in literature. LS-DYNA (version 971)[1] has
several concrete material models. The concrete models available include (the notation in
parentheses indicates the keyword used to invoke them in LS-DYNA)[1].
a) Modified Soil Model Applied to Concrete (mat_soil_concrete, MAT 78),
b) Winfrith Concrete Model (mat_winfrith_concrete, MAT 84)
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c)Winfrith Concrete Model with Reinforcement (mat_winfrith_concrete_reinforcement, MAT 85)
d) Holmquist Johnson Concrete Model (mat_johnson_holmquist_concrete, MAT 111)
e) Continuous Surface Cap Model (mat_cscm, MAT 159)
f) Continuous Surface Cap Model for Concrete (mat_cscm_concrete, MAT 159)
g) Eurocode based Concrete Material Model (mat_concrete_ec2, MAT 172)
h) Karagozian and Case Concrete Damage Model Release 3 (mat_concrete_damage_rel3, MAT 72 R3)
Of all these concrete material models, Karagozian and Case Concrete Damage Model
Release 3[7] and Winfrith Concrete Model[12] have been chosen for this study. This choice
was based on the conclusions of a preliminary work done by Yaramada (2010)[2] in our
laboratory using several of the models listed above.
Unified Facilities Criteria (UFC) 3-340-02[3] presents methods of design for
protective construction used in facilities for development, testing, production, storage,
maintenance, modification, inspection, demilitarization, and disposal of explosive materials.
In doing so, it establishes design procedures and construction techniques whereby
propagation of explosion (from one structure or part of a structure to another) or mass
detonation can be prevented and personnel and valuable equipment can be protected. Chapter
2 of the document provides information on the effect of external blast loads on structures.
Furthermore, information regarding the various pressures generated such as incident pressure
and reflected pressure generated during a blast wave is presented.
Ganchai et al.[4] presented results that compared numerical simulation results with
experimental responses of concrete panels subjected to blast loading. LS-DYNA was used in
the numerical analysis for blast load and Concrete Damage Model Release 3 was used to
4
define the concrete material properties. In the study, the results showed that the maximum
deflection obtained from LS-DYNA was17 % less than experimental values.
Hao et al.[5] conducted a study of the dynamic behavior of reinforced concrete (RC)
slabs and factors that influence the behavior, such as the concrete strength ratio, slab
thickness, steel reinforcement ratio when subjected to the blast loading. The analysis was
performed using LS-DYNA and based on this numerical analysis principles for blast-
resistant design are proposed, such as increasing the slab thickness which is preferred over
concrete strength enhancement, to improve the behavior of RC slabs subjected to blast
loading.
Broadhouse.B.J[6] has presented theoretical information on the Winfrith Concrete
Model. He also describes the various input parameters in the model and the effect of strain
rate enhancement. In the latter part of his paper, he describes the methodology to output
cracks in LS-DYNA also. An example problem is also provided to understand the various
concepts explained in the paper. This paper provides enough information to use the Winfrith
Concrete Model with its crack plotting capability to study the behavior of concrete under
various load and stress conditions.
Material type 72R3 (concrete damage REL3) [7] is a three-invariant model, uses three
shear failure surfaces, includes damage and strain-rate effects, and has origin based on the
Pseudo-Tensor Model (Material Type 16).[1] The model has the inbuilt ability to generate the
required model input parameters based on providing the unconfined compressive strength
alone. Model details and its applicability to blast simulations are described in Malvar et al [7].
The Concrete Damage REL 3 material model provides no direct way to turn the strain rate
5
effect on or off. Instead, user should define and include the strength enhancement versus
strain rate curve in the program.
Sangi et al.[8] have compared the behavior of the reinforced concrete slabs with
Winfrith Concrete Model and Concrete Damage Model Release 3, when subjected to drop
weights. Impact tests were done on six reinforced concrete slabs of which the dimensions of
four slabs were 30 in. square (775 mm square) and 3 inch (76 mm) thick and two were 91 in.
square (2320 mm square) and 6 inch (150 mm) thick. The results obtained from the
experimental output were compared with the two models from LS- DYNA. From this study,
they concluded that the damage pattern obtained from the Winfrith Concrete Model was in
agreement with the experiment. Also, the impact force histories obtained from the
experiment was in agreement with both the models. They also have suggested the use of
these two models for finite element studies on reinforced concrete slabs.
Algaard et al.[9] have performed perforation studies by evaluating low velocity
impacts of heavy objects on reinforced concrete floor slabs. An explicit finite element
analysis has been performed in LSDYNA using non-linear material properties for both steel
and concrete. Winfrith Concrete and Winfrith Concrete Reinforcement Models are used to
model the reinforced concrete slab along with Mat_Add_Erosion option to simulate failure.
The finite element (FE) analysis is then validated with an empirical approach and an
experimental program performed at Heriot-Watt University. The authors have concluded that
there was a very good correlation of results between the FE analysis, empirical approach and
the experimental program.[9]
Xu et al.[10] have presented a numerical simulation study on the concrete spallation in
reinforced concrete slabs under various blast loading and structural conditions. The Pseudo-
6
Tensor concrete material model[1] is employed, taking into account the strain rate effect. The
erosion technique is adopted to model the spallation process. The principal tensile strain is
adopted as the criteria for erosion in the numerical simulation. From this study, the authors
have concluded that the simulation results using the erosion criterion mentioned above for
concrete spallation show a consistent comparison with the relevant experimental
observations.
Torres Alamo, J O.[11] conducted experiments on ten doubly reinforced concrete slabs
at the U.S. Army Engineering Research and Development Center, Vicksburg; MS. The
objective of the experiments was to investigate the potential weight, space, cost savings and
system improvements in the form of protection level resulting from the substitution of high-
performance materials for conventional materials when the slabs are subject to blast loads.
Based on these experimental results, he concluded that the use of high strength concrete and
doubly reinforced HSLA-V reinforcement gave a good combination of protection level. This
experimental report has been used in this thesis for validating the material models.
1.2 Objective
The primary objective of this research is to study numerically, the response of both
high strength concrete and normal strength concrete panels reinforced with double mat high
strength low alloy vanadium (HSLA-V) reinforcement. An experimental validation using
two pre-defined concrete material models namely, Winfrith Concrete Model and Concrete
Damage Model Release 3 in LSDYNA is performed in order to study their capabilities and
limitations of the models so that these material models may be used as an alternative to
expensive field testing for blast protection in structures
7
1.3 Scope
The scope of the work is outlined below,
a) To perform explicit finite element analysis is done in LSDYNA on a 64 in. (1625
mm) × 34 in. (864 mm) × 4 in. (101.6 mm) reinforced concrete panel with double mat
reinforcement to evaluate the performance of high strength materials when subjected
to extreme loading conditions such as explosions.
b) Study four types of reinforced concrete panels namely High Strength Concrete with
HSLA-V Steel Reinforcing bars (HSC-VR), High Strength Concrete with
Conventional Steel Reinforcing bars (HSC-NR), Normal Strength Concrete with
HSLA-V Steel Reinforcing bars (NSC-VR), and Normal Strength Concrete with
Conventional Steel Reinforcing bars (NSC-NR) were chosen from the experiments.
c) Uses two predefined concrete models namely Winfrith Concrete Model and Concrete
Damage Model Release 3 were chosen in LS-DYNA® for comparing the numerical
behavior of the above mentioned panel types.
d) Study numerical models with two mesh sizes such as 1 in. (25.4 mm); ½ in. (12.7
mm) to perform mesh size sensitivity studies. Also, ¼ in. (6.35 mm) mesh size
models were used for qualitative comparison of cracks developed on the panel.
e) Compare the deformation and damage results from the panels obtained from the
Shock Tube experiments with the results from the numerical models developed using
LSDYNA.
f) Perform crack propagation studies on the numerical models to understand the slab’s
tolerance to damage and the spalling mechanisms, and compare with the damage
patterns obtained from the experiment.
8
g) Draw conclusions related to high strength materials and the two numerical material
models based on this study and recommendations for future work .
1.4 Thesis Organization
a) Chapter 2 gives a detailed description of the experimental program associated with
this research. The information presented in this chapter includes the experimental set
up, the reason behind the use of HSLA-V reinforcement and the details of the
reinforced concrete slab. This experimental study was not part of the thesis and was
performed by army researchers and the data obtained from them is used here as a
collaborative work.
b) Chapter 3 provides information regarding the numerical modeling procedure which
includes the theoretical basis of the two pre-defined models in LS-DYNA and the
parameters used as input. It also gives information regarding the boundary conditions
and various other assumptions used in the modeling and analysis of the RC slab.
c) Chapter 4 provides details on the results and observations of the two concrete models
with and without the use of Constrained Lagrange in Solid (CLS) formulation and for
two different mesh sizes 1 in. (25.4 mm) and ½ in. (12.7 mm) and these have been
compared with the experimental observations.
d) Chapter 5 is the analysis of the observations and results obtained from Chapter 4. The
behavior of the two pre-defined models in LSDYNA have been compared and
discussed.
9
e) Chapter 6 is written to discuss the various conclusions that can be deduced from the
observations and the experimental comparisons. It also provides brief information
regarding the future work.
10
CHAPTER 2
EXPERIMENTAL PROGRAM
Dynamic testing of ten 1/3 scale reinforced concrete panels was performed using the
Blast Load Simulator (BLS) at ERDC-Vicksburg[11]. The experimental work is not a part of
the thesis and is described here in order to outline the parameters and input used for
numerical comparison. This experimental study was not part of the thesis and was performed
by Torres Alamo, J O. under the guidance of Robert, S at the U.S Army Engineering and
Research and Development Center, Vicksburg , MS. and the data obtained from them is used
here as a collaborative work.
The Blast Load Simulation (BLS) system, as shown in Figure 2.1, is a mechanical
device capable of subjecting targets to dynamic loads representative of blast waves. The
purpose of the BLS system is to generate realistic blast pulses on a target with peak pressures
and impulses considered representative of blast environments. The system provides the
ability to generate pulses with time-histories representative of a variety of blast waves,
including negative phase parameters.
The reinforced concrete panels used for the study consisted of double mat
conventional Grade 60 reinforcement or High Strength Low Alloy –Vanadium (HSLA-V)
reinforcement in combination with 4 ksi (27.6 MPa) or 15.5 ksi (107 MPa) concrete. Tests
were performed using varying blast pressures and impulses to determine the performance of
the different reinforced concrete slab combinations. The center span deflection, average blast
pressure, and average impulse were recorded.
2.1 Rationale Behind Using High Strength Low Alloy
The most common procedure to mitigate blast effects on buildings is to add more
mass to it and to use high strength concrete. However, in addition to high strength concrete, it
is important to use reinforcement which retain its ductility with increased str
system and provide a balanced cross sectional behavior. The use of
Alloy-Vanadium (HSLA-V)
protection level in structures.
Figure 2.1
11
High Strength Low Alloy-Vanadium (HSLA-V)
The most common procedure to mitigate blast effects on buildings is to add more
mass to it and to use high strength concrete. However, in addition to high strength concrete, it
is important to use reinforcement which retain its ductility with increased str
system and provide a balanced cross sectional behavior. The use of High Strength Low
) steel reinforcement is seen as an alternative
.
2.1: BLS shock tube used for experimental studies(Courtesy: US Army ERDC) [11]
) Reinforcement.
The most common procedure to mitigate blast effects on buildings is to add more
mass to it and to use high strength concrete. However, in addition to high strength concrete, it
is important to use reinforcement which retain its ductility with increased strength to the
High Strength Low
steel reinforcement is seen as an alternative to improve the
: BLS shock tube used for experimental studies
12
A comparison of the stress vs. strain curves (Figure 2.2) obtained from the ASTM E8-
01 testing standards show that the yield strength of vanadium steel reinforcement is 83 ksi
(572 MPa), which is greater than that of the conventional reinforcement which has yield
strength of 60 ksi (415 MPa). Also, it can be seen that the failure strain of HSLA-V
reinforcing bar is slightly higher than that of conventional reinforcing bar. From the Figure
2.2, it can be concluded that the introduction of vanadium into the chemical composition of a
steel reinforcement bar has the advantages of increased strengths without compromising on
ductility or formability and has good fracture toughness and weldability.
Figure 2.2: Stress vs. Strain behavior of conventional reinforcement and vanadium reinforcement. (Courtesy: US Army ERDC)
0
138
276
414
552
690
828
0
20
40
60
80
100
120
0 5 10 15
Str
ess
(MP
a)
Str
ess
(ksi
)
Strain (%)
HSLA-V and Conventional #3 Reinforcement (Stress vs Strain)
Conventional (60 ksi)
ReinforcementHSLA-V Reinforcement
13
2.3 Experimental Data
Four slabs were considered for the study from a matrix of ten for numerical studies
performed in this thesis, due to symmetry in configuration. The following nomenclatures are
used to designate each slab for convenience of use.
a) High Strength Concrete with HSLA-V Steel Reinforcing bars (HSC-VR).
b) High Strength Concrete with Conventional Steel Reinforcing bars (HSC-NR).
c) Normal Strength Concrete with HSLA-V Steel Reinforcing bars (NSC-VR).
d) Normal Strength Concrete with Conventional Steel Reinforcing bars (NSC-NR).
The data recorded from the experimental program included pressures at various
locations, mid-span displacements from accelerometers and laser devices, and observed
damage patterns. The basic input data that were used for the numerical simulations were the
pressure vs. time plots. Figures 2.3 to 2.6 provide pressure and impulse histories recorded
from the slabs under consideration. These pressure histories were digitized using a standard
graph digitizing software and the pressure vs. time values obtained from the graphs were
added to the LS-DYNA input deck and the pressure was distributed uniformly over the entire
face of the slab.
14
Figure 2.3: Pressure and impulse histories for slab HSC-NR(Courtesy: US Army ERDC) [11]
Figure 1.4 : Pressure and impulse histories for slab HSC-VR(Courtesy: US Army ERDC) [11]
IMPULSE,
Psi- mse
c
PRESSURE, Psi
TIME, msec
PRESSURE, Psi
IMPULSE,
Psi- mse
c
TIME, msec
965 Psi-msec
56 Psi
1091 Psi-msec 58.7 Psi
15
Figure 2.6: Pressure and impulse histories for slab NSC-VR (Courtesy: US Army ERDC) [11]
Figure 2.5: Pressure and impulse histories for slab NSC-NR (Courtesy: US Army ERDC) [11]
PRESSURE, Psi
PRESSURE, Psi
IMPULSE,
Psi- mse
c
IMPULSE,
Psi- mse
c
TIME, msec
TIME, msec
1118 Psi-msec 56.9 Psi
1061 Psi-msec 56.5 Psi
The rectangular reinforced concrete slab
(1652 mm x 863mm x 101.6 mm)
reinforcement bars of size 3/8”
were used at a spacing of 4 in. (101.6 mm) on centers and the shrinkage steel reinforcement
were used at 12 in. (304.8mm) on centers.
Figure 2.7: Concrete slab in plan and its dimensions
4” (101.6 mm)
12” (304.8
4” (101.6 mm)
Figure 2.8: Concrete slab at section
1” (25.4 mm)
2” (50.8 mm)
16
The rectangular reinforced concrete slab with the dimensions 64 in.
(1652 mm x 863mm x 101.6 mm) as shown in Figure 2.7 was used in the experiments
of size 3/8” (# 3 bars) were used in the slab. The main steel reinforcement
spacing of 4 in. (101.6 mm) on centers and the shrinkage steel reinforcement
at 12 in. (304.8mm) on centers.
Concrete slab in plan and its dimensions (Courtesy: US Army ERDC)
64” (1652 mm)
12” (304.8 mm)
34” (863 mm)
Concrete slab at section A-A with double-mat reinforcement.
A
A
dimensions 64 in. x 34 in. x 4 in.
was used in the experiments. Steel
in the slab. The main steel reinforcement
spacing of 4 in. (101.6 mm) on centers and the shrinkage steel reinforcement
(Courtesy: US Army ERDC)
34” (863 mm)
mat reinforcement.
1” ( 25.4 mm)
1” ( 25.4 mm)
17
The concrete slab with the dimensions shown in Figures 2.7 and 2.8 was subject to
blast pulses from pre-determined charge weights and stand-off distances and the peak
pressures and impulses as shown in Figures 2.3 to 2.6 were recorded along with center span
deflections. These recorded values were later used in the numerical modeling and validation
phase of the thesis.
18
CHAPTER 3
NUMERICAL MODELING
The primary objective of this thesis is to study the differences in behavior of
reinforced concrete slabs using combinations of normal strength concrete and high strength
concrete along with two different types of steel reinforcement. This objective is achieved by
comparing numerical simulations with the experimental data outlined in the previous section
in LS-DYNA and validation of the pre-defined concrete and steel material models. The
numerical model, its geometry, loading conditions and the model boundary conditions are
described in this chapter.
The numerical model consists of a rectangular reinforced concrete slab modeled with
eight noded hexahedron elements .The constant stress solid element formulation was used
with a uniform mesh size of 1 in. (25.4 mm), ½ in. (12.7 mm) and ¼ in. (6.35 mm), with
dimensions being 64 in. × 34 in. x 4 in. (1652 mm x 863mm x 101.6 mm) as shown in Figure
3.1. The geometry was chosen to be consistent with the experimental specimen. The steel
reinforcements in the slab were modeled as circular Hughes-Liu beam elements (Figure 3.2)
in two layers at a distance of 1 in. (25.4 mm) between the layers and a concrete cover of 1in.
(25.4 mm) from the either face. The main steel reinforcement were modeled at a spacing of 4
in. (101.6 mm) on centers and the shrinkage steel reinforcement were modeled at 12 in.
(304.8mm) on centers. The model with 1 in. (25.4 mm) mesh size consists of 11,376 nodes,
8,704 solid elements and 1,560 beam elements. The model with a ½ in. (12.7 mm) mesh size
consists of 83151 nodes, 69632 solid elements and 3120 bean elements. Also, the model with
¼ in. (6.35 mm) mesh size consists of 598,554 nodes, 557,056 solid elements and 6,240
beam elements.
19
3.1MODEL BOUNDARY CONDITIONS
In order to be consistent with the boundary conditions used in the experiment, the following boundary conditions were adopted in the numerical model
Figure 3.1: Reinforced Concrete Slab Model with Solid Elements. 1 in. (25.4 mm) mesh size.
Figure 3.2: Double layer Steel Reinforcement Modeled as Hughes-Liu beam Elements
20
i. As shown in figure 3.3, the top and bottom nodes of the slab were restrained to move in the Y- direction.
ii. A 6 in. restraint in the Z- direction or the pressure direction, from the top was provided on the back face of the slab as shown in Figure 3.4.
iii. In order to provide stability to the slab on the blast face, one strip of nodes as shown in figure 3.5, within the experimental 3 in. strip was restrained to move in the Z- direction only.
3.2 LSDYNA Material Models
Figure 3.3: Boundary conditions on the top and bottom faces.
Figure 3.4: Boundary conditions on the back face.
Figure 3.5: Boundary conditions at the front face of the slab.
Y Y
X Z X
21
LS-DYNA (version 971) has several concrete material models. As outlined in chapter
1 and their ability to provide details on cracks and its propagation, the Winfrith Concrete
Model and the Concrete Damage Model Release 3 were chosen for the study. The parameters
of the material models have been tabulated in Appendix A.
The Winfrith Concrete Model also called the smeared crack model was originally
developed in response to the requirement of the nuclear industry for a finite element analysis
capability to predict the local and global response of reinforced concrete structures subjected
to explosive and impact loadings [12] . The hydrostatic stress state in the model is determined
from a pressure vs volumetric strain curve (Volume Compaction Curve) which is input as
part of the model parameters and is shown in Table 3 of appendix A. The deviatoric stress
state in the concrete are incremented elastically, using a locally rate dependent modulus.. The
yield surface expands with increasing hydrostatic stress, and its radii at the compressive and
the tensile meridian are determined by the locally rate sensitive compressive and tensile
strengths. This surface is described analytically by a function of the stress and stress deviator
tensors in the equations (Eqn. 1-4) below. [6] .
The constants A, B, K1 and K2 are called the
shape parameters in the model. The constants A and B control the meridional shape of the
shear failure surface and the constants K1 and K2 define the shape of the shear failure
surface in the octahedral plane.
1 0---------------------------------------------------------------
Eqn. 1
Where,
cos cos cos 3 !" cos 3 # 0 ------------------------------Eqn.2
22
cos $ 1/3 cos cos 3 !" cos 3 & 0 ----------------------Eqn.3
cos 3 √(.* + ------------------------------------------------------------------------Eqn.4
Where,
S2 and S3 are the deviatoric stress components.
Θ is referred to as the lode angle.
And A, B, K1 & K2 are all functions of,-,.
.
Where, σ_c & σ_t are the compressive and tensile strengths respectively.
For the Winfrith Concrete Model the following material properties of concrete were
used: mass density=2.24e-4 lb s2/in4 (2400 kg/m3); tangent modulus of concrete=3.6e6 psi
(24.8 MPa); Poisson’s ratio=0.18; uniaxial compressive strength of 4 ksi (27.6 MPa) and
uniaxial tensile strength of concrete=475 psi (3.3 MPa).The material parameters are shown in
Table 2 of appendix A. The material parameters were the same for the high strength concrete
simulations with the exception of the compressive and tensile strength values. The rest of the
parameters that were related to the reinforcement were taken as zero since they were modeled
using a different material model described in detail later in this chapter.
The release 3 of the Karagozian and Case (K&C) Concrete model also called
Concrete Damage Model Release 3 is a three invariant plasticity and damage based
constitutive model which is used for lightweight and normal concrete applications to
compute quasi-static and blast loads on structures. Inputs for the Concrete Damage Model
Release 3 have the ability to generate parameters based solely on the uniaxial compressive
strength value. The material parameters are shown in Table 1 of appendix A. The uniaxial
compressive strength and the tensile strength were input as -4 ksi (27.6 MPa) and 475 psi
23
(3.3 MPa) respectively, and the rest of the parameters were taken as zero, allowing the model
to generate damage function values on its own. The strain rate enhancement effects in this
model were also turned off since the model tends exhibit stiff behavior due to dynamic
increase in strength in concrete.
In order to simulate the response of steel reinforcement represented as beam
elements in the model, a plastic kinematic model was chosen in order to consider the effects
of isotropic and kinematic hardening of beam elements[1]. This is also a very cost effective
model when used for beam elements. The parameters used for the model were: mass
density=0.00073 lb s2/in.4 (7.83e3 kg/m3); Young`s modulus= 29e6 psi (200,000 MPa);
Poisson’s ratio=0.3; yield strength of HSLA-V steel=83 ksi (572 MPa); tangent
modulus=29e5 psi (20,000 MPa). Kinematic hardening effect was taken in to consideration
and the strain rate effects in the model were not considered.
3.3 Blast Load Application
In the design of protective structures to resist the effects of accidental explosions, the
principal effects of the explosive output to be considered are blast pressures, fragments
generated by the explosion and the shock loads produced by the shock wave transmitted
through the air or ground. Of these three parameters, the blast pressures are usually the
governing factor in the determination of the structure response.
The effects of an explosion are in the form of a shock wave composed of a high
intensity shock front which expands outward from the surface of the explosive into the
surrounding air. As the wave expands in air, the front impinges on structures located within
its path and then the entire structure is engulfed by the shock pressures. The magnitude and
24
distribution of the blast loads on the structure arising from these pressures are a function of
the following factors: (1) explosive properties, namely type of explosive material, energy
output (high or low order detonation), and weight of explosive; (2) the location of the
detonation relative to the protective structures; and (3) the magnitude and reinforcement of
the pressure by its interaction with the ground barrier, or the structure itself.[3]
The blast wave phenomenon and its application on the structure is a very complex
process is ideally not unifrom across the panels under consideration. The blast wave is
categorized into incident wave, reflected wave and the mach wave.The intersection of these
waves is called the triple point.The height of the triple point increases as the blast pressure
moves away from the source.[3]In this research, the height of this triple point is assumed to
occur at a point higher than that of the slab and hence the blast pressures obtained from the
shock tube in the form of pressure vs time plots as show in figures 2.3 to 2.6 is assumed to
uniformly distributed across the face of the panel as shown in figure 3.6.
Figure 3.6: Blast Load Applied Uniformly on the Slab
25
3.4 Constrained Lagrange In Solid Formulation.
In order to achieve good interaction between concrete and steel elements, a proper
coupling mechanism needs to be used. In this study, the reinforcement is modeled in a
discreet manner as shown in Figure 3.2. There are various ways to achieve coupling in
LSDYNA such as merging the reinforcing beam elements with solid concrete elements in the
form of shared nodes. Secondly, the beam elements can be tied to the concrete elements
using 1-D contact which accounts for bond-slip between concrete and steel. Since the loads
under consideration are that of explosive in nature and the rate of loading is very high, bond-
slip can be neglected for blast and impact studies.[10] Furthermore, the reinforcing beam
elements can be coupled to concrete elements through the
*CONSTRAINED_LAGRANGE_IN_SOLID formulation[1]. This method when used with the
fluid-structure coupling mechanism of CTYPE = 2, couples concrete with reinforcement in
an efficient manner and it removes the burden of having to align the beam nodes to the solid
element nodes.
In this research, the CONSTRAINED_LAGRANGE_IN_SOLID (CLS) is used to
couple concrete solid elements with reinforcing beam elements.
26
3.5 DAMAGE AND CRACK ANALYSIS.
The Winfrith Concrete Model, also called the smeared crack model, is provided with
an option to depict the propagation of cracks on the concrete surface. When a concrete
element fails with a tensile stress component, a crack is flagged in a plane normal to the
maximum principal stress. This phenomenon represents the onset of crack propagation in
concrete and it initiates the decay of crack – normal stress as the crack continues to open
up.[6]
The inbuilt crack model present in the Winfrith Concrete Model can be invoked in
LS-DYNA by adding a line (q= “Crack Filename”) in the execution line. Adding this option,
generates an additional binary output file containing information related to cracks which
include crack widths, location and direction.[1] Also, LS-DYNA has the capability of
providing various information such as minimum and maximum crack widths that are
developed with this model in the “Model Info” section.
In order to simulate the physical cracks in concrete, in a material model such as the
Concrete Damage Model Release 3, which does not have in built erosion and crack
simulating mechanism, an external erosion algorithm needs to be implemented. An additional
material model called Mat_Add_Erosion is used along with the Concrete Damage Model
Release 3 to include failures in concrete. This erosion model is based on the concept that the
concrete element is deleted when the material response in an element reaches certain critical
value. The Mat_Add_Erosion model has various criteria to include erosion and failure in the
model and each of these criteria is applied independently and the elements get deleted from
the simulation as soon as one of the criteria is satisfied.
27
Based on empirical studies performed by Xu et al. (2005), it is found that the typical
concrete strain at peak tensile stress under static loading is around 0.0002. Considering the
softening phase, the concrete at fracture with practically complete loss of tensile strength, it
may be assumed as 5 times 0.0002 = 0.001. For the explosion case under consideration, with
very high strain rates and taking into consideration, the confinement effect from the
reinforcement and in conjunction with trial parametric analysis, it is found that the dynamic
tensile fracture strain should be around 0.01 for spallation of RC material.[10] Thus, for this
research, the principal tensile strain reaching 0.01 is adopted as the governing criterion in the
implementation of the erosion algorithm in the numerical simulation.
28
CHAPTER 4
NUMERICAL RESULTS AND EXPERIMENTAL COMPARISONS
This chapter presents the comparison of experimental data with those from
numerical simulations. Only the deflection history data and damage data are available from
experimental results and are compared with numerical simulations. The numerical
comparison has been performed for four slabs comprising of double mat conventional Grade
60 reinforcement or HSLA-V reinforcement in combination with 4 ksi (27.6 MPa) or 15.5 ksi
(107 MPa) concrete.
Three parameters were used in comparing numerical deflections with that of the
deflection obtained from the experiment. The comparison was made between two mesh sizes,
namely 1 in.(25.4 mm) and ½ in.(12.7 mm) [the ¼ in. ( 6.35 mm) mesh size was used to
compare cracks only], two concrete material models namely, Winfrith Concrete Model and
Concrete Damage Model Release 3 and two types of coupling between steel and concrete
elements, with “Constrained Lagrange in Solid” and without “Constrained Lagrange in
Solid”.
4.1 Normal Strength Concrete with HSLA-V Steel Reinforcing bars (NSC-VR).
The first configuration of slab used in the numerical simulation consists of normal
strength concrete with a compressive strength of 4 ksi (27.6 MPa) reinforced with HSLA-V
bars with a yield strength of 83 ksi (572.7 MPa). A comparison of results obtained from the
numerical analyses with that of the ones obtained from the experiment have been shown in
the following sections.
4.1.1 With “Constrained Lagrange in Solid”.
Deflection results obtained from models having two different mesh sizes, namely 1
in. (25.4 mm) and ½ in. (12.7 mm
Lagrange in Solid” formulation was used to couple the steel nodes to the concrete nodes.
Figure 4.1: Deflection Comparison for 1 in
The deflection results obtained from the two LS
in.(25.4 mm) mesh sizes has been compared in Figure
from the experiment was 5.1 in. (129.5 mm). The peak
Damage Model Release 3 with 1 in.
deflection obtained from the Winfrith Concrete Model with 1 in.
0
1
2
3
4
5
6
0 20
Def
lect
ion
(in.)
29
With “Constrained Lagrange in Solid”.
Deflection results obtained from models having two different mesh sizes, namely 1
(12.7 mm) have been compared in this study. The “Constrained
Lagrange in Solid” formulation was used to couple the steel nodes to the concrete nodes.
Deflection Comparison for 1 in. (25.4) Mesh Size with Constrained
Solid.(NSC-VR)
The deflection results obtained from the two LS-DYNA concrete models with
mesh sizes has been compared in Figure 4.1. The average deflection obtained
from the experiment was 5.1 in. (129.5 mm). The peak deflection obtained from the Concrete
Damage Model Release 3 with 1 in. (25.4 mm) mesh size was 5.1 in. (129.5
deflection obtained from the Winfrith Concrete Model with 1 in.(25.4 mm)
40 60 80 100 120
Time (msecs)
Concrete Damage Model Rel 3
Winfrith Concrete Model
Experimental
Deflection results obtained from models having two different mesh sizes, namely 1
have been compared in this study. The “Constrained
Lagrange in Solid” formulation was used to couple the steel nodes to the concrete nodes.
onstrained Lagrange in
DYNA concrete models with 1
. The average deflection obtained
deflection obtained from the Concrete
5 mm). The peak
(25.4 mm) mesh size was
0
25.4
50.8
76.2
101.6
127
152.4
140 160
Def
lect
ion
(mm
)
Concrete Damage Model Rel 3
Winfrith Concrete Model
30
5.4 in. (137.2 mm). The deflections obtained from models with 1 in.(25.4 mm) mesh size
were within the limits when compared to the deflection obtained from the experiment as the
Winfrith Concrete Model showed only a 5% increase and the Concrete Damage Rel 3 model
showed no changes in deflection when compared with the experimental values. However, it
is to be noted that the time at which peak deflection occurred was at 0.015 secs. 0.035 secs.
and 0.060 secs. for the experimental, Winfrith Concrete Model and Concrete Damage Model
Release 3 respectively. The prediction time from the Winfrith Concrete Model was closer to
the experimental results. Also, the total time of simulation for the 1 in. (25.4 mm) models
were 600 secs.
Figure 4.2: Deflection Comparison for 0.5 in. 3(12.7 mm) mesh size with Constrained
Lagrange in Solid.(NSC-VR)
0
25.4
50.8
76.2
101.6
127
152.4
177.8
203.2
228.6
254
0
1
2
3
4
5
6
7
8
9
10
0 20 40 60 80 100 120 140 160
Def
lect
ion(
mm
)
Def
lect
ion
(in.)
Time(msecs)
Concrete Damage Model Rel 3
Winfrith Concrete Model
Experimental
1 in. = 25.4 mm
31
As depicted in Figure 4.2, the magnitude of peak deflection obtained from the
Concrete Damage Model Release 3 with a 1/2 in. (12.7 mm) mesh size was 8.6 in. (218.5
mm), an increase by 40 % when compared to the experimental value. The Winfrith Concrete
Model with 1/2 in. (12.7 mm) mesh size gave a deflection value of 8.1 in. (205.7 mm), an
increase by 37 %. Also in Figure 4.2, similar to the observations made in the previous Figure
4.1, it is to be noted that the time at which peak deflection occurred was at 0.015 secs. 0.035
secs. and 0.065 secs. for the experimental, Winfrith Concrete Model and Concrete Damage
Model Release 3 respectively. The total time of simulation for ½ in .( 12.7 mm) was about
1500 secs.
4.1.2 Without “Constrained Lagrange in Solid.”
Deflection results obtained from models having two different mesh sizes, namely 1
in.(25.4 mm) and ½ in.(12.7 mm) have been compared in this study. The “Constrained
Lagrange in Solid” formulation was not used to couple the steel nodes to the concrete nodes.
The nodes of reinforcing beam elements were shared with concrete nodes.
32
Figure 4.3: Deflection Comparison for 1 in.(25.4 mm) Mesh Size without Constrained
Lagrange in Solid.(NSC-VR)
Figure 4.3 provides information on the numerical comparison of experimental
deflection in LSDYNA without the use of the “Constrained Lagrange in Solid” formulation
for 1 in. (25.4 mm) mesh size. The deflection obtained from the Concrete Damage Model
Release 3 with 1 in. (25.4 mm) mesh size was very low at 0.6 in. (15.2 mm). The peak
deflection obtained from the Winfrith Concrete Model with 1 in. (25.4 mm) mesh size was 4
in. (101.6 mm). The Concrete Damage Model release 3 gave a stiff response for this
condition. However, the deflection results obtained from the Winfrith Concrete Model was
better and was closer to the experimental deflection.
0
25.4
50.8
76.2
101.6
127
152.4
0
1
2
3
4
5
6
0 20 40 60 80 100 120 140 160
Def
lect
ion(
mm
)
Def
lect
ion(
in.)
Time(msecs)
Concrete Damage Model Rel 3
Winfrith Concrete Model
Experimental
1 in. = 25.4 mm
33
Figure 4.4: Deflection Comparison for 0.5 in. (12.7 mm) Mesh Size without Constrained
Lagrange in Solid.(NSC-VR)
The magnitude of peak deflection obtained from the Concrete Damage Model
Release 3 with a ½ in. mesh size was 2.0 in. (50.8 mm) as shown in Figure 4.4. The Winfrith
Concrete Model with ½ in. mesh size gave a deflection value of 4.3 in. (109.2 mm). In the ½
in. mesh size simulations, the Winfrith Concrete Model performed better than the Concrete
Damage Model Release 3, which gave lower deflections.
4.1.3 Overall Observations:
From the observations made from Figures 4.1 to 4.4, a brief summary is depicted
below which compares mesh size effect, the two material models, Constrained Lagrange in
Solid Formulation Study and Crack propagation studies.
0
25.4
50.8
76.2
101.6
127
152.4
0
1
2
3
4
5
6
0 20 40 60 80 100 120 140 160
Def
lect
ion(
mm
)
Def
lect
ion(
in.)
Time (msecs)
Concrete Damage Model Rel 3
Winfrith Concrete Model
Experimental
1 in. = 25.4 mm
34
4.1.3.1 Mesh Size Effect:
A variation of mesh size from 1 in. (25.4 mm) to ½ in. (12.7 mm) saw an increase in
deflections in both concrete and steel coupling categories, i.e., with and without “Constrained
Lagrange in Solid”. From Figures 4.1 and 4.2, when the “Constrained Lagrange in Solid”
formulation was used, varying the mesh size from 1 in. (25.4 mm) to ½ in. (12.7 mm)
showed an increase in deflection by 3 in. (76.2 mm) in both Concrete Damage Model
Release 3 Model and Winfrith Concrete Model. Also, for the models without “Constrained
Lagrange in Solid Formulation” formulation as depicted in Figures 3 and 4, a reduction in
mesh size from 1 in. (25.4 mm) to ½ in. (12.7 mm) showed an increase in deflection by 1.6
in. (40.6 mm) for the Concrete Damage Model Release 3 and 0.3 in. (7.6 mm) increase for
the Winfrith Concrete Model. It can be concluded that a 1 in. (25.4 mm) mesh size can be
used for an accurate prediction of deformation in comparison with the experimental
deformation.
4.1.3.2 Concrete Material Model Study:
Among the two concrete material models namely, Concrete Damage Model Release 3
and Winfrith Concrete Model, which were used in this study, the Concrete Damage Model
Release 3 with a 1 in. (25.4 mm) mesh size and with the incorporation of “Constrained
Lagrange in Solid” formulation gave the closest prediction of deflection when compared to
the experimental deflection. However, the predictions of this model were not consistent as
the mesh sizes were varied along with variations in the concrete and steel coupling as seen in
Figures 4.1 to 4.4. Furthermore, the Winfrith Concrete Model with a 1 in. (25.4 mm) mesh
size and with “Constrained Lagrange in Solid” formulation gave a marginal increase in
deflection of 0.3 in. (7.6 mm) than the Concrete Damage model Release 3 when compared
35
with the experimental deflection. But, the predictions of the Winfrith Concrete Model were
better in other mesh size categories too, Although it gave a lesser deflection of 0.6 in. (15.2
mm) and 1 in. (25.4 mm) for mesh sizes of ½ in.(12.7 mm) and 1 in.(25.4 mm) respectively,
than the experimental deflection when the “Constrained Lagrange in Solid” formulation was
not used. This was not the case with the Concrete Damage Model Release 3 Model.
4.1.3.3 “Constrained Lagrange in Solid” Formulation Study:
It can be observed from Figures 4.1 to 4.4 that the numerical response of the slab
shows considerable variations with and without the use of the ALE concrete and steel
coupling parameter called “Constrained Lagrange in Solid”. The peak experimental
deflection can be seen to occur at 18 milliseconds. In the Concrete Damage Model Release 3,
when the ALE coupling card is used, the peak deflection is attained between 60 to 70
milliseconds and the peak deflections for the Winfrith Concrete Model can be seen at 30
milliseconds. Also, the slab shows a smooth reduction in deflection by 2 in. (50.8 mm) after
attaining its peak deflections for both the concrete material models. However, when the ALE
coupling card is not used and the concrete and steel nodes are shared, the deformation
response of the slab is closer to the experimental response for the Winfrith Concrete Model.
The peak deflection is obtained at 20 milliseconds which are close to the experimental value
of 18 milliseconds. Also, the behavior of the slab beyond the peak deflection is similar to the
experimental behavior as the slab does not show a considerable reduction in deflection.
4.1.3.4 Crack Propagation Studies:
Figure 4.5depicts the actual cracks that were observed during the experiment at
maximum deflection. The numerical simulation of these cracks for the Winfrith Concrete
Model with a 1 in. (25.4 mm) mesh size has been depicted in Figure 4.6, which is a good
match with the experimental results. Also, the numerical simulation showed that the cracks
first start appearing at the center of the slab
with the application of the load. By default, LS
slab due to the loading. However, in order to neglect very narrow cracks, the minimum crack
width was set as 0.0125 in. (0.3175 mm) and the maximum crack width that was observed on
the slab was 0.165 in. (4.2 mm).
Figure 4.5: Cracks obtained during the experiment
36
match with the experimental results. Also, the numerical simulation showed that the cracks
first start appearing at the center of the slab and propagate to the periphery of the slab along
with the application of the load. By default, LS-DYNA depicts all cracks that appear on the
slab due to the loading. However, in order to neglect very narrow cracks, the minimum crack
5 in. (0.3175 mm) and the maximum crack width that was observed on
the slab was 0.165 in. (4.2 mm).
Cracks obtained during the Figure 4.6: Cracks from Winfrith Concrete Model with 1 in. (25.4mm)VR)
match with the experimental results. Also, the numerical simulation showed that the cracks
and propagate to the periphery of the slab along
DYNA depicts all cracks that appear on the
slab due to the loading. However, in order to neglect very narrow cracks, the minimum crack
5 in. (0.3175 mm) and the maximum crack width that was observed on
Cracks from Winfrith Concrete (25.4mm) mesh size.(NSC-
Figures 4.7 to 4.10 depict the damage pattern obtained from the Concrete Damage
Model Release 3 used in conjunction with the Mat_Add_Erosion model with an erosion
governing criteria of maximum principal strain of
damage and crack patterns obtained from the models from all three mesh sizes are compared
with crack patterns obtained from the experiment.
The damage pattern obtained from the 1 in.
of the experimental pattern .The damage patterns obtained from the ½ in.
size and the ¼ in.(6.35 mm)
from the experiment. The propagation of flexural c
in the ½ in.(12.7 mm) and
Figure 4.7: Cracks obtained during the experiment
37
depict the damage pattern obtained from the Concrete Damage
Model Release 3 used in conjunction with the Mat_Add_Erosion model with an erosion
maximum principal strain of 0.01 as explained in section 3.5.
s obtained from the models from all three mesh sizes are compared
with crack patterns obtained from the experiment.
The damage pattern obtained from the 1 in.(25.4 mm) mesh size does not match that
of the experimental pattern .The damage patterns obtained from the ½ in.
) mesh size are a close match to the damage patterns obtained
The propagation of flexural cracks can be seen clearly in the simulation
Cracks obtained during the Figure 4.8: Cracks obtained Damage Model Release 3 with 1 in. (25.4 mm) mesh size (NSC-VR)
depict the damage pattern obtained from the Concrete Damage
Model Release 3 used in conjunction with the Mat_Add_Erosion model with an erosion
0.01 as explained in section 3.5. The
s obtained from the models from all three mesh sizes are compared
mesh size does not match that
of the experimental pattern .The damage patterns obtained from the ½ in.(12.7 mm) mesh
mesh size are a close match to the damage patterns obtained
racks can be seen clearly in the simulation
Cracks obtained from Concrete Damage Model Release 3 with 1 in. (25.4
the ¼ in.(6.35 mm) models; however, the 1 in.
accurate crack propagation behavior.
in.(6.35 mm) model gives the closes
that of the experiment. The disadvantage of using Mat_Add_Erosion is that the concrete slab
breaks away as the simulation progresses and the deformation results are lost. This is not
seen in the Winfrith Concrete Model, which provides both deformation results along with a
smeared crack propagation behavior on the slab.
lot of information on the crack width and its propagation which is essential for any damage
tolerance study.
Figure 4.9: Cracks obtained from Concrete Damage Model Release 3 withmesh size.(NSC-VR)
38
models; however, the 1 in.(25.4 mm) model does not depict a very
accurate crack propagation behavior. Among all the three models, it can be seen that the ¼
model gives the closest prediction of cracks and damage when compared with
that of the experiment. The disadvantage of using Mat_Add_Erosion is that the concrete slab
breaks away as the simulation progresses and the deformation results are lost. This is not
Concrete Model, which provides both deformation results along with a
smeared crack propagation behavior on the slab. Also, the smeared crack model provides a
lot of information on the crack width and its propagation which is essential for any damage
from Concrete Damage Model Release 3 with ½ in.(12.7 mm)
Figure 4.10: Cracks obtained Damage Model Release 3 with ¼ in.(6.35mm) mesh size (NSC-VR)
model does not depict a very
can be seen that the ¼
of cracks and damage when compared with
that of the experiment. The disadvantage of using Mat_Add_Erosion is that the concrete slab
breaks away as the simulation progresses and the deformation results are lost. This is not
Concrete Model, which provides both deformation results along with a
Also, the smeared crack model provides a
lot of information on the crack width and its propagation which is essential for any damage
Cracks obtained from Concrete Damage Model Release 3 with ¼ in.(6.35mm)
VR)
39
From this study, it can also be observed that the use of CLS (change) improves the
deflection values and consequently, the numerical simulations are closer to the experimental
simulations. Hence, for the next set of numerical comparisons, simulations without the use of
CLS were neglected.
4.2 Normal Strength Concrete with Conventional Steel Reinforcing bars (NSC-NR).
The next configuration of slab used in the numerical simulation consists of normal
strength concrete with a compressive strength of 4 ksi (27.6 MPa) reinforced with
conventional bars with a yield strength of 60 ksi (415 MPa).A comparison of results obtained
from the numerical analysis with that of the ones obtained from the experiment have been
shown in the following sections.
4.2.1 Deformation Results.
Deflection results obtained from models having two different mesh sizes, namely 1
in. (25.4 mm) and ½ in. (12.7 mm) has been compared in this study. The “Constrained
Lagrange in Solid” formulation was used to couple the steel nodes to the concrete nodes.
40
Figure 4.11: Deflection Comparison for 1 in. (25.4 mm) Mesh Size with Constrained
Lagrange in Solid.(NSC-NR)
The deflection results obtained from the two LS-DYNA concrete models with 1 in.
(25.4 mm) mesh sizes has been compared in Figure 4.11. The average deflection obtained
from the experiment was 8.7 in. (220.9 mm). The peak deflection obtained from the Concrete
Damage Model Release 3 with 1 in. (25.4 mm) mesh size was 5.6 in. (142.24 mm), which
was 35% less than the experimental value. The peak deflection obtained from the Winfrith
Concrete Model with 1 in. (25.4 mm) mesh size was 6.3 in. (160.1 mm) which was a 27%
reduction from the experimental value. The deflections obtained from the Winfrith Concrete
Model and the Concrete Damage Model Release 3 were lower than the experimental
deflection by 2.5 in. (63.5 mm) and 3.1 in. (78.8 mm) respectively.
0
25.4
50.8
76.2
101.6
127
152.4
177.8
203.2
228.6
254
0
1
2
3
4
5
6
7
8
9
10
0 20 40 60 80 100 120 140 160
Def
lect
ion(
mm
)
Def
lect
ion(
in.)
Time (msecs)
Winfrith concrete Model
Concrete Damage Model
Release 3Experimental
41
Figure 4.12: Deflection Comparison for 0.5 in. (12.7 mm) Mesh Size with Constrained
Lagrange in Solid.(NSC-NR)
As depicted in Figure 4.12, the magnitude of peak deflection obtained from the
Concrete Damage Model Release 3 with a 1/2 in. (12.7 mm) mesh size was 8.9 in. (226.6
mm) which was similar to the experimental deflection. The Winfrith Concrete Model with
1/2 in. (12.7 mm) mesh size gave a deflection value of 9.9 in. (251.5 mm) which was 13%
higher than the experimental deflection.
4.2.2 Overall Observations:
By taking into account the three parameters used for the comparison, the following
observations can be made from Figures 4.11 and 4.12.
0
50.8
101.6
152.4
203.2
254
304.8
0
2
4
6
8
10
12
0 20 40 60 80 100 120 140 160
Def
elct
ion(
mm
)
Def
lect
ion(
in.)
Time(msecs)
Winfrith Concrete Model
Concrete Damage Model
Release 3
Experimental
42
4.2.2.1 Mesh Size Effect:
From Figures 4.11 and 4.12, when the “Constrained Lagrange in Steel” formulation
was used, varying the mesh size from 1 in. (25.4 mm) to ½ in. (12.7 mm) showed an increase
in deflection by 3.3 in. (83.82 mm) in both Concrete Damage Model Release 3 Model and
Winfrith Concrete Model. Based on the comparison between Figures 4.11 and 4.12, a
conclusion can be drawn that for normal strength concrete with conventional reinforcement,
the deflections obtained from models with ½ in. (12.7 mm) mesh size models were within the
limits of the experimental values, when compared to the deflection obtained from the 1 in.
(25.4 mm) mesh size models, as the later produced lower deflection values.
4.2.2.2 Concrete Material Model Study:
Among the two concrete material models namely, Concrete Damage Model Release 3
and Winfrith Concrete Model, which were used in this study, the Concrete Damage Model
Release 3 with a ½ in. (12.7 mm) mesh size and with the incorporation of “Constrained
Lagrange in Solid” formulation gave the closest prediction of deflection when compared to
the experimental deflection. Furthermore, the Winfrith Concrete Model with a ½ in. (12.7
mm) mesh size and with “Constrained Lagrange in Solid” formulation gave an increase in
deflection by 11 % when compared with the Concrete Damage Model Release 3.
4.2.2.3 Crack Propagation Studies:
Figure 14.13 depicts the actual cracks that were observed during the experiment at
maximum deflection. The numerical simulation of these cracks for the Winfrith Concrete
Model with a 1 in. (25.4 mm) mesh size has been depicted in Figure 4.14, which is a good
match with the experimental results. Also, the numerical simulation showed that the cracks
first start appearing at the center of the slab and propagate to the periphery of the slab along
with the application of the load. By default, LS
slab due to the loading. However, in order to neglect very narrow cracks, the minimum crack
width was set as 0.0125 in. (0.3175 mm) and the maximum crack width that was observed on
the slab was 0.24 in. (4.2 mm).
Figure 4.15 depicts the da
Release 3 used in conjunction with the Mat_Add_Erosion model with an erosion governing
criteria of maximum principal strain of
crack patterns obtained from the models from
crack patterns obtained from the experiment.
Figure 4.13: Cracks obtained during the experiment.(NSC-NR)
43
with the application of the load. By default, LS-DYNA depicts all cracks that appear on the
slab due to the loading. However, in order to neglect very narrow cracks, the minimum crack
width was set as 0.0125 in. (0.3175 mm) and the maximum crack width that was observed on
in. (4.2 mm).
the damage pattern obtained from the Concrete Damage Model
used in conjunction with the Mat_Add_Erosion model with an erosion governing
maximum principal strain of 0.01 as explained in section 3.5. The damage and
crack patterns obtained from the models from ¼ in. (6.35 mm) mesh size are compared with
crack patterns obtained from the experiment.
Cracks obtained during NR)
Figure 4.14: Cracks from Winfrith Concrete Model with 1 in.(25.4 mm)NR)
YNA depicts all cracks that appear on the
slab due to the loading. However, in order to neglect very narrow cracks, the minimum crack
width was set as 0.0125 in. (0.3175 mm) and the maximum crack width that was observed on
obtained from the Concrete Damage Model
used in conjunction with the Mat_Add_Erosion model with an erosion governing
0.01 as explained in section 3.5. The damage and
mesh size are compared with
Cracks from Winfrith Concrete (25.4 mm) mesh size.(NSC-
44
The damage patterns obtained from ¼ in. (6.35 mm) mesh size depict some vertical
cracks along with the horizontal cracks. These vertical cracks propagate orthogonally in the
same plane of that of the horizontal cracks. The propagation of flexural cracks can be seen
clearly at the tension zone of the slab in the simulations.
4.3 High Strength Concrete with Conventional Steel Reinforcing bars (HSC-NR).
The next configuration of the slab used in the numerical simulation consists of high
strength concrete with a compressive strength of 15.5 ksi (106.95 MPa) reinforced with
conventional bars with a yield strength of 60 ksi (415 MPa).A comparison of results obtained
from the numerical analysis with that of the ones obtained from the experiment have been
shown in the following sections.
Figure 4.15: Cracks obtained from Concrete Damage Model Release 3 with ¼ (6.35 mm) in. mesh size.(NSC-NR)
45
4.3.1 Deformation Results
Deflection results obtained from models having two different mesh sizes, namely 1
in. (25.4 mm) and ½ in. (12.7 mm) have been compared in this study. The “Constrained
Lagrange in Solid” formulation was used to couple the steel nodes to the concrete nodes.
Figure 4.16: Deflection Comparison for 1 in. (25.4 mm) Mesh Size with Constrained
Lagrange in Solid.(HSC-NR)
The deflection results obtained from the two LS-DYNA concrete models with 1
in.(25.4 mm) mesh sizes has been compared in Figure 4.16. The average deflection obtained
from the experiment was 5.5 in. (139.7 mm). The peak deflection obtained from the Winfrith
Concrete Model with 1 in. (25.4 mm) mesh size was 4.9 in. (124.2 mm), 10 % less than the
experimental value..However, the Concrete Damage Model Release 3 gave a stiff response
with negligible deflection values because previous compressive strength comparison studies
with the model has shown that its deformation response is limited to 10 ksi (69 MPa) beyond
which , the model becomes stiff.
0
50.8
101.6
152.4
203.2
254
304.8
0
2
4
6
8
10
12
0 20 40 60 80 100 120 140 160
Def
lect
ion(
mm
)
Def
lect
ion(
in.)
Time(msecs)
Winfrith Concrete Model
Concrete Damage Model Release 3
Experimental
46
Figure 4.17: Deflection Comparison for 0.5 in. (12.7 mm) Mesh Size with Constrained
Lagrange in Solid.(HSC-NR)
As depicted in Figure 4.17, the magnitude of peak deflection obtained from the
Winfrith Concrete Model with a 1/2 in. (12.7 mm) mesh size was 4.9 in. (124.2 mm). The
Concrete Damage Model Release 3 gave a stiff response with negligible deflection values for
the ½ in. (12.7 mm) mesh size model also.
4.3.2 Overall Observations:
By taking into account the three parameters used for the comparison, the following
observations can be made from Figures 4.16 and 4.17.
0
50.8
101.6
152.4
203.2
254
304.8
0
2
4
6
8
10
12
0 20 40 60 80 100 120 140 160
Def
lect
ion(
mm
)
Def
lect
ion(
in.)
Time(msecs)
Winfrith Concrete Model
Concrete Damage Model Release 3
Experimental
47
4.3.2.1 Mesh Size Effect:
From Figures 4.16 and 4.17, when the “Constrained Lagrange in Steel” formulation
was used, varying the mesh size from 1 in.(25.4 mm) to ½ in.(12.7 mm), did not depict
variations in deflection in both Concrete Damage Model Release 3 Model and Winfrith
Concrete Model. Based on the comparison between Figures 4.18 and 4.19, a conclusion can
be drawn that for high strength concrete with conventional reinforcement, any variation in
mesh size does not produce variations in deflection, which was not the case in the other
simulations.
4.3.2.2 Concrete Material Model Study:
Among the two concrete material models namely, Concrete Damage Model Release 3
and Winfrith Concrete Model, which were used in this study, the Winfrith Concrete Model
with both 1 in. (25.4 mm) mesh size and ½ in.(12.7 mm) mesh size gave the closest
prediction of deflection when compared to the experimental deflection. On the contrary,
Concrete Damage Model Release 3 gave a very stiff response in both the mesh size
categories.
4.3.2.3 Crack Propagation Studies:
Figure 4.18 depicts the actual cracks that were observed during the experiment at
maximum deflection. The numerical simulation of these cracks for the Winfrith Concrete
Model with a 1 in. (25.4 mm) mesh size has been depicted in Figure 4.19, which is a good
match with the experimental results. Also, the numerical simulation showed that the cracks
first start appearing at the center of the slab and propagate to the periphery of the slab along
with the application of the load. By default, LS-DYNA depicts all cracks that appear on the
slab due to the loading. However, in order to neglect very narrow cracks, the minimum crack
width was set as 0.0125 in. (0.3175 mm) and the maximum crack width that was observed on
the slab was 0.26 in. (4.2 mm)
Figures 4.20 depict the damage pattern obtained from the Concrete Damage Model
Release 3 used in conjunction with the Mat_Add_Erosion model with an erosion governing
criteria of maximum principal strain of
crack patterns obtained from the models from all three mesh sizes are compared with crack
patterns obtained from the experiment.
Figure 4.18: Cracks obtained during the experiment
48
was set as 0.0125 in. (0.3175 mm) and the maximum crack width that was observed on
in. (4.2 mm).
depict the damage pattern obtained from the Concrete Damage Model
Release 3 used in conjunction with the Mat_Add_Erosion model with an erosion governing
maximum principal strain of 0.01 as explained in section 3.5. The damage and
s obtained from the models from all three mesh sizes are compared with crack
patterns obtained from the experiment.
Cracks obtained during the Figure 4.19: Cracks from Winfrith Concrete Model with 1 in.(25.4 mm)NR)
was set as 0.0125 in. (0.3175 mm) and the maximum crack width that was observed on
depict the damage pattern obtained from the Concrete Damage Model
Release 3 used in conjunction with the Mat_Add_Erosion model with an erosion governing
0.01 as explained in section 3.5. The damage and
s obtained from the models from all three mesh sizes are compared with crack
Cracks from Winfrith Concrete (25.4 mm) mesh size.(HSC-
49
Though the ¼ in. (6.35 mm) mesh model depicts the crack patterns in the HSC-NR
category, the patterns are not a very close match to the experimental patterns and as effective
as the ones seen in the normal strength concrete categories. This is due to the slab being very
stiff with almost negligible deformation, the maximum principal strain value is reached only
at a very few places on the tension zone of the slab.
4.4 High Strength Concrete with HSLA-V Steel Reinforcing bars (HSC-VR).
The final configuration of the slab used in the numerical simulation consists of high
strength concrete with a compressive strength of 15.5 ksi (106.95 MPa) reinforced with
conventional bars with a yield strength of 83 ksi (572.5 MPa).A comparison of results
obtained from the numerical analysis with that of the ones obtained from the experiment have
been shown in the following sections.
Figure 4.20: Cracks obtained from Concrete Damage Model Release 3 with 1/4 in.(6.35 mm) mesh size.(HSC-NR)
50
4.4.1 With “Constrained Lagrange in Solid”.
Deflection results obtained from models having two different mesh sizes, namely 1
in.( 25.4 mm) and ½ in.( 12.7 mm) have been compared in this study. The “Constrained
Lagrange in Solid” formulation was used to couple the steel nodes to the concrete nodes.
Figure 4.21: Deflection Comparison for 1 in.(25.4 mm) Mesh Size with Constrained
Lagrange in Solid.(HSC-VR).
The deflection results obtained from the two LS-DYNA concrete models with 1 in.
(25.4 mm) mesh sizes has been compared in Figure 4.21. The average deflection obtained
from the experiment was 4.8 in. (121.9 mm), 37 % less than the experimental value. The
peak deflection obtained from the Winfrith Concrete Model with 1 in. ( 25.4 mm) mesh size
0
25.4
50.8
76.2
101.6
127
152.4
0
1
2
3
4
5
6
0 20 40 60 80 100 120 140 160
Def
lect
ion(
mm
)
Def
lect
ion(
in.)
Time(msecs)
Winfrith Concrete Model
Concrete Damage Model Release
3
Experimental
51
was 3 in. (76.2 mm). However; the Concrete Damage Model Release 3 gave a stiff response
with negligible deflection values.
Figure 4.22: Deflection Comparison for 0.5 in. (12.7 mm) Mesh Size with Constrained
Lagrange in Solid.(HSC-VR)
As depicted in Figure 4.22, the magnitude of peak deflection obtained from the
Winfrith Concrete Model with a 1/2 in. (12.7 mm) mesh size was 4.3 in. (109.2 mm), 10%
less than the experimental value. The Concrete Damage Model Release 3 gave a stiff
response with negligible deflection values for the ½ in.(12.7 mm) mesh size model also.
4.4.2 Overall Observations:
By taking into account the three parameters used for the comparison, the following
observations can be made from Figures 4.21 and 4.22.
0
0.2
0.4
0.6
0.8
1
1.2
0
1
2
3
4
5
6
0 20 40 60 80 100 120 140 160
Def
lect
ion(
mm
)
Def
lect
ion(
in.)
Time(msecs)
Winfrith Concrete Model
Concrete Damage Model Release 3
Experimental
52
4.4.2.1 Mesh Size Effect:
From Figures 4.21 and 4.22, when the “Constrained Lagrange in Steel” formulation
was used, varying the mesh size from 1 in. (25.4 mm) to ½ (12.7 mm) in increased the
deflection values by 1.2 in (30.5 mm) in the Winfrith Concrete Model. But, the Concrete
Damage Model Release 3 did not show any change in deflection due to variation in mesh
size.
4.4.2.2 Concrete Material Model Study:
Among the two concrete material models namely, Concrete Damage Model Release 3
and Winfrith Concrete Model, which were used in this study, the Winfrith Concrete Model
with ½ in.(12.7 mm) mesh size gave the closest prediction of deflection when compared to
the experimental deflection. The same model with 1 in. (25.4 mm) mesh size gave deflection
lower by 2.5 in. (63.5mm) Also, the Concrete Damage Model Release 3 gave a very stiff
response in both the mesh size categories.
4.4.2.3 Crack Propagation Studies:
Figure 4.23 depicts the actual cracks that were observed during the experiment at maximum
deflection. The numerical simulation of these cracks for the Winfrith Concrete Model with a
1 in. (25.4 mm) mesh size has been depicted in Figure 4.24, which is a good match with the
experimental results. Also, the numerical simulation showed that the cracks first start
appearing at the center of the slab and propagate to the periphery of the slab along with the
application of the load. By default, LS-DYNA depicts all cracks that appear on the slab due
to the loading. However, in order to neglect very narrow cracks, the minimum crack width
was set as 0.0125 in. (0.3175 mm) and the maximum crack width that was observed on the
slab was 0.135 in. (4.2 mm).
Figure 4.25 depicts the damage pattern obtained from the Concrete Damage Model
Release 3 used in conjunction with the Mat_Add_Erosion model with an erosion governing
criteria of maximum principal strain of 0.01
crack patterns obtained from the models from all three mesh sizes are compared with crack
patterns obtained from the experiment.
Figure 4.23: Cracks obtained during the experiment
53
the damage pattern obtained from the Concrete Damage Model
Release 3 used in conjunction with the Mat_Add_Erosion model with an erosion governing
maximum principal strain of 0.01 as explained in section 3.5. The damage and
ned from the models from all three mesh sizes are compared with crack
patterns obtained from the experiment.
Cracks obtained during the Figure 4.24: Cracks from Winfrith Concrete Model with 1 in.(25.4 mm)VR)
the damage pattern obtained from the Concrete Damage Model
Release 3 used in conjunction with the Mat_Add_Erosion model with an erosion governing
as explained in section 3.5. The damage and
ned from the models from all three mesh sizes are compared with crack
Cracks from Winfrith Concrete (25.4 mm) mesh size.(HSC-
54
Though the ¼ in. (6.35 mm) mesh model depicts the crack patterns in the HSC-VR
category, the patterns are not a very close match to the experimental patterns and as effective
as the ones seen in the normal strength concrete categories. This is due to the slab being very
stiff with almost nil deformation, the maximum principal strain value is reached only at a
very few places on the tension zone of the slab.
Figure 4.25: Cracks obtained from Concrete Damage Model Release 3 with 1/4 in.(6.35 mm) mesh size.(HSC-VR)
55
CHAPTER 5:
ANALYSIS OF RESULTS
The objective of this research effort has been to validate and compare the behavior of
NSC/HSC and NR/VR with that of the experimental behavior. With the help of validation
efforts like this, any research organization can substantially reduce the number tests that need
to be performed to understand the behavior of reinforced concrete materials and structures
when subjected to blast loads and explosion type situations. The experimental validation has
been performed at the material level and also at the response level.
5.1 Analytical Behavior of High Strength Materials When Compared To Conventional
Materials.
The deformation results obtained from the experiment indicates that the use of high
strength concrete with HSLA-V rebar (HSC-VR) gave a deflection of 4.8 in (121.9 mm).
Also, the defection obtained from the slab consisting of normal strength concrete with
conventional rebar (NSC-NR) gave a deflection of 8.7 in (220.8 mm). This indicates that use
of high strength materials in the slab provided 55 % less response than normal strength
materials. This also indicates that the use of normal strength materials require more level of
protection in explosive type scenarios.
At the computational level, a similar kind of behavior was seen in the slabs modeled
in LSDYNA. For instance, the Winfrith Concrete Model with HSC-VR gave a deflection of 3
in. (76.2 mm) when compared to a deflection of 6.3 in. (160.1 mm) using the same model
with NSC-NR parameters. This shows that the response of the structure reduced by 48 %
which is close to the value obtained from the experiment. However, a similar comparison
56
could not be performed with the Concrete Damage Model Release 3 as the responses of this
model for the HSC-VR category was stiff.
5.2 Effect of Mesh Size on Experimental Validation.
From Table A 6 in appendix A, it can be seen that, mesh size sensitivity is
substantially higher when normal strength concrete is used. When the mesh size is reduced
form 1 in. (25.4 mm) to ¼ in. (6.35 mm), there is a 40 % increase in deflection in the NSC-
VR category with Concrete Damage Model Release 3. Also, there is a 33 % increase in the
Winfrith Concrete Model. In the NSC-NR category, there is a 37 % increase in deflection
with Concrete Damage Model Release 3 and an increase in deflection by 36 % when the
Winfrith Concrete Model is used. There is no substantial increase in deflection in the HSC-
NR and HSC-VR categories when both the material models are taken into consideration.
5.3 Comparison of Winfrith Concrete Model with Concrete Damage Model Release 3.
Table A1 and A2 in appendix A, gives a comparison of the parameters that were used
in the two concrete material models. Also, Table A7 provides information on the percentage
difference in the two concrete material models when compared with experimental behavior.
Taking into consideration 1 in. (25.4 mm) mesh size models, in the normal strength concrete
and HSLA-V rebar (NSC-HR) category, the Winfrith Concrete Model gave a 5 % higher
deflection than the experimental deflection. The Concrete Damage Model Release 3 showed
a deflection similar to that of the experimental value. In the normal strength concrete with
conventional rebar (NSC-NR) category, the Winfrith concrete model and the Concrete
Damage Model Release 3 showed a lesser deflection of 27 % and 35 % respectively, when
compared to the experimental deflection. In the high strength concrete with conventional
rebar (HSC-NR) category, the Winfrith Concrete Model, showed a deflection 10 % less than
57
the experimental value and in the high strength concrete with HSLA-V rebar (HSC-VR)
category, the Winfrith Concrete Model showed a deflection 37 % less than the experimental
value. However, the Concrete Damage Model Release 3 provided a stiff response in both
HSC-NR and HSC-VR categories.
Similarly, taking into consideration ½ in. (12.7 mm) mesh size models, in the normal
strength concrete and HSLA-V rebar (NSC-VR) category, the Winfrith Concrete Model gave
a 37 % higher deflection than the experimental deflection. The Concrete Damage Model
Release 3 showed a deflection 40 % higher when compared to that of the experimental value.
In the normal strength concrete with conventional rebar (NSC-NR) category, the Winfrith
Concrete Model gave a 13 % higher deflection than the experimental deflection. The
Concrete Damage Model Release 3 showed a deflection similar to that of the experimental
value. In the high strength concrete with conventional rebar (HSC-NR) category, the
Winfrith Concrete Model, showed a deflection 10 % less than the experimental value and in
the high strength concrete with HSLA-V rebar (HSC-VR) category, the Winfrith Concrete
Model showed a deflection 10 % less than the experimental value. However, similar to the 1
in. (25.4 mm) models, the Concrete Damage Model Release 3 provided a stiff response in
both HSC-NR and HSC-VR categories.
5.4 Comparison of Damage and Crack patterns with experimental crack patterns.
It is important to study and understand crack propagation in reinforced concrete
structures when subjected to blast loads because, cracks provide a lot of information on the
action of reinforcement to provide tensile strength to concrete as concrete has very low
tensile strength and deformation capacity.
58
Among the two material models used for the study, the Winfrith Concrete Model has
the ability to show the propagation of cracks on the surface of the reinforced concrete slab,
without being sensitive to mesh sizes. The observations presented in chapter 4 indicated than
the cracks developed using the Winfrith Concrete Model were a close match to the
experimental crack patterns. However, the Concrete Damage Model Release 3 does not have
an inbuilt crack feature, and needs to be coupled with an external material model called
MAT_Add_Erosion, which takes into account the maximum principal strain in the material
to provide information on initiation and propagation of cracks. The cracks produced by the
Concrete Damage Model Release 3 with a ¼ in. (6.35 mm) mesh size were a close match to
the crack produce during the experiments.
59
CHAPTER 6:
CONCLUSIONS
From the observations and the analysis presented in chapters 4 and 5, some
conclusions can be drawn regarding the behavior of the two material models namely,
Winfrith Concrete Model and Concrete Damage Model Release 3, in an attempt to validate
the models with experimental data involving the response of reinforced concrete slabs subject
to blast loads in a Shock Tube apparatus.
I. In the normal strength concrete NSC-VR and NSC-NR categories with 1 in.(25.4
mm) mesh size, when CLS was used, both the Winfrith Concrete Model and the
Concrete Damage Model Release 3 performed well and gave deflection predictions
that were close to the experimental values and hence both the models could be used
for validation purposes.
II. In the normal strength concrete NSC-VR and NSC-NR categories with 1 in. (25.4
mm) mesh size, when CLS was not used, though the Winfrith Concrete Model
performed better than the Concrete Damage Model Release 3.However, both gave
lower deflections than the experimental value.
III. In the HSC-VR and HSC-NR categories with 1 in.(25.4 mm) mesh size, the Winfrith
Concrete Model provided deflection values that were close to the experimental
values, however, the Concrete Damage Model Release 3 gave very low deflections.
IV. In the NSC-VR category with ½ in. (12.7 mm) mesh size, both the Winfrith Concrete
Model and the Concrete Damage Model Release 3 showed deflection values that were
higher than that of the experimental value and in the NSC-NR category, Both the
60
models gave deflection predictions that were close to the experimental values and
hence both the models could be used for experimental validation purposes in the ½ in.
(12.7 mm) mesh size also.
V. In the HSC-VR and HSC-NR categories with ½ in.(12.7 mm) mesh size, the Winfrith
Concrete Model provided deflection values that were close to the experimental
values, however, the Concrete Damage Model Release 3 was very stiff and gave very
low deflections.
VI. The crack patterns obtained from the Winfrith Concrete Model with a 1 in. (25.4 mm)
mesh size was similar to that of the experiment and does not require an additional
material model to initiate cracks. In the case of Concrete Damage Model Release 3, it
not only requires an additional material model to generate cracks, but also is very
sensitive with 1 in. (25.4 mm) mesh and requires a ¼ in. (6.35 mm) mesh or lower to
generate cracks effectively which increases the use of time and resources for the
simulation.
VII. Overall, for the above considered configuration of the slab and the loading condition,
Winfrith Concrete Model provides a better response in terms of deflection and crack
propagation than the Concrete Damage Model Release 3. It can also be used for a
wide range of concrete strengths with the help of the volume compaction curve which
is not possible in Concrete Damage Model Release 3.
61
6.1 Future Work
Based on the conclusions obtained from analyzing the behavior of the two concrete
material models, the following future work could be suggested.
a) The Concrete Damage Rel 3 model gave very low deflections compared to the
Winfrith model in the high strength criteria; hence this model needs to be studied
more at the source code level to understand the various input parameters and its effect
on higher concrete strengths.
b) A damage criterion may be established for the slabs through pressure impulse
diagrams.
c) From a broader perspective, a cost analysis can be performed in order to understand
the reduction in the number of field tests to be performed on the slabs.
62
Appendix A
Tables of Summaries
Table A1: Input Parameters for Concrete Damage Model Release 3
Concrete Damage Model Release 3
Parameters Description Values Units
RHO Mass Density 2.32E-04 lb-
s/in3 PR Poisson`s Ratio 0.15
FT Uniaxial Tensile Strength 475/935 Psi
A0 /-fc’ Uniaxial Compressive Strength -
4000.00/-15500
Psi
(A1) Maximum shear surface parameter Default
(A2) Maximum shear failure parameter Default
(B1) Damage Scaling Parameter Default
(Ω) Fractional dilatancy Default
(A1F) Residual Failure Coefficient Default
(λs) Stretch factor Default
(NOUT) Output selector for effective plastic strain 2
(RSIZE) Unit Conversion factor for length 1
(UCF) Unit conversion factor for stress 1
LCRATE Load Curve for strain rate effects Default
LOCWID Maximum aggregate diameter Default
λ01 – λ13 Damage Functions Default
B3 Damage scaling coefficient for tri-axial tension Default
A0Y Initial yield surface cohesion Default
A1Y Initial yield surface coefficient Default
η01 – η13 Scale factor Default
B2 Tensile Damage scaling coefficient Default
A2F Residual failure surface coefficient Default
A2Y Initial yield surface coefficient Default
63
Table A2: Input Parameters for Winfrith Concrete Model
Winfrith Concrete Model
Parameters Description Values Units RHO Mass Density 2.32E-04 lb-
s/in3 PR Poisson’s Ratio 0.15
TM Tangent Modulus 3.60E+06 Psi
UCS Uniaxial Compressive Strength 4000.00 Psi
UTS Uniaxial Tensile Strength 475 Psi
FE Fracture Energy 2.00E-04
ASIZE Aggregate Size 0.125 in.
E Young`s Modulus of Rebar Default
YS Yield`s stress of rebar Default
EH Hardening Modulus of rebar Default
UELONG Ultimate elongation before rebar fails Default
RATE Rate effects 1
CONM Factor to convert model mass units to Kg -1
CONL Factor to convert model length units to meters 0.0254
CONT Factor to convert model length units to seconds 1
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Table A3: Input Parameters for Volume Compaction Curve in the Winfrith Concrete Model for 15.5 ksi and 4 ksi Concretes.
15.5 ksi
Volumetric Strain
Pressure(Mpa) [ x*P1]
P1 x*P1 Mpa to Ksi conversion
factor
x*P1
x (Mpa) (Mpa) (Ksi)
-0.000019 1 35.62 35.6 0.145 5.17 -0.002 1.5 35.62 53.4 0.145 7.75 -0.004 3 35.62 106.9 0.145 15.50 -0.01 4.8 35.62 171.0 0.145 24.80 -0.02 6 35.62 213.7 0.145 31.00 -0.03 7.5 35.62 267.2 0.145 38.75
-0.041 9.45 35.62 336.6 0.145 48.82
-0.051 11.55 35.62 411.4 0.145 59.67 -0.062 14.25 35.62 507.6 0.145 73.62 -0.094 25.05 35.62 892.3 0.145 129.41
4 ksi
Volumetric Strain
Pressure(Mpa) [ x*P1]
P1 x*P1 Mpa to Ksi conversion
factor
x*P1
x (Mpa) (Mpa) (Ksi)
-0.000019 1 9.19 9.2 0.145 1.33 -0.002 1.5 9.19 13.8 0.145 2.00 -0.004 3 9.19 27.6 0.145 4.00 -0.01 4.8 9.19 44.1 0.145 6.40 -0.02 6 9.19 55.1 0.145 8.00 -0.03 7.5 9.19 68.9 0.145 10.00
-0.041 9.45 9.19 86.8 0.145 12.60 -0.051 11.55 9.19 106.1 0.145 15.39 -0.062 14.25 9.19 131.0 0.145 18.99 -0.094 25.05 9.19 230.2 0.145 33.39
65
Table A4: Input Parameters for Plastic Kinematic Model for Steel Rebar
Plastic Kinematic Model
Parameters Description Values Units RO Mass Density 7.30E-04 lb-s/in3
E Young`s Modulus of Rebar 2.90E+07 Psi
PR Poisson`s Ratio 3.00E-01 Psi
SIGY Yield`s Strength of Rebar 60000/83000 Psi
ETAN Tangent Modulus Default
BETA Hardening parameter Default
SRC Strain Rate Parameter Default
SRP Strain Rate Parameter Default
FS Failure Strain for Eroding Elements Default
VP Visco-Elastic Parameter Default
Table A5: Analytical and Experimental Deflection Summary
Slab ID Deflections
66
1 in. Mesh 1/2 in. Mesh Experimental Winfrith Damage Release 3 Winfrith Damage Release 3 NSC-VR
5.4 in. 5.1 in. 8.1 in. 8.6 in. 5.1
NSC-NR
6.3 in. 5.6 in. 9.9 in. 8.9 in. 8.7
HSC-VR
3 in. Stiff 4.3 in. Stiff 4.8
HSC-NR
4.9 in. Stiff 4.9 in. Stiff 5.5
Table A 6: Percentage change in deflection when the mesh size was reduced from 1 in. (25.4 mm) to 1/2 in. (12.7 mm).
Slab id. Deflection Percentage
Winfrith Damage Rel 3
NSC-NR ↑ 36% ↑ 37%
NSC-VR ↑33% ↑40%
HSC-NR Nil Nil
HSC-VR ↑30% Nil
67
Table A 7: Percentage comparison of deflections with experimental value.
Slab id. 1 in. Mesh Size ½ In. Mesh Size
Winfrith Damage Rel 3 Winfrith Damage Rel 3
NSC-NR ↓ 27 % ↓ 35 % ↑13% ↑2%
NSC-VR ↑5% Same
Deflection ↑37% ↑40%
HSC-NR ↓ 10 % Stiff ↓ 10 % Stiff
HSC-VR ↓ 37 % Stiff ↓ 10 % Stiff
68
Appendix B
Input File Description
Figure B1: Input and Output Control Parameters
69
Figure B2: Input parameters for Concrete Damage Model Release 3
Figure B2: Input parameters generated by Concrete Damage Model Release 3
70
Figure B4: Input Parameters for Winfrith Concrete Model for 4 ksi Concrete
Figure B6: Input parameters for Constrained Lagrange in Solid Formulation
Figure B5: Input Parameters for Plastic Kinematic Model
71
Figure B7: Input parameters for Mat Add Erosion Material Model
'MAT m EROSION
" ~" excl mxpres mneps effeps voleps numflp occ , 0.000 0.000 0.00000 0.000 0.000 1.000000 1.000000
" mnpres slgp1 c,~ mxeps epssh slgth mpulse falltm 0.000 0.000 0.000 0.0100e 0.000 0.000 0.000 0.000
72
References
1. LSDYNAV970, 971 Keyword manual Vol. 1 and Vol. 2, Livermore Software
Technology Corporation.2007 a & b.
2. Yaramada, V.K.R., Numerical Response of Steel Reinforced Concrete Slab Subjected
to Blast and Pressure Loadings in LSDYNA, A Thesis in Civil and Mechanical
Engineering. 2010, University of Missouri Kansas City.
3. (DoD), D.o.D., Unified facilities criteria (UFC), DoD minimum antiterrorism
standards for buildings.” Department of Defense, UFC 4-010-01. 2007.
4. Tanapornraweekit, G., et al., Modeling of a Reinforced Concrete Panel Subjected to
Blast Load by Explicit Non-linear FE Code. In Proceedings. AEES Conference.2007.
5. D.U.Hao, L.Z., Numerical Analysis of Dynamic Behavior of RC slabs Under BLast
Loading. Transactions of Tianjin University, 2008. 15(1): p. 61-64.
6. Broadhouse, B. and G. Attwood. Finite element analysis of the impact response of
reinforced concrete structures using dyna3d. Proceedings of Structural Mechanics in
Reactor Technology (SMiRT) 12, University of Stuttgart Germany Elsevier Science
Publishing. 1993.
7. Malvar L, C.J., Morrill K., K&C concrete material model, release III: automated
generation of material model input. Karagozian & Case Structural Engineers, 2000.
Report TR-99-24.
8. Sangi, A. and I. May, High-Mass, Low-Velocity Impacts on Reinforced Concrete
Slabs. In proceeding . 7th European LSDYNA Conference.2009.Dynamore GMBH.
9. Algaard, W., Lyle, J. and Izatt, C., Perforation of Composite Floors. In proceedings
.5th European LS-DYNA User's Conference, 2005.
73
10. Xu, K. and Y. Lu, Numerical simulation study of spallation in reinforced concrete
plates subjected to blast loading. Computers & Structures, 2006. 84(5-6): p. 431-438.
11. Jorge O. Torres Alamo and Robert, S.D, Dynamic Blast Load Simulator Micro-Alloy
Vanadium Steel Reinforced Concrete Slab Experiments. US Army Corps of Engineers
Research and Development Center, 2008.
12. Broadhouse, B., The Winfrith Concrete Model in LS-DYNA3D. Report: SPD/D (95).
363.
13. Schwer, L. and L. Malvar, Simplified concrete modeling with*
MAT_CONCRETE_DAMAGE_REL3. In proceedings. LS-DYNA Anwenderforum,
Bamberg, 2005.
74
VITA
Anirudha Vasudevan was born in Mysore, in the state of Karnataka, India on April
7th, 1987. He joined University Visvesvaraya College of Engineering, Bangalore, India for
his Bachelor`s. He completed Bachelor`s in Civil Engineering in July 2008. He worked as a
Project Engineer in hydroelectric power for 8 months in India till June 2009.
He came to the USA in August 2009 and joined the Master’s program in Civil
Engineering at UMKC. He was awarded graduate research assistantship from the civil and
mechanical engineering department of UMKC. He is the recipient of the ACI 2010-11
Honorary “DJ” Belarbi Graduate Scholarship for 2010-2011. He is the co-author of a paper
in 2011 ACI SP Vol. 281 journal titled “Numerical modeling of concrete slabs reinforced
with high strength low alloy vanadium (HSLA-V) steel bars subjected to blast loads”.
He plans to pursue his research activities in the field of finite element analysis and
structural dynamics after M.S. along with working as a Structural Engineer.