FATIGUE BEHAVIOR OF HIGH VOLUME FLY ASH CONCRETE UNDER CONSTANT AMPLITUDE AND COMPOUND LOADING by iaemedu

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									  INTERNATIONAL Engineering and Technology ENGINEERING AND
International Journal of Civil JOURNAL OF CIVIL(IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME
                             TECHNOLOGY (IJCIET)
ISSN 0976 – 6308 (Print)
ISSN 0976 – 6316(Online)
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        FATIGUE BEHAVIOR OF HIGH VOLUME FLY ASH
       CONCRETE UNDER CONSTANT AMPLITUDE AND
                 COMPOUND LOADING
                        Aravindkumar.B.Harwalkar1 and Dr.S.S.Awanti2
              1
               Associate Professor, Department of Civil Engineering, P.D.A.College of
                        Engineering, Gulbarga, Karnataka State, India.
                                 e-mail: harwalkar_ab@yahoo.co.in
              2
                Professor and Head, Department of Civil Engineering, P.D.A.College of
                        Engineering, Gulbarga, Karnataka State, India.
                                    e-mail: ssawanti@yahoo.co.in

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. This
paper 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
75mm×100mm×500mm 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 Miner’s hypothesis for high
volume fly ash concrete was verified. It was found that Miner’s hypothesis gives both unsafe
and over safe predictions of failure. Miner’s sum was found to be dependent on type of
compound loading and sequence of loading.



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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME

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 Miner’s hypothesis. Miner’s hypothesis assumes that
damage accumulates linearly with the number of cycles applied at a particular stress level. As
per Miner’s 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 Miner’s
rule. But the studies carried out by Holmen (9) found variable amplitude loading to be more
damaging than that predicted by Miner’s 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% using
third 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 test
results of HVFAC were compared with that of reference concrete (PCC). To investigate the fatigue
behavior a series of prism specimens of size 75mm×100mm×500mm 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 of
100 PCC prism specimens were tested under constant amplitude fatigue loading. For HVFAC, 95
prism 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 Miner’s 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 strength
requirements [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 range
water 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 optimum
replacement 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 in
water 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). Mixture
proportions of the two types of concrete are shown in table 1.

                            Table 1 Mixture Proportions of Concrete
                             Mixture                     PCC        HVFAC
                          Components
            Cement (OPC 53 grade) in kg/m3               440         176
            Class F fly ash in kg/m3                      0          264
            Water in kg/m3                               132         132
            Superplasticizer in liter/m3                 15.4         3.5
                                              3
            Saturated surface dry sand in kg/m          937.6       858.2
            Saturated surface dry coarse aggregate      1059         1059
            in kg/m3




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3.3 Test Procedure and Test Results
3.3.1 Static Testing
        Cube specimens of size 150mm×150mm×150mm were used for determining compressive
strength. For static flexural strength, specimens of similar size to that of fatigue specimens have been
used. 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/       28 day compressive strength 28 day static flexural strength
       Type of concrete            in MPa                       in MPa

       Conventional concrete               62.3*                              6.9*
       HVFAC60                             40.8*                              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 at
pavement 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 were
tested 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. Minimum
stress 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 of
application 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 are
tabulated 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 Levels
 Test        S=0.85    S=0.81    S=0.76    S=0.71    S=0.65   S=0.61     S=0.57     S=0.53
 specimen
 no.
      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        S=0.80 S=0.75 S=0.70 S=0.65 S=0.60 S=0.54                  S=0.50
       specimen
       no.
       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 stage
fatigue loading three stress levels have been applied to the test specimen. Fixed numbers of load
cycles 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 at
fourth 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 were
used 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 the
probability 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 µ and σ 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 different
stress levels are shown in table 5. It can be seen that the parameters of lognormal distribution are
dependent 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
                                                        µ                       σ
                      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                0.6321
                                     0.57             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 hypothesized
distribution 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
Nj         j   FO(Nj)   FN(Nj)         D2            for   Maximum        D2 for 5%         Inference
               = j/m    from           lognormal           D2      from   significanc
                        lognormal      distribution=       lognormal      e level and
                        distribution   |    FO     (Nj)-   distribution   m=10
                                       FN(Nj)|
  22      1      0.1      0.0113            0.0887
  43     2       0.2      0.1443            0.0557
  69      3      0.3      0.4201            0.1201                                       Lognormal
  78      4      0.4      0.5085            0.1085                                        model for
  82      5      0.5      0.5447            0.0447           0.1449          0.41        fatigue life
  94      6      0.6      0.6408            0.0408                                      distribution is
 102     7       0.7      0.6946            0.0054                                         accepted
 110     8       0.8      0.7409            0.0591
 122     9       0.9      0.7980            0.1020
 138     10       1       0.8551            0.1449

     Table 7 Kolmogorov-Smirnov Test for Lognormal Distribution at Different Stress Levels
             Type of     Stress level     Maximum D2      D2 for 5%      Inference
            concrete                     from lognormal significance
                                           distribution     level
              PCC            0.81            0.1583         0.41
                             0.76            0.0781         0.41       Lognormal
                             0.71            0.1230         0.41       models for
                             0.65            0.0739         0.34       fatigue life
                             0.61            0.1628         0.34       distributions
                             0.57            0.1609         0.34       are accepted
            HVFAC            0.80            0.1445         0.41       in all the
                             0.75            0.0901         0.41       cases
                             0.70            0.0868         0.34
                             0.65            0.0757         0.34
                             0.60            0.1208         0.34
                             0.54            0.1462         0.34


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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 R2 values 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
                                            1

                                                                                              y = -0.0358Ln(x) + 0.9948
                                      0.9
                                                                                              R2 = 0.9332 -- Eqn for PCC
                                                                                              y = -0.0338Ln(x) + 0.9389
                                      0.8
                                                                                              R2 = 0.8759 -- Eqn for HVFAC
                   Stress Level (S)




                                      0.7                                                                                            S-N Curve
                                                                                                                                     for PCC
                                      0.6
                                                                                                                                     S-N Curve
                                      0.5                                                                                            for HVFAC


                                      0.4                                                                                            Log. (S-N
                                                                                                                                     Curve for
                                                                                                                                     PCC)
                                      0.3
                                                0     20000           40000     60000          80000       100000          120000    Log. (S-N
                                                                                                                                     Curve for
                                                               Fatigue Life in No. of Cycles of Loading
                                                                                                                                     HVFAC)


                                                    Figure 3. S-N Curves for PCC and HVFAC

                                                                                                                                    S-N Curve
                                                              S-N Curve and 95% Confidence Limits for PCC

                                            1
                                                                                                                                    Upper 95%
                                       0.9                                                  y = -0.0358x + 0.9948                   confidence
                                                                                            2                                       limit
                                                                                           R = 0.9332 -- S-N curve
                                       0.8                                                                                          Lower 95%
                                                                                                                                    confidence
                         Stress Level (S)




                                                                                                                                    limit
                                       0.7
                                                                                                                                    Linear (S-N
                                                         y = -0.0358x + 1.0439                                                      Curve)
                                       0.6
                                                       -- Upper 95% confidence limit eqn
                                       0.5                                                                                          Linear
                                                          y = -0.0358x + 0.9457                                                     (Upper 95%
                                                          -- Lower 95% confidence limit eqn                                         confidence
                                       0.4                                                                                          limit)
                                                                                                                                    Linear
                                                                                                                                    (Lower 95%
                                       0.3
                                                                                                                                    confidence
                                                0     2           4           6 Ln(N) 8            10         12           14       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

                                       1
                                                                                                                                S-N Curve
                                                                                             y = -0.0338x + 0.9389
                                      0.9                                                    R2 = 0.8759 -- S-N curve

                                                                                                                                Upper 95%
                                                                                                                                confidence
                                      0.8
                                                                                                                                limit


                   Stress Level (S)
                                                                                                                                Lower 95%
                                      0.7
                                                                                                                                confidence
                                                                                                                                limit
                                      0.6                                                                                       Linear (S-N
                                                                                                                                Curve)
                                                y = -0.0338x + 0.9977
                                      0.5        -- Upper 95% confidence limit eqn
                                                                                                                                Linear (Upper
                                                y = -0.0338x + 0.8801                                                           95%
                                      0.4                                                                                       confidence
                                                 -- Lower 95% confidence limit eqn
                                                                                                                                limit)
                                                                                                                                Linear (Lower
                                      0.3                                                                                       95%
                                        0.000    2.000      4.000      6.000        8.000     10.000     12.000     14.000      confidence
                                                                               Ln(N)                                            limit)

                   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., Miner’s sum varied between 0.824 and 2.103. Miner’s 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
                                      No. of load cycles applied at                   Fatigue Life at                   Cumulative damage
        Specimen                               Stress level                            Stress Level                          factor
           no.                         S=0.55            S=0.6                       S=0.55    S=0.6

                                         (n1)                  (n2)                   N1           N2               M=(n1/N1)+(n2/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
                     No. of load cycles    Fatigue Life at Cumulative damage
           Specimen applied at Stress       Stress Level         factor
              no.    level
                     S=0.65      S=0.6    S=0.65     S=0.6 M=(n1/N1)+(n2/N2)
                       (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
                                         Fatigue Life at Stress    Cumulative
 Specimen No. of load cycles applied     Level                     damage factor
 no.      at Stress level                                          M=(n1/N1)+(n2/N2)
          S=0.55 S=0.6        S=0.65     S=0.55   S=0.6     S=0.65    +(n3/N3)
          (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
Specimen No. of load cycles applied at Fatigue Life at Stress Level      Cumulative
no.        Stress level                                                  damage factor
           S=0.55 S=0.6 S=0.65 S=0.7 S=0.55 S=0.6 S=0.65 S=0.7 M=(n1/N1)+
                                                                         (n2/N2)+(n3/N3)
           (n1)      (n2) (n3)    (n4)    (N1)   (N2)     (N3)      (N4) +(n4/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 to
       be satisfactory for both PCC and HVFAC at all stress levels.
   • Parameters of lognormal model were found to be dependent on type of concrete and
       the stress level.
   • There is an upper limit for stress level in fatigue loading which is dependent on type
       of concrete, beyond which fatigue life value was insignificant.
   • S-N relations obtained from regression analysis were found to be dependent on type
       of 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
   • Miner’s sum varied between 0.824 and 2.103. Hence Miner’s hypothesis gives both
       unsafe and over safe predictions for failure of HVFAC under compound fatigue
       loading.
   • Miner’s sum shows dependency on type of compound fatigue loading and also on
       sequence of loading.




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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
(Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME

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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