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Publication Number: FHWA-HRT-10-079
Date: November 2010

Finite Element Analysis of UHPC:Structural Performance of an AASHTO Type II Girder and a 2nd-Generation Pi-Girder

FHWA Contact: Ben Graybeal,
HRDI-40, (202) 493-3122, benjamin.graybeal@dot.gov

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This document is a technical summary of the unpublished Federal Highway Administration (FHWA) report, Finite Element Analysis of Ultra-High Performance Concrete: Modeling Structural Performance of an AASHTO Type II Girder and a 2nd Generation Pi-Girder, available only through the National Technical Information Service, www.ntis.gov.

OBJECTIVE

This TechBrief highlights the results of a research program that developed finite element analysis modeling techniques applicable to ultra-high performance concrete (UHPC) structural components.

INTRODUCTION

UHPC is an advanced cementitious composite material that tends to exhibit superior properties such as exceptional durability, increased strength, and long-term stability.(1–3)

This research program is aimed at developing general finite element concepts within a commercially available finite element package to facilitate the development of UHPC structural systems. This investigation focused on calibrating the proposed finite element models to a series of completed full-scale structural tests on existing UHPC structural components, including a prestressed UHPC American Association of State Highway Transportation Officials (AASHTO) Type II girder and a prestressed UHPC second-generation pi-girder.

FINITE ELEMENT MODELS AND UHPC

Table 1 presents example mechanical properties for the type of UHPC investigated in this study. The properties far surpass those normally associated with concrete. The concrete damaged plasticity (CDP) model was primarily employed to model the constitutive behaviors of UHPC.(4,5) It assumes isotropic damage elasticity combined with isotropic tensile and compressive plasticity to represent the inelastic behavior of concrete. Formation of tensile microcracks is represented macroscopically with a softening stress-strain relationship, and the compressive plastic response is represented by stress hardening followed by strain softening beyond the ultimate compressive strength.

Table 1. UHPC Material Properties.

This research program is aimed at developing general finite element concepts within a commercially available finite element package to facilitate the development of UHPC structural systems. This investigation focused on calibrating the proposed finite element models to a series of completed full-scale structural tests on existing UHPC structural components, including a prestressed UHPC American Association of State Highway Transportation Officials (AASHTO) Type II girder and a prestressed UHPC second-generation pi-girder.

Table 1. UHPC Material Properties.

Property

Value

Unit weight

160 lb/ft3
(2565 kg/m3)

Modulus of elasticity

7,650–8,000 ksi
(53–55 GPa)

Poisson’s ratio

0.18

Compressive strength

29 ksi
(200 MPa)

Post-cracking
tensile strength

1.4–2.3 ksi
(9.7–15.9 MPa)

Ultimate tensile strain

0.007–0.010

Figure 1 depicts the typical assumed uniaxial stress-strain relationship of UHPC. The CDP parameters were calibrated through comparison to experimental structural test results, including three on an I-girder and a series on the second-generation pi-girder. The three-dimensional (3-D) finite element models of the I-girder and pi-girder test specimens are illustrated in figure 2 and figure 3.

Figure 1. Graph. UHPC Uniaxial Material Model. This figure shows the assumed unaxial stress-strain relationship of ultra-high performance concrete (UHPC). The concrete's compressive relationship is obtained from compression test cylinder response results and is linear until the ultimate strength of 28 ksi (193 MPa). Its tensile relationship assumes a simple elastic-perfectly-plastic stress-strain response. The assumed tensile strength falls in a range of 1.4 to 2.3 ksi (9.7 to 15.9 MPa) and the ultimate tensile strain is approximately 0.01, according to the physical tests and model calibrations. Its Young's modulus is approximately 7,650-8,000 ksi (53-55 GPa). This uniaxial material response is represented in the concrete damaged plasticity (CDP) model to describe the three-dimensional (3-D) response of UHPC in both elastic and plastic stages.

Figure 1. UHPC Uniaxial Material Model.

Figure 2. Illustration. 3-D Finite Element Models of I-Girders 80F, 24S, and 14S. This figure presents the three-dimensional (3-D) finite element models of three I-girders. The girder section used the American Association of State Highway Transportation Officials (AASHTO) Type II girder shape, which is 3 ft (0.91 m) deep and has a 12 inch (305 mm) wide top and an 18-inch (457 mm) wide bottom flange. The girder web is 15 inches (381 mm) deep and is 6 inches (152 mm) thick. The girder contains 26 0.5-inch, 270 ksi (12.7 mm, 1,862 MPa) low-relaxation prestressing strands. Twenty-four of these strands are located in the bottom flange, spaced in a grid pattern on 2-inch (51-mm) spacing. I-girder 80F is considered a simply supported flexure member with a span of 78.5 ft (24 m) and loaded symmetrically by two point loads each located 3 ft (0.914 m) from midspan. Tests on I-girders 24S and 14S focused on shear response of the same AASHTO shape and strand reinforcement. An I-girder 24S specimen with a span of 24 ft (7.3 m) was obtained from the east portion of the tested I-girder 80F specimen after the conclusion of the I girder 80F test. The I-girder 14S specimen was part of a 30-ft (9.2 m)-long girder and was tested on a span of 14 ft (4.3 m). All of the finite element models were built to replicate the tests.

Figure 2. 3-D Finite Element Models of I-Girders 80F, 24S, and 14S.

Figure 3. Illustration. 3-D Finite Element Models of Pi-Girder and Pi-Girder with Joint. This figure shows the three-dimensional (3-D) finite element models of a pi-girder and a pi-girder with joint. The pi-girder is 2.75 ft (0.84 m) deep, 8.33 ft (2.54 m) wide, 25 ft (7.6 m) long and can contain up to 16 prestressing strands in each bulb. The integral deck of the girder is 4.1 inches (104 mm) thick, and webs range from 3.2 to 3.5 inches (81 to 89 mm) thick. A 5.2-inch (132-mm)-deep shear key runs the length of each flange tip to allow for connection of the modular components. The girder was prestressed through the use of 0.6-inch, 270-ksi (15.2-mm, 1,862 MPa) low-relaxation prestressing strands. The girder contained 22 strands, with 9 strands in each of the two bulbs and 2 in the deck above each web. The strands in the bulbs were all stressed to 42.5 kips (189 kN), and the strands in the deck were each pulled to 5 kips (22 kN). The pi-girder test specimens each included two steel diaphragms within the span. The diaphragms are each located 6.33 ft (1.93 m) from midspan. A peak total load of 340 kips (1,512 kN) was applied vertically downward through two hydraulic jacks situated near midspan. In the test, loads were transmitted to the deck through two 10-by-20-inch (0.25-by-0.51-m) elastomeric pads located along the centerline of the girder and situated 2 ft (0.61 m) on either side of midspan. The pi-girder test focused on transverse flexure behavior of the pi-girder when subjected to loads applied between the girder's legs. The test on the pi-girder with a longitudinal joint was similar to the test on the pi-girder in many ways. The test specimen was created by saw-cutting the pi-girder specimen along the longitudinal center line after the conclusion of tests. A high-performance magnesium phosphate grout or field-cast UHPC was used to fill the longitudinal joint between the half-girders. The test on the pi-girder with joint focused on transverse flexural and shear behaviors of the pi-girder in presence of the longitudinal joint, a joint which would repeat itself between adjacent pi-girders in a bridge structure.

Figure 3. 3-D Finite Element Models of Pi-Girder and Pi-Girder with Joint.

In the pi-girder models, nonlinear springs replaced actual diaphragms and linear springs replaced elastomeric pads in order to facilitate modeling. Some idealized scenarios were also investigated to complement the experimental results and to suggest potential future optimizations. Parametric studies were presented to address issues such as mesh sensitivity, concrete smeared cracking model, different tension stiffening definitions, grouting material, and contact interaction. Finite element model-predicted results were compared with experimentally captured measurements.

Figure 4 and figure 5 present a comparison of midspan deflection and strain responses of the I girder 80F.

Figure 4. Graph. I-Girder 80F: Deflection at Midspan. This graph demonstrates that the proposed finite element model accurately replicates the experimental response of the vertical displacement of I girder 80F at midspan.

Figure 4. I-Girder 80F: Deflection at Midspan.

Figure 5. Graph. I-Girder 80F: Longitudinal Strains at Midspan. This graph demonstrates that the proposed finite element model accurately replicates the experimental response of the longitudinal strain on the top and bottom surfaces of I girder 80F at midspan.

Figure 5. I-Girder 80F: Longitudinal Strains at Midspan.

Figure 6 and figure 7 present the predicted deflections of the I-girders 24S and 14S along six instrumentation lines spaced in the longitudinal direction in comparison with the experimental measurements that were modified by excluding possible linear elastic deformation of the test supporting systems. In figure 7, the slippage of the prestressing strands accounts for the larger nonlinear deflection observed in the experiment.

Figure 6. I-Girder 24S: Deflection Along Specified Instrumentation Lines.

Figure 6. Graph. I-Girder 24S: Deflection Along Specified Instrumentation Lines. This figure presents the predicted and observed vertical deflection of I-girder 24S along the six instrumentation lines. A uniform vertical displacement appears to be a result of vertical deformation of the supporting systems and was excluded from the experimental measurements.

Figure 6. Graph. I-Girder 24S: Deflection Along Specified Instrumentation Lines. This figure presents the predicted and observed vertical deflection of I-girder 24S along the six instrumentation lines. A uniform vertical displacement appears to be a result of vertical deformation of the supporting systems and was excluded from the experimental measurements.

Figure 7. I-Girder 14S: Deflection Along Specified Instrumentation Lines.

Figure 7. Graph. I-Girder 14S: Deflection Along Specified Instrumentation Lines. This figure presents the predicted and observed vertical deflection of I-girder 14S along the six instrumentation lines. Similarly to I-girder 24S, a uniform vertical displacement appears to be a result of vertical deformation of the supporting systems and was excluded from the experimental measurements. The effects of slippage of prestressing strands were observed and retained in the experimental results.

Figure 7. Graph. I-Girder 14S: Deflection Along Specified Instrumentation Lines. This figure presents the predicted and observed vertical deflection of I-girder 14S along the six instrumentation lines. Similarly to I-girder 24S, a uniform vertical displacement appears to be a result of vertical deformation of the supporting systems and was excluded from the experimental measurements. The effects of slippage of prestressing strands were observed and retained in the experimental results.

Figure 8 through figure 13 present the experimental and finite element results on deflection, longitudinal strain, leg spreading at midspan, and diaphragm force for the pi-girder. Figure 14 through figure 19 show the experimental and finite element results for the pi-girder with joint.

Figure 8. Graph. Pi-Girder: Deflection of Bulb at Midspan. This graph provides a comparison of the finite element model (FEM) and experimental results on the deflection of the bulbs at midspan. The midspan vertical deflection of the bulbs is fairly linear and is primarily representative of the global longitudinal flexure of the girder.

Figure 8. Pi-Girder: Deflection of Bulb at Midspan.

Figure 9. Graph. Pi-Girder: Deflection of Middeck at Midspan. This graph provides a comparison of the finite element model (FEM) and experimental results on the deflection of the middeck at midspan. The vertical deflection response at the middeck midspan location gradually displays an increasing difference between the FEM and experimental results.

Figure 9. Pi-Girder: Deflection of Middeck at Midspan.

Figure 10. Graph. Pi-Girder: Longitudinal Strain on Bulb Bottom Surface at Midspan. This graph provides a comparison of the finite element model (FEM) and experimental results on the longitudinal strain on the bulb bottom surface at midspan. Excellent agreement was obtained between the FEM and experimental results on the longitudinal strains on the bottom of the north bulb at midspan. These portions of girder concrete primarily experienced longitudinal flexural deformation. The concurrence of results lends support to the chosen Young's modulus of 7,650 ksi (53 GPa) for the ultra-high performance concrete (UHPC).

Figure 10. Pi-Girder: Longitudinal Strain on Bulb Bottom Surface at Midspan.

Figure 11. Graph. Pi-Girder: Longitudinal Strain on Deck Surface Immediately Above Web at Midspan. This graph provides a comparison of the finite element model (FEM) and experimental results on the longitudinal strain on the deck surface above web at midspan. Excellent agreement was obtained between the FEM and experimental results on the longitudinal strains on the deck immediately above the north web at midspan. These portions of girder concrete primarily experienced longitudinal flexural deformation. The concurrence of results lends support to the chosen Young's modulus of 7,650 ksi (53 GPa) for the ultra-high performance concrete (UHPC).

Figure 11. Pi-Girder: Longitudinal Strain on Deck Surface Immediately Above Web at Midspan.

Figure 12. Graph. Pi-Girder: Bulb Lateral Spreading at Midspan. This graph provides a comparison of the finite element model (FEM) and experimental results on the bulb lateral spreading at midspan. Agreement between FEM and experimental results on the bulb lateral spreading at midspan is observed during nearly all of the loading process.

Figure 12. Pi-Girder: Bulb Lateral Spreading at Midspan.

Figure 13. Graph. Pi-Girder: Diaphragm Force. This graph provides a comparison of the finite element model (FEM) and experimental results on the diaphragm force for the pi-girder test. Agreement between FEM and experimental results on the diaphragm force is observed during nearly all of the loading process.

Figure 13. Pi-Girder: Diaphragm Force.

Figure 14. Graph. Pi-Girder with Joint: Deflection of Bulbs at Midspan. This graph presents the modeling result of the deflections of both bulbs at midspan in comparison to the experimental results of the pi-girder grouted by field-cast ultra-high performance concrete (UHPC) in its longitudinal joint. The results of the UHPC-joint model case agree well with the experimental results on both bulbs in terms of midspan deflection.

Figure 14. Pi-Girder with Joint: Deflection of Bulbs at Midspan.

Figure 15. Graph. Pi-Girder with Joint: Deflection of Deck near Joint at Midspan. This graph presents the modeling result of the midspan middeck deflections in comparison to the experimental results of the pi-girder grouted by field-cast ultra-high performance concrete (UHPC) in its longitudinal joint. The midspan middeck deflections compare favorably.

Figure 15. Pi-Girder with Joint: Deflection of Deck Near Joint at Midspan.

Figure 16. Graph. Pi-Girder with Joint: Longitudinal Strain on Bulb Bottom Surface at Midspan. This graph presents the modeling result of the longitudinal strain on the bottom surfaces of the bulbs at midspan in comparison to the experimental results of the pi-girder grouted by field-cast ultra-high performance concrete (UHPC) in its longitudinal joint. The finite element model replicates the longitudinal strain on the bottom surfaces of the bulbs at midspan quite well.

Figure 16. Pi-Girder with Joint: Longitudinal Strain on Bulb Bottom Surface at Midspan.

Figure 17. Graph. Pi-Girder with Joint: Longitudinal Strain on Deck Top Surface Immediately Above Webs at Midspan. This graph presents the modeling result of the longitudinal strain on the deck top surface immediately above webs at midspan in comparison to the experimental results of the pi-girder grouted by field-cast ultra-high performance concrete (UHPC) in its longitudinal joint. The finite element model (FEM) replicates the longitudinal strain on the deck immediately above webs at midspan quite well.

Figure 17. Pi-Girder with Joint: Longitudinal Strain on Deck Top Surface Immediately Above Webs at Midspan

Figure 18. Graph. Pi-Girder with Joint: Bulb Lateral Spreading at Midspan. This graph presents the modeling result of the bulb lateral spreading at midspan in comparison to the experimental results of the pi-girder grouted by field-cast ultra-high performance concrete (UHPC) in its longitudinal joint.

Figure 18. Pi-Girder with Joint: Bulb Lateral Spreading at Midspan.

Figure 19. Graph. Pi-Girder with Joint: Diaphragm Force. This graph presents the modeling result of diaphragm force in comparison to the experimental results of the pi-girder grouted by field-cast ultra-high performance concrete (UHPC) in its longitudinal joint. The diaphragm behavior corresponds reasonably well until the modeled girder appears to collapse after an applied load of 363 kips (1,614 kN).

Figure 19. Pi-Girder with Joint: Diaphragm Force.

Figure 20 presents the finite element-predicted maximum principal stress contours of the pi girder and pi-girder with joint at midspan cross section in deformed shapes under applied loads of 340 kips (1,512 kN) and 428 kips (1,904 kN), respectively.

Figure 20. Illustration. Stress Contours from Modeled Pi-Girder Test Simulations. This figure presents the finite element-predicted maximum principal stress contours of the pi girder and the pi-girder with joint at midspan cross section in deformed shapes under the maximum applied model loads of 340 kips (1,512 kN) and 428 kips (1,904 kN), respectively. The deformed shapes of both pi girders are amplified by a factor of five against their undeformed profiles. The areas of stress concentration can be observed.

Figure 20. Stress Contours from Modeled Pi-Girder Test Simulations.

The results show that CDP models using appropriate parameters in any of the three types of tension stiffening definitions can capture both linear and nonlinear behaviors of the I-girders and pi-girders reasonably well. The assumed elastic-perfectly-plastic tensile stress-strain relationship for UHPC used in the CDP models is reasonable.

CONCLUSIONS

The CDP model replicates the observed responses better than the concrete smeared cracking model in the prestressed UHPC I-girders and second-generation pi-girders. The CDP model, using appropriate parameters in any of three types of tension stiffening definitions, can capture both linear and nonlinear behaviors of the modeled tests. The proposed modeling techniques, including nonlinear spring diaphragms, linear spring pads, automatic stabilization, and contact interaction, were demonstrated to be effective. The failure mechanics in the physical tests have been investigated with additional information provided by the models.

FUTURE RESEARCH

The research completed in this study has led to the initiation of a number of related studies. A family of UHPC pi-girder cross sections applicable to a range of span lengths and configurations is under development. Combined effects of discrete and fiber reinforcements on UHPC are under investigation. Other full-scale UHPC structural component tests are being modeled in order to gain a greater understanding of the performance of precast UHPC components and field-cast UHPC connections.

REFERENCES

  1. Graybeal, B. (2006). Material Property Characterization of Ultra-High Performance Concrete, Report No. FHWA-HRT-06-103, Federal Highway Administration, McLean, VA.

  2. Graybeal, B. (2006). Structural Behavior of Ultra-High Performance Concrete Prestressed I Girders, Report No. FHWA-HRT-06-115, Federal Highway Administration, McLean, VA.

  3. Graybeal, B. (2009). Structural Behavior of a 2nd Generation Ultra-High Performance Concrete Pi-Girder, Federal Highway Administration, McLean, VA.

  4. Chen, W.F. (1982). Plasticity in Reinforced Concrete, McGraw-Hill, New York

  5. SIMULIA™. (2009). Abaqus Software and Documentation, Version 6.9-1, Dassault Systèmes, Providence, RI.

 

Researchers—This study was completed by contract staff at the Turner-Fairbank Highway Research Center under the direction of Ben Graybeal. Additional information can be gained by contacting him at 202-493-3122 or in the FHWA Office of Infrastructure Research and Development located at 6300 Georgetown Pike, McLean, VA 22101.

Distribution—The unpublished report covered in this TechBrief is being distributed through the National Technical Information Service, www.ntis.gov.

Availability—The report will be available in November 2010 and may be obtained from the National Technical Information Service, www.ntis.gov.

Key Words—Ultra-high performance concrete, UHPC, Finite element analysis, FEA, Abaqus, Concrete smeared cracking, and Concrete damaged plasticity.

Notice—This document is disseminated under the sponsorship of the U.S. Department of Transportation in the interest of information exchange. The U.S. Government assumes no liability for the use of the information contained in this document. The U.S. Government does not endorse products or manufacturers. Trademarks or manufacturers' names appear in this TechBrief only because they are considered essential to the objective of the document.

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