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
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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
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)
3
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