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October 2005
Vanadium Rebar Case Study
by Beverly P. DiPaolo, Bradley W. Foust, Edward F. ONeil, Photios Papados, and
Stanley C. Woodson
U.S. Army Corps of EngineersEngineer Research and Development Center
3909 Halls Ferry Road
Vicksburg, MS 39180-6199
Prepared for Advanced Technology Institute
5300 International Boulevard
North Charleston, SC 29418
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Contents
Preface................................................................................................................................ iv
Conversion Factors, Non-SI to SI Units of Measurement .................................................. v1: Introduction.................................................................................................................... 1
1.1 Background............................................................................................................... 11.2 Objective................................................................................................................... 1
1.3 Scope ........................................................................................................................ 1
2: Parametric Study............................................................................................................ 32.1: Purpose of Study...................................................................................................... 3
2.2: Approach ................................................................................................................. 3
2.3: Results ..................................................................................................................... 62.4: Summary ............................................................................................................... 13
3: Experimental Results ................................................................................................... 14
3.1 General.................................................................................................................... 143.2 Concrete Materials Testing..................................................................................... 183.3 Steel Rebar Materials Testing................................................................................. 25
3.4 Concrete Components Testing................................................................................ 27
3.5 Summary of Testing Program................................................................................. 314: Computations............................................................................................................... 32
4.1: Introduction ........................................................................................................... 32
4.2: Material constitutive models ................................................................................. 334.3: Numerical Analysis ............................................................................................... 35
5: Usage and Risk ............................................................................................................ 42
5.1: Environmental Statement ...................................................................................... 42
6: Conclusions.................................................................................................................. 466.1: Conclusions ........................................................................................................... 46
Acknowledgements ....................................................................................................... 48
References......................................................................................................................... 49Appendix 4.1..................................................................................................................... 51
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Preface
The study reported herein was performed by members of the staff of the Geotechnicaland Structures Laboratory (GSL) of the U.S. Army Engineer Research and Development
Center (ERDC) located at the Waterways Experiment Station in Vicksburg, Mississippi.The investigation was sponsored by the Army Research Laboratory in collaboration with
Advanced Technology Institute and the Vanadium Technology Program underCooperative Research and Development Agreement (CRADA-04-GSL-02). The principal
investigator for this effort was Dr. Paul Mlakar.
This study was performed under the general supervision of Dr. David W. Pittman,
Director, GSL, Dr. William P. Grogan, Deputy Director, GSL, Dr. Robert L. Hall, Chief,
Geosciences and Structures Division (GSD), and Mr. Frank D. Dallriva, Chief, StructuralMechanics Branch (SMB), GSL.
At the time of publication of this report, Director of ERDC was Dr. James R. Houston,and Commander and Executive Director was COL James R. Rowan, EN.
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1: Introduction
1.1 BACKGROUND
Due to recent terrorist activities, structural performance to protect building occupants
during a blast event, and residual structural integrity to increase survivability after theexplosion are becoming design criteria for specific buildings. For designs using
conventional construction materials, as the protection level increases, the structural
system space, weight, and costs also increase. Very high-strength concretes could be usedto mitigate these increases, but may require high-strength reinforcement with high
ductility to adequately balance cross-sectional behavior, to achieve the design strength or
to provide the required deformation performance. Vanadium steel rebar may offer thiscombination of high strength and high ductility. Vanadium-alloy high-strength steel
rebar will be investigated to determine its performance when coupled with very high-
strength concrete. Vanadium is widely used as a grain refining element in the mini-millsteel industry. The introduction of vanadium into the chemical composition of a steelreinforcement bar provides higher strengths without compromising on ductility or
formability.
1.2 OBJECTIVE
The overall objective of this study was to research very high strength concrete and highstrength vanadium steel reinforcement bar for newly constructed reinforced concrete
protective structures for United States Army use and also for conventional construction.
1.3 SCOPE
The case study was initiated with a parametric analysis to investigate the potential for
weight, space, and cost savings, and system improvement in the form of increasedprotection level resulting from the substitution of high-performance materials for
conventional materials. The high-performance materials consisted of high-strength
concrete (fc 15 ksi) and vanadium steel rebar with a yield stress of at least 75 ksi. Alaboratory experimental program and computational simulations evaluating design
concepts for structural elements subjected to severe dynamic loadings were alsoconducted.
Two representative structural components were considered in the parametric analysis; areinforced concrete blast-resistant exterior wall and a reinforced concrete first-floor
column. Several high-performance material combinations were examined. These
combinations include the following: 15 ksi compressive strength concrete in conjunctionwith 75 ksi steel reinforcement bar, 15 ksi concrete with 85 ksi steel reinforcement, and
30 ksi concrete with 100 ksi steel reinforcement. The performances of these material
combinations were then compared to that of a conventional strength material
combination; 5 ksi compressive strength concrete with 60 ksi steel reinforcement.
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2: Parametric Study
2.1 PURPOSE OF PARAMETRIC STUDY
The analytical parametric study was performed to compare the effectiveness of the high-performance materials of interest with that of standard materials with regard to the blastresponse of reinforced concrete walls and columns.
2.2 APPROACH
The U.S. government-owned computer programs ConWep and Wall Analysis Code
(WAC) were the analytical tools used for the parametric study. Both computer programs
were developed at ERDC.
ConWep has many capabilities with regard to predicting the effects of conventionalweapons. For this study, ConWepwas used only for a good approximation of the blast
loading (pressure and impulse) on selected structural components. ConWep considers the
effects of the airblast clearing the loaded element in determining the impulse distribution.
For example, the wall of one bay of a building can be considered as the target area for the
computation of loads. The dimensions of the entire building can be used as the reflecting
surface as shown in Figure 2.1.
Figure 2.1 ConWep Geometry
WAC was developed initially to compute the SDOF response of masonry walls. It has
since been adapted to analyze reinforced concrete members (e.g., columns, beams, and
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walls) and allow the use of a user-defined resistance function. Figure 2.2 presents an
idealized SDOF model of the type used in WAC. Various support conditions
(combinations of simple, fixed, and free) can be modeled. WAC solves the equation of
motion for the equivalent system by numerical integration to determine the response-time
history of a critical point on the structural element (usually at mid-height and mid-width).
Figure 2.2 Typical SDOF Model
For this study, analyses were performed for reinforced concrete walls and columns. In
order to compare the effects of the material strengths on the blast response of the
elements, it was necessary to define reasonable levels of response to serve as standardsfor comparison. Table 2.1 was taken from the Unified Facilities Criteria (UFC) DoD
Minimum Antiterrorism Standards for Buildings, and describes potential damage and
injury for defined levels of protection. In general, a low level of protection corresponds
to a high level of damage, but not to the point of likely progressive collapse. Conversely,
a high level of protection corresponds to essentially no structural damage.
RANGE
CHARGE
WALL
BLAST LOADED WALL
SDOF MODEL
kF
x
M
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Level of
Protection
Potential Structural Damage Potential Door and Glazing
Hazards
Potential Injury
Low Damaged unrepairable.
Major deformation of non-
structural elements andsecondary structural members
and minor deformation of
primary structural members, but
progressive collapse is unlikely.
Glazing will break, but fall
within 1 meter of the wall or
otherwise not present asignificant fragment hazard.
Doors may fail, but they will
rebound out of their frames
presenting minimal hazards.
Majority of
personnel suffer
significant injuries.There may be a few
(
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HLOP High Level of Protection
MLOP Medium Level of Protection
LLOP Low Level of Protection
VLLOP Very Low Level of Protection
- Ductility Ratio
- Support Rotation
Table 2.2 Response Limits
2.3 RESULTS
2.3.1 Concrete Wall
The following structural parameters were used in the analyses of concrete wall elements.
Building Height = 120
Building Width = 200 Wall Height = 13 Wall Width = 20 Two Thickness and Reinforcing Schemes:
a. doubly reinforced 12-inch thick wall
b. singly reinforced 6-inch thick wall Simple Support End Conditions Standard Building Materials
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- 5 ksi Conventional Concrete- 60 ksi Steel Reinforcement
High-Performance Building Materials Combinations
- 15 ksi High-Strength Concrete and 75 ksi Vanadium Steel Reinforcement
- 15 ksi High-Strength Concrete and 85 ksi Vanadium Steel Reinforcement- 25 ksi High-Strength Concrete and 100 ksi Vanadium Steel Reinforcement
- 30 ksi High-Strength Concrete and 100 ksi Vanadium Steel Reinforcement
The original task for the study was to compare the standard building materials with the 15
ksi concrete and 75 ksi steel (15/75). Later, supplemental calculations were performed
for higher performance materials. Thus, the results presented below typically use eitherthe standard materials or the 15/75 combination as baselines for comparison.
Two other parameters required for the study were the explosive charge weight and thestandoff (distance from center of explosive charge to face of structural element). Charge
weights of 1000, 4000, and 10,000 lbs of TNT were used. The standoff varied dependingon the response limit being achieved, as will be discussed herein.
Table 2.3 presents the analytical results for concrete walls that are reinforced with #5
reinforcing bars spaced at 12 inches on-center, in each face of the wall. Such a
reinforcing scheme is typically termed doubly-reinforced. For each of the two chargeweights (4000 lbs and 10,000 lbs), a standoff was determined that would produce a
support rotation of approximately 4 degrees for use of the 15/75 materials. The 4-degree
support rotation corresponds to the defined Low Level of Protection for a wall that doesnot have any special end conditions and is probably typical of most conventional walls of
similar proportion. For comparison, the same standoffs were used for the wall with the5/60 (5 ksi concrete and 60 ksi reinforcement), the 15/85 (15 ksi concrete and 85 ksi
reinforcement), and the 25/100 (25 ksi concrete and 100 ksi reinforcement) materials.
The increasein response (as defined by support rotation) for the 5/60 wall was 34% and38% respectively for the 4000-lb and the 10,000-lb charge weights in comparison to the
15/75 wall. The responses for 15/85 and 25/100 walls were approximately 12 to 20%less(as indicated by negative signs in the table) than the 15/75 wall.
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Explosive
Wt.
TNT
(lbs)
Standoff
(ft)
Concrete
Strength
(ksi)
Rebar
Strength
(ksi)
Support
Rotation
(deg.)
Percent
Diff.
Support
Rotation
(%)
Deflectio
n (in.)
Peak
Pressure
(psi)
Peak
Impulse
(psi-
msec)
4000 100 15 75 4.1 5.6 79 492
4000 100 5 60 5.5 34 7.5 79 492
4000 100 15 85 3.6 -11 5.0 79 492
4000 100 25 100 3.4 -18 4.6 79 492
10000 170 15 75 4.0 5.4 42 513
10000 170 5 60 5.5 38 7.5 42 513
10000 170 15 85 3.5 -12 4.8 42 513
10000 170 25 100 3.2 -20 4.4 42 513
Table 2.3 Comparison of Response (4-degree baseline) for 2 Layers of #5 rebar at 12
Spacing in a 12 thick wall
Table 2.4 also presents analytical results for concrete walls that are reinforced with no. 5
reinforcing bars spaced at 12 inches on-center, in each face of the wall. However, for
each of the two charge weights (4000 lbs and 10,000 lbs), a standoff was determined thatwould produce a support rotation of approximately 12 degrees of the 15/75 materials.
The 12-degree support rotation corresponds to the defined Low Level of Protection for a
wall that is of normal proportions, but doeshave end conditions that would allow thedevelopment of large deformation response, including a mechanism known as tension
membrane. In pure tension membrane, all reinforcement is in tension such that theelement resembles a catenary. The reinforcement must be well anchored into strongsupports in order to develop the tension forces. Such characteristics are somewhat typical
for blast resistant structures, but sometimes can be found in conventional construction.
For comparison, the same standoffs were used for the wall with the 5/60, 15/85, and25/100 materials. For the 5/60 material, the increase in response (as defined by support
rotation) was 29% and 31% respectively for the 4000-lb and the 10,000-lb charge
weights. As expected, the response was less for the 15/85 (approximately 10%) and
25/100 (approximately 17%) materials than for the 15/75 material.
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Explosive
Wt.
TNT
(lbs)
Standoff
(ft)
Concrete
Strength
(ksi)
Rebar
Strength
(ksi)
Support
Rotation
(deg.)
Percent
Diff.
Support
Rotation
(%)
Deflectio
n (in.)
Peak
Pressure
(psi)
Peak
Impulse
(psi-
msec)
4000 64 15 75 12.1 16.7 305 849
4000 64 5 60 15.6 29 21.8 305 849
4000 64 15 85 10.8 -10 14.9 305 849
4000 64 25 100 10.1 -16 14.0 305 849
10000 111 15 75 12.0 16.6 143 851
10000 111 5 60 15.7 31 21.9 143 851
10000 111 15 85 10.8 -10 14.9 143 851
10000 111 25 100 10.1 -16 13.9 143 851
Table 2.4 Comparison of Response (12-degree baseline) for 2 Layers of #5 rebar at 12
Spacing in a 12 thick wall
The results presented in Table 2.5 are intended for consideration of the quantity of
reinforcing steel required to achieve a given support rotation for a given explosive threat.
For each wall, the area of steel was determined that would allow a response ofapproximately 4 degrees support rotation for a 4000-lb explosive charge at a standoff of
60 ft. This explosive threat was selected to allow the use of no. 8 reinforcing bars at a
reasonable spacing. For the 5/60 materials, the total area of required reinforcing steelwas approximately 40% greater than that required for the wall with the 15/75 materials.
The required area of reinforcing was reduced approximately 11 and 22% for the 15/85and the 25/100 material, respectively.
Concrete
Strength
(ksi)
Rebar
Strength
(ksi)
Spacing
(in)
Area of
Rebar
(in/ft)
Percent
Diff.
Area of
Rebar
(%)
Support
Rotation
(deg.)
Deflectio
n (in.)
Peak
Pressure
(psi)
Peak
Impulse
(psi-
msec)
15 75 7 2.69 4.2 5.7 370 922
5 60 5 3.76 40 4.3 5.9 370 922
15 85 8 2.37 -12 4.2 5.7 370 92225 100 9 2.10 -22 4.0 5.4 370 922
Table 2.5 Comparison of Required Area of Rebar to Achieve Support Rotation of 4
Degrees for Doubly Reinforced 12 Thick Wall Subjected to 4000# TNT at 60
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Concrete
Strength
(ksi)
Rebar
Strength
(ksi)
RebarSpacing
(in)
Area of
Rebar
(in/ft)
Percent
Diff.
Area of
Rebar
(%)
Deflection
(in.)
15 75 #10 3.5 8.69 0.8
5 60 #11 3 12.49 44 0.8
15 85 #9 3 8.00 -8 0.77
30 100 #9 3.75 6.40 -26 0.68
Table 2.7 Comparison of Required Area of Rebar to Achieve a Ductility Ratio of One
for a 12 Thick Wall When Subjected to 4000# TNT at 100
2.3.2 Reinforced Concrete Column
Reinforced concrete columns are a primary structural component of reinforced concrete
buildings and are susceptible to blast damage. The analytical results presented hereincompare the response of columns constructed with the material strengths of interest.
Experimental results reported by Woodson and Baylot (1999) demonstrated that
conventional reinforced concrete columns will incur heavy damage when subjected to theblast effects of 1000 lbs of C-4 explosives at a standoff of 14 ft. The response is
considerably less at a standoff of 20 ft. Thus, explosive threats in range of 1000 lbs at 15
to 20 ft of standoff were considered of interest for this study. Also, larger explosivecharge weights at greater standoff distances were evaluated.
Table 2.8 indicates the change in response for a 14-inch by 14-inch column reinforced
with 6 no. 8 reinforcing bars for the 1000 lbs of TNT threat. This column design wasused in all of the column analyses and might be expected in a typical of 4-story office
building in low seismic zones. The clear height of the column was taken as 12 ft. The
protective design community has yet to develop definitive criteria for allowable responselimits of reinforced concrete columns; however, for purposes of this study 4 degrees will
be taken as the baseline. The 20-ft standoff is considered in Table 2.8 as a standoff that
will cause damage levels typically not considered to cause catastrophic failure of the
structure. It is observed that the high performance materials decrease the columnresponse (support rotation) by approximately 23 to 42 percent compared to the
conventional materials. A similar result was observed for the standoff of 15 ft, which
should be considered to cause heavy damage. It is interesting that the column with the15/75 materials is somewhat optimum for resisting this threat with the baseline response
of 4 degrees support rotation.
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Standoff
(ft)
Concrete
Strength
(ksi)
Rebar
Strength
(ksi)
Support
rotation
(deg.)
Percent
Diff.
(Support
Rotation)
Deflection
(in.)
Peak
Pressure
(psi)
Peak
Impulse
(psi-msec)
20 5 60 2.78 2.7 2157 1438
20 15 75 2.15 -23 3.5 2157 1438
20 15 85 1.93 -31 2.4 2157 1438
20 30 100 1.61 -42 2 2157 1438
15 5 60 5.2 5 3692 1956
15 15 75 4 -23 6.5 3692 1956
15 15 85 3.52 -32 4.4 3692 1956
15 30 100 2.94 -43 3.7 3692 1956
Table 2.8 Comparison of Support Rotations for Explosive Threat of 1000 lbs of C-4
A larger explosive charge weight (4000 lbs TNT) was considered for the results
presented in Table 2.9. The standoff of 37 ft was determined to induce a support rotationof 4 degrees for the column of conventional materials. Decreases in support rotation of
28 to 46 percent were observed for the high performance materials.
Concrete
Strength
(ksi)
Rebar
Strength
(ksi)
Support
rotation
(deg.)
Percent
Diff.
(Support
Rotation)
Deflection
(in.)
5 60 4 5
15 75 2.9 -28 3.69
15 85 2.61 -35 3.28
30 100 2.15 -46 2.7
Table 2.9 Comparison of Support Rotations for Explosive Threat of 4000 lbs of TNT at
37
Table 2.10 presents similar results to that of Table 2.9, but Table 2.10 is for a 10,000-lbcharge weight.
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Concrete
Strength
(ksi)
Rebar
Strength
(ksi)
Support
rotation
(deg.)
Percent
Diff.
(Support
Rotation)
Deflection
(in.)
5 60 4 3.7
15 75 3 -25 5
15 85 2.6 -35 3.3
30 100 2.1 -48 2.6
Table 2.10 Comparison of Support Rotations for Explosive Threat of 10,000 lbs of TNT
at 63
2.4 SUMMARY
The SDOF analyses consistently indicated significant enhancement to the blast resistance
of the selected typical reinforced concrete wall and column structural elements. Theresults indicate that a typical 12-inch thick reinforced concrete wall constructed of
standard concrete and reinforcing materials will incur roughly 30% more response (in
terms of support rotation) than a similar wall constructed of the 15/75 materials.Additional performance can be expected for the higher level performance 15/85 and
25/100 materials with a decrease in response of roughly 10 and 20% from that of the
15/75 material. Even greater percentage differences can be observed in comparison ofthe reduction of reinforcement needed to limit wall response to a specified level.
For the columns, response of the columns with the high-performance materials was
compared against that of a column with the standard materials. Somewhat consistently
over the range of explosive charge weights considered, the 15/75, 15/85, and 30/100materials respectively incurred support rotations approximately 30, 35, and 45 percent
less than that for the standard materials.
Whether one considers the standard material or the 15/75 material as a baseline,
enhancement to blast resistance on the order of at least 30% can be expected for the highperformance materials over the standard material.
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3: Experimental Program
3.1 GENERAL
The experimental program was based on two material combinations that each consisted
of a concrete material and a steel reinforcement bar material. The combinations wereconventional concrete and conventional rebar and very high strength concrete and high
strength rebar and were designated as Cc-Cr and VHSc-HSr, respectively. The
combinations were based on mechanical properties of the materials: the compressivestrength of the concrete and the yield strength of the steel rebar material and are as
described in Figure 3.1.
The objectives of the experimental program were to:
Perform required tests of the concrete and steel reinforcement bar (rebar)materials for quality assurance purposes
Determine actual mechanical properties of materials and compare to standardspecifications
Verify performance of materials Gain relevant experience with the material combinations prior to determining theexperimental program for the Demonstration Project
ERDC mix designs for the concrete materials were chosen based on a design concrete
compressive strength of fc= 5,000 psi (28 day cure) for the conventional concrete and fcof 15,000 psi (56 day cure) for the very high strength concrete. The concrete mix
constituents and an example of the hardened concrete mesostructure are shown in Figure3.2a and Figure 3.2b for the conventional concrete and the very high strength concrete,respectively.
Conventional concrete and rebar (Cc-Cr)
Concrete with compressive strength of fc= 5,000 psiA 615 rebar with yield stress of fy= 60,000 psi
Very High Strength Concrete and High Strength Rebar (VHSc-HSr)
Concrete with compressive strength of fc= 15,000 psi
Rebar with yield stress of fy= 75,000 psi
Figure 3.1 Concrete Material Steel Reinforcement Bar Material Combinations
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Conventional Concrete Mix Constituents
1. Type 1 Portland cement2. Fine aggregatesand3. Coarse aggregatelimestone4. Defoaming agent5. High range water reducing agent
6. Water reducing agent7. Air8. Water
Very-High-Strength Concrete Mix Constituents
1. Type 1 Portland cement2. Fine aggregatelimestone3. Coarse aggregatelimestone4. Silica fume5. Fly ash6. High range water reducing agent7. Air8. Water
Example of Hardened Concrete
1.5 inch square cross-sectionfrom 6 inch diameter cylinder
Example of Hardened Concrete
1.5-inch diameter core cross-section
from 6 inch diameter cylinder
(a) Conventional Concrete
(b) Very High Strength Concrete
Figure 3.2 Concrete Mix Constituents and Hardened Concrete Appearances
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The steel material used for the reinforcement bars or rebar for the Cc-Cr material
combination was conventional steel rebar that met the ASTM A615 Grade 60 rebarminimum specified yield stress of fy= 60,000 psi. As high strength vanadium steel rebar
could not be located in time for the scheduled concrete mixing, batch and placement of
test specimens, the steel material used for the rebar for the VHSc-HSr material
combination was 316LN stainless steel Grade 75 rebar that met the ASTM A955 Grade75 rebar minimum specified yield stress of fy= 75,000 psi. For each steel material,
several 20-ft lengths of #3 and #6 deformed rebar were purchased from commercial
metals suppliers [ONEAL, Salit].
The experimental program included mechanical property testing of the concrete and the
steel materials and small component testing. All testing was quasi-static. The programconsisted of three parts:
Concrete Materials Testing Steel Rebar Materials Testing Concrete Component Testing
For the concrete material testing part, tests were performed on hardened concrete
specimens to determine strengths in major stress/strain states and verify quality control.The tests included:
Compressive strength of cylindrical concrete specimens tests Tensile strength tests
Direct tensile strength of cylindrical concrete specimens tests Splitting tensile strength of cylindrical concrete specimens tests Flexural strength of concrete (modulus of rupture) tests beams
with square cross-sections
For the steel rebar materials testing, uniaxial tensile strength tests were performed to
determine yield stress, ultimate strength and ductility of the conventional and highstrength rebar materials.
Miscellaneous testing was performed on small hardened reinforced concrete components.The tests included:
Rebar and bolt pullout tests Reinforced concrete beam flexure strength tests
Four-point bend 3rd-point loading
For the test specimens, the mixing and placement of the concrete in the formwork, the
curing of the concrete test specimens and all testing was performed in the Concrete and
Materials Branch of the Geotechnical and Structure Laboratory of ERDC in Vicksburg,Mississippi. For each concrete material, the amount of concrete needed for all test
specimens was 4 cubic feet and due to the size of mixers available, forms were divided
into three sets and concrete was mixed and placed in three batches. The concrete mixer is
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diameter by 6 inch long cylinder forms and small one-half inch and one inch diameter by
one inch deep plastic specimen forms for miscellaneous material specimens. Theseforms are shown in Figure 3.4a. Figure 3.4b shows a 6-inch wide by 6-inch deep by 21-
inch long plastic beam form for a concrete flexure test. A double 12 inch square by 24
inch deep form and a single 12 inch cube form for embedded rebar pullout testing and a
12 inch cube form for embedded bolt pullout testing are shown in Figure 3.4c. For thereinforced concrete beam bend test, a 6-inch wide by 6 inch deep by 36-inch long metal
beam forms is shown in Figure 3.4d.
Specimens from a specific form were assigned specimen numbers. The numbers
consisted of a letters representing the concrete or concrete and rebar material type
designation a batch number and (-if applicable, a sequence number of the specimen in
the batch, if multiple specimens were placed in the same form type), e.g. Cc2-5 for thefifth cylinder of Cc concrete in batch 2.
3.2 CONCRETE MATERIALS TESTING
3.2.1 Compressive Strength of Cylindrical Concrete Specimens Tests
For each concrete material, compressive strength tests were performed on three 6-inch
diameter by 12-inch long cylinders. One specimen was used from each batch. Reference
test methods used were ASTM C 39 03 Standard Test Method for CompressiveStrength of Cylindrical Concrete Specimens and ASTM C 469 - 02 Standard Test
Method for Static Modulus of Elasticity and Poissons Ratio of Concrete in Compression.
As stated in ASTM C39, the compressive strength as determined by this test method is
(a) Cylinder Forms
(b) Small Plastic Beam Form for
Plain Concrete Beam Specimens
(d) Large Metal Beam Form
for RC Beam Specimens
(c) Forms for Rebar and Bolt
Pullout Test Specimens
Figure 3.4 Forms for the Concrete Test Specimens
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not a fundamental or intrinsic property of the specific concrete, because compressive
strength depends on the size and shape of the test specimens, the batching and mixingprocedures, the methods used for sampling, the type of molding and fabrication, the
temperature, and moisture conditions during curing and the age at testing. However, the
test was used for quality assurance purposes and values of the compressive strength, fc,
are used in engineering practice for design purposes.
The test procedure consists of applying a compressive axial load to a cylinder at a rate
within a prescribed range specified in the standard test method. The specimen is loadeduntil failure occurs by fracture. All testing was performed using the Baldwin 440,000 lbs
Universal Testing Machine. The test setup is shown in Figure 3.5a. Specimen
preparation included demolding of the cylinders and end preparation to ensure parallelend surfaces and axial loading. For the Cc specimens, ends were capped with a sulfur
compound. A Cc specimen after failure is shown in Figure 3.5b.
Because the sulfur compound compressive strength is approximately 12,000 lbs andtherefore, less than the expected strength of the VHSc material, the ends of the VHSc test
specimen cylinders were ground flat. The grinding of a specimen is shown in Figure
3.6a. For the VHSc material, failure of the cylinders is sudden with the potential fordebris flying outside the boundary of the machine. Therefore, a cage (Figure 3.6b) was
placed around the specimen to contain pieces that might fracture off at failure of the
specimen. Figure 3.6b also shows the strain gages that were attached to the specimen andthat were used to obtain data for the static modulus of elasticity and Poissons ratio of
concrete in compression. As stated in ASTM C469, this data is used in sizing structural
members, determining quantity of reinforcement and computing stress in the working
(a) Test Machine and Specimen
Prior to Compression Test
(b) Cc Specimen in Machineafter Compression Test
Figure 3.5 Compressive Strength of Concrete Cylinder Specimens Test Setup and Results
fc= 4P/d2
where fc= compressive strength, (psi)
P= maximum load, (lbs)
d= diameter, (in)
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stress range of 0-40% of ultimate concrete strength. It was obtained in the case study for
the computational effort.
For each test, the compressive strength was calculated by the formula given in Figure 3.5.
The results of the testing are given in Table 1 and an example of engineering compressive
stress versus crosshead displacement for the Cc and the VHSc materials is given inFigure 3.7. The compressive strengths of the Cc specimens exceed the design stress of
5,000 psi. However, all of the compressive strength values for the VHSc specimens are
less than the design stress of 15,000 psi. On fracture surfaces of specimens of the VHScmaterial, it was discovered that large hydrated cement pieces were contained in the
concrete matrix and this could account for the reduced strength values. It isrecommended that better quality control of the mixing including sifting of the cement be
performed in the Demonstration Project to ensure the design concrete compressive
strength.
0
2000
4000
6000
8000
10000
12000
14000
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
Position (in.)
Stress(psi)
VHSc
Cc
(b) VHSc Specimen: with Strain Gages and with Cage for Specimen
Debris Containment
Figure 3.6 VHSc Concrete Cylinder Specimen Preparation and Test Setup
(a) VHSc Cylindrical Specimenin Grinder
Figure 3.7 Compressive Strength TestResults - Example: Engineering Stress vs.
Cross-head Displacement Cc and VHSc
Cylinder f'c Design
Concrete Material Specimen Age Compressive Compressive
ID (days) Strength (psi) Strength (psi)
Conventional Cc1-1 28 5,500 5,000
Cc2-1 28 5,900
Cc3-1 28 5,500
Very High Strength VHSc1-1 56 13,400 15,000VHSc2-1 56 13,200
VHSc3-1 56 11,600
Note 1: ASTM -C39/C 39m-03 and C469-02
Table 1. Compressive Strength Test Results
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3.2.2 Tensile Strength Tests of Concrete
Three types of tests were performed to obtain tensile strength data on hardened concrete
specimens. The tests were:
Direct Tensile Strength of Cylindrical Concrete to obtain the tensilestrength, S Splitting Tensile Strength of Cylindrical Concrete to obtain the
splitting tensile strength, T
Flexural Strength of Concrete (Using Simple Beam with Third-PointLoading) to obtain Modulus of Rupture,R
3.2.2.1 Direct Tensile Strength of Cylindrical Concrete Specimens Tests
For each concrete material, direct tensile strength tests were performed on three 6-inchdiameter by 12-inch long cylinders with one cylinder from each batch. The reference test
methods used was CRD-C 164-92 Standard Test Method for Direct Tensile Strength ofCylindrical Concrete or Mortar Specimens. The test consists of applying an axial tensile
load at a constant rate within a specified range until failure by fracture of the concreteoccurs. This test is considered to be the most basic test for determining tensile strength.
For this test, metal caps are required to be cemented to the ends of specimens to provide
grips and to ensure alignment of the test specimen. However, these caps act as holdingdevices and induce secondary stresses. Because of the capping requirement, this test has
added expense due to the time and effort involved in the capping process. Another
disadvantage is that for high strength concrete, failure may occur in the cement betweenthe cap and the concrete and the test then becomes invalid.
The testing was performed using the Baldwin 440,000 lbs Universal Testing Machine.The test setup is shown in Figure 3.8a with a Cc concrete specimen during loading andjust after fracture. A tested specimen that failed in the concrete is shown in Figure 3.8b.
(a) Example of Direct Tensile Strength of Cc ConcreteDuring Loading and just after Fracture
(b) Cc Direct Tensile
Test Specimen
Figure 3.8 Direct Tensile Strength Test Setup and Test Specimen
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The splitting tensile strength is calculated by the formula:
The results of the splitting tensile strength testing are given in Table 3 for both the Cc and
the VHSc materials. The percent that each splitting tensile strength value is of thecorresponding design compressive strength was calculated and also given in the table.
(a) Splitting Tensile Test Specimen Holder
T= 2P/ld
where T= splitting tensile strength, (psi)
P= failure load, (lbs)l= length, (in)
d= diameter, (in)
(b) Example of Splitting Tensile Strength of Concrete Specimens Test
Specimen in Test Machine - before and after Test
(c) Cc Splitting Tensile
Test Specimen
Figure 3.9 Splitting Tension Test Setup and Test Specimen
Cylinder T, Splitting
Concrete Material Specimen Age Tensile Strength % f'cID (days) (psi)
Conventional Cc1-2 28 450 9
Cc2-2 28 435 9
Cc3-2 28 460 9
Very High Strength VHSc1-4 56 660 4
VHSc2-4 56 700 5
VHSc3-4 56 725 5
Note 1: ASTM A496/C496M-04
Table 3. Splitting Tensile Strength Test Results
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3.2.2.3 Flexural Strength of Concrete (Modulus of Rupture) Tests
For each concrete material, flexural strength tests were performed on three 21 inch long
plain concrete beams with 6 inch wide by 6 inch deep square cross-sections to determine
the modulus of rupture. The reference test method was ASTM C 78 - 02 Standard Test
Method for Flexural Strength of Concrete (using Simple Beam with Third-PointLoading). Each beam is simply supported and third point loading is applied at a constant
rate within a specified range and through bearing blocks until rupture occurs. The test is
considered valid if the fracture occurs in the middle third of the span length. All of thetesting was performed using the Baldwin 440,000 lbs Universal Testing Machine and the
test setup is shown in Figure 3.10
For all test specimens, fracture occurred in the middle third of the span length. Themodulus of rupture was calculated using the following formula:
Table 4 gives the modulus of rupture and the percent of the design fcfor both the Cc and
the VHSc materials.
Figure 3.10 Flexure Strength Test Setup
R=PL/bd2
where R= modulus of rupture, (psi)
P= maximum load, (lbs)L= span length, (in)
d= depth of specimen, (in)
Flexure R, ModulusConcrete Material Specimen Age of Rupture % f'c
ID (days) (psi)
Conventional Cc1 28 665 13Cc2 28 685 14
Cc3 28 685 14
Very High Strength VHSc1 56 1370 9
VHSc2 56 1195 8
VHSc3 56 1340 9
Note 1: ASTM C 78-02
Table 4. Flexure Strength Test Results
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Results of all three tensile strength tests are consistent with the observations that usually
values of tensile strength determined by the these test methods are approximately 5-10%of the compressive strength determined by compression tests on cylindrical concrete
specimens and that strength magnitudes are in the following order:
S < T < Rdirect tensile splitting tensile modulus of rupture
3.3 STEEL REBAR MATERIALS TESTING
Uniaxial tension testing was performed on the conventional and the high strength steel
rebar materials to determine yield strength, ultimate strength and ductility of thecommercially produced rebar. The reference test methods were ASTM A 370 01
Standard Test Methods and Definitions for Mechanical Testing of Steel Products and E 8
01 Standard Test Methods for Tension Testing of Metallic Materials.
Testing was performed at 70F (room temperature) using an MTS Universal TestingMachine (100 kip load frame and load cell), a one-inch gage length extensometer with a
maximum percent strain of 18%, and a MTS computer-based data acquisition system.
The test setup is shown in Figure 3.11a and b. Testing was performed in displacementcontrol mode at a rate of 1/16 inch per minute. The testing conditions are summarized in
Figure 3.11d. For each material, specimens included No. 6 deformed bars in the as-
received condition, No. 3 deformed bars in the as-received condition and No. 3deformed bars with a machined necked-down region. Examples of the test specimens for
both materials are shown in Figure 3.11c
MTS Universal Testing Machine100 kip Load frame and Load cellQuasi-static Testing
Displacement ControlRoom Temperature
Extensometer
(a) MTS Machine with Test Specimen
(b) Test Specimen with
Extensometer
(d) Test Conditions
(c) Cr and HSr Test
Specimen Types
Figure 3.11 Uniaxial Rebar Tension Test Setup and Conditions
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The engineering stress-engineering strain curves for the No. 3 and the No.6 deformed
bars in the as-received conditions are given for both the Cr and the HSr materials inFigure 3.12a and Figure 3.12b, respectively. The corresponding tension test data is
summarized in Table 5. The ASTM minimum yield stress and ultimate strength values
are also shown in the table. The results indicate that there can be a wide variation in yield
stress and ultimate strength values; that minimum values may not be acquired, and also,that as-received material may significantly exceed minimum specified values. As the
rebar in the Demonstration Project will be used in the as-received condition, actual
strength values should be obtained and used in reinforced component designs instead ofspecified minimum values.
The engineering stress-engineering strain curves for the No. 3 deformed bars with
machined necked-down central regions are given for both the Cr and the HSr materials in
Figure 3.13. The corresponding tension test data is summarized in Table 6. The ASTM
minimum yield stress and ultimate strength values for unmachined rebar tests are alsoshown in the table. For both materials, yield stress and ultimate strength values are above
Figure 3.12 Engineering Stress-Engineering Strain Curves Nos. 3 & 6 Deformed Rebars
- as-received Condition
0
20000
40000
60000
80000
100000
120000
140000
160000
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20
Engineering Strain (in/in)
En
gineeringStress(psi)
0
20000
40000
60000
80000
100000
120000
140000
160000
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20
Engineering Strain (in/in)
En
gineeringStress(psi)
(a) No. 3 Rebars (b) No. 6 Rebars
HSr #6d
Cr #6d
HSr #3d
Cr #3d
fy, Yield Stress Ultimate Strength % Elongation
Bar Size Rebar type Specimen Test ASTM min. Test ASTM min. Test
ID (ksi) (ksi) (ksi) (ksi)
No. 3 Conventional 3C3d 69 60 107 90 >18
3C4d 68 106 >18
3C5d 43 81 >13
High Strength 3H1d 109 75 140 100 >18
3H2d note 2 139 note 2
3H3d 111 141 >18
No. 6 Conventional 6C1d 53 60 66 90 >16
6C3d 61 100 >18
High Strength 6H1d 65 75 101 100 >18
6H2d 74 109 >18
Note 1: ASTM - minimum values from ASTM A 615 Grade 60 and ASTM A955 Grade 75; Note 2: Error in acquiring strain data
Table 5 Uniaxial Tension Test Results Nos. 3 & 6 Deformed Rebars as-received Condition
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the minimum specified values and there is little variation in strength value for a given
material.
3.4 CONCRETE COMPONENTS TESTING
As indicated in the test results above, concrete material is much stronger in compression
than in tension and therefore, reinforcement is needed to resist the tensile stresses
resulting from induced loads on structural components.Rebar and bolt pullout testing andreinforced beam bending tests were performed to work with embedded metal and
reinforcement in both of the concrete materials prior to the demonstration project.
Rebar Pullout Tests: Rebar pullout test specimens were prepared for both material
combinations. The reference test standards are ASTM C 234 91a and CRD-C 24-01Standard Test Method for Comparing Concretes on the Basis of the Bond Developed
with Reinforcing Steel. Both single block specimens and specimens split from double
blocks were used. The forms are shown in Figure 3.4c. For the single block forms, therebars are oriented vertically during concrete placement. The double blocks had two
embedded rebars. The rebars were in horizontal positions in these forms. One week after
placement, the double blocks were split along the central horizontal plane into two cube
specimens with each cube having a centrally located rebar. The blocks were designatedtop and bottom. The cubes from the double forms were used to test if there was a
difference in pullout strength due to distance that a horizontally oriented bar was
vertically located during placement of the concrete. Each material combination had fivesingle blocks with embedded rebars and there were three and two double blocks for the
Cc-Cr and the VHSc-HSr material combinations, respectively.
The test setup is shown in Figure 3.14a. For the test, the block specimen with the rebar
oriented vertically is placed on a thin base ring, a square plate with a square cutout for the
blocks top surface is screwed onto the sides of the block, a fixture to hold the twoLVDTs for displacement measurement is attached by screws to the rebar, a multi-piece
alignment fixture (shown in Figure 3.14b) is placed on top of the cube, and a hydraulic
jack is positioned on top of the fixture and connected to the upper end of the rebar by a
Bar Size - No. 3 fy Ultimate %
Rebar type Specimen Yield Stress Strength ElongationID (ksi) (ksi)
Conventional 3C1n 71 113 >18
3C2n 69 112 >18
3C3n 73 115 >18
ASTM A615 Gr601
60 90
High Strength 3H1n 89 126 >18
3H2n 84 124 >18
3H3n 88 123 >18
ASTM A955 Gr751
75 100
Note 1: ASTM - minimum values for comparison purposes only
Figure 3.13 Engineering Stress-Engineering
Strain Curves - No. 3 Deformed
Rebars Necked Specimens
0
20000
40000
60000
80000
100000
120000
140000
160000
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20
Engineering Strain (in/in)
EngineeringStress(psi)
Cr #3n
HSr #3n
Table 6 Uniaxial Tension Test Results Nos. 3
Necked Specimens
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segmented nut. The LVDTs are inserted into their holding fixture and put into contact
with the square plate and zeroed. The rebar is pulled upward as the jack bears on theblock until failure of the concrete occurs. Force and displacement data are recorded. The
results of the rebar testing for both material combinations are shown in Table 7 and a
tested specimen is shown in Figure 3.14c.
(a) Test Specimen with Measuring andTesting Fixtures
(b) Alignment Pieces
Figure 3.14 Rebar Pullout Test Setup
(c) Example - VHSc HSr Rebar PulloutTest Specimen - after Testing
P, Maximum
Concrete Material Specimen Rebar Specimen Age Load P averageType
LocationID (days)
(lbs) (lbs)Conventional Single - Cc-Cr 1 +56 13,000
- Cc-Cr 2 +56 13,400
- Cc-Cr 3 +56 9,800 12,100
Double Top Cc-Cr 1T +56 16,300
Cc-Cr 2T +56 13,200
Cc-Cr 3T +56 14,700 14,800
Bottom Cc-Cr 1B +56 20,800
Cc-Cr 2B +56 15,800
Cc-Cr 3B +56 18,400 18,300
Very High Strength Single - VHSc-HSr 1 +56 no data
- VHSc-HSr 2 +56 22,300- VHSc-HSr 3 +56 20,500 21,400
Double Top VHSc-HSr 1T +56 23,800
VHSc-HSr 2T +56 29,800 26,800
Bottom VHSc-HSr 1B +56 27,600
VHSc-HSr 2B +56 25,200 26,400
Note 1: ASTM C 900 - 01
Table 7 Rebar Pullout Test Results
Note 1: ASTM C 234-91a
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The tabulated values show a variation in pullout force magnitudes for most of the
specimen type and rebar location combinations. However, in general, higher averageloads were obtained for specimens that had rebars oriented in the horizontal position
during the concrete placement. For these specimens, the Cc-Cr material combination also
showed differences in the vertical rebar placement in that pullout forces for the top blocks
were less than those for the bottom blocks. As rebar bond strength is an importantperformance issue, it is recommended that rebar-concrete bond experiments be performed
in the Demonstration Project.
Bolt Pullout Tests: Bolt pullout testing was performed for both the Cc and the VHSc
concrete materials. The reference test standard is ASTM C 900 - 01 Standard Test
Method for Pullout Strength of Hardened Concrete. For each concrete material, fiveblock specimens were prepared with two specimens in batch 1 and batch 2 and one
specimen in batch 3. For each test specimen, a high-strength bolt with a hexagonal head
and a threaded end was used and the bolt head was embedded in the concrete to aspecified depth. For testing of a specimen, a machined high-strength steel connector rod
was screwed onto the bolt end and the same procedure was used for the pullout test ashad been used in the rebar pullout tests. The maximum pullout load test results are given
in Table 8 and show that the VHSc average pullout loads were slightly higher than the Ccloads. Figure 3.15 shows a VHSc bolt pullout test specimen after testing with the
fractured concrete block and the bolt with concrete material.
Although the bolt pullout tests provide some information on type of fracture, quality and
strength of a concrete with shallow embedded inserts, there is significant time and effortinvolved in the testing. Also, further testing would require machined inserts instead of
bolts to relate test results to the compressive (tension) strength of the concrete. Theseadvantages and disadvantages need to be taken into account if this test method is to be
considered for inclusion in the Demonstration Project testing program.
Cube with Bolt P, MaximumConcrete Material Specimen Age Load P average
ID (days) (lbs) (lbs)
Conventional Cc1-1 +56 5,100Cc1-2 +56 5,700
Cc2-1 +56 5,600
Cc2-2 +56 5,500
Cc3-1 +56 4,200 5,200
Very High Strength VHSc1-1 +56 5,200
VHSc1-2 +56 5,900
VHSc2-1 +56 6,400
VHSc2-2 +56 6,400
VHSc3-1 +56 5,800 5,900
Note 1: ASTM C 900 - 01
Table 8 Bolt Pullout Test Results
Figure 3.15 Bolt Pullout Test Specimens -Example: VHSc Bolt Pullout Concrete
Test Specimen and Concrete Cone on
Bolt head after Testing
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Reinforced Concrete Beam Flexure Strength Tests: Concrete beam specimens withtensile reinforcement only were prepared for four-point (3rd-point loading) bend testing.
The testing method was similar to that in the ASTM C 78 - 02 Standard Test Method for
Flexural Strength of Concrete (using Simple Beam with Third-Point Loading) referencetest standard. The purpose of these tests was to gain experience with concrete placement
with respect to workability, flowability and compaction of the concretes in forms withreinforcement and in testing reinforced components for the selected concrete mixes. Thedesign of reinforced beams was done on under-reinforced beam basis to try to ensure
rebar yielding before concrete failure. The manufacturers specified minimum yieldstresses for the No. 3 rebars were used in the design.
The test setup is shown in Figure 3.16a and testing was performed using the Baldwin440,000 lbs Universal Testing Machine. For both material combinations, the specimens
underwent some tensile side cracking in the central section before shear failure occurred
near the support.
The maximum loads are given in Table 9 and example load time histories are shown inFigure 3.17 for both material combinations. From these results, it is recommended that
rebar material be tested to obtain actual mechanical properties that then should be used to
design the reinforced components in the Demonstration Project.
(b) VHSc-HSr Tested Specimen(a) Test Specimen in Test Machineprior to Testing
Figure 3.16 Pullout Test Specimens after Testing
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
18,000
20,000
0 103 203 303
Time (sec)
Load(lbs)
Figure 3.17 Reinforced Concrete Beam
Flexure Test Results Example
RC Beam P, Maximum P, AverageMaterial Specimen Age Load Paverage
Combination ID (days) (lbs) (lbs)
Conventional Cc-Cr 1 +56 15,900
Cc-Cr 2 +56 15,200
Cc-Cr 3 +56 15,500 15,500
Very High Strength VHSc-HSr 1 +56 13,200
VHSc-HSr 2 +56 15,000
VHSc-HSr 3 +56 12,600 13,600
Note 1: ASTM C 78-02
Table 9. RC Beam Test Results - Maximum Loads
Cc-Cr
VHSc-HSr
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4: Computations
4.1 INTRODUCTION
4.1.1 Objective
The objective of this effort was to conduct a preliminary assessment of the applicability
of currently-available constitutive models to the case of high-strength steel reinforcing in
conjunction with high-strength concrete.
4.1.2 Technical Background
Typically, the numerical solution of the continuum equations proceeds by discretizing thespace-variables using the finite element (FE) methods which include incorporating
constitutive equations and failure models. The constitutive equations and underlying
failure models are based on actual experiments and vary from purely phenomenologicalto micro-structurally based prediction procedures. Problems with high rates of loading
(e.g., structures under blast conditions) require such that the solution is advanced in time
using an explicit time integration scheme. The explicit method, however, is onlyconditionally stable, i.e, the size of the time step is limited by the Courant stability
criteria and is usually very small.
ParaDyn is the FE code used in this study. The steps involved in solving applications
using ParaDyn on scalable computers are: 1) Mesh/grid generation using pre-processing
software, 2) Partition or spatial decomposition of the solution domain on to desirednumber of processors, 3) Execution of the problem on scalable computers, and 4)
Gathering and Post-processing results from all the processors, usually referred to by themnemonic abbreviation MPEG.
Domain decomposition and gathering of results are the primary differences betweenserial and scalable methods. The objective behind partitioning is to balance the
computational load and optimize communications between processors. For description of
the implementation of ParaDyn on scalable computers refer to [Appendix 4.1].
4.1.3 Approach
Initially, a number of constitutive models were evaluated for both the concrete matrix andthe reinforcement. Due to the nature of the applications to be addressed in this program,
the constitutive models were restricted to those suited for explicit integration FEanalyses. Special care was given such that these models include the capability of
differing behavior in tension and compression in the case of the concrete matrix, theinclusion of failure mechanisms and erosion schemes for both the reinforcement and the
concrete, as well as the inclusion of enhanced material strengths due to strain-rate
dependencies. It is noted that the concrete constitutive model is suited for normalstrength-concretes or up to 10 ksi (70 Mpa). Experimental data were gathered for the
normal strength concrete and the reinforcement. These data were obtained either from
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new tests conducted in the laboratory at ERDC or from the literature. The data were
fitted to the numerical constitutive models and tested such that the behavior of thematerial is replicated within a tolerable limit for simple numerical models. Numerical
benchmark experiments were also carried out to ensure the valid behavior of these
models for more complex geometries and load conditions. Subsequently, a FE model was
generated for the normal strength-steel bar embedded in normal strength-concrete matrix.A pre-test analysis was conducted to estimate the bars pullout force. It is noted that the
analysis was carried out in a scalable fashion, i.e., the mesh was partitioned and
distributed to a number of processors and once the actual analysis was completed themesh was reassembled for visualization and numerical-data extraction purposes. In
addition, a preliminary constitutive model was developed for high strength-concrete. The
basis for this model is found in the original normal strength-concrete constitutive modelchosen for the study described above. At this point, this constitutive model requires
further validation that can be derived from controlled laboratory tests under different
stress/strain environments. Once the validation is completed, the constitutive model canbe used to predict events under quasi-static and dynamic loading conditions.
4.2 MATERIAL CONSTITUTIVE MODELS
For the numerical simulations carried out for this study, the concrete matrix is
represented using a modified nonlinear, elastoplastic, three-invariant, three-parametermodel which was specifically developed for use with concrete [2]. The reinforcement is
simulated using a modified elastic-plastic model with isotropic hardening and failure
based on a limiting strain level.
4.2.1 Concrete
A modified version of the geologic/concrete model (Model 16) available in DYNA3D-LLNL [3] is used as the constitutive model for the concrete. This is a nonlinear elastic-
plastic, three-invariant, three-failure surface model as suggested by Willam and Warnke
[4] and as further modified and implemented to account for dynamic loadingenvironments. This model uses a partly non-associative flow rule, a pressure-volume
dependent failure criterion in compression, and a fracture energy-based failure in tension.
The concrete model remains the same for all the analyses carried out for this study. Itshould be noted that rate enhancements for this material are used in all the FE analyses
conducted. Independent strain rate enhancements are used for the compressive and tensile
regime, as illustrated in Figure 4.1. These rates are readily available in the literature
although the fitting methodology of the available data may give rise to slightly differentrate enhancement values (curves).
In general, for this constitutive model the plastic flow is governed by a failure surfacewhose compressive meridian is determined in part by two of the three functions:
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4.2.2 Reinforcing steel model
The constitutive model used for the reinforcing steel is an elastic-plastic model with
isotropic hardening that accounts for strain rate enhancements and failure considerations
of the reinforcement once a threshold level of strain is reached (Model 24 in
ParaDyn/Dyna3D). The failure criterion is based on the ultimate effective plastic strainaccumulation limit provided in advance. The equation governing the effective plastic
strain accumulation is:
wherepl
eff and pl are the effective plastic and plastic strains, respectively. It should be
noted that the original model, as found in the original code, is neither suited to be usedwith one-dimensional elements nor providing ultimate strain-level considerations. The
modified Model 24 was developed specifically to meet these needs under the auspice of a
Defense Thread Reduction Agencys (DTRA) Conventional Weapons Effects program.ERDC was instrumental in developing and validating this material model in collaboration
with APTEC, Inc. Both the original and modified models account for strain rate
enhancements.
4.3 NUMERICAL ANALYSIS
4.3.1 Constitutive Model for Normal Strength Concrete:
A plethora of constitutive models of normal strength concretes are available in the
literature [5]. Only a few, however, can capture the behavior of concrete accurately in
both tension and compression by making a distinct effort to precisely model the tensileand compressive meridian. Even fewer, can predict the behavior of concrete structures
under loadings of interest to the US Army and the Corps of Engineers. The concrete
model described in an earlier section of this chapter has been scrutinized, numerically
tested and experimentally verified for simple and complex states of stress and loadingenvironments (ranging from quasi-static to highly non-linear dynamic). One more
desirable aspect of this model is the fact that although numerically cumbersome, it is,
nevertheless, a practical model when incorporated correctly in the numerical arena. Inaddition, the experience of using this particular model by the investigators at ERDC and
the fact that the source code is available for modifications and enhancements makes the
model even more attractive and applicable for this particular study.
4.3.2 Constitutive Model Modification for Normal Strength Steels
As mentioned in section 4.2.2 the constitutive model used for the reinforcing steel is the
modified models 24 currently found in the ParaDYn/Dyna3D codes. No modificationswere deemed necessary. The parameters extracted from the experimental data, such as
elastic modulus, yield strength, pairs of pl and pl that describe the plastic regime of
plplpl
eff
tpl
eff
pl
eff dddd 3
2,
0== (7)
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the stress-strain curve, and the maximum strain attained before fracture, were directly
used as input parameters of the numerical model, model 24.
4.3.3 Constitutive Model Modification for High Strength Steels
As with the previous case, no modifications were deemed necessary. The parametersextracted from the experimental data for the high strength steel, such as elastic modulus,
yield strength, pairs of pl and pl that describe the plastic regime of the stress-strain
curve, and the maximum strain attained before fracture, were directly used as input
parameters of the numerical model, model 24. In addition, a best fit values for the pl
and pl pairs gave an estimate of the tangent modulus of the material which in
conjunction with the maximum strain can be used to describe the behavior of the material
in the plastic region.
Modeling of the steel reinforcement can be accomplished using much more sophisticated
constitutive relations. The fact that the behavior of the model described above is kept to
the minimum possible complexity and at the same time yields reliable results promptedthe investigator in using this model versus a more sophisticated one
4.3.4 Preliminary Constitutive Model for High Strength Concrete
The current constitutive model for normal strength-concrete is only applicable up to 10-ksi compressive strength levels of concrete. The new high strength-concrete is demanding
compressive strength levels of the order of 15-20 ksi and higher. Thus, the mathematical
formulation of the current normal strength-constitutive model needs to be enhanced such
that these levels of strength are included. It is envisioned that the new high strength-
concrete model will be treated separately compared to that of the normal strength-concrete model. At this time, the formulation of the high strength-constitutive model has
been completed at the preliminary level. The fact that there are no experimental dataavailable in the biaxial and triaxial states of stress/strain for both compression and tension
makes the development of this model very preliminary and without validation. The
volumetric and deviatoric responses of the high strength-concrete need to be investigatedexperimentally and the results implemented in the new numerical model since (as with
the normal strength-concrete) a three-invariant model is necessary.
For this study, the approach taken included the modification of the normal strength-concrete mathematical formulae describing the three independent failure surfaces as well
as other mathematical parameters, e.g. lodes angle which describe the location andmagnitude of these surfaces in stress space. As a first approximation, the tensile meridianwas expanded such that it can accommodate uniaxial, biaxial, and triaxial strengths as
high as twice as that of the normal strength-concrete envelopes. In addition, the
compressive meridian was expanded such that the compressive strength magnitude canbe enhanced to two and one-half times the limit strength of the normal strength-concrete
envelope. The 2:5:2 ratio of the maximum compressive to tensile enhancement was
necessary to avoid singularity of the two meridians at their intersecting location.
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Figure 4.2. Representative Material fittings in Compression and Tension
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Figure 4.3. Two views of the numerical model used to simulate the pullout test full
option
Figure 4.4. Numerical model used to simulate the pullout test half option
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Figure 4.5. Preliminary analysis for normal strength concrete/steel pull-out test damage
levels at four stages
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Figure 4.6. Damage evolution and transition from symmetric (at early time) to non-
symmetric (at late time) of the pullout test simulation
Figure 4.7. Partition of the pullout test for a 16-processor analysis
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5: Usage and Risk
5.1 ENVIRONMENTAL STATEMENT
The environmental benefits of using vanadium steel rebar were investigated in the case
study. This investigation was directly related to the results of the parametric analysis thatwas conducted on two representative structural members. It was concluded that the area
of rebar required for a given threat was decreased by 29-37% for a structural wall slab
with double reinforcement when utilizing high-strength materials rather thanconventional materials. In this case, the only parameters that were changed were the
material strengths and the spacing of #8 rebar. The structural members were designed to
undergo a target support rotation of about 4 degrees, when subjected to the given threat.Figure 5.1 shows the results from this analysis. The figure shows four different material
combinations ranging from 5 ksi concrete compressive strength coupled with 60 ksi steel
reinforcement yield stress up to 25 ksi concrete compressive strength coupled with 100ksi steel reinforcement yield stress. From the figure, one can determine that as theconcrete and steel reinforcement strengths increase, the area of rebar required to obtain
the targeted 4 degree support rotation decreases. This scenario was also the case in
analyzing a structural wall slab with a single layer of reinforcement. The only differencein this analysis was that the targeted support rotation was 2 degrees instead of 4 degrees.
Figure 5.2 shows the same trend as Figure 5.1, as the material strengths increase the area
of rebar required decreases. However, in this case the decrease is even more significant.The percent decrease of the area of rebar required to obtain 2 degrees support rotation for
a singly reinforced wall slab ranges from 50-70% when higher strength materials are
utilized.
From this analysis, one can conclude that using high strength material combinations will
significantly reduce the total area of steel reinforcement required to meet specifications in
blast design. In turn, it can be concluded that the less steel that has to be produced in thesteel mill; the less pollution will be distributed into the atmosphere. The energy
consumption at the steel mill, CO2emissions into the atmosphere, and the number of
trucks transporting the rebar to the jobsite would all decrease, which should result in apositive impact on the environment.
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5.2MANUFACTURING ASSESSMENT
Several steel mini-mills across the United States and even Canada were contacted to
determine which mills are able to produce the vanadium rebar that meets researched
specifications of this project. This was a collaborative process between key technical
advisors of the Cooperative Agreement Management Committee (CAMC) and ERDCpersonnel. A request for quote was sent to four mini-mills that specifically stated the
chemical composition and mechanical properties that were required. Two of the four
mills responded they could produce the rebar to meet our specifications. Of the two mills,SMI-South Carolina was chosen as the preferred mill. This choice was based on their
previous experience and their production schedule.
The non-availability of vanadium rebar could be a potential risk associated with
vanadium-alloyed steel reinforcement. Currently, very few steel mills produce vanadium
rebar as an everyday operation. Many have the possibility to do so, but it is not aneveryday occurrence due to lack of demand. One situation where this could be a potential
risk is a time-dependant project. If a structure needs to be constructed in a timely manner,in todays market, finding a mill to produce the vanadium rebar required would be an
obstacle due to their production schedules.
5.3FINANCIAL CHARACTERIZATION
The costs benefits of using vanadium rebar were considered. Figure 5.3 demonstrates the
level of protection provided by the same four material combinations as used before. Inthis case, the area of reinforcement was held constant along with member geometry.
From the figure, one can determine as the material strength increases the support rotationdecreases. For a given threat, area of rebar, and member geometry, the higher strength
material provides 25-38% decrease in support rotation. If the level of protection of the
structure required a support rotation no greater than 3.5 degrees, the conventionalmaterial combination would not be sufficient. In order to provide a sufficient facility, one
would have to increase the member size and the amount of rebar, therefore, increasing
material and labor cost.
The higher strength material combination allows the designer to use the smaller member
sizes while not compromising on protection level provided. In turn, the smaller member
sizes provide more space to be utilized inside a structure. From an architecturalstandpoint, this could be very important. It could also lead to more savings for the owner
because less purchased property will be required to build their structure on. In
conclusion, the less material one has to deal with, the less expensive the facility will be.
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Increased Protection with Same Area of Steel Reinforcement
Given Threat at 100'
0
0.25
0.5
0.75
1
1.251.5
1.75
2
2.25
2.5
2.75
3
3.25
3.5
3.75
4
4.25
4.5
4.75
5
5.25
5.5
5.75
6
Material Combinations
SupportRotation(degrees)
5 ksi / 60 ksi
15 ksi / 75 ksi
15 ksi / 85 ksi
25 ksi/100 ksi
Figure 5.3. Increased Protection Provided
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6: Conclusions
6.1CONCLUSIONS
The research conducted in this case study provided valuable information for theadvancement of vanadium alloyed steel reinforcement bar and its use as primary
reinforcement in high-strength concrete. The parametric analysis portrayed the potentialfor weight, space, and cost savings. An increased level of protection can also be obtained
when utilizing the higher-strength material combination. The results concluded that a
typical 12-inch thick reinforced concrete wall constructed of standard concrete andreinforcing materials will incur roughly 30% more response (in terms of support rotation)
than a similar wall constructed of the 15/75 materials. The increased level of response
gained from using higher-strength materials could lead to the design of smaller membersizes to obtain the same level of response. This could be critical when restrictions on
member sizes or available space control the design. These savings not only affect the cost
of the structure, but also have positive implications on the environment. Theadvantageous effects attributable to the reduction in materials result in a healthierenvironment due to less CO2emissions into the atmosphere at the steel mill. Less
material also results in less transportation of the reinforcement to the jobsite, which in
turn, results in less fuel consumption and less pollution into the air from the freightcarriers.
The mechanical properties and hands on experience gained through the experimentaltesting program provided critical information as the program advances into the
demonstration phase. Necessary quality assurance measures became apparent throughout
the testing process. These measures will be critical in the demonstration phase in order to
obtain a quality product and also to design the structural components correctly. Specificmaterial property testing, specifically dynamic material property testing of both the high-
strength concrete and steel reinforcement, is considered necessary in the demonstration
phase of the project. These properties are necessary due to the strain-rate sensitivity ofthe concrete and steel materials.
The computational effort consisted of a preliminary assessment of the applicability ofcurrently-available constitutive models to the case of high-strength steel reinforcing in
conjunction with high-strength concrete. The initial evaluation concluded that theconcrete constitutive model is suited for normal strength-concretes up to 10 ksi (70 Mpa).
Experimental data was gathered for the normal strength concrete and reinforcement then
fitted to the numerical constitutive model and tested such that the behavior of the materialis replicated within a tolerable limit for simple numerical models. Subsequently, a FE
model was generated for the normal strength-steel bar embedded in normal strength-
concrete and a pre-test analysis was conducted to estimate the bars pullout force. Inaddition, a preliminary constitutive model was developed for high strength-concrete
based on the original normal strength-concrete constitutive model. This model requires
further validation that can be derived from controlled laboratory tests under different
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stress/strain environments. Once the validation is completed, the model will be used to
predict events under quasi-static and dynamic loading conditions.
In conclusion, through an extensive parametric, computational, and experimental
investigation, the mechanical properties of a high-strength and extremely ductile
vanadium-alloyed steel reinforcement bar were shown to be advantageous when used toreinforce a very-high-strength-concrete. This innovative combination will now be
investigated for use in newly-constructed reinforced concrete protective structures for
United States Army use, as well as for conventional construction.
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Acknowledgements
We gratefully acknowledge the contributions of Billy D. Neeley in the selection of and
providing of the concrete mix designs, Rudy Andreatta in the mixing and placement of
the concrete specimens, Michael K. Lloyd for specimen preparation, Dan E. Wilson and
Joe G. Tom for data acquisition setup and specimen testing, Stephen D. Robert forassistance in the parametric analysis, and the ERDC Directorate of Public Works (DPW)
machine shop personnel for fabrication of test fixtures.
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References
Standard Methods of Testing:
ASTM American Society of Testing and Materials, West Conshohocken, PA USA
ASTM Designation -
A 370 01 - Standard Test Methods for Mechanical Testing of Steel Products
A 615/A 615M 03a Standard Specification for Deformed and Plain Billet-Steel
Bars for Concrete Reinforcement
A 706/A 706M 03 Standard Specification for Low-Alloy Steel Deformed andPlain Bars for Concrete Reinforcement
A 955/A955M 05a Standard Specification for Deformed and Plain Stainless-
Steel Bars for Concrete Reinforcement
C39/D39M 03 - Standard Test Method for Compressive Strength of Cylindrical
Concrete Specimens
C79 02 Standard test Method for Flexural Strength of Concrete (Using Simple
Beam with Third-Point Loading)
C 234 91a Standard Test Method for Comparing Concretes on the Basis of theBond Developed with Reinforcing Steel (CRD-C24-01)
C 469 02 Standard Test Method for Static Modulus of Elasticity and PoissonsRatio of Concrete in Compression
C 496/C 496M 04 Standard Test Method for Splitting Tensile Strength ofCylindrical Concrete Specimens
C 900 01 Standard Test Method for Pullout Strength of Hardened Concrete
E 8 - 01 Standard Test Methods for Tension Testing of Metallic Materials
CRD C 164-92 Standard Test Method for Direct Tensile Strength of Cylindrical
Concrete or Mortar Specimens
Chen, W.F. Plasticity in Reinforced Concrete, McGraw Hill, New York, 1982.
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Hoover, C.G., DeGroot, A.J., and Pocassini, R.J. ParaDyn: DYNA3D for massivelyparallel computers, Lawrence Livermore National Laboratory, UCRL 53838-94, 1995.
Logicon RDA. Joint DNA UTP Precision Test Modeling and CEW Structural BenchmarkMeeting, Meeting Proceedings, 1994.
Malvar, L.J., Crawford, J.E., and Wesevich, J.W. A New Concrete Material Model forDYNA3D, Karagozian and Case, TR 94-14.1, 1994.
ONEAL Steel, Pearl, MS, ASTM A 615 Deformed Reinforcement Bars: No. 3 and No. 6
Grade 60, Heat numbers J4-3907 and C4-1060, September 14, 2004.
Salit Specialty Rebar, Niagara Falls, N.Y., Reinforcement Bars: No. 3 and No. 6 Grade
75 Type 316LN, Heat numbers G7446, G7907, Invoice 316668, September 13, 2004.
Whirley, R.G., and Engelmann, B.E. DYNA3D-A Nonlinear, Explicit, Three-Dimensional Finite Element Code for Solid and Structural Mechanics-Users Manual,UCRL-MA-107254 Rev. 1, 1993.
Woodson, Stanley C. and Baylot, James T., Structural Collapse: Quarter-Scale Model
Experiments, U.S. Army Engineer Research and Development Center, August 1999.
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APPENDIX 4.1
Dyna3D: A Nonlinear, Explicit, Three-Dimensional Finite Element Code for Solid
and Structural MechanicsDyna3D is an explicit finite element code for analyzing the transient dynamic response of
three dimensional solids and structures. The element formulations available include one-dimensional truss and beam elements, two-dimensional quadrilateral and triangular shell
elements, two-dimensional delamination and cohesive interface elements, and three-
dimensional continuum elements.
Many material models are available to represent a wide range of material behavior,
including elasticity, plasticity, composites, thermal effects, and rate dependence. Inaddition, Dyna3D has a sophisticated contact interface capability, including frictional
sliding and single surface contact, to handle arbitrary mechanical interactions between
independent bodies or between two portions of one body. Also, all element types support
rigid materials for modeling rigid body dynamics or for accurately representing thegeometry and mass distribution of a complex body at minimum cost.
ParaDyn: A Parallel Nonlinear Explicit, Three-Dimensional Finite-Element Code
for Solid and Structural Mechanics
ParaDyn is a parallel version of the Dyna3D computer program, a three-dimensionalexplicit finite-element program for analyzing the dynamic response of solids and
structures. The ParaDyn program has been used as a production tool for several years for
analyzing problems which range in size from a few tens of thousands of elements to
several million elements. ParaDyn runs on parallel computers provided by theDepartment of Defense and the High Performance Computing and Modernization
Program, Department of Energy Advanced Simulation and Computing Program, and the
Atomic Weapons Establishment in the UK. In addition to these massively parallelcomputers, ParaDyn has recently been installed on several Linux cluster computers.
Advances in the development of parallel algorithms for explicit finite-element analysis
and domain partitioning techniques have led to scalable production applications usingParaDyn. New models are being generated for mesh sizes between one-million and ten-
million elements. This is an order of magnitude larger than the largest models possible in
the past. Longer time simulations (problems running for a few million steps) are now
being run on both massively parallel computers and Linux clusters.
ParaDyn is a production program and includes a suite of software for automating thepreparation of models and the analysis of results. The DynaPart preprocessing tool
automates the task of model partitioning and is coupled directly to the research inscalable parallel contact algorithms developed in the ParaDyn program. The development
of the GRIZ4 visualization tool based on the Mili (Mesh I/O Library) software provides a