TECHBRIEF Finite Element Analysis of UHPC:

Structural Performance of an 

AASHTO Type II Girder and a 

2nd-Generation Pi-Girder

FHWA Publication No. of this TechBrief: FHWA-HRT-10-079

NTIS Accession No. of the report covered in this TechBrief: 

PB2011-100864

FHWA Contact: Ben Graybeal, HRDI-40, 202-493-3122, 

benjamin.graybeal@dot.gov

This document is a technical summary of the unpublished 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 secondgeneration pi-girder.

Research, Development, and 

Technology

Turner-Fairbank Highway 

Research Center

6300 Georgetown Pike

McLean, VA 22101-2296

www.tfhrc.gov
2

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.

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 threedimensional (3-D) finite element models of the 

I-girder and pi-girder test specimens are illustrated in figure 2 and figure 3.

Table 1. UHPC Material Properties.

Property Value

Unit weight

160 lb/ft3

(2,565 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 to 15.9 MPa)

Ultimate tensile strength 0.007–0.010 -30

-25

-20

-15

-10

-5

0

5

-0.004 -0.002 0 0.002 0.004 0.006 0.008 0.01 0.012

Stress (ksi (MPa))

Strain

(-34)

(-69)

(-103)

(-138)

(-172)

(-207)

(34) TENSION

COMPRESSION

Figure 1. UHPC Uniaxial Material Model.

 

I-Girder 80F I-Girder 24S I-Girder 14S

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

 

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

0

200

400

600

800

0

50

100

150

200

-4000 0 4000 8000 12000

Applied Load (kN)

Applied Load (kips)

Longitudinal Strain at Midspan (microstrain)

EXP-Top

EXP-Bottom

FEM-Top

FEM-Bottom

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

0

200

400

600

800

0 100 200 300 400 500

0

50

100

150

200

0 5 10 15 20

Applied Load (kN)

Deflection at Midspan (mm)

Applied Load (kips)

Deflection at Midspan (in.)

EXP

FEM

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

0

500

1000

1500

2000

2500

3000

0 10 20 30 40 50

0

100

200

300

400

500

600

700

0.0 0.5 1.0 1.5 2.0

Applied Load (kN)

Deflection at Instrumentation Line (mm)

Applied Load (kips)

Deflection at Instrumentation Line (in.)

EXP 1-M

FEM 1

EXP 2-M

FEM 2

EXP 3-M

FEM 3

0

500

1000

1500

2000

2500

3000

0 10 20 30 40 50

0

100

200

300

400

500

600

700

0.0 0.5 1.0 1.5 2.0

Applied Load (kN)

Deflection at Instrumentation Line (mm)

Applied Load (kips)

Deflection at Instrumentation Line (in.)

EXP 4-M

FEM 4

EXP 5-M

FEM 5

EXP 6-M

FEM 6

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

0

500

1000

1500

2000

2500

3000

3500

0 2 4 6 8 10 12

0

100

200

300

400

500

600

700

800

0.0 0.1 0.2 0.3 0.4 0.5

Applied Load (kN)

Deflection at Instrumentation Line (mm)

Applied Load (kips)

Deflection at Instrumentation Line (in.)

EXP 1-M

FEM 1

EXP 2-M

FEM 2

EXP 3-M

FEM 3

0

500

1000

1500

2000

2500

3000

3500

0 2 4 6 8 10 12

0

100

200

300

400

500

600

700

800

0.0 0.1 0.2 0.3 0.4 0.5

Applied Load (kN)

Deflection at Instrumentation Line (mm)

Applied Load (kips)

Deflection at Instrumentation Line (in.)

EXP 4-M

FEM 4

EXP 5-M

FEM 5

EXP 6-M

FEM 6

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

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 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 
4

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100 120 140

0

50

100

150

200

250

300

350

0 5 10 15 20 25 30 35

Applied Load (kN)

Diaphragm Force (kN)

Applied Load (kips)

Diaphragm Force (kips)

EXP

FEM (CDP)

FEM (CSC)

Figure 13. Pi-Girder: Diaphragm Force.

0

200

400

600

800

1000

1200

1400

0 5 10 15 20 25

0

50

100

150

200

250

300

350

0.0 0.2 0.4 0.6 0.8 1.0

Applied Load (kN)

Bulb Lateral Spreading at Midspan (mm)

Applied Load (kips)

Bulb Lateral Spreading at Midspan (inches)

EXP

FEM (CDP)

FEM (CSC)

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

0

200

400

600

800

1000

1200

1400

0 5 10 15 20 25

0

50

100

150

200

250

300

350

0.0 0.2 0.4 0.6 0.8 1.0

Applied Load (kN)

Deflection of Bulb at Midspan (mm)

Applied Load (kips)

Deflection of Bulb at Midspan (inches)

EXP NORTH

EXP SOUTH

FEM (CDP)

FEM (CSC)

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

0

200

400

600

800

1000

1200

1400

0 5 10 15 20 25

0

50

100

150

200

250

300

350

0.0 0.2 0.4 0.6 0.8 1.0

Applied Load (kN)

Deflection at Midspan and Middeck (mm)

Applied Load (kips)

Deflection at Midspan and Middeck (inches)

EXP

FEM (CDP)

FEM (CSC)

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

0

200

400

600

800

1000

1200

1400

0

50

100

150

200

250

300

350

0 200 400 600 800

Applied Load (kN)

Applied Load (kips)

Longitudinal Strain on Bulbs (Bottom) at Midspan (microstrain)

EXP

FEM (CDP)

FEM (CSC)

Figure 10. Pi-Girder: Longitudinal Strain on Bulb 

Bottom Surface at Midspan.

0

200

400

600

800

1000

1200

1400

0

50

100

150

200

250

300

350

-300 -250 -200 -150 -100 -50 0

Applied Load (kN)

Applied Load (kips)

Longitudinal Strain above Webs (Top) at Midspan (microstrain)

EXP

FEM (CDP)

FEM (CSC)

Figure 11. Pi-Girder: Longitudinal Strain on Deck 

Surface Immediately Above Web at Midspan.

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 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 20 presents the finite elementpredicted 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.

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.
5

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, 

Figure 20. Stress Contours from Modeled Pi-Girder 

Test Simulations.

Figure 8. Pi-Girder with Joint: Deflection, Longitudinal Strain on Bulb Bottom Surface, Leg Spreading at

Midspan, and Diaphragm Force.

0

500

1000

1500

2000

0 50 100 150 200

0

100

200

300

400

500

0 10 20 30 40

Applied Load (kN)

Diaphragm Force (kN)

Applied Load (kips)

Diaphragm Force (kips)

EXP

FEM

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

0

500

1000

1500

2000

0 5 10 15

0

100

200

300

400

500

0.0 0.2 0.4 0.6

Applied Load (kN)

Bulb Lateral Spreading at Midspan (mm)

Applied Load (kips)

Bulb Lateral Spreading at Midspan (inches)

EXP

FEM

Figure 18. Pi-Girder with Joint: Bulb Lateral 

Spreading at Midspan.

0

500

1000

1500

2000

0 5 10 15 20 25 30

0

100

200

300

400

500

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Applied Load (kN)

Deflection of Bulbs at Midspan (mm)

Applied Load (kips)

Deflection of Bulbs at Midspan (inches)

EXP SOUTH

EXP NORTH

FEM SOUTH

FEM NORTH

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

Midspan.

0

500

1000

1500

2000

0 5 10 15 20 25 30

0

100

200

300

400

500

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Applied Load (kN)

Deflection of Deck near Joint at Midspan (mm)

Applied Load (kips)

Deflection of Deck near Joint at Midspan (inches)

EXP SOUTH

EXP NORTH

FEM SOUTH

FEM NORTH

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

Near Joint at Midspan.

0

500

1000

1500

2000

0

100

200

300

400

500

0 500 1000 1500 2000 2500

Applied Load (kN)

Applied Load (kips)

Longitudinal Strain on Bulbs (Bottom) at Midspan (microstrain)

EXP SOUTH

EXP NORTH

FEM SOUTH

FEM NORTH

Figure 16. Pi-Girder with Joint: Longitudinal Strain 

on Bulb Bottom Surface at Midspan.

0

500

1000

1500

2000

0

100

200

300

400

500

-600 -400 -200 0

Applied Load (kN)

Applied Load (kips)

Longitudinal Strain above Webs (Top) at Midspan (microstrain)

EXP SOUTH

EXP NORTH

FEM SOUTH

FEM NORTH

Figure 17. Pi-Girder with Joint: Longitudinal Strain on

Deck Top Surface Immediately Above Webs at Midspan.
6

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.

Quality Assurance Statement—The Federal Highway Administration provides high-quality 

information to serve Government, industry, and the public in a manner that promotes public 

understanding. Standards and policies are used to ensure and maximize the quality, objectivity, 

utility, and integrity of its information. FHWA periodically reviews quality issues and adjusts its 

programs and processes to ensure continuous quality improvement.

November 2010 FHWA-HRT-10-079

HRDI-40/11-10(150)E

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. SIMULIATM. (2009). Abaqus Software and 

Documentation, Version 6.9-1, Dassault 

Systèmes, Providence, RI.