FATIGUE ANALYSIS OF STEEL FIBRE REINFORCED CONCRETE CONTAINING CEMENT ADDITIVES

G Kaur1, S P Singh1, S K Kaushik2

1. Dr B R Ambedkar National Institute of Technology Jalandhar, India 2. Indian Institute of Technology Roorkee, India

ABSTRACT. Based upon the statistical distribution of flexural fatigue life data and flexural fatigue strength of the Steel Fibre Reinforced Concrete (SFRC) containing blends of Silica fume (SF), Metakaolin (MK), Limestone powder (LP) and Fly ash (FA), the influence of these inserts on the flexural fatigue performance of concretes is probed. An extensive experimental work has been carried out to obtain the flexural fatigue lives of concretes containing cement additives and control concrete incorporating 1.0% steel fibre volume fraction. In total 7 concrete mixes were cast, with 100% Portland cement (PC) mix referring as control mix. Other six mixes were proportioned to replace 30% PC with these cement additives in binary and ternary style to demonstrate their effect on flexural fatigue properties. Approximately 294 flexural fatigue tests were conducted supplemented by approximately 168 static flexural strength tests on all the concrete mixes. The fatigue test data thus obtained has been modeled by two-parameter Weibull distribution. The two-million cycles endurance limit / fatigue strength has been estimated based upon the percentage of the ultimate strength of concretes under static loading as well as in terms of actually applied flexural stress. Keywords: Cement additives, Weibull distribution, Fatigue strength Gurbir Kaur is a Research Associate in Dr B R Ambedkar National Institute of Technology Jalandhar, India. Her research interests include reinforced concrete, recycling of materials in concrete. Dr S P Singh is a Professor of Civil Engineering at Dr B R Ambedkar National Institute of Technology Jalandhar, India. He has worked as a Commonwealth Research Fellow at the Concrete Technology Unit of the University of Dundee, UK from October 2006 to March 2007. His research interests are fatigue behaviour of concrete composites, reinforced concrete, recycling of materials in concrete. Dr S K Kaushik is Fellow of National Academy of Engineering and formerly Professor of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee, India. He has been very active in research and consultancy. His research interests are fibre reinforced concrete- behaviour and applications, sifcon, high performance concretes, non-destructive testing and evaluation of concrete structures.

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INTRODUCTION The last few years have been very productive in the development of cement based composites from different viewpoints: increasing interest in environmental-friendly concretes, for the sake of sustainable development, applications in outstanding civil engineering structures, increase of mass constructions and many others. Concrete should satisfy various requirements that were not imposed in the past century or that did not have the importance earlier. This refers to various ecological aspects and sustainability which are of worldwide concerns these days. Sustainability has become an increasingly important characteristic for concrete infrastructure, as the production of Portland cement (the most common binder in concrete) is an energy-intensive process that accounts for a significant portion of global carbon dioxide emissions and other greenhouse gases. As such, even slight improvements in the design, production, construction, maintenance of plants and equipment and materials performance of concrete can have enormous social, economic and environmental impacts [1]. Large quantities of industrial and agricultural by-products are generated from manufacturing processes and service industries, resulting in major environmental concerns. With the increasing awareness about the environment, scarcity of land-fill space and due to its ever increasing cost, the utilization of waste materials and by-products in concrete technology / construction has become an attractive alternative to disposal. In literature the addition of mineral admixtures or cement additives to concrete either as an ingredient of cement or as partial replacement of cement are also termed as secondary raw materials, supplementary cementitious materials, fillers or powders depending upon their role in the fresh and hardened state of concrete. The use of cement additives as a raw material in cement, concrete, and other construction materials is to be expected because of their voluminous availability; economical manufacture of concrete due to lower cement content; minimizing the environmental impact due to green house gases, which would otherwise have been produced in the process of cement production. These cement additives possess in themselves little or no cementitious value, but will in finely divided form and in the presence of moisture react with cement at ordinary temperatures to form compounds possessing cementitious properties. Further, their utilization improves the microstructure, mechanical and durability properties of mortar and concrete, which cannot be easily achieved by the use of Portland cement (PC) alone. The cement additives contribute to the improved properties of concrete through chemical activity (usually pozzolanic activity) and microfiller effect [2, 3, 4, 5, 6, 8]. Fatigue loading is of concern in the design of concrete bridges, offshore structures and concrete pavements for roads and airfields. Fatigue is a process of progressive, permanent structural change occurring in a material which is subjected to conditions which produce time fluctuating stresses and strains. The structural changes may culminate in cracks or complete fracture after a sufficient number of fluctuations and as a result the structural member may fail at a load well below its strength under statically applied loads. Parameters such as loading conditions, load frequency, boundary conditions, stress level, number of cycles, matrix composition and environmental conditions will influence the fatigue performance of concrete. The fatigue behaviour of concrete during its service life is an important characteristic for assessing its useful life. The degree of damage and the sustaining time in the cycles depend on the character and structure of components, and the characteristic and effect of the interface, the dimension of original crack and resistance to crack extension and propagation under repeated load. Although the effect of steel fibres on fatigue performance is remarkable, it is difficult for the steel fibres to play their full role in strengthening concrete, if there are weaknesses in the interface between the fibre and the matrix [9].

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RESEARCH SIGNIFICANCE The attempts to study the benefits of using cement additives in various fields of concrete research i.e. workability, mechanical or durability properties, are continuously increasing. Although several mechanical and durability related properties of concrete containing cement additives have been discussed till now, very few studies have been devoted to the flexural fatigue properties of composites containing such materials. It is well established that a material subjected to fatigue loads fails well below its static strength. Therefore, it is of paramount interest to investigate the fatigue performance of concrete containing cement additives. The significance of the present research is to examine the effect of substituting PC in different proportions by FA, LP, SF and MK on the flexural fatigue performance of different mix combinations. This experimental work recommends the local materials and industrial wastes for use in modern construction jobs which are predominantly subjected to fatigue loading.

EXPERIMENTAL PROGRAMME

Materials and Mix Proportions The properties of different materials used were determined in the laboratory as per relevant codes of practice. The materials used in this research programme are 43 Grade Portland cement (PC), crushed gravel as coarse aggregates and natural sand as fine aggregates. The cement additives which were used as partial replacement of PC to produce binary and ternary mixes are FA, LP, MK and SF. Figure 1 presents the particle size distribution of all powders used in the study. To maintain workability, Glenium 51 was used as superplasticizer. Corrugated rectangular shaped steel fibres (35 mm long, 2.0 mm wide and 0.6 mm thick), supplied by M/s Stewols Pvt. Ltd., Nagpur (India) were employed at a constant volume fraction of 1.0% in all the mixes. This study examines the contribution of cement additives on the flexural fatigue performance of SFRCs where steel fibres are considered as a constant parameter.

Figure 1 Particle size analysis of the powders used in the study

0

20

40

60

80

100

0.1 1 10 100 1000

CUM

MU

LATI

VE

SIZE

, %

PARTICLE SIZE, µm

Limestone powder (LP)

Metakaolin (MK)

Silica fume (SF)

Fly ash (FA)

Portland cement (PC )

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The present investigation on the flexural fatigue performance of SFRC mixes containing LP, FA, MK and SF as cement additives in different proportions, involved preparing 7 mixes - control concrete (100% PC); binary blended mix combinations (70% PC + 30%LP) designated as ‘CL’ and (70% PC + 30% FA) designated as ‘CF’; ternary blended mix combinations (70% PC + 20% LP + 10% SF) designated as ‘CLS’; (70% PC + 20% LP +10% MK) designated as ‘CLM’; (70% PC + 20% FA + 10% SF) designated as ‘CFS’ and (70% PC + 20% FA + 10% MK) designated as ‘CFM’ respectively. The reference concrete mix proportions used was 1: 1.53: 1.89 (PC: fine aggregate: coarse aggregate) with water/binder ratio of 0.46. Table 1 summarizes the concrete mix combinations used in this investigation.

Table 1 Mix combinations considered in the study

MIX WATER/ BINDER RATIO

SAND/ BINDER RATIO

AGGREGATE/ BINDER RATIO

LP/PC RATIO

FA/PC RATIO

MK/PC RATIO

SF/PC RATIO

Control: (100%PC) 0.46 1.53 1.89 -

- - -

CL: (70%PC+30%LP) 0.46 1.53 1.89 0.43

- - -

CLM: (70%PC+20%LP+10%MK)

0.46 1.53 1.89 0.29 - 0.14 -

CLS: (70%PC+20%LP+10%SF)

0.46 1.53 1.89 0.29 - - 0.14

CF: (70%PC+30%FA) 0.46 1.53 1.89 - 0.43 - -

CFM: (70%PC+20%FA+10%MK)

0.46 1.53 1.89 - 0.29 0.14 -

CFS: (70%PC+20%FA+10%SF)

0.46 1.53 1.89 - 0.29 - 0.14

The cube and beam moulds were cleaned, brushed and oiled well before the commencement of the casting. The homogenous concrete mix was poured into the specimen moulds in two layers, each layer vibrated properly. The specimens were marked with their respective designations after three or four hours of setting and were allowed to set in the moulds for 24 hours. Subsequently the specimens were demoulded and immersed in fresh water for curing until the age of test. The cube and beam specimens were water cured for 28- and 90-days respectively. Subsequently, the beam specimens were kept in laboratory condition for about two months before being tested. The higher curing age of 90 days was chosen for specimens top be tested in static flexure and flexural fatigue tests so as to minimize the possible strength gain during fatigue tests. The specimens for each mix type were cast in nine batches, with each batch comprising of three cube specimens of size 150x150x150 mm for static compressive strength tests and nine beam specimens of size 100x100x500 mm for static and flexural fatigue tests. The average 28 days static compressive strength values for CL, CLM and CLS are 36.96, 48.65 and 46.70

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MPa respectively, whereas, the average 28 days static compressive strength values for CF, CFM and CFS are 38.44, 45.84 and 44.78 MPa respectively. The average static compressive strength for control concrete was observed to be 40.18 MPa. The average static flexural strength values for CL, CLM and CLS are 6.74, 9.79 and 9.45 MPa respectively, whereas, the average static flexural strength values for the CF, CFM and CFS concretes are 8.67, 9.43 and 8.84 MPa respectively. The average static flexural strength for control concrete was observed to be 8.08 MPa.

FLEXURAL FATIGUE ANALYSIS

The main thrust of the present investigation was on the flexural fatigue testing of beam specimens. After the static flexural strength testing of a particular batch was over, the remaining specimens from the same batch were tested in flexural fatigue. The flexural fatigue tests were conducted on the same machine as the static flexural strength test. In the fatigue tests also, the specimens were simply supported over an effective span of 450 mm and loaded at the third points. The fatigue parameters include static flexural strength (fr), stress level (S), stress ratio (R) and the loading frequency. The load cycle characteristic value or stress ratio

‘R’ is expressed asmax

min

ffR = , where fmin and fmax refer to the minimum and maximum fatigue

stress respectively. The stress level ‘S’ is expressed asrf

f max , where fr is the static flexural

strength. The fatigue tests were performed with stress levels ranging from 0.90 to 0.75, at a constant stress ratio value of 0.1. The tests were carried out in load or force control mode using a constant amplitude non-reversed sinusoidal waveform with a loading frequency of 10 Hz. Since fatigue testing is a very expensive and time consuming procedure and a large number of specimens were proposed to be tested, an upper limit of two-million cycles was selected. The machine was set so that it terminates the test as and when the specimen failed or the upper limit was reached. However, most of the specimens failed below this limit. Probabilistic Analysis of Fatigue Life Data of Concretes

The analysis of fatigue life data requires techniques from statistics, especially probabilistic analysis and linear regression. The fatigue design is clouded with uncertainties arising from the assumptions made in analysis as well as the inherent material variability [10]. So, the probabilistic reliability theory is an efficient way to adequately account for the uncertainties. Various mathematical models like the logarithmic-normal distribution and the Weibull distribution have been suggested for the statistical description of fatigue life data. On the basis of physically valid assumptions, sound experimental verifications, relative ease in its use, and better developed statistics, the Weibull distribution is most commonly employed for the statistical description of fatigue data [10, 11, 12, 13, 14]. The Weibull cumulative distribution function Pf (N) can be expressed as two-parameter Weibull distribution i.e. Eq. (1) in following way [12, 13]:

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−−=

α

uNNPf exp1)( (1)

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While most researchers prefer to use the distribution function, the survivorship function has a simpler form and has been used in present study. The probability of survival or survivorship function or reliability function, LN, may be defined as: LN = 1 – Pf (2) Substitute the value of Pf(N) from Eq. (1) into Eq. (2) to get Eq. (3). The reliability function LN can be written in the following manner [10, 11, 12, 13, 14, 15]:

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−=

α

uNLN exp (3)

The distribution of fatigue life of plain concrete, at a particular stress level approximately follows the two-parameter Weibull distribution [10, 11, 13, 14]. Fatigue life distributions of SFRC at 0.5%, 1.0% and 1.5% fibre volume fraction can also be modeled by the two-parameter Weibull distribution [16]. The two-parameter Weibull distribution has also been successfully used by various researchers in their respective investigations [16, 17, 18]. Therefore, the two parameter Weibull distribution was used in the present study to model the fatigue life data of SFRC containing binary and ternary blends of cement additives in the following section. Establishing fatigue life distributions The fatigue life data obtained for the tested beam specimens for all concretes corresponding to four different stress levels (0.90, 0.85, 0.80 and 0.75) and at a constant stress ratio (0.1) have been arranged in an ascending order at all stress levels. Table 2 presents the fatigue life data of CFS concrete and its analysis at all stress levels. In same manner, other concrete mixes were also analysed at all stress levels. The graphical method has been employed to establish two-parameter Weibull distribution for fatigue life data of concretes at a particular stress level. Three methods namely: the graphical method, the method of moments and the maximum likelihood estimate are presented to estimate the distribution parameters. The probability distributions for the fatigue life data of all concretes at different stress levels has been established in the following sections. Chauvenet’s criterion [19] was applied to all data points at each stress level and points meeting this criterion were identified and excluded from further analyses. Analysis of fatigue life data by the Graphical method

The graphical method has been employed to show that the statistical distribution of fatigue life of a concrete at a certain stress level, follows the two-parameter Weibull distribution. Equation (3) is reproduced here for reference.

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−=

α

uNLN exp (3)

Taking the logarithm twice on both sides of Eq. (3)

)ln()ln(1lnln uNLN

αα −=⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ (4)

Setting⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛=

NLY 1lnln , )ln(NX = , )ln(uαη =

We get ηα −= XY (5) Equation (5) represents a linear relationship between Y and X. In order to obtain the graphic form of Eq. (5), the fatigue life data at a given stress level was arranged in ascending order of

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cycles to failure. The empirical survivorship function LN for each fatigue life data at a given stress level is calculated as follows [10, 11, 12, 13, 16, 17, 18]:

Table 2 Fatigue life data and its analysis at different stress levels for CFS mix.

i Ni ln (Ni) ( )1kiPf +

= ⎟⎟⎠

⎞⎜⎜⎝

⎛

NL1lnln

Stress level (S) = 0.90 1 56971 10.9503 0.0909 -2.35062 67091 11.1138 0.1818 -1.60613 71382 11.1758 0.2727 -1.14434 79971 11.2894 0.3636 -0.79415 87971 11.3847 0.4545 -0.50076 96024 11.4723 0.5454 -0.23777 111091 11.6181 0.6363 0.01158 125526 11.7403 0.7272 0.26189 153544 11.9417 0.8181 0.5334

10 162544 11.9987 0.9090 0.8746Stress level (S) = 0.85

1 157173 11.9651 0.0909 -2.35062 185436 12.1305 0.1818 -1.60613 236342 12.3730 0.2727 -1.14434 273544 12.5192 0.3636 -0.79415 320291 12.6769 0.4545 -0.50076 385903 12.8633 0.5454 -0.23777 439714 12.9939 0.6363 0.01158 571134 13.2554 0.7272 0.26189 657618 13.3964 0.8181 0.5334

10 728044 13.4981 0.9090 0.8746Stress level (S) = 0.80

1 260710 12.4712 0.0909 -2.35062 343158 12.7459 0.1818 -1.60613 414754 12.9354 0.2727 -1.14434 425432 12.9609 0.3636 -0.79415 507262 13.1368 0.4545 -0.50076 891058 13.7002 0.5454 -0.23777 975658 13.7909 0.6363 0.01158 1105498 13.9158 0.7272 0.26189 1198675 13.9967 0.8181 0.5334

10 1357473 14.1211 0.9090 0.8746Stress level (S) = 0.75

1 306063 12.6315 0.1000 -2.2504 2 351857 12.7709 0.2000 -1.4999 3 735240 13.5079 0.3000 -1.0309 4 914230 13.7258 0.4000 -0.6717 5 1201435 13.9990 0.5000 -0.3665 6 1826043 14.4177 0.6000 -0.0874 7 1957542 14.4872 0.7000 0.1856 8 1987259 14.5023 0.8000 0.4759 9 1996374 14.5068 0.9000 0.8340

10 2000000** * Rejected as outliers by Chauvenet’s criterion, not included in analysis ** Specimen treated as run out, not included in analysis

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( )1+=

kiLN

(6) where ‘i’ represents the failure order number and ‘k’ represents the number of fatigue data or sample size under consideration at a particular stress level S. When a graph is plotted

between ⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛=

NLY 1lnln and )ln(NX = and the data falls approximately along a straight

line, it indicates that the two-parameter Weibull distribution is a reasonable assumption for the fatigue behaviour of concrete. The best fit straight line is drawn through the data using the method of regression analysis, such as the least square technique. The parameters (the shape parameter α and the characteristic life u) can be obtained from the regression coefficients directly. Figure 2 presents the graphical analysis of fatigue life data for CFS mix at all stress levels.

Figure 2 Graphical analysis of fatigue life data at all stress levels for CFS mix.

Analysis of fatigue life data by the Method of Moments To obtain the parameters of the Weibull distribution by this method, an estimation of appropriate sample moments, such as sample mean and sample variance are required. Wirsching and Yao (1970, 1982); Oh (1986); Singh and Kaushik (2000); Mohammadi and Kaushik (2005) used the same method to obtain the Weibull distribution parameters. The shape parameter α can be deduced from an expression given below (Wirsching and Yao 1982; Oh 1986, 1991):

( ) 08.1CV −=α (7) The characteristic life u can be estimated from the Eq. (8) as follows:

R² = 0.97

R² = 0.99

R² = 0.96

R² = 0.93

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

9 10 11 12 13 14 15

lnln

(1/(1

1/L N

))

ln(N)

S=0.90

S=0.85

S=0.80

S=0.75

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⎟⎠⎞

⎜⎝⎛ +Γ

=11

α

μu (8)

Equations (7) and (8) can be used to estimate the values of the parameters of the Weibull distribution for all concretes at various stress levels. The calculations to estimate parameters for all concretes by this method are not presented in the paper. Analysis of fatigue life data by Method of Maximum-likelihood Estimate

The distribution parameters of the Weibull distribution can also be obtained using the method of maximum likelihood estimate. The probability density function of Weibull distribution can be written as follows [11, 14]: f (n) = n exp − (9)

where θ = uα (10)

The maximum likelihood equations can be modified as follows: θ∗ = ∑ n ∗ (11) ∑ ∗ ( )∑ ∗ − ∗ = ∑ ln (n ) (12)

where α* and θ* are the maximum likelihood estimates of α and θ respectively. The shape parameter α is first obtained from Eq. (12) by a trial and error procedure using a simple computer program. The average value of shape parameter α calculated by the graphical method and the method of moments can be used as a first trial. Then the maximum-likelihood estimator for the fatigue life data, at a particular stress level, is calculated from Eq. (11). Finally, the parameter u is determined from Eq. (10). The average value of estimated parameters (shape parameter α and scale parameter u) of the Weibull distribution using different methods of analysis for fatigue life of control concrete and LP and FA based concretes at all stress levels are presented in Table 3.

Table 3 The Weibull parameters of fatigue life at different stress levels for control and LP based concretes

STRESS LEVEL

(S)

WEIBULL PARA-METER

CONTROL CONCRETE CL CLM CLS CF CFM CFS

0.90 α 2.142 2.416 2.606 2.713 2.579 2.786 2.990 u 1787 30604 40108 66824 49131 68455 113665

0.85 α 1.396 1.649 1.772 1.834 1.698 1.902 2.075

u 36906 117328 235715 256506 163310 408030 450508

0.80 α 1.270 1.4817 1.698 1.763 1.592 1.732 1.905

u 168982 409900 511199 577219 559363 718492 855169

0.75 α 1.184 1.379 1.482 1.630 1.499 1.571 1.687

u 772430 914842 1035779 1311790 1120080 1363611 1442866

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Examining variability in the fatigue life distributions of different concretes It can be observed from Tables 3 that for concretes containing cement additives, the average values of the shape parameters were higher than that of the control concrete. The increased values of the shape parameters for concretes containing cement additives reduce the variability in the distribution of fatigue life to different extents as compared to the control concrete. From Table 3 it can be observed that the average values of the shape parameters for the fatigue life distribution of LP based concretes ranged from 2.416 to 1.379, 2.606 to 1.482 and 2.713 to 1.630 for the CL, CLM and CLS mixes respectively. The maximum increase in the values of the shape parameters for CL, CLM and CLS mixes with respect to the control concrete was found to be 18.12% (at S=0.85), 33.70% (at S=0.80) and 38.82% (at S=0.80) respectively. A maximum decrease of about 18.36% (at S=0.80), 28.55% (at S=0.80) and 30.79% (at S=0.75) in the coefficient of variation in the fatigue life data of CL, CLM and CLS mix was observed as compared to the control concrete. Clearly, the CLS mix has performed better against other LP based mixtures in terms of reduction in variability in the distribution of fatigue life. The average values of the shape parameter of the Weibull distribution for the fatigue life of CF, CFM and CFS concrete ranged from 2.579 to 1.499, 2.786 to 1.571 and 2.990 to 1.687 respectively as S moved from 0.90 to 0.75 as shown in Table 3. The maximum increase in the values of the shape parameter for CF, CFM and CFS mixes with respect to the control concrete was found to be 26.60% (at S= 0.75), 36.38% (at S=0.80), 50.00% (at S=0.80) respectively. A maximum decrease of about 25.02% (at S=0.75), 30.51% (at S=0.75) and 35.75% (at S=0.75) in the coefficient of variation in the fatigue life data of CF, CFM and CFS mixes was observed as compared to the control concrete. Based upon the reduced variability in the fatigue life distributions of FA based concrete, the CFS mix performed the best among other FA based mixes.

Figure 3 The variation in shape parameters of LP and FA based concrete mixes with respect

to control concrete at different fatigue stress levels

0

0.5

1

1.5

2

2.5

3

Control CL CLM CLS CF CFM CFS

SHA

PE P

ARA

MET

ER

S=0.90

S=0.85

S=0.80

S=0.75

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Two Million Cycles Endurance Limit/Flexural Fatigue Strength

Fatigue strength is the highest stress that a material can withstand for a given number of cycles without breaking. It is also called as endurance strength. The ASTM defines fatigue life as the number of stress cycles of a specified character that a specimen sustains before failure of a specified nature occurs. In the present case, the endurance limit was defined as the maximum flexural fatigue stress at which the beam specimen could withstand two-million cycles of non-reversed fatigue loading, expressed as a percentage of the corresponding static flexural strength or modulus of rupture. The two-million cycle limit was chosen to approximate the life span of a structure that may typically be subjected to fatigue loading. It has been reported that if the specimen could withstand two-million cycles without failure, it could last for all practical purposes forever [20]. The fatigue behaviour of concrete is generally expressed in terms of the S-N curves. The S-N curves have been plotted to determine the two-million cycles fatigue strength/endurance limit of the concrete mixes. The fatigue test data have been presented as S-N relationships, with the maximum fatigue stress expressed as a percentage of the strength under static flexural loading, and as relationships between the actually applied fatigue stress and number of loading cycles to failure. The predicted fatigue strengths for two-million cycles of load application for the CL and CF mixes are 71% and 73% of the static flexural strength respectively whereas the two-million cycles fatigue strength for control concrete is 73%. Hence, it can be affirmed that the CF mix has equal fatigue strength to that of control concrete, the CL mix however, has slightly reduced performance on the other hand. Substituting 30% PC content with equal amount of FA in concrete and yet achieving quite similar fatigue strength/endurance limit favours the use of CF mix as compared to the control concrete mix. It has been observed that the two-million cycles fatigue strength/endurance limit for the CLM and CLS concrete mixes were 73% and 74% of its static flexural strength respectively. This contributes towards similar or slightly enhanced performance of concrete containing cement additives as compared to that of control concrete. The predicted two-million cycles endurance limit for the CFM and CFS concrete mixes were 75% and 76% of its static flexural strength respectively. Figure 3 summarizes the fatigue performance based upon stress as a percentage of static flexural strength for all concrete mixes of the present investigation. Among different concrete mixes the highest value of the fatigue strength at two-million cycles of load application i.e. 76% of the static flexural strength was achieved for the CFS concrete mix. The two-million cycles fatigue strength/endurance limit can also be represented in terms of actually applied fatigue stress. The two-million cycles fatigue strength/endurance limit for the CL and CF concrete mixes in terms of actually applied stress were 4.8 MPa and 6.1 MPa respectively. The ternary based LP concrete mixes has shown better performance as compared to control concrete. The two-million cycles fatigue strength/endurance limit for the CLM and CLS concrete mixes in terms of actually applied stress were 7.2 MPa and 7.0 MPa respectively. The two-million cycles fatigue strength/endurance limit for the CFM and CFS concrete mixes in terms of applied stress were 7.2 MPa and 6.6 MPa respectively. Clearly, the results of the two-million cycles fatigue strength/endurance limit in terms of actually applied stress differs from the two-million cycles fatigue strength/endurance limit based on applied maximum fatigue stress expressed as a percentage of corresponding static flexural strength. Figure 4 shows the fatigue performance of different control and LP ternary concretes at two million cycles based on actually applied flexural stress. The concrete that performs best in terms of absolute strength is the CLM mix as observed from the S-N curves.

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Figure 3 Comparison of fatigue performance based upon stress as a percentage of static

flexural strength for all concretes.

Figure 4 Comparison of fatigue performance based on actually applied flexural stress for all

mix concretes.

0.7

0.75

0.8

0.85

0.9

0.95

2 3 4 5 6 7

STRE

SS L

EVEL

, S

LOG10(N)

Control (100%PC)

CL (70%PC+30%LP)

CF (70%PC+30%FA)

CLM (70%PC+20%LP+10%MK)

CFM (70%PC+20%FA+10%MK)

CLS (70%PC+20%LP+10%SF)

CFS (70%PC+20%FA+10%SF)

4

5

6

7

8

9

10

2 2.5 3 3.5 4 4.5 5 5.5 6 6.5

APP

LIED

FLE

XU

RAL

STRE

SS, M

Pa

LOG10(N)

CL (70%PC+30%LP)CF (70%PC+30%FA)CLM (70%PC+20%LP+10%MK)CLS (70%PC+20%LP+10%SF)Control (100%PC)CFM (70%PC+20%FA+10%MK)CFS (70%PC+20%FA+10%SF)

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ACKNOWLEDGEMENTS The financial assistance in the form of fellowship to the first author from the Ministry of Human Resource Development (MHRD), Government of India is gratefully acknowledged. The authors also acknowledge the support of the staff of Structures Testing Laboratory at Dr B R Ambedkar National Institute of Technology, Jalandhar, India during the experimentation work reported in the paper.

CONCLUDING REMARKS

1. The probabilistic distributions for the fatigue life of concrete containing binary and ternary blends of cement additives and control concrete have been established. With the higher values of correlation coefficients at all stress levels, the successful modeling of fatigue life data by the two-parameter Weibull distribution has been confirmed. The distribution parameters i.e. ‘shape parameter’ and ‘characteristic life’ used to define the fatigue life distributions have been estimated by the different methods of analysis.

2. There has been reduction in variability in the distribution of fatigue life of concretes containing cement additives as compared to control concrete. This can be interpreted from the fact that higher values of the shape parameters indicate lower variability in the distribution of fatigue life. The maximum increase in the values of the shape parameters for CL, CLM and CLS mixes with respect to the control concrete was found to be 18.12%, 33.70% and 38.82% respectively whereas, maximum decrease of about 18.36%, 28.55% and 30.79% in the coefficient of variation for the fatigue life data of CL, CLM and CLS mix was observed as compared to the control concrete. Clearly, the CLS mix has performed better against other LP based mixtures in terms of reduction in variability in the distribution of fatigue life.

3. Similarly, for FA based concretes, the maximum increase in the values of the shape parameter for CF, CFM and CFS mixes with respect to the control concrete was found to be 26.60%, 36.38%, 50.00% respectively. A maximum decrease of about 25.02%, 30.51% and 35.75% in the coefficient of variation in the fatigue life data of CF, CFM and CFS mixes was observed as compared to the control concrete. Based upon the reduced variability in the fatigue life distributions of FA based concrete, the CFS mix performed the best among other FA based mixes.

4. The fatigue test data has been presented in the form of S-N diagrams to examine the fatigue performance of control concrete and concrete containing cement additives in terms of the two-million cycles fatigue strengths/endurance limits. The two-million cycle fatigue strengths/endurance limits for all concretes were estimated in terms of the maximum applied fatigue stress expressed as a percentage of the static flexural strength (i.e. level S) as well as in terms of actually applied maximum fatigue stress (fmax). The two-million cycles fatigue strengths/endurance limits for LP based concretes i.e. CL, CLM and CLS mix are estimated as 71%, 73% and 74% of the static flexural strength respectively. The same for control concrete was found to be 73% of its static flexural strength. Whereas, in terms of actually applied fatigue stress, the two-million cycles fatigue strength/endurance limit for CL, CLM and CLS concretes are found to be 4.8 MPa, 7.0 MPa and 7.2 MPa as compared to 6.0 MPa for control concrete signifying a comparable fatigue performance for LP based concretes except the CL mix.

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5. The estimated two-million cycles fatigue strengths/endurance limits are found to be 73%, 75% and 76% of the corresponding static flexural strength for CF, CFM and CFS mixes respectively, compared to 73% for control concrete. Whereas, in terms of actually applied fatigue stress, the two-million cycles fatigue strengths/endurance limits for CF, CFM and CFS concretes are found to be 6.0 MPa, 6.6 MPa and 7.2 MPa as compared to 6.0 MPa for control concrete. These results signify a comparable and slightly enhanced fatigue performance for FA based concretes as compared to control concrete.

6. Based upon the results of present investigation, in general, it can be observed that the concrete containing cement additives demonstrate better fatigue performance in terms of reduction in the variability of their fatigue lives and improved or comparable two-million cycles fatigue strengths/endurance limits. Through this investigation, the benefits of using cement additives as partial replacement to PC in fibre reinforced concretes in civil engineering applications wherein fatigue loading is predominant, is established. Replacing 30% cement content with equal amount of cement additives in concrete and yet achieving comparable or higher flexural fatigue performance favours the use of concretes containing cement additives over the control concrete while contributing towards the sustainable construction and economical challenges at different levels.

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