October 2005

Vanadium Rebar Case Study by Beverly P. DiPaolo, Bradley W. Foust, Edward F. O’Neil, Photios Papados, and

Stanley C. Woodson U.S. Army Corps of Engineers Engineer Research and Development Center 3909 Halls Ferry Road Vicksburg, MS 39180-6199 Prepared for Advanced Technology Institute 5300 International Boulevard North Charleston, SC 29418

1

iii

Contents

Preface................................................................................................................................ iv Conversion Factors, Non-SI to SI Units of Measurement .................................................. v 1: Introduction.................................................................................................................... 1

1.1 Background............................................................................................................... 1 1.2 Objective................................................................................................................... 1 1.3 Scope ........................................................................................................................ 1

2: Parametric Study............................................................................................................ 3 2.1: Purpose of Study...................................................................................................... 3 2.2: Approach ................................................................................................................. 3 2.3: Results ..................................................................................................................... 6 2.4: Summary ............................................................................................................... 13

3: Experimental Results ................................................................................................... 14 3.1 General.................................................................................................................... 14 3.2 Concrete Materials Testing..................................................................................... 18 3.3 Steel Rebar Materials Testing................................................................................. 25 3.4 Concrete Components Testing................................................................................ 27 3.5 Summary of Testing Program................................................................................. 31

4: Computations ............................................................................................................... 32 4.1: Introduction ........................................................................................................... 32 4.2: Material constitutive models ................................................................................. 33 4.3: Numerical Analysis ............................................................................................... 35

5: Usage and Risk ............................................................................................................ 42 5.1: Environmental Statement ...................................................................................... 42

6: Conclusions.................................................................................................................. 46 6.1: Conclusions ........................................................................................................... 46 Acknowledgements ....................................................................................................... 48

References......................................................................................................................... 49 Appendix 4.1..................................................................................................................... 51

iv

Preface

The study reported herein was performed by members of the staff of the Geotechnical and 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 under Cooperative 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, Structural Mechanics 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.

v

Conversion Factors, Non-SI to SI Units of Measurement Non-SI units of measurement used in this report can be converted to SI units as follows: Multiply By To Obtain degrees (angle) 0.01745 radians feet 0.3048 meters inches 25.4 millimeters kips (force) per square inch 6.894757 megapascals pounds 4.448222 newtons pounds (force) per square inch 0.006894757 megapascals

1

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 the explosion 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 used to 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 this combination 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-mill steel industry. The introduction of vanadium into the chemical composition of a steel reinforcement 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 high strength 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 increased protection level resulting from the substitution of high-performance materials for conventional materials. The high-performance materials consisted of high-strength concrete (f’c ≥ 15 ksi) and vanadium steel rebar with a yield stress of at least 75 ksi. A laboratory experimental program and computational simulations evaluating design concepts for structural elements subjected to severe dynamic loadings were also conducted. Two representative structural components were considered in the parametric analysis; a reinforced 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 conjunction with 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.

2

The experimental effort was conducted to gain relevant experience with the material combinations. The objectives of the experiment were to perform the required material property tests for quality assurance, determine actual mechanical properties of materials and compare to specifications, verify performance of materials, and select tests of importance for the follow-up demonstration project. Computational simulations were conducted to address aspects of the experimental program. The objective of the computational 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.

3

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 blast response 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 conventional weapons. For this study, ConWep was 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

4

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 standards for 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

xM

5

Level of Protection

Potential Structural Damage Potential Door and Glazing Hazards

Potential Injury

Low Damaged – unrepairable. Major deformation of non-structural elements and secondary 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 a significant 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 (<10%) fatalities.

Medium Damaged- repairable. Minor deformation of non-structural elements and secondary structural members and no permanent deformation in primary structural members.

Glazing will break, but will remain in the window frame. Doors will stay in frames, but will not be reusable.

Some minor injuries, but fatalities are unlikely.

High Superficially damaged. No permanent deformation of primary and secondary structural members or non-structural members.

Glazing will not break. Doors will be reusable.

Only superficial injuries are likely.

Table 2.1 Levels of Protection

Table 2.2 presents typical response limits associated with a level of protection. Thus, the general approach in this study was to compare structural component designs using the different material strength properties to achieve a selected response limit. The levels of protection provide some qualitative understanding of the quantitative response limits.

6

• HLOP – High Level of Protection

• MLOP – Medium Level of Protection

• LLOP – Low Level of Protection

• VLLOP – Very Low Level of Protection

• µ - Ductility Ratio

• θ - 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

7

- 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 either the standard materials or the 15/75 combination as baselines for comparison. Two other parameters required for the study were the explosive charge weight and the standoff (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 depending on 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 charge weights (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 does not 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 the 5/60 (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 increase in response (as defined by support rotation) for the 5/60 wall was 34% and 38% 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.

8

Explosive Wt.

TNT (lbs)

Standoff (ft)

Concrete Strength

(ksi)

Rebar Strength

(ksi)

Support Rotation

(deg.)

Percent Diff.

Support Rotation

(%)

Deflection (in.)

Peak Pressure

(psi)

Peak Impulse

(psi-msec)

4000 100 15 75 4.1 5.6 79 4924000 100 5 60 5.5 34 7.5 79 4924000 100 15 85 3.6 -11 5.0 79 4924000 100 25 100 3.4 -18 4.6 79 492

10000 170 15 75 4.0 5.4 42 51310000 170 5 60 5.5 38 7.5 42 51310000 170 15 85 3.5 -12 4.8 42 51310000 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 that would 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 does have end conditions that would allow the development of large deformation response, including a mechanism known as tension membrane. In pure tension membrane, all reinforcement is in tension such that the element resembles a catenary. The reinforcement must be well anchored into strong supports 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, and 25/100 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.

9

Explosive Wt.

TNT (lbs)

Standoff (ft)

Concrete Strength

(ksi)

Rebar Strength

(ksi)

Support Rotation

(deg.)

Percent Diff.

Support Rotation

(%)

Deflection (in.)

Peak Pressure

(psi)

Peak Impulse

(psi-msec)

4000 64 15 75 12.1 16.7 305 8494000 64 5 60 15.6 29 21.8 305 8494000 64 15 85 10.8 -10 14.9 305 8494000 64 25 100 10.1 -16 14.0 305 849

10000 111 15 75 12.0 16.6 143 85110000 111 5 60 15.7 31 21.9 143 85110000 111 15 85 10.8 -10 14.9 143 85110000 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 of approximately 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 steel was 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 15/85 and the 25/100 material, respectively.

Concrete Strength

(ksi)

Rebar Strength

(ksi)

Spacing (in)

Area of Rebar (in²/ft)

Percent Diff.

Area of Rebar (%)

Support Rotation

(deg.)

Deflection (in.)

Peak Pressure

(psi)

Peak Impulse

(psi-msec)

15 75 7 2.69 4.2 5.7 370 9225 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’

10

Since some conventional walls are only reinforced with one layer (singly reinforced) of reinforcing, Table 2.6 compares the areas of reinforcing required for the different material strengths to allow a support rotation of 2 degrees. The 2-degree support rotation corresponds to the Low Level of Protection for singly reinforced walls. Singly reinforced walls are typically considered incapable of sustaining tension membrane behavior. The area of steel required for the wall with the 5/60 materials is approximately twice (100% increase) that required for the wall with the 15/75 materials. However, decreases of 14 and 39% were computed for the 15/85 and the 30/100 materials, respectively.

Concrete Strength

(ksi)

Rebar Strength

(ksi)

Spacing (in)

Area of Rebar (in²/ft)

Percent Diff. Area of Rebar

(%)

Support Rotation

(deg.)

Deflection (in.)

15 75 6 1.57 2 2.75 60 3 3.14 100 1.9 2.6

15 85 7 1.35 -14 1.98 2.730 100 10 0.95 -40 1.93 2.6

Table 2.6 Comparison of Required Area of Rebar (using # 8 bars) to Achieve Support Rotation of 2 Degrees for Singly Reinforced 6” Thick Wall When Subjected to 4000# at 160’ In order to consider the High Level of Protection category, Table 2.7 presents results for comparing the area of steel required to limit the wall response of elastic behavior, i.e. a ductility ratio of 1. Of course, reinforcing requirements are rather large in order to achieve the high level of protection; thus rebar sizes and spacing combinations were selected to represent walls that are constructible. A 44% increase in reinforcement is required for the wall with the 5/60 materials compared to the wall with the 15/75 materials. This is less than for the 100% case at the Low Level of Protection (Table 2.6). Again, reductions in reinforcement area can be allowed for the 15/85 and 30/100 materials.

11

Concrete Strength

(ksi)

Rebar Strength

(ksi)Rebar Spacing

(in)

Area of Rebar (in²/ft)

Percent Diff.

Area of Rebar (%)

Deflection (in.)

15 75 #10 3.5 8.69 0.85 60 #11 3 12.49 44 0.8

15 85 #9 3 8.00 -8 0.7730 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 herein compare 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 the blast 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 explosive charge 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 was used 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 response limits 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 column response (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 the 15/75 materials is somewhat optimum for resisting this threat with the baseline response of 4 degrees support rotation.

12

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 143820 15 75 2.15 -23 3.5 2157 143820 15 85 1.93 -31 2.4 2157 143820 30 100 1.61 -42 2 2157 143815 5 60 5.2 5 3692 195615 15 75 4 -23 6.5 3692 195615 15 85 3.52 -32 4.4 3692 195615 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 rotation of 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 4 515 75 2.9 -28 3.6915 85 2.61 -35 3.2830 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-lb charge weight.

13

Concrete Strength

(ksi)

Rebar Strength

(ksi)

Support rotation (deg.)

Percent Diff.

(Support Rotation)

Deflection (in.)

5 60 4 3.715 75 3 -25 515 85 2.6 -35 3.330 100 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. The results 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 of the 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 30/100 materials 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 high performance materials over the standard material.

14

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 were conventional 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 compressive strength 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 standard specifications • Verify performance of materials • Gain relevant experience with the material combinations prior to determining the experimental program for the Demonstration Project

ERDC mix designs for the concrete materials were chosen based on a design concrete compressive strength of f’c = 5,000 psi (28 day cure) for the conventional concrete and f’c of 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 Figure 3.2a 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 f’c = 5,000 psi A 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 f’c = 15,000 psi Rebar with yield stress of fy = 75,000 psi

Figure 3.1 Concrete Material – Steel Reinforcement Bar Material Combinations

15

Conventional Concrete Mix Constituents

1. Type 1 Portland cement 2. Fine aggregate–sand 3. Coarse aggregate–limestone 4. Defoaming agent 5. High range water reducing agent 6. Water reducing agent 7. Air 8. Water

Very-High-Strength Concrete Mix Constituents

1. Type 1 Portland cement 2. Fine aggregate–limestone 3. Coarse aggregate–limestone 4. Silica fume 5. Fly ash 6. High range water reducing agent 7. Air 8. Water

Example of Hardened Concrete

1.5 inch square cross-section from 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 ConcreteFigure 3.2 Concrete Mix Constituents and Hardened Concrete Appearances

16

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 rebar minimum 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 Grade 75 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 program consisted 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 high strength 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

17

shown in Figure 3.3a. For each batch of each concrete material, slump tests were performed and unit weights were measured for quality control of the mixes. The start and end of a slump test for the VHSc material is shown in Figure 3.3b and a unit weight container is shown in Figure 3.3c. The forms for all test specimens of a given concrete material are shown in Figure 3.3d and will be described individually below. After placement of a given concrete material in the forms, moist curing was performed in the fog room shown in Figure 3.3e. For the conventional concrete specimens, curing time was 28 days and for the very high strength concrete specimens, curing time was 56 days. The molds or forms for the different test specimens of concrete are shown in Figure 3.4. Cylindrical concrete forms included five 6 inch diameter by 12 inch long cylinder forms for compressive strength and direct and splitting tensile strength, one to two 3 inch

(d) Forms for Each Concrete and Rebar Material Combination -Placement Performed

in Three Batches

Figure 3.3 Concrete Mixing Facility, Specimen Forms and Fog Room

(a) Concrete Mixer

(b) Slump Test on a Concrete Batch Very High Strength Concrete Example

(c) Unit Weight Determination

(e) Fog Room Used for Moist Curing and Storage of Concrete Specimens

18

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. These forms 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 the reinforced 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 the fifth 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 Compressive Strength of Cylindrical Concrete Specimens and ASTM C 469 - 02 Standard Test Method for Static Modulus of Elasticity and Poisson’s 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

19

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 mixing procedures, 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, f’c, 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 loaded until 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 parallel end 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 and therefore, 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 for debris 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 and that were used to obtain data for the static modulus of elasticity and Poisson’s 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 Machine after Compression Test

Figure 3.5 Compressive Strength of Concrete Cylinder Specimens Test Setup and Results

f’c = 4P/πd2 where f’c = compressive strength, (psi) P = maximum load, (lbs)

d = diameter, (in)

20

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 in Figure 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 VHSc material, it was discovered that large hydrated cement pieces were contained in the concrete matrix and this could account for the reduced strength values. It is recommended 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.)

Stre

ss (p

si)

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 Specimen in Grinder

Figure 3.7 Compressive Strength Test Results - Example: Engineering Stress vs. Cross-head Displacement – Cc and VHSc

Cylinder f'c DesignConcrete Material Specimen Age Compressive Compressive

ID (days) Strength (psi) Strength (psi)

Conventional Cc1-1 28 5,500 5,000Cc2-1 28 5,900Cc3-1 28 5,500

Very High Strength VHSc1-1 56 13,400 15,000VHSc2-1 56 13,200VHSc3-1 56 11,600

Note 1: ASTM -C39/C 39m-03 and C469-02

Table 1. Compressive Strength Test Results

21

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 tensile strength, S

• Splitting Tensile Strength of Cylindrical Concrete to obtain the splitting tensile strength, T

• Flexural Strength of Concrete (Using Simple Beam with Third-Point Loading) 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-inch diameter 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 of Cylindrical 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 concrete occurs. 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 “holding devices” 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 between the 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 and just after fracture. A tested specimen that failed in the concrete is shown in Figure 3.8b.

(a) Example of Direct Tensile Strength of Cc Concrete During Loading and just after Fracture

(b) Cc Direct Tensile Test Specimen

Figure 3.8 Direct Tensile Strength Test Setup and Test Specimen

22

The direct tensile strength is calculated by dividing the maximum load by the cross-sectional area of the specimen: All specimens failed in the concrete and therefore, the tests were valid. The strength results of the direct tensile strength testing are given in Table 2 for both the Cc and the VHSc materials. The percent that each direct tensile strength value is of the corresponding design compressive strength was calculated and is also given in Table 2. The direct tensile strengths of the Cc materials are 6-7% and for the higher strength VHSc material, the percents are 4% of the design compressive concrete strength. 3.2.2.2 Splitting Tensile Strength of Cylindrical Concrete Specimens For each concrete material, splitting tensile strength tests were performed on three 6-inch diameter by 12-inch long cylinders. For each concrete material, one cylinder specimen was used from each batch. The reference test method used was ASTM C 496 - 04 Standard Test Method for Splitting Tensile Strength of Cylindrical Specimen. As required in the standard, the test consists of applying a diametral compressive force along the length of a horizontal cylindrical concrete specimen at a constant rate within a specified range until the specimen fails by fracture. Two views of the test fixture for holding a specimen are shown in Figure 3.9a. All of the testing was performed using the Baldwin 440,000 lbs Universal Testing Machine. Figure 3.9b shows a specimen being tested during loading and just after failure. An example of a tested specimen is shown in Figure 3.9c.

S = 4P/πd2

where S = direct tensile strength, (psi) P = failure load, (lbs)

d = diameter, (in)

Cylinder ft, DirectConcrete Material Specimen Age Tensile Strength % f'c

ID (days) (psi)

Conventional Cc1-3 28 320 6Cc2-3 28 345 7Cc3-3 28 320 6

Very High Strength VHSc1-5 56 630 4VHSc2-5 56 600 4VHSc3-5 56 630 4

Note 1: CRD-C 164-92

Table 2. Direct Tensile Strength Test Results

23

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 the corresponding design compressive strength was calculated and also given in the table.

(a) Splitting Tensile Test Specimen Holder

T = 2P/πld

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, SplittingConcrete Material Specimen Age Tensile Strength % f'c

ID (days) (psi)

Conventional Cc1-2 28 450 9Cc2-2 28 435 9Cc3-2 28 460 9

Very High Strength VHSc1-4 56 660 4VHSc2-4 56 700 5VHSc3-4 56 725 5

Note 1: ASTM A496/C496M-04

Table 3. Splitting Tensile Strength Test Results

24

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-Point Loading). 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 the testing 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. The modulus of rupture was calculated using the following formula: Table 4 gives the modulus of rupture and the percent of the design f’c for 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 14Cc3 28 685 14

Very High Strength VHSc1 56 1370 9VHSc2 56 1195 8VHSc3 56 1340 9

Note 1: ASTM C 78-02

Table 4. Flexure Strength Test Results

25

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 < R

direct 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 the commercially 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 70° F (room temperature) using an MTS Universal Testing Machine (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 displacement control 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. 3 deformed bars with a machined necked-down region. Examples of the test specimens for both materials are shown in Figure 3.11c

MTS Universal Testing Machine 100 kip Load frame and Load cell

Quasi-static Testing Displacement Control Room 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

26

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 in Figure 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 of specified 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 also shown 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)

Eng

inee

ring

Str

ess (

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)

Eng

inee

ring

Str

ess (

psi)

(a) No. 3 Rebars (b) No. 6 Rebars

HSr #6d

Cr #6d

HSr #3d

Cr #3d

fy, Yield Stress Ultimate Strength % ElongationBar Size Rebar type Specimen Test ASTM min. Test ASTM min. Test

ID (ksi) (ksi) (ksi) (ksi)

No. 3 Conventional 3C3d 69 60 107 90 >183C4d 68 106 >183C5d 43 81 >13

High Strength 3H1d 109 75 140 100 >183H2d note 2 139 note 2

3H3d 111 141 >18

No. 6 Conventional 6C1d 53 60 66 90 >166C3d 61 100 >18

High Strength 6H1d 65 75 101 100 >186H2d 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

27

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 and reinforced 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 24-01 Standard 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, the rebars 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 designated “top” 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 five single 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 block’s top surface is screwed onto the sides of the block, a fixture to hold the two LVDT’s 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 Elongation

ID (ksi) (ksi)

Conventional 3C1n 71 113 >183C2n 69 112 >183C3n 73 115 >18

ASTM A615 Gr60 1 60 90

High Strength 3H1n 89 126 >183H2n 84 124 >183H3n 88 123 >18

ASTM A955 Gr75 1 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)

Eng

inee

ring

Str

ess (

psi)

Cr #3n

HSr #3n

Table 6 Uniaxial Tension Test Results – Nos. 3 – Necked Specimens

28

segmented nut. The LVDT’s 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 the block 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 and Testing Fixtures

(b) Alignment Pieces

Figure 3.14 Rebar Pullout Test Setup

(c) Example - VHSc – HSr Rebar Pullout Test Specimen - after Testing

P, MaximumConcrete Material Specimen Rebar Specimen Age Load P average

Type Location ID (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 16,300Cc-Cr 2T +56 13,200Cc-Cr 3T +56 14,700 14,800

Bottom Cc-Cr 1B +56 20,800Cc-Cr 2B +56 15,800Cc-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 23,800VHSc-HSr 2T +56 29,800 26,800

Bottom VHSc-HSr 1B +56 27,600VHSc-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

29

The tabulated values show a variation in pullout force magnitudes for most of the specimen type and rebar location combinations. However, in general, higher average loads 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 important performance 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, five block 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 a specified 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 as had 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 Cc loads. 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 effort involved 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. These advantages 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 5,700Cc2-1 +56 5,600Cc2-2 +56 5,500Cc3-1 +56 4,200 5,200

Very High Strength VHSc1-1 +56 5,200VHSc1-2 +56 5,900VHSc2-1 +56 6,400VHSc2-2 +56 6,400VHSc3-1 +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

30

Reinforced Concrete Beam Flexure Strength Tests: Concrete beam specimens with tensile 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) reference test 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 with reinforcement and in testing reinforced components for the selected concrete mixes. The design of reinforced beams was done on under-reinforced beam basis to try to ensure rebar yielding before concrete failure. The manufacturers’ specified minimum yield stresses 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 Baldwin 440,000 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 in Figure 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 Machine

prior 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 15,900Cc-Cr 2 +56 15,200Cc-Cr 3 +56 15,500 15,500

Very High Strength VHSc-HSr 1 +56 13,200VHSc-HSr 2 +56 15,000VHSc-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

31

3.5 SUMMARY OF TESTING PROGRAM Experience was obtained in handling, producing and testing the individual materials and components of the Cc-Cr and the VHSc-HSr material combinations. Tests were performed for quality assurance purposes and to obtain actual mechanical property data from purchased and as-produced concrete materials. Strength data was consistent with standard specification minimum values with a few exceptions. The lower strength values for the VHSc material may be due to hydrated cement particles that could be eliminated by cement seiving prior to mixing of the concrete batches. Variation in strength levels for the rebar materials indicates that testing of purchased materials is required not only to ensure adequate minimum strength levels, but also to obtain strength values of the actual materials to be used in the research. These valuse are needed for the design of the reinforced components in the testing program and for the computational modelling efforts. It is recommended that the test methods used in the Case Study experimental program be performed in the Demonstration Project with the possible exclusion of the bolt pullout and the small reinforced beam bending tests. Although the direct tension test has additional cost and effort due to the capping requirement, the hydrated cement inclusions in the specimens affected the test data for the VHSc material in this study and more accurate data is required for this material. Also, as stated in the Case Study proposal, the Demonstration Project should include dynamic mechanical properties testing because of the strain-rate sensitivity of the concrete and steel materials.

32

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 the space-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 phenomenological to 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 only conditionally 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 desired number 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 the mnemonic abbreviation MPEG. Domain decomposition and gathering of results are the primary differences between serial 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 and the 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 FE analyses. 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, the inclusion 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 normal strength-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

33

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 the material 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 bar’s 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 the mesh 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 model chosen 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 can be 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-parameter model 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 loading environments. 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. It should 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 different rate enhancement values (curves). In general, for this constitutive model the plastic flow is governed by a failure surface whose compressive meridian is determined in part by two of the three functions:

34

The tensile meridian, at an equivalent stress point represented by the reflection of the compressive meridian with respect to the hydrostatic axis, is merely a fraction of the latter. This ratio of the two radii with respect to this axis, increases from 0.5 at low confinements to 1.0 at high confinements. Thus the overall failure surface transitions from an ellipse at low confinements to a circle at high confinements. In each case, once the stress point reaches the initial yield surface, but prior to reaching the maximum failure surface, the current surface is obtained via a linear interpolation between these two surfaces. This is represented by equation 5, which is stress and strain dependent as well as strain rate sensitive:

where η varies from 0 to 1, depending on the non-decreasing damage parameter λ. After reaching the maximum surface, the current failure surface is similarly interpolated between the maximum and the residual, except η varies from 1 (maximum) to 2 (residual):

The function η(�) is input as a series of (η, �) pairs. The values of λ must start at 0 and increase in sequence. The values of � would normally begin at 0 when λ=0, increase to 1 at some intermediate value λ=λm , and then decrease to 0 at some larger value of λ (thus, permitting ∆σ to reach sequentially the values ∆σy , ∆σm , and ∆σr). As with all softening models, the material properties are “fitted” numerically so that the stress-strain behavior is captured for a wide spectrum of confinements. The problem is element size dependent and requires a number of numerical iterations prior to accomplishing an acceptable material fit. Furthermore, the situation becomes more complicated when the element under consideration is of non-uniform aspect ratio, i.e., one size is different than the other. This poses added problems especially in fitting the tensile material properties (fracture energy). The element choice in this problem was fitted to continuum elements of sizes varying from 0.33 to 1.00 in. in both compression and tension. The material properties used were fc’ = 6.00 ksi and ft = 595 psi. The model fit was done so that accuracy prevails in the lower confining pressure regime (0-2.0 ksi). The compression fittings shown are for 0, 20 ksi respectively. The tension fitting shown is for fracture energy of approximately 0.6 in.-lb/in.2 (Figure 4.2).

surface) failure (residual

surface) failure (maximum

surface) yield (initial

21

210

210

pa+a

p=

pa+a

p + a =

pa+a

p+a =

ffr

m

yyyy

σ

σ

σ

∆

∆

∆

(4)

rrm σσσησ ∆+∆−∆=∆ )( (6)

yym σσσησ ∆+∆−∆=∆ )( (5)

35

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 strain accumulation limit provided in advance. The equation governing the effective plastic strain accumulation is:

where pl

effε and plε 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 used with 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 Agency’s (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 tensile and 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 loading environments (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. In addition, 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 modifications were deemed necessary. The parameters extracted from the experimental data, such as elastic modulus, yield strength, pairs of plε and plσ that describe the plastic regime of

plplpleff

t pleff

pleff dddd εεεεε

32 ,

0== ∫ (7)

36

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 parameters extracted from the experimental data for the high strength steel, such as elastic modulus, yield strength, pairs of plε and plσ 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 plε and plσ 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 prompted the 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 data available 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 investigated experimentally 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. lode’s angle which describe the location and magnitude of these surfaces in stress space. As a first approximation, the tensile meridian was 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 can be 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.

37

Once again, since this is more of a speculative constitutive model, it needs to be validated and verified experimentally and numerically. 4.3.5 Preliminary Pullout Tests of Normal Strength Concrete/Steel The experimental setup of the pullout test of normal strength-concrete and steel section is described elsewhere in this report (Chapter 3). Two simulations were carried out. The first one uses half symmetry (symmetric structure and load) and the second one uses the full model. The disadvantage of using half symmetry with highly non-linear constitutive models is that beginning at the onset of softening, the behavior of the structure may vary substantially from the full model. This is due to the fact that numerical softening is an instability which may occur anywhere in the medium under plasticity conditions. If only half of the model is considered, locations experiencing softening will likely differ from that experienced by a full model. The half-symmetry model is much faster than the full model as far as CPU time is concerned, therefore more sensitivity studies can be conducted. FE models and select results from this experiment are presented in Figures 4.3 - 4.8 below. The reader should note that the numerical results from the half-space simulations indicate a pullout force on the rebar of 4,700 lbs for the .001 1/s loading stain rate and 5,150 lbs for the .01 per-sec strain rate of loading. Each numerical simulation uses approximately 0.45 hour of CPU using 16 processing units of the SGI 3900 located at the Major Shared Resource Center (MSRC), Vicksburg, MS Supercomputing Center. The full model analysis yields results of approximately a factor of two in terms of the pull out force for the two cases noted earlier. The CPU time, however, quadruples for each calculation.

Figure 4.1. Strain rate enhancements for tension and compression

Rate (1/sec)

Enha

ncem

ent F

acto

r

1.E-7 1.E-6 1.E-5 1.E-4 .001 .01 0.1 1.0 10 1000.

1.5

3

4.5

6

7.5

9

CompressionTension

38

Figure 4.2. Representative Material fittings in Compression and Tension

39

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

40

Figure 4.5. Preliminary analysis for normal strength concrete/steel pull-out test damage levels at four stages

41

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

42

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 that was 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 than conventional 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 100 ksi steel reinforcement yield stress. From the figure, one can determine that as the concrete 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 difference in 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 the steel mill; the less pollution will be distributed into the atmosphere. The energy consumption at the steel mill, CO2 emissions into the atmosphere, and the number of trucks transporting the rebar to the jobsite would all decrease, which should result in a positive impact on the environment.

43

Area of Rebar (double layer) Reduction for Given Threat

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

2.5

2.75

3

3.25

3.5

3.75

4

Material Combinations

(Are

a of

Reb

ar (i

n2 /ft

)5 ksi / 60 ksi

15 ksi / 75 ksi

15 ksi / 85 ksi

25 ksi/100 ksi

4.29º Support Rotation

4.21º Support Rotation

4.17º Support Rotation

3.57º Support Rotation

Figure 5.1. Reductions in Area of Rebar (double layer)

Area of Rebar (single layer) Reduction for Given Threat

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

2.5

2.75

3

3.25

Material Combinations

(Are

a of

Reb

ar (i

n2 /ft)

5 ksi / 60 ksi

15 ksi / 75 ksi

15 ksi / 85 ksi30 ksi/100 ksi

1.92º Support Rotation

1.98º Support Rotation

1.96º Support Rotation

1.93º Support Rotation

Figure 5.2 Reductions in Area of Rebar (single layer)

44

5.2 MANUFACTURING 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 ERDC personnel. 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 an everyday 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 today’s market, finding a mill to produce the vanadium rebar required would be an obstacle due to their production schedules. 5.3 FINANCIAL 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. In this 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 rotation decreases. 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 conventional material 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 architectural standpoint, 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.

45

Increased Protection with Same Area of Steel Reinforcement Given Threat at 100'

00.250.5

0.751

1.251.5

1.752

2.252.5

2.753

3.253.5

3.754

4.254.5

4.755

5.255.5

5.756

Material Combinations

Supp

ort R

otat

ion

(deg

rees

)5 ksi / 60 ksi

15 ksi / 75 ksi

15 ksi / 85 ksi

25 ksi/100 ksi

Figure 5.3. Increased Protection Provided

46

6: Conclusions 6.1 CONCLUSIONS The research conducted in this case study provided valuable information for the advancement of vanadium alloyed steel reinforcement bar and its use as primary reinforcement in high-strength concrete. The parametric analysis portrayed the potential for 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 and reinforcing 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 member sizes 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. The advantageous effects attributable to the reduction in materials result in a healthier environment due to less CO2 emissions 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 freight carriers. The mechanical properties and hands on experience gained through the experimental testing 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. Specific material 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 of the concrete and steel materials. The computational effort consisted of 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. The initial evaluation concluded that the concrete 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 material is 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 bar’s pullout force. In addition, 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

47

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 to reinforce 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.

48

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 for assistance in the parametric analysis, and the ERDC Directorate of Public Works (DPW) machine shop personnel for fabrication of test fixtures.

49

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 and Plain 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 the Bond Developed with Reinforcing Steel (CRD-C24-01) C 469 – 02 – Standard Test Method for Static Modulus of Elasticity and Poisson’s Ratio of Concrete in Compression C 496/C 496M – 04 – Standard Test Method for Splitting Tensile Strength of Cylindrical 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.

50

Hoover, C.G., DeGroot, A.J., and Pocassini, R.J. ParaDyn: DYNA3D for massively parallel computers, Lawrence Livermore National Laboratory, UCRL 53838-94, 1995. Logicon RDA. Joint DNA UTP Precision Test Modeling and CEW Structural Benchmark Meeting, Meeting Proceedings, 1994. Malvar, L.J., Crawford, J.E., and Wesevich, J.W. A New Concrete Material Model for DYNA3D, 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.

51

APPENDIX 4.1

Dyna3D: A Nonlinear, Explicit, Three-Dimensional Finite Element Code for Solid and Structural Mechanics Dyna3D 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. In addition, 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 the geometry 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-dimensional explicit 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 the Department 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 parallel computers, 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 using ParaDyn. 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 the preparation of models and the analysis of results. The DynaPart preprocessing tool automates the task of model partitioning and is coupled directly to the research in scalable 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 flexible, self-defining format to use for the large databases generated during a parallel simulation.