20320140503020 2-3

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online) Volume 5, Issue 3, March (2014), pp. 187-194 © IAEME
187
STRESS STRAIN BEHAVIOUR OF ULTRA HIGH PERFORMANCE
CONCRETE UNDER UNIAXIAL COMPRESSION
S. Lavanya Prabha1
, J.K.Dattatreya2
, M.Neelamegam3
1
Professor & Head, Department of Civil Engineering, Easwari Engineering College, chennai
2
Former Assistant Director, Concrete Composite Lab, SERC, Chennai, India,
3
Professor, Department of Civil Engineering, Easwari Engineering College, Chennai
ABSTRACT
Ultra High Performance Concrete (UHPC), which is a type of improved high strength
concrete, is a recent development in concrete technology. The stress-strain behaviour of UHPC under
compression is of considerable interest in the design of UHPC members because the material is
intrinsically strong in compression, and accurate prediction of their structural behaviour. An attempt
has been made in the present study to determine the complete stress-strain curves from uniaxial
compression tests and to develop stress-strain models representing this behaviour. The effect of
material composition on the stress-strain behaviour and the consequent variation in the model
parameters and the compression toughness are presented in the paper. The highest cylinder
compressive strength of 171.3 MPa and elastic modulus of 44.8 GPa were recorded for 2% 13 mm
fibers. The optimum fiber content was found to be 3% of 6mm or 2% of 13mm.
A new measure of compression toughness known as MTI (modified toughness index) is
proposed and it is found to range from 2.64 to 4.65 for UHPC mixes. It appears to be a better
measure of the reinforcing action of fibers and their crack bridging action than some of the earlier
measures proposed by other investigators. For modelling of the complete stress-strain curve, several
stress-strain behavioural models were examined and a modification of model adopted by earlier by
Voo et al [2003] was found to provide the best fit for all the mixes and provided very good
agreement with the experimental results.
Keywords: UHPC, Fiber, Stress, Strain, Elastic modulus, Uniaxial Compression, Toughness
1.0 INTRODUCTION
Ultra High Performance Concrete (UHPC) represents one of the most recent technological
leaps witnessed by the construction industry. Among already built outstanding structures, UHPC
structures lie at the forefront in terms of innovation, aesthetics and structural efficiency. Many
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Volume 5, Issue 3, March (2014), pp. 187-194
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researchers have investigated the various aspects of UHPC like Richard and Cherezy1
, Jörg
Jungwirth2
, Voo. et al3
, Chang. et al4
and Malik. et al5
,. However, proper selection of materials,
their proportioning and process of production influence the rheological properties and mechanical
performances of UHPC. For the design of UHPC structural components, one of the important
requirements is the stress-strain behavioural model. Not much published information is available
about the stress-strain characteristics of UHPC. The paper focuses on the stress-strain behaviour of
UHPC under uniaxial compression and its modelling. The proposed equation for modeling the stress-
strain behaviour uses only two parameters, which are functions of the material properties and
compositional parameters expressed by the term reinforcement index and generates both the
ascending and descending segments of the stress-strain curves of UHPC reinforced with straight steel
fibers.
2.0 RESEARCH SIGNIFICANCE
One of the basic prerequisites for the analysis and design of reinforced concrete is the
constitutive model of the materials. UHPC is a recent development in concrete technology.
Therefore, the behaviour of UHPC under compression is of considerable interest in the design of
UHPC members and prediction of their structural behaviour. However, only a few studies have been
undertaken on the stress-strain behaviour of UHPC. An attempt has been made to in the present
study to determine the complete stress-strain curves from uniaxial compression tests and to develop
stress-strain models representing this behaviour. The effect of material composition on the model
parameters and the compression toughness properties of UHPC were determined.
3.0 NEED FOR THE PRESENT STUDY
Very few investigations reported the complete stress-strain behaviour of UHPC. A research
program was undertaken by Graybeal., et., al.,6
to characterize many of the behaviors relevant to the
use of UHPFRC(Ultra High Performance Fiber Reinforced Concrete) in the highway bridge
industry. Full compression stress-strain response data was also collected for cylinder specimens. The
results clearly indicated the change in the behavior of for untreated UHPFRC as the curing of the
concrete progresses.There is considerable difference in the test procedures and the stress-strain
pattern reported in the literature. Modelling of stress-strain curve has not been dealt in detail. The
effect of different parameters on stress-strain characteristics are not investigated in detail. No report
is available on the effect of fibre content and the toughness index in compression for UHPCs.
4.0 EXPERIMENTAL PROGRAM
4.1 Formulation and properties of UHPC
An Ultra High Performance Concrete formulation developed at the Structural Engineering
Research Center, Chennai based on extensive investigations [Dattatreya et al7
] was used for
production of UHPC cylinders of 100mm diameter and 200mm height. The stress-strain behaviour of
cylinders with various combinations of fibre content was investigated under uniaxial compressive
loading. The various experimental activities involved in this study are presented in the following
paragraphs.
4.1.1 Mix Composition
The mix proportion per m3
of ultra high performance concrete mix formulation are shown in
Table1.

189
Table 1 Mixture proportions
Mix ID Fibre Length
Mix proportions of UHPC
C SF Q FA W SP
SteelFib
re
UHPC -1% 6mm 1 0.25 0.4 1.1 0.17 1.2% 1%
UHPC -2% 6mm 1 0.25 0.4 1.1 0.17 2.25% 2%
UHPC - 3% 6mm 1 0.25 0.4 1.1 0.20 2.5% 3%
UHPC - 1% 13mm 1 0.25 0.4 1.1 0.17 1.2% 1%
UHPC -2% 13mm 1 0.25 0.4 1.1 0.17 2.25% 2%
UHPC - 3% 13mm 1 0.25 0.4 1.1 0.20 2.5% 3%
UHPC -
1%+1%
6mm+13mm 1 0.25 0.4 1.1 0.17 2.25% 2%
UHPC -
1%+2%
6mm+13mm 1 0.25 0.4 1.1 0.20 2.5% 3%
Note: C – Cement, SF – Silica fume, Q – Quartz, FA – Fine aggregate, CA – Coarse aggregate, W –
Water, SP – Superplasticizers (quantity of SP represented in percentage by weight of cement
material), SF – Steel Fibres (quantity of SF is represented in percentage by volume of the total
mixture)
4.1.2 Casting
The UHPC cylinders of 100mm diameter and 200mm height were cast with various fibre
content and combinations as shown in Table 2.
4.2 Testing
For determining the stress-strain characteristics of UHPC in compression, uniaxial
compression tests were carried out on concrete cylinder specimens of size 100 mm dia. X 200mm
high in the MTS Universal Testing Machine at CSIR-SERC, Chennai. The specimen was also
instrumented with two LVDTs for measurement of axial deformation (Fig.1) between the platens as
recommended by RILEM Technical Committee TC 1489
, “on strain softening of concrete for the
post peak strain monitoring”. In addition, two electrical resistance strain gauges fixed at the mid-
height of the specimen one in horizontal and another one placed vertically, to measure the axial and
circumferential strains. A HBM data logger connected to the control system recorded the readings
automatically. The specimens were tested under cross head control at a constant deformation rate of
0.2mm/minute until the peak load was reached and after that the load started decreasing (post-peak
stage), and the deformation rate was reduced to about 0.05 mm/minute. The test was continued until
the load dropped to m than 50% of peak load or until failure.
Fig-1 Testing of cylinders for uniaxial compression

190
5.0 TEST RESULTS AND DISCUSSIONS
The data on mechanical properties in compression for the mixes are reported in Table 2.
Table 2 Stress-strain Parameters
S.
No
Mix
Type
Fibre content
Stress
at
peak
load
(MPa)
Elastic
Modulus
GPa
Compression toughness
Index
Strain at
peak
load
X 106
έp
Ultimate
Strain x
106
έu
Strain
Ratio
, έu/έp
Up to
0.0075
Up to
έu
MTI
1 UHPC 1% 6mm 122.7 39 0.623 0.604 2.51 3820 9258 2.42
2 UHPC 2% 6mm 145.8 42 0.675 0.639 3.474 4442 14600 3.29
3 UHPC 3% 6mm 161.8 44 0.660 0.589 3.945 4851 18007 3.71
4 UHPC 1%13 mm 136.9 41 0.672 0.655 3.285 4252 12098 2.85
5 UHPC 2% 13mm 171.3 44.8 0.659 0.617 3.634 4501 17232 3.83
6 UHPC
2%6mm+1%
13mm
156.1 38 0.647 0.595 2.784 4751 12541 2.64
7 UHPC
2%
13mm+1%
6mm
156.3 42 0.64 0.64 4.654 4900 20636 4.21
6.0 STRESS-STRAIN PARAMETERS
Table 2 shows the important stress-strain parameters viz., the peak stress, the corresponding
strain, the elastic modulus, the ultimate strain and the toughness indices for different mixes. The
compressive strength generally increased with increase in Fibre content in case of UHPC mixes with
6mm fibres and 13 mm fibres. The highest compressive strength of 171.3 MPa was recorded for 2%
13 mm fibres. However, when for the fibre combinations of 6mm and 13 mm fibre, there was a
reduction in compressive strength compared to highest compressive strength obtained for single size
fibres. This could have attributed the reduced workability and lower compaction density as indicated
by the density ratios show in Table 2. Therefore 3% of 6mm and 2% of 13 mm seem to be the
optimum fibre contents as observed from the results obtained in the present
6.1 Elastic modulus
The elastic modulus of UHPC mixes is found to be 44.8 GPa with 2%-13mm Fibre. The
highest value of 46.5 is obtained for UHPC mix with 2% 13 mm + 1% 6mm Fibres which had a
reinforcement index RI of 2.[RI=Vf(lf/df)].
6.2Toughness Index
Toughness is a measure of the energy absorption capacity of the material and is used to
charcterize the materials ability to resist fracture. The toughness in compression is computed as the
area under the stress-strain curve. Many nondimensional toughness indices have been proposed by
the reaserachers for Fibre reinforced concrete. Ezeldin and Balaguru10
defined the toughness index
as the ratio of the area up to a strain of 0.15 to the area of a perfectly plastic material (expressed in
MPa. mm/mm) with an yield strength equal to the peak strength and plastic strain of 0.15 (i.e.,
σcux0.15). In the present, study, definition of Ezheldin and Balaguru10
has been used considering
two strain limits 0.0075 and the ultimate strain. A modified toughness index (MTI) was defined as
the ratio of the area of stress-strain curve to pre-peak area of the curve. As seen from Table 2, the
value of MTI ranges from 2.64 to 4.65 for UHPC mixes and appears to be a better measure of the
reinforcing action of Fibres and their crack bridging action.

191
The ultimate strain values show the dominant effect of reinforcement effect and the length of
fibre and it is interesting to note that 13 mm fibres enable higher ultimate strain to be reached as the
6mm Fibres have a lower aspect ratio and may fail by fibre fracture rather than pull out. The ratio of
ultimate to peak strain is the highest for fibre combination of 2% 13 mm and 1% 6mm(4.65)
followed by 2% 13 mm(3.81) mix and 3% 6mm (3.73) mixes.
6.3 Crack Pattern
Fig. 2 Failure patterns of specimens with different Fibre contents in compression
Failure Patterns of typical fibre reinforced UHPC specimens is shown in Fig.9. It may be
noted here that Jungwirth2
observed that the failure pattern was characterized by a typical diagonal
crack. From Fig. 2, it is observed that failure of specimens with higher fibre volume fractions is
associated with multiple cracking and while more localized failure is evident in case of lower fibre
volume fractions. The multiple cracking leads to higher failure strain and the redistribution of
stresses leads to higher residual strength.
7.0 CONSTITUTIVE MODELLING
The most common parameters with physical significance used to define the stress-strain
relationship of steel Fibre concrete include σcu = the maximum stress of the fibre concrete, usually
considered as the material strength; Єcp = corresponding strain to the maximum stress or the secant
modulus Es, initial tangent modulus E0 and failure strain Єcu; and RI the reinforcing index by
volume. Some of the important stress-strain models developed for concrete under uniaxial
compression was used for modelling the stress-strain data obtained in the present study. To model
the UHPC stress-strain behaviour Voo. et. al.,2
used Thornfeldt11
model which is similar to that
proposed by Collins. et. al.,12
and Carriera and Chu13
except for the expressions for the parameters
n and k. While Thornfeldt. et. al.,11
expressed n and k as function of only peak compressive stress,
Voo., et., al.,3
expressed n as a function of initial tangent and secant modulus at the peak stress and
used a constant value of k=1 for both pre-peak and post peak portions. Fig. 3 shows a comparison of
the various models. It is observed that the Collins et al12
and Voo., et., al.,3
models are very near to
the experimental curve while they are rather inadequate in the post peak portion. The Desayi and
Krishnan14
, Tulin and Gerstle15
and Saenz16
models exhibit very mild post peak behaviour and
steeper pre-peak curve than the actual experimental curve. The post peak behaviour was improved by
modifying the parameter k to reduce the steepness of the post peak portion of the Voo et al3
model.
As seen in the Fig.3, the modified Voo model as used in the present study gives the best agreement

192
with the experimental data. This is confirmed from the comparison of presented in Fig. 4. In general,
the coefficient of determination (R2
) ranged from 0.95 to 0.98 for the various mixes investigated
indicating a satisfactory agreement. The following expressions were found to be appropriate for the
parameters n and k.
fc/fcp= nηηηη/(n-1+ηηηηnk
) -------------------(1)
n=E0/(E0-ESP)
k=0.75-0.075*RI
Where, E0=Initial tangent modulus,
ESP= Secant modulus at the peak stress,
RI= Vf(lf/df)
fc, έc/=compressive stress and strain
fcp, έcp/=compressive stress and strain at peak stress
η=έc/έcp=Strain ratio
Since the factor K regulates the post peak slope, it should be appropriate that it should depend
on the Fibre content and aspect ratio. Similarly, the following formulae were derived from the
experimental data for the peak stress, elastic modulus and the ultimate strain as a function of the
reinforcement index and density ratio for the UHPC mixes.
X = DR.x (RI) 1.25
------------ (2)
Peak stress, σcu = 105+1.0294X3
-15.595X2
+65.817X ------------ (3)
Where, DR =Density Ratio= Ratio of wet density of Fibreed UHPC to that of plain UHPC
Initial tangent modulus, E = 34.74+8.2681X-2.0018X2
+0.1388X3
--------- (4)
Failure strain, Єcu = 7135.4+11567X-3349.3X2
+261.47X3
--------- (5)
Secant modulus, Es=29.784+6.441X-1.5722X2
+0.1022X3
--------- (6)
Softening Factor , K=0.989-0.7393X+0.5157X2
-0.105X3
+0.0064X4
---------(7)
Fig. 3 Comparison of Different stress-strain Models for UHPC

193
Fig. 4 Comparison of the Modified Voo Model and Experimental Stress –strain Curves
8.0 CONCLUSIONS
The following are the observations made from the present study
• The highest compressive strength of 171.3 MPa was recorded for 2% 13 mm fibres. However,
when fibre combinations of 6mm and 13 mm fibre were used, there was a reduction in
compressive strength compared to highest compressive strength obtained for single size fibres.
This could be attributed to the reduced workability and lower compaction density achieved as
indicated by the density ratios.
• The elastic modulus of UHPC mixes is found to be 44.8 Gpa with the UHPC mix with 2%-13mm
Fibre.
• The value of MTI(modified toughness index) ranges from 2.64 to 4.65 for UHPC mixes and
appears to be a better measure of the reinforcing action of Fibres and their crack bridging action.
• The ratio of ultimate to peak strain is the highest for fibre combination of 2% 13 mm and 1%
6mm(4.65) followed by 2% 13 mm(3.81) mix and 3% 6mm (3.73) mixes.
• The crack pattern shows formation of vertical cracks for lower percentage of small fibre
reinforcement and diagonal cracks for higher percetages.of fibre reinforcement
• A modified Voo model was found to be appropriate for modelling of stress-strain curve of
UHPC has been suggested.
REFERENCES
1. Richard p. and Cheyrezy M.H., (1995), Cement and concrete research 25(7): pp.1501-1511
2. Jungwirth J.,(2002) 4th International PhD Symposium in Civil Engineering, Munich,
Germany,2002
3. Voo,J. Y., Foster.S.J., and Gilbert, R. I., (2003) University Report No. R-421 November
2003,, The University Of New South Wales, Sydney 2052 Australia

194
4. Chang, T.P., Chen, B.T., Wang, J.J., and Wu, C.S., (2009)“ Proc., Concrete Repair,
Rehabilitation and Retrofitting I, Ed. Alexander et al, Taylor and Francis Group, London,
pp1203-1207
5. Malik, Adnan R, Foster, and Stephen J.,(2010),ACI Structural Journal, May 2010
6. Benjamin A.Graybeal,(2007), ACI Materials Journal, March/April(2007), pp:146-152.
7. Dattatreya, J.K., Harish, K. V. , and Neelamegam,M., The Indian Concrete Journal ,
September (2007), pp 31-45
8. Harish,K.V., Dattatreya,J.K., Sabitha,D. and Neelamegam,M.,(2008) , Journal of
Structural Engineering, Vol.34, No.6, February-March (2008), pp.421-428
9. RILEM TC 148-SSC, (2000) Recommendations of TC 148-SSC: Materials and Structures,
Vol. 33, pp 347-351.
10. Ezheldin, AS and Balaguru, PN, (1999), , Journal of Materials in Civil Engineering, Vol. 4,
No. 4, (1999), pp 415-429
11. Thornfeldt D., Tomaszewicz,A., and Jenson,J.J, International Symposium on utilization of
high strength concrete, Stavanger, Norway,June(1987), pp:149-259.
12. Collins.M.P, Mitchell.D and MacGregor.J.G., (1993), Concrete International,Design
construction,1993,15(5) ,pp 27-34.
13. Carreira.D.J. Chu, Kuang-Han, ACI journal, ,(1986) 84 , pp21-28.
14. Desayi.P. and Krishnan.S , ,ACI Journal Vol.61,(1964), pp345-350.
15. Tulin.L.G. and Gerstle.K.H “Discussion of equation for stress-strain curve of concrete by
Desayi and Krishnan”,American Concrete Institute Journal. .,(1964) 61(6), 1236-1238.
16. Sanez, L.P. (1964)”Discussion of ’Equation for the stress-strain curve of concrete’ by Desayi
and Krishnan, ACI. J. Proc., 61(1964)1229-1235.
17. Ervind Hognestad.A., (1951),Bulletin 399. University of Illinois Engineering Experiment
Station. UrbanaIII,November -1951,128.
18. Tsai.W.T.(1988), journal of Engineering Mechanics ASCE, 114(1988)2133-2136.
19. M. Vijaya Sekhar Reddy, Dr.I.V. Ramana Reddy and N.Krishna Murthy, “Experimental
Evaluation of The Durability Properties of High Performance Concrete Using Admixtures”
International Journal of Advanced Research in Engineering & Technology (IJARET), Volume
4, Issue 1, 2014, pp. 96 - 104, ISSN Print: 0976-6480, ISSN Online: 0976-6499.
20. Vinod P, Lalumangal and Jeenu G, “Durability Studies on High Strength High Performance
Concrete” International Journal of Civil Engineering & Technology (IJCIET), Volume 4,
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