Fatigue Strength of Hybrid Steel-Polypropylene Fibrous Concrete Beams in Flexure

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ProcediaEngineering

Procedia Engineering 00 (2011) 000–000

www.elsevier.com/locate/procedia

The Twelfth East Asia-Pacific Conference on Structural Engineering and Construction

Fatigue Strength of Hybrid Steel-Polypropylene Fibrous Concrete Beams in Flexure

SURINDER PAL SINGH1

1 Department of Civil Engineering, Dr B R Ambedkar National Institute of Technology,Jalandhar – 144 011, India

Abstract

The paper presents results of an investigation on the flexural fatigue strength of Hybrid Fibre Reinforced Concrete (HyFRC) containing different proportions of steel and polypropylene fibres. An experimental programme was conducted to obtain the fatigue lives of HyFRC specimens at different stress levels in which approximately 115 flexural fatigue tests were conducted. Approximately 58 complimentary static flexural tests were also conducted to facilitate the fatigue tests. The specimen incorporated different proportions of steel and polypropylene fibres i.e. 25–75%, 50–50% and 75–25% by volume at a total fibre content of 0.5%. The fatigue test data has been used to determine a relationship between fatigue stress level S, fatigue life N and probability of failure Pf and to generate family of S-N-Pf curves for HyFRC. The experimental coefficients of the fatigue equation have also been obtained from the fatigue test data to represent the S-N-Pf curves analytically.

Keywords: Flexural strength; Fatigue strength; Hybrid fibre reinforced concrete; Probability of failure

1. INTRODUCTION

The applications of fibre reinforced concrete in pavements, airfield runways, road surfaces, bridge decks, offshore structures etc. have increased extensively in the past decade due to its improved mechanical properties. The increase in use has led to greater demand of knowledge of fibre reinforced concrete under fatigue loading conditions since these structures are predominantly subjected to such loads.

The modeling of the scatter or variability in the distribution of fatigue life of plain concrete and SFRC has been a subject of interest to many researchers (Oh 1986 and 1991; Singh and Kaushik 2000). It has been shown that the variability in the distribution of fatigue life at a particular stress level can approximately be described by the two parameters Weibull distribution. Recently considerable interest has developed in hybrid fibre reinforced concrete (HyFRC) – particularly hybridization of metallic and

1877–7058 © 2011 Published by Elsevier Ltd.doi:10.1016/j.proeng.2011.07.307


SURINDER PAL SINGH / Procedia Engineering 14 (2011) 2446–2452 2447Available online at www.sciencedirect.com

ProcediaEngineering


www.elsevier.com/locate/procedia

The Twelfth East Asia-Pacific Conference on Structural Engineering and Construction

Fatigue Strength of Hybrid Steel-Polypropylene Fibrous Concrete Beams in Flexure

SURINDER PAL SINGH1

1 Department of Civil Engineering, Dr B R Ambedkar National Institute of Technology,Jalandhar – 144 011, India

Abstract

The paper presents results of an investigation on the flexural fatigue strength of Hybrid Fibre Reinforced Concrete (HyFRC) containing different proportions of steel and polypropylene fibres. An experimental programme was conducted to obtain the fatigue lives of HyFRC specimens at different stress levels in which approximately 115 flexural fatigue tests were conducted. Approximately 58 complimentary static flexural tests were also conducted to facilitate the fatigue tests. The specimen incorporated different proportions of steel and polypropylene fibres i.e. 25–75%, 50–50% and 75–25% by volume at a total fibre content of 0.5%. The fatigue test data has been used to determine a relationship between fatigue stress level S, fatigue life N and probability of failure Pf and to generate family of S-N-Pf curves for HyFRC. The experimental coefficients of the fatigue equation have also been obtained from the fatigue test data to represent the S-N-Pf curves analytically.

Keywords: Flexural strength; Fatigue strength; Hybrid fibre reinforced concrete; Probability of failure

1. INTRODUCTION

The applications of fibre reinforced concrete in pavements, airfield runways, road surfaces, bridge decks, offshore structures etc. have increased extensively in the past decade due to its improved mechanical properties. The increase in use has led to greater demand of knowledge of fibre reinforced concrete under fatigue loading conditions since these structures are predominantly subjected to such loads.

The modeling of the scatter or variability in the distribution of fatigue life of plain concrete and SFRC has been a subject of interest to many researchers (Oh 1986 and 1991; Singh and Kaushik 2000). It has been shown that the variability in the distribution of fatigue life at a particular stress level can approximately be described by the two parameters Weibull distribution. Recently considerable interest has developed in hybrid fibre reinforced concrete (HyFRC) – particularly hybridization of metallic and

2 Author name / Procedia Engineering 00 (2011) 000–000

non-metallic fibres. The mechanical properties such as compressive strength, flexural strength under statically applied loads and flexural toughness etc. of the resulting composite have been investigated by different researchers (Ahmed et al. 2007; Banthia and Gupta 2005; Banthia and Sappakittipakorn 2007; Banthia and Soleimani 2005; Hsie at al. 2008; Qian and Stroeven 2000; Sivakumar and Santhanam 2007 and Yao et al. 2003). The different types of fibres used are steel, glass, polyester, carbon and macro and micro polypropylene fibres. However, the common type of hybridization consisted of steel and polypropylene fibres in most of these investigations.

Review of literature indicates that a number of research studies have been conducted on the mechanical properties of HyFRC containing metallic and non-metallic fibres under statically applied loads. Mostly, a combination of steel and polypropylene fibres is used. To the knowledge of the authors, very limited information is available on the fatigue strength of HyFRC containing combinations of metallic and non-metallic fibres. Therefore, this investigation was planned to study the flexural fatigue strength of HyFRC containing different proportions of steel and polypropylene fibres. It is proposed to generate a family of S-N-Pf curves for HyFRC with different proportions of steel and polypropylene fibres and to develop a mathematical model to represent the S-N-Pf curves analytically.

2. EXPERIMENTAL PROGRAMME

The concrete mix proportions used in this investigation are shown in Table 1. Portland Pozzolanic Cement, crushed stone coarse aggregates with maximum size of 12 mm and locally available river sand were used. The materials conformed to the relevant Indian Standard Specifications. Corrugated steel fibres 35 mm long, 2 mm wide and 0.6 mm in thickness and homopolymer fibrillated polypropylene fibres were used. The specimens incorporated different proportions of steel and polypropylene fibres by volume i.e. 75-25%, 50-50% and 25-75%. The total volume fraction of fibres was kept at 0.5%. Table-2 presents the details of various fibre concrete mixes used in this investigation. The specimens used for compressive strength tests were 150 x 150 x 150 mm3 standard size cubes whereas standard prisms of size 100 x 100 x 500 mm3 were used for static flexural and flexural fatigue tests. The specimens were cast in different batches, each batch containing nine standard prisms for static flexural and flexural fatigue tests and three cubes for compressive strength tests. Appropriate dose of super-plasticizer was used to maintain workability.

Table 1: Concrete mix proportion

Water/Cement Ratio Sand/Cement Ratio Coarse Aggregate/Cement Ratio

0.46 1.52 1.88

Table 2: Fibre mix combinations

Type of Fibres Fibre Mix Proportion by Volume (%)

Total Volume Fraction, Vf = 0.5%

Steel Fibres 25 50 75

Polypropylene Fibres 75 50 25

Three specimens from each batch were tested to obtain its static flexural strength prior to fatigue tests. The remaining beams in a particular batch were tested in flexural fatigue wherein the static flexural strength obtained earlier was used to select suitable load levels for fatigue tests. Non-reversed sinusoidal loads were applied at a frequency of 10 Hz. Flexural fatigue tests were conducted at different stress levels 'S' ranging from 0.90 to 0.70 of corresponding static flexural strength. The fatigue stress ratio ‘R’ was

2448 SURINDER PAL SINGH / Procedia Engineering 14 (2011) 2446–2452 Author name / Procedia Engineering 00 (2011) 000–000 3

kept constant at 0.10. The number of cycles to failure of each specimen under different loading conditions was noted as fatigue life N. All the static flexural tests and flexural fatigue tests were conducted on a 100 kN servo-controlled actuator. Approximately 115 flexural fatigue tests and 58 static flexural tests were conducted.

Average compressive strength of 36.40 MPa, 44.20 MPa and 46.10 MPa was obtained for HyFRC containing 25% steel fibres + 75% polypropylene fibres, 50% steel fibres + 50% polypropylene fibres and 75% steel fibres + 25% polypropylene fibres respectively. The average static flexural strength of 5.60 MPa, 5.85 MPa and 6.80 MPa was achieved for HyFRC containing 25% steel fibres + 75% polypropylene fibres, 50% steel fibres + 50% polypropylene fibres and 75% steel fibres + 25% polypropylene fibres respectively.

3. ANALYSIS OF FATIGUE LIFE DATA

The determination of fatigue strength has been based on experimental studies. Large variability usually occurs in the fatigue life data of concrete even at a given stress level under carefully controlled test procedures. The variability or scatter in the fatigue life data of fibre reinforced concrete is expected to be larger than that of plain concrete. Therefore, incorporation of probability of failure into the fatigue test data is an important aspect.

To incorporate failure probability into the fatigue test data, a method employed previously to develop S-N-Pf diagram has been used here (McCall 1958; Singh et al. 2005). First a family of S-N-Pf curves has been developed for HyFRC containing different proportions of steel and polypropylene fibres. Secondly, a mathematical relation to represent the family of S-N-Pf curves analytically has been developed.

A typical family of S-N-Pf curves for HyFRC containing 25% steel fibres + 75% polypropylene fibres is shown in Fig. 1. The fatigue test data at each stress level has been ranked in the ascending order of magnitude and the probability of failure is calculated. First of all, lower part is generated in which the probability of failure Pf is plotted against number of cycles to failure N corresponding to different values of the stress levels tested, and is denoted as a family of N-Pf curves. In the next step, a family of S-N curves has been plotted using the previously generated N-Pf curves. This is shown in the upper right part of the Figure 1. These S-N curves can be used to predict the flexural fatigue strength of HyFRC for the desired level of probability of failure. The upper left part presents a family of S-Pf curves that have been obtained using the S-N curves presented in the upper right part of Figure 1. In the same manner, S-N-Pf

diagrams have also been constructed for HyFRC containing 50% steel fibres + 50% polypropylene fibres and 75% steel fibres + 25% polypropylene fibres. These families of S-N-Pf curves are not shown.

To represent the S-N-Pf curves analytically, following expression proposed by McCall (1958) for plain concrete and subsequently used by Singh et al. (2005) for steel fibre reinforced concrete has been employed here for HyFRC

( )cb )N(log)S(a10L −= (1)

where a, b and c are experimental coefficients and L is the probability of survival, which equals unity minus the probability failure Pf.

The coefficients of Eq. (1) can be obtained from the fatigue test data of HyFRC obtained in this investigation. Taking logarithm twice on both sides of Eq. (1)

( ) ( ) ( ) ( )NloglogcSlogbalogLloglog ++=−

SURINDER PAL SINGH / Procedia Engineering 14 (2011) 2446–2452 24494 Author name / Procedia Engineering 00 (2011) 000–000

Probability of Failure 'Pf'0.00.20.40.60.81.0

Cyc

les

to F

ailu

re 'N

'103

104

105

106

Cycles to Failure 'N'

103 104 105 106

Stre

ss L

evel

'S'

0.70

0.75

0.80

0.85

Probability of Failure 'Pf'0.00.20.40.60.81.0

Stre

ss le

vel '

S'

0.65

0.70

0.75

0.80

0.85

0.90LEGEND

Pf = 0.10Pf = 0.30Pf = 0.50Pf = 0.70

S = 0.85

S = 0.80

S = 0.75

S = 0.70

N = 1000 cycles

N = 4000

N = 20000

N = 100000

N = 1000000 cycles

Pf = 0.90

PredictedPf = 0.10Pf = 0.90

Typical Predicted Curves

Curves from Test Data

Figure 1: S-N-Pf curves for HyFRC (75% steel fibres + 25% polypropylene fibres).

which can be written in the following form

Y = A + bX + cZ (2)

in which Y = ( )Lloglog − , A = ( )alog , X = ( )Slog and Z = ( )NloglogSince Z has to be determined from X and Y, Eq. (2) can be modified and written as follows

YCXBAZ ′+′+′= (3)

here ,cA

A −=′ ,cb

B −=′ ,c1

C =′

It is more convenient to work with the mean values of the variables rather than values of the variables,therefore, the following relationship can be written

∑ ∑′+∑′+∑ ′= YCXBAZ

nY

CnX

BAZn1 ∑′+∑′+′=∑


YCXBAZ ′+′+′= (4)

Subtracting Eq. (4) from Eq. (3), following expression is obtained

( ) ( )YYCXXBZZ −′+−′=−

or

ycxbz ′+′= (5)

where ZZz −= , XXx −= , YYy −=The fatigue life data of HyFRC containing 75% steel fibres + 25% polypropylene fibres has been

analysed using the above equations and the following expression is obtained

z = - 2.660001x + 0.05257y (6)

or in the following form

Z = 0.64298 - 2.660001X + 0.05257Y (7)

The coefficients a, b and c of Eq. (1) have been evaluated and the final equation for HyFRC containing 75% steel fibres + 25% polypropylene fibres can be written in the following form

( ) 10.24)N(log22.57S101012.1)10(L−×−= (8)

In the same way, the fatigue life data of HyFRC for other combinations of steel fibres and polypropylene fibres has been analysed and the equations which are developed to represent the S-N-Pf

curves are as follows For HyFRC with 50% steel fibres + 50% polypropylene fibres

( ) 78.2272.4212 )N(logS1048.2)10(L−×−= (9)

and for HyFRC with 25% steel fibres + 75% polypropylene fibres

( ) 02.1960.508 )N(logS1009.7)10(L−×−= (10)

Equations (8), (9) and (10) represent theoretical relationships for the family of S-N-Pf curves for HyFRC and can be used to predict its flexural fatigue strength for the desired level of probability of failure. The coefficients of Eq. (1) obtained in this investigation for different combinations of steel and polypropylene fibres are listed in Table 3. The coefficients of Eq. (1) obtained previously for SFRC containing single size fibres are also listed for comparison.

To represent the family of S-N-Pf curves theoretically, the analysis to obtain the material coefficients of Eq. (1) is based upon the approximate assumption that the fatigue test data, at a particular stress level, conforms to a symmetric probability density function. Using the material coefficients of Eq. (1) as obtained in this investigation, some typical predicted curves have been plotted alongside the curves obtained from test data as shown in Fig. 1 for HyFRC incorporating 75% steel fibres + 25% polypropylene fibres. It can be observed that the predicted curves are quite close to the experimental curves, which indicates that the assumption of an approximate symmetric probability density function is not unjustified. A comparison of the results with Steel Fibre Reinforced Concrete (SFRC) indicates that the gradual replacement of steel fibres by polypropylene fibres is beneficial as it reduces the

SURINDER PAL SINGH / Procedia Engineering 14 (2011) 2446–2452 24516 Author name / Procedia Engineering 00 (2011) 000–000

variability/scatter in the fatigue life data of HyFRC at a particular stress level. The detailed results on this issue will be published in a separate paper.

It may, however, be noted that the coefficients of Eq. (1) obtained in this investigation for HyFRC containing different proportions of steel and polypropylene fibres are valid for the type and size of fibres used in this investigation. Additional research work is required to estimate these coefficients for other type and size of the fibres which are available.

4. CONCLUSION

Experiments have been conducted to obtain the flexural fatigue lives of HyFRC with 0.5% fibre volume fraction incorporating different combinations of steel and polypropylene fibres. The test data has been used to develop S-N-Pf curves for HyFRC and a relationship between stress level, fatigue life and survival probability has been determined. The material coefficients of the fatigue equation representing family of S-N-Pf curves have been obtained for HyFRC containing different proportions of steel and polypropylene fibres. The equation can be used to predict the flexural fatigue strength of HyFRC using the coefficients obtained in this investigation. However, the results obtained are applicable to the type and size of the fibres used and additional research work is required to develop equations for other type and size of the fibres.

Table 5: Material coefficients a, b and c of Eq. (1) for SFRC and HyFRC

Fibre Size/Combination

Volume Fraction,

Vf (%)

Coefficients of Eq. (1)

a b c

SFRC – Mono steel fibres - Rectangular corrugated

fibres (Singh et al. 2005) 30 x 2.0 x 0.6 mm 0.5

5.47 x 10-8

45.78 17.90

HyFRC – Present investigation –

(Steel Fibres + Polypropylene Fibres)

75% steel fibres + 25% polypropylene fibres

0.57.09 x 10-8

50.60 19.02


0.52.48 x 10-12

42.72 22.78


0.5 1.12 x 10-7 57.22 24.10

5. Acknowledgement

This research work reported herein is part of the UKIERI (UK-India Education and Research Initiative) Collaborative Research Project currently in progress. The support received from UKIERI and the Ministry of Human Resource Development (MHRD), Government of India is gratefully acknowledged.

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Fatigue Strength of Hybrid Steel-Polypropylene Fibrous Concrete Beams in Flexure

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