20320140503020 2-3

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20320140503020 2-3

  1. 1. 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 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: www.iaeme.com/ijciet.asp Journal Impact Factor (2014): 7.9290 (Calculated by GISI) www.jifactor.com IJCIET ©IAEME
  2. 2. 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 188 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.
  3. 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 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
  4. 4. 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 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.
  5. 5. 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 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
  6. 6. 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 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
  7. 7. 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 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
  8. 8. 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 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, Issue 1, 2013, pp. 16 - 25, ISSN Print: 0976 – 6308, ISSN Online: 0976 – 6316.

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