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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 6308
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FATIGUE BEHAVIOR OF HIGH VOLUME FLY ASH
CONCRETE UNDER CONSTANT AMPLITUDE AND
COMPOUND LOADING
Aravindkumar.B.Harwalkar1
andDr.S.S.Awanti
2
1
Associate Professor, Department of Civil Engineering, P.D.A.College ofEngineering, Gulbarga, Karnataka State, India.
e-mail: [email protected] and Head, Department of Civil Engineering, P.D.A.College of
Engineering, Gulbarga, Karnataka State, India.
e-mail: [email protected]
ABSTRACT
Road projects in future have to be environmental friendly and cost effective apart
from being safe so that society at large is benefited by the huge investments made in the
infrastructure projects. To achieve this, component materials of the pavement system have to
be optimized with reference to cost effectiveness, sustainability and fatigue behavior. Thispaper presents a study on fatigue behavior of high volume fly ash concrete (HVFAC) and
conventional concrete (PCC) under constant amplitude fatigue loading. Also behavior of
HVFAC was studied under compound fatigue loading. In the present investigation HVFAC
mix with cement replacement level of 60% with low calcium fly ash has been used.
A total number of 95 prism specimens of HVFAC were tested under constant
amplitude fatigue loading. Also 100 prism specimens of PCC were tested under constant
amplitude fatigue loading for comparative studies. All prism specimens were of size
75mm100mm500mm and were tested under flexural fatigue loading using haiver sine
wave loading. Frequency of fatigue loading was kept at 4Hz. Lognormal model was verified
for probability distribution of fatigue life. Studies indicated that lognormal model was
acceptable for fatigue life distributions at all stress levels for both HVFAC and PCC. The
parameters of distribution exhibited dependency on stress levels and type of concrete.
Relations between stress level and fatigue life were developed for both HVFAC and PCC.
These relations were found to be dependent on type of concrete.
A total number of 24 prism specimens were tested under compound fatigue loading.
Based on the results of compound fatigue loading the validity of Miners hypothesis for high
volume fly ash concrete was verified. It was found that Miners hypothesis gives both unsafe
and over safe predictions of failure. Miners sum was found to be dependent on type of
compound loading and sequence of loading.
INTERNATIONAL JOURNAL OF CIVIL ENGINEERING AND
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ISSN 0976 6308 (Print)
ISSN 0976 6316(Online)
Volume 3, Issue 2, July- December (2012), pp. 404-415
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Keywords: Compound fatigue loading; High volume fly ash concrete; Probability
distribution; lognormal.
1. INTRODUCTION
Fatigue strength is an important property which has to be taken into account in the
design of various concrete structures requiring long fatigue life. Especially the understanding
of the behavior of a concrete road under fatigue loading is vital for the design and the
performance prediction. Also there is a need for optimization of materials in the rigid
pavement system with regard to long term fatigue resistance at lowest cost and ecologically
sound choices.
Many researchers have carried out studies on developing fatigue models for plain
concrete. Majority of the researchers [1-3] have developed the fatigue model relating the
stress level (S) which is defined as the ratio of maximum stress applied in cyclic loading to
static flexural strength, to number load cycles to failure (N), termed as fatigue life. This
relation is commonly called as Wholer equation. The second form of fatigue model given by
Vesic et al [4] and Treybig et al [5] is a power equation relating S and N. Jakobsen et al [6]
included the effect of ratio of minimum stress to maximum stress in cyclic loading, which is
known as stress range (R), in the S-N relation for fatigue. Hsu [7] developed a more general
expression for fatigue strength involving four variables i.e., S, N, R and period of cyclic
loading (T). But the most commonly used fatigue model for design of concrete pavements is
the one given by Wholer equation.
In literature [8-9] variable amplitude fatigue studies have been carried out on plain
concrete to verify the validity of Miners hypothesis. Miners hypothesis assumes that
damage accumulates linearly with the number of cycles applied at a particular stress level. As
per Miners hypothesis the failure criterion is written as:
-----------
----- (1)
Where ni = number of cycles applied at stress level i
Ni = number of cycles to failure at stress level i
k = number of stress levels used
Studies carried out by Siemes (8) on plain concrete proved the validity of Miners
rule. But the studies carried out by Holmen (9) found variable amplitude loading to be more
damaging than that predicted by Miners hypothesis.
As per the definition given by Mehta [10], a concrete having minimum cement
replacement level of 50% by fly ash is termed as high volume fly ash concrete (HVFAC).
Limited studies [11-13] are available on fatigue behavior of HVFAC. Ramkrishnan et al [13]
have developed an S-N relation for HVFAC with cement replacement level of 58% usingthird point flexural fatigue loading at a frequency of 20Hz.
In the development of S-N model it has been assumed that the non dimensional term
S eliminates the influence of static ultimate strength of concrete and hence eliminates the
effect of water-cement ratio, type and gradation of aggregate, type and amount of cement, age
of concrete. But there are concerns over influence of static strength of concrete on S-N
relation due to variation in fracture toughness. There is also very limited literature available
on fatigue behavior of HVFAC under compound and variable amplitude fatigue loading.
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2. RESEARCH SIGNIFICANCE AND SCOPE
In the present investigation an attempt has been made to study the fatigue behavior of
HVFAC under constant amplitude and compound fatigue loading. Multistage constant amplitude
loading has been used as compound fatigue loading in the present investigation. The fatigue testresults of HVFAC were compared with that of reference concrete (PCC). To investigate the fatiguebehavior a series of prism specimens of size 75mm100mm500mm were tested under flexural
fatigue loading.In the present investigation HVFAC mix satisfying the criteria of pavement quality concrete
was developed using a cement replacement level of 60% with low calcium fly ash. A total number of100 PCC prism specimens were tested under constant amplitude fatigue loading. For HVFAC, 95prism specimens were tested under constant amplitude fatigue loading. Probability distributions were
developed for experimental results of fatigue lives. S-N relations were established from regression
analysis of fatigue data. A total number of 24 specimens of HVFAC have been tested under
compound fatigue loading to verify the validity of Miners hypothesis.
3. LABORATORY TESTS
3.1 Materials
The ordinary Portland cement from single batch has been used in the present investigation.The coarse fraction consisted of equal fractions of crushed stones of maximum size 20mm and 12mm.
Low calcium fly ash satisfying the criteria of fineness, lime reactivity and compressive strengthrequirements [14] has been used in the investigation. Fine aggregate used was natural sand with
maximum particle size of 4.75mm. Polycarboxylic based superplasticizer has been used as high rangewater reducing admixture (HWRA) to get the desired workability. The optimum dosage of
superplasticizer for each type of concrete was fixed by carrying out compaction factor test.
3.2 Mixture Proportions
A minimum grade of M30 which results in a minimum static flexural strength of 3.8N/mm2
has been specified for pavement quality concrete by Indian Roads Congress [15]. Trial mixes were
developed to achieve M35 grade HVFAC at cement replacement of 60%, which was the optimumreplacement percentage with water to cementitious ratio of 0.3. Water to cementitious ratio utilized in
the investigation i.e., 0.3 was the lowest value that could be used from the limitation of reduction inwater content that can be achieved using HWRA and usage of conventional means of mixing and
compaction. Corresponding conventional concrete was used as reference concrete (PCC). Mixtureproportions of the two types of concrete are shown in table 1.
Table 1 Mixture Proportions of Concrete
Mixture
Components
PCC HVFAC
Cement (OPC 53 grade) in kg/m3
Class F fly ash in kg/m3
Water in kg/m3Superplasticizer in liter/m
3
Saturated surface dry sand in kg/m3
Saturated surface dry coarse aggregate
in kg/m3
440
0
13215.4
937.6
1059
176
264
1323.5
858.2
1059
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3.3 Test Procedure and Test Results
3.3.1 Static Testing
Cube specimens of size 150mm150mm150mm were used for determining compressive
strength. For static flexural strength, specimens of similar size to that of fatigue specimens have beenused. An effective span of 400mm has been used for both static flexural strength and fatigue strength
determination. All the strength properties were determined after a curing period of 28days. Static
compressive strength and flexural strength values are shown in table 2.
Table 2 Mechanical Properties of Concrete
Property of concrete/
Type of concrete
28 day compressive strength
in MPa
28 day static flexural strength
in MPa
Conventional concrete
HVFAC60
62.3*
40.8*
6.9*
5.3*
* Mean value of six specimens
3.3.2 Fatigue Testing
3.3.2.1 Constant Amplitude Fatigue Testing: Fatigue test specimens were tested under one-third
point loading using frequency of loading as 4Hz. Since the present investigation was aimed atpavement application haiver sine wave form of cyclic loading was used. Typical fatigue test set up
and loading pattern used are shown in figures 1 and 2 respectively. All the fatigue specimens weretested after 90 days from casting so as to give allowance for sufficient strength gain. Specimens were
cured for 28 days by ponding method and then covered with polythene bags up to 90 days. Minimumstress in fatigue loading was maintained at 1% of maximum stress. Minimum stress was used mainly
to prevent any possible movement of specimens at support during testing and to simulate residual
stresses in the pavement to a certain degree. Beyond the upper limits of stress levels used for different
types of concrete in the present investigation, the fatigue life values were insignificant to be recorded
i.e., they were typically less than 10. For HVFAC at all cement replacement levels the lower limit of
stress level used was based on the criteria, when none of the test specimens failed even after ofapplication of one lakh cycles of fatigue loading. PCC was tested for eight stress levels and HVFAC
was tested at seven stress levels. Constant amplitude Fatigue test results for PCC and HVFAC aretabulated in table 3 and 4 respectively. Fatigue life values have been arranged in the increasing order
so as to facilitate probability analysis.
Figure 1 Flexural fatigue test setup Figure 2. Typical constsant amplitude fatigue loading
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Table 3 Fatigue Life of PCC at Different Stress LevelsTestspecimenno.
S=0.85 S=0.81 S=0.76 S=0.71 S=0.65 S=0.61 S=0.57 S=0.53
1 22 84 158 1327 5289 16488 46582 100000*2 43 97 284 1489 7213 20312 48270 100000*3 69 105 312 2596 8863 22268 52164 100000*4 78 152 382 3642 10322 34511 54416 100000*5 82 184 411 4149 12723 39920 56005 100000*6 94 198 474 5218 16523 46718 66012 100000*7 102 288 578 6629 18708 51512 73676 100000*
8 110 432 694 8383 20391 61512 80520 100000*9 122 682 916 9558 21262 77812 81891 100000*
10 138 730 1182 12009 23992 81800 100000* 100000*11 ---- ---- ---- ---- 24771 92477 100000* 100000*
12 ---- ---- ---- ---- 27344 100000* 100000* 100000*
13 ---- ---- ---- ---- 32811 100000* 100000* 100000*14 ---- ---- ---- ---- 40887 100000* 100000* 100000*15 ---- ---- ---- ---- 44816 100000* 100000* 100000*
*specimen did not fail after the application of given number of cycles of loading
-- data not available
Table 4 Fatigue Life of HVFAC at Different Stress Levels
Test
specimen
no.
S=0.80 S=0.75 S=0.70 S=0.65 S=0.60 S=0.54 S=0.50
1 44 78 312 4159 5324 18785 100000*
2 48 102 422 5802 6852 19084 100000*3 52 146 584 6802 7102 21039 100000*
4 65 182 886 7759 8404 22259 100000*
5 72 212 1092 8759 12723 29384 100000*
6 88 292 1109 9259 14785 32911 100000*
7 92 344 1243 10014 15680 45512 100000*
8 99 459 1422 12008 22348 62214 100000*
9 112 582 1586 14620 28109 68743 100000*
10 120 889 1704 14882 36891 76544 100000*
11 ---- ---- 1959 16822 45841 82477 100000*
12 ---- ---- 2390 16822 49869 86792 100000*
13 ---- ---- 3532 18826 52113 100000* 100000*14 ---- ---- 4426 23426 59641 100000* 100000*
15 ---- ---- 3962 28110 65869 100000* 100000*
* specimen did not fail after the application of given number of cycles of loading
-- data not available
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3.3.2.2. Compound Fatigue Testing: Compound fatigue testing was carried out on HVFAC
specimens only. Two stage, three stage and four stage constant amplitude fatigue loadings have been
used as compound fatigue loading. In two stage loading test specimen was subjected to a fixed
number of load cycles at a particular stress level in the first stage and after the first stage amplitude
was changed corresponding to second stress level and maintained constant up to failure. In three stagefatigue loading three stress levels have been applied to the test specimen. Fixed numbers of loadcycles were applied for two stress levels and testing was continued up to failure at the third stress
level. In four stage loading fixed numbers of load cycles were applied for three stress levels and atfourth stress level specimen was tested up to failure. Minimum stress was maintained at 1% of the
corresponding maximum stress for all the specimens. Test results of compound fatigue loading wereused to check the validity of Miners hypothesis for HVFAC.
4. PROBABILITY ANALYSIS OF CONSTANT APLITUDE FATIGUE TEST RESULTS
Since the fatigue lives for both types of concrete showed larger scatter, an attempt to
determine the probabilistic distributions was made. Few researchers [16-17] have developed Weibull
distribution models for fatigue lives at different stress levels in case of conventional concrete. In the
present study lognormal distribution models were developed and verified for different stress levels.Conservatively for few specimens which did not fail after the application of one lakh cycles of
loading at some of the stress levels fatigue life value has been taken as one lakh cycles in theprobability analysis.
4.1 Determination of Lognormal Distribution Model
The probability density function of lognormal distribution model is given by equation (2).The parameters of lognormal distributions are and which are mean and standard deviation of
observed ln (N) values. In the equation (2), X represents ln(N) values.
(2)
The values lognormal distribution parameters for all the types of concretes and at differentstress levels are shown in table 5. It can be seen that the parameters of lognormal distribution aredependent on type of concrete and the stress level.
Table 5 Lognormal Distribution Parameters for Fatigue Lives at Different Stress Levels
Type of concrete Stress level Parameters of log normal distribution
PCC 0.85 4.3450 0.5501
0.81 5.4036 0.7867
0.76 6.1377 0.5925
0.71 8.3841 0.7565
0.65 9.7882 0.6293
0.61 10.8915 0.63210.57 11.2150 0.3007
HVFAC 0.80 4.3158 0.3599
0.75 5.5329 0.7742
0.70 7.2237 0.7795
0.65 9.3603 0.5369
0.60 9.9538 0.8700
0.54 10.7820 0.6580
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4.2 Model Verification
Probabilistic models developed in the present investigation were tested using
Kolmogorov-Smirnov test. For conducting this test, the test statistic D2 was calculated using
equation (3) in which FO
(Nj) is the observed distribution of N and FN (Nj) is the hypothesizeddistribution of N and m is the total number of specimens.
.. (3)
The D2 values were compared with critical D2 for the given sample size and
significance level of 5%. If calculated value is less than critical D2, model is accepted. The
basic calculations for verification of lognormal model for PCC at stress level of 0.85 are
shown in table 6. The D2 values and verification of lognormal distributions for both types of
concretes at different stress levels are shown in table 7. It can be seen that lognormal model
was accepted for both types of concretes at all stress levels.
Table 6 Kolmogorov-Smirnov Test for Lognormal Distribution for PCC at Stress Level of 0.85
Table 7 Kolmogorov-Smirnov Test for Lognormal Distribution at Different Stress Levels
Type of
concrete
Stress level Maximum D2
from lognormaldistribution
D2 for 5%
significancelevel
Inference
PCC 0.81 0.1583 0.41
Lognormalmodels for
fatigue lifedistributions
are acceptedin all the
cases
0.76 0.0781 0.41
0.71 0.1230 0.41
0.65 0.0739 0.340.61 0.1628 0.34
0.57 0.1609 0.34
HVFAC 0.80 0.1445 0.41
0.75 0.0901 0.41
0.70 0.0868 0.34
0.65 0.0757 0.34
0.60 0.1208 0.34
0.54 0.1462 0.34
Nj j FO(Nj)
= j/m
FN(Nj)
from
lognormaldistribution
D2 for
lognormal
distribution=| F
O(Nj)-
FN(Nj)|
Maximum
D2 from
lognormaldistribution
D2 for 5%
significanc
e level andm=10
Inference
22 1 0.1 0.0113 0.0887
0.1449 0.41
Lognormal
model forfatigue life
distribution is
accepted
43 2 0.2 0.1443 0.0557
69 3 0.3 0.4201 0.1201
78 4 0.4 0.5085 0.1085
82 5 0.5 0.5447 0.0447
94 6 0.6 0.6408 0.0408102 7 0.7 0.6946 0.0054
110 8 0.8 0.7409 0.0591
122 9 0.9 0.7980 0.1020
138 10 1 0.8551 0.1449
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5. DETERMINATION OF S-N RELATION
S-N relations were developed by carrying out regression analysis on fatigue test data
of constant amplitude loading. The S-N curves determined for the two types of concretes are
shown in figure 3. S-N relations for PCC and HVFAC are shown in equations (4) and (5)respectively along with R
2values where R is the coefficient of correlation. It can be seen that
S-N relations are dependent on type of concrete i.e., on the strength of concrete. In the
present investigation existence of upper limits of stress levels for fatigue loading, dependent
on type of concrete, was observed. The 95% confidence limits using constant variance were
determined for both PCC and HVFAC. Upper and lower confidence limits along with S-N
curve for PCC and HVFAC are shown in figures 4 and 5 respectively. Lower confidence
limits are important in design of structures.
S = -0.0358Ln(N) + 0.9948 (R2=0.9332) --------------- (4)
S = -0.0338Ln(N) + 0.9389 (R2=0.8759) --------------- (5)
S-N Curve for PCC and HVFAC
y = -0.0358Ln(x) + 0.9948
R2 = 0.9332 -- Eqn for PCC
y = -0.0338Ln(x) + 0.9389
R2 = 0.8759 -- Eqn for HVFAC
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20000 40000 60000 80000 100000 120000
Fatigue Life in No. of Cycles of Loading
Stress
Level(S)
S-N Curve
for PCC
S-N Curve
for HVFAC
Log. (S-N
Curve for
PCC)
Log. (S-N
Curve for
HVFAC)
Figure 3. S-N Curves for PCC and HVFAC
S-N Curve and 95% Confidence Limits for PCC
y = -0.0358x + 0.9948
R2
= 0.9332 -- S-N curve
y = -0.0358x + 1.0439
-- Upper 95% confidence limit eqn
y = -0.0358x + 0.9457
-- Lower 95% confidence limit eqn
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 2 4 6 8 10 12 14Ln(N)
Stress
Leve
l(S)
S-N Curve
Upper 95%
confidence
limit
Lower 95%
confidence
limit
Linear (S-N
Curve)
Linear
(Upper 95%
confidence
limit)Linear
(Lower 95%
confidence
limit)
Figure 4. S-N Curve and 95% confidence limits for PCC
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S-N Curve and 95% Confidence Limits for HVFAC
y = -0.0338x + 0.9389
R2 = 0.8759 -- S-N curve
y = -0.0338x + 0.9977
-- Upper 95% confidence limit eqn
y = -0.0338x + 0.8801
-- Lower 95% confidence limit eqn
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.000 2.000 4.000 6.000 8.000 10.000 12.000 14.000
Ln(N)
StressLevel(S)
S-N Curve
Upper 95%confidence
limit
Lower 95%confidencelimit
Linear (S-N
Curve)
Linear (Upper
95%confidencelimit)Linear (Lower
95%confidencelimit)
Figure 5. S-N Curve and 95% confidence limits for HVFAC
6. ANALYSIS OF TEST RESULTS OF COMPOUND FATIGUE LOADING
Test results of compound fatigue testing along with calculation of cumulative damage
factor for HVFAC are shown in tables 8 to 11. Stress levels shown in the tables 8 to 11 are
given in the order in which they have been applied to the specimens during testing. Fatigue
lives at different stress levels in tables 8 to 11 have been calculated from equation (5).
Cumulative damage factor i.e., Miners sum varied between 0.824 and 2.103. Miners sum
showed dependency on type of compound fatigue loading and also on the sequence of
loading.
Table 8. Cumulative Damage Factors for HVFAC for Two Stage Compound Fatigue Loading
Specimen
no.
No. of load cycles applied at
Stress level
Fatigue Life at
Stress Level
Cumulative damage
factor
M=(n1/N1)+(n2/N2)
S=0.55 S=0.6 S=0.55 S=0.6
(n1) (n2) N1 N2
1 20000 20672 99302 22621 1.115
2 20000 21453 99302 22621 1.150
3 20000 24550 99302 22621 1.287
4 40000 27683 99302 22621 1.627
5 40000 25894 99302 22621 1.548
6 40000 19527 99302 22621 1.266
Table 9. Cumulative Damage Factors for HVFAC for Two Stage Compound Fatigue Loading
Specimen
no.
No. of load cycles
applied at Stress
level
Fatigue Life at
Stress LevelCumulative damage
factor
M=(n1/N1)+(n2/N2)S=0.65 S=0.6 S=0.65 S=0.6
(n1) (n2) (N1) (N2)
1 2000 9861 5153 22621 0.824
2 2000 15683 5153 22621 1.081
3 2000 13187 5153 22621 0.971
4 1000 17122 5153 22621 0.951
5 1000 15566 5153 22621 0.882
6 1000 19891 5153 22621 1.073
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Table 10. Cumulative Damage Factors for HVFAC for Three Stage Compound Fatigue Loading
Specimen
no.
No. of load cycles applied
at Stress level
Fatigue Life at Stress
LevelCumulative
damage factor
M=(n1/N1)+(n2/N2)
+(n3/N3)S=0.55 S=0.6 S=0.65 S=0.55 S=0.6 S=0.65(n1) (n2) (n3) (N1) (N2) (N3)
1 40000 6000 2838 99302 22621 5153 1.219
2 40000 6000 3836 99302 22621 5153 1.412
3 40000 6000 4126 99302 22621 5153 1.469
4 20000 10000 3645 99302 22621 5153 1.351
5 20000 10000 3358 99302 22621 5153 1.295
6 20000 10000 5372 99302 22621 5153 1.686
Table 11. Cumulative Damage Factors for HVFAC for Four Stage Compound Fatigue Loading
Specimenno.
No. of load cycles applied atStress level
Fatigue Life at Stress Level Cumulativedamage factor
M=(n1/N1)+
(n2/N2)+(n3/N3)
+(n4/N4)
S=0.55 S=0.6 S=0.65 S=0.7 S=0.55 S=0.6 S=0.65 S=0.7
(n1) (n2) (n3) (n4) (N1) (N2) (N3) (N4)
1 40000 5000 1000 911 99302 22621 5153 1174 1.594
2 40000 5000 1000 811 99302 22621 5153 1174 1.509
3 40000 5000 1000 1025 99302 22621 5153 1174 1.691
4 20000 10000 2000 1258 99302 22621 5153 1174 2.103
5 20000 10000 2000 852 99302 22621 5153 1174 1.757
6 20000 10000 2000 1042 99302 22621 5153 1174 1.919
7. CONCLUSIONS
Based on experimental investigations following conclusions were made.
For probability distribution of fatigue life lognormal distribution model was found tobe satisfactory for both PCC and HVFAC at all stress levels.
Parameters of lognormal model were found to be dependent on type of concrete andthe stress level.
There is an upper limit for stress level in fatigue loading which is dependent on typeof concrete, beyond which fatigue life value was insignificant.
S-N relations obtained from regression analysis were found to be dependent on typeof concrete i.e., mainly on the static strength of concrete. Following are the S-N
relations for PCC and HVFAC
S = -0.0358Ln(N) + 0.9948 -------- for PCC
S = -0.0338Ln(N) + 0.9389 -------- for HVFAC
Miners sum varied between 0.824 and 2.103. Hence Miners hypothesis gives bothunsafe and over safe predictions for failure of HVFAC under compound fatigue
loading.
Miners sum shows dependency on type of compound fatigue loading and also onsequence of loading.
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8. ACKNOWLEDEGEMENT
The financial support under Research Promotion Scheme from All India Council for
Technical Education, New Delhi, India, is gratefully acknowledged.
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Flexural Stresses.ACI Journal Proceedings, Vol. 63, No. 10, 1966, pp. 1059-1076.
2. Ballinger, C.A. Cumulative Fatigue Damage Characteristics of Plain Concrete.
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Sub-Jected To Alternate Wetting And Drying International Journal of Civil Engineering &
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19. A.S Jeyabharathy, Dr.S.Robert Ravi and Dr.G.Prince Arulraj Finite Element
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20. M.N.Bajad, C.D.Modhera and A.K.Desai, Influence Of A Fine Glass Powder OnStrength Of Concrete Subjected To Chloride Attack International Journal of Civil
Engineering & Technology (IJCIET), Volume 2, Issue 2, 2011, pp. 01-12, Published by
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Reinforced Concrete Columns By The Transfer-Matrix Method International Journal of
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by IAEME.
22. P.A. Ganeshwaran, Suji and S. Deepashri, Evaluation Of Mechanical Properties
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of Civil Engineering & Technology (IJCIET), Volume 3, Issue 2, 2012, pp. 60 - 69,
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Containing Silicafume And Fly Ash Reinforced With Chicken Mesh International Journal of
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by IAEME.