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A technical look at ‘Individual test result’ criterion for concrete acceptance as per IS 456:2000

N.P. Rajamane, M.C. Nataraja and T.P. Ganesan

The provisions of IS 456:2000 help practical engineers to decide the acceptance of concrete based on the test data of four samples, using the principles of statistics considering the compressive strength as a ‘random variable’ representable by ‘Normal Distribution Curve’. This technical note is prepared to understand the use of the Codal provisions to decide whether the given test data on samples is indicative of acceptable concrete using the criterion related to ‘Individual Test Result’. A quick mathematical analysis suggests that the probability of occurrence of strength lower than that corresponding to ‘Individual Test Result’ criterion is not uniform for same grade of concrete with different standard deviations. This is in contrast to the characteristic strength, fck , where the probability of occurrence of strength lower than that corresponding to fck is always 5% (or 1 in 20) and this value is independent of standard deviation.

Heterogeneity of cement concrete invariably causes recording of different strengths in samples collected from any given concrete.1,2 This means that a statistical test on strengths is required.3,4 This is done usually by assuming a ‘normal distribution’ (ND) and the parameters to describe this curve, namely, average strength (‘population’ mean) and standard deviation (SD) are obtained from a very large number of the

test results.5 The concrete strength is considered mathematically as a ‘random variable’ for the Normal Distribution Curve and plotted as abscissa (x-axis) on this curve.1 The task now, as taken up in this paper, is to determine whether the quality of concrete is acceptable based on the given set of four test results, using the acceptance criteria recommended in IS 456:2000.6 The statistical rationale behind the codal provisions on acceptability criteria are examined briefly here.

The present paper examines the ‘individual test result’ (ITR) of a sample against the requirement of corresponding grade of concrete. Accordingly five sets of test data (each set consisting of four test results of samples) were checked against a single concrete, M30 grade with standard deviation (SD) of 5 MPa.

The codal stipulations was interpreted to mean that if any one of the criteria given is not satisfied, then, the concrete representing the samples was deemed to be not acceptable. Notably for each grade of concrete, there is a possibility of more values of SD due to different levels of control in the production of concrete, yet, one value representing the characteristic strength is used for structural design purposes.

So the subject matter of this paper is statistical in nature than technical, since many items such as the actual

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process of mix design, concreting conditions, sampling procedure, testing conditions etc are not covered in the discussions. The main purpose of the paper is to present sets of test sample data and use them to describe and discuss the BIS Code provision on Individual Test Result (ITR) criterion. It was the experience of the authors that many engineers feel that the statistical nature of concrete and the provisions of IS 456 need to be discussed explicitly so that the interpretation of test data on site becomes more rational and scientific.

Problem statementThe average 28 day compressive strength obtained from tests on 3 numbers of 150 mm cube specimens is given under each test data set under the heading 'Typical test data sets'. One may note that to accept the one data point from tests on 3 numbers of 150 mm cube specimens, the clause 15.4 of IS 456:2000 should be satisfied. It states that:

“The test results of the sample shall be the average of the strength of three specimens. The individual variation should not be more than ±15 percent of the average. If more, the test results of the sample are invalid.”

It is assumed that each of the test result in the data given under paragraph 'Typical test data sets' given below is recorded after satisfying the above mentioned Clause 15.2 of IS 456:2000.

Typical test data sets The following test data sets were obtained from the field (Figure 1):

Test data set A (i) 35, (ii) 33, (iii) 33, (iv) 34 MPa

Test data set B (i) 35, (ii) 27, (iii) 40, (iv) 34 MPa

Test data set C (i) 35, (ii) 25, (iii) 41, (iv) 34 MPa

Test data set D (i) 38, (ii) 26, (iii) 27, (iv) 44 MPa

Test data set E (i) 38, (ii) 28, (iii) 29, (iv) 44 MPa

Table 1a. Failure rate for ‘Individual test result’ criterion before Amendment No. 3 to IS 456:2000

SD ITRf1 z AFL %AFL Failure Rate = 1/ AFL2 4 -3.65 0.00013 0.013 7627

2.5 4 -3.25 0.00058 0.058 17333 4 -2.98 0.00143 0.143 701

3.5 4 -2.79 0.00261 0.261 3834 4 -2.65 0.00402 0.402 248

4.5 4 -2.54 0.00556 0.556 1805 4 -2.45 0.00714 0.714 140

5.5 4 -2.38 0.00872 0.872 1156 4 -2.32 0.01026 1.026 97

6.5 4 -2.27 0.01174 1.174 857 4 -2.22 0.01316 1.316 76

7.5 4 -2.18 0.01451 1.451 698 4 -2.15 0.01578 1.578 63

Table 1b .Failure rate for ‘Individual test result’ criterion after Amendment No. 3 to IS 456:2000

SD ITRf2 z AFL %AFL Failure rate = 1/ AFL2 3 -3.15 0.00082 0.082 1225

2.5 3 -2.85 0.00219 0.219 4573 3 -2.65 0.00402 0.402 248

3.5 3 -2.51 0.00609 0.609 1644 3 -2.40 0.0082 0.820 122

4.5 3 -2.32 0.01026 1.026 975 3 -2.25 0.01222 1.222 82

5.5 3 -2.20 0.01407 1.407 716 3 -2.15 0.01578 1.578 63

6.5 3 -2.11 0.01736 1.736 587 3 -2.08 0.01883 1.883 53

7.5 3 -2.05 0.02018 2.018 508 3 -2.03 0.02143 2.143 47

ITRf1 = Factor in ‘ITR’ criterion of IS 456:2000 before Amendment No 3=4 MPa since ITR criterion for acceptability was fck-4 MPa for grade M20 and aboveITRf2 = Factor in ‘ITR’ criterion of IS 456:2000 after Amendment No 3=3 MPa since ITR criterion for acceptability was fck-3 MPa for Grade M15, Grade M20 and aboveSD = Standard Deviation, MPa; z = X-coordinate of ‘standard normal distribution’ curve = ( x – μ ) / σ = ( fc – fm ) / SD = ( ( fck –ITRf ) – fm ) / SD where fm = fck + 1.65 * SDAFL = Fraction of the area to the left of fc considering the total area under curve as 1%AFL = %age of the area to the left of fc considering the total area under curve as 100= Percentage of specimens with value less than fcFailure Rate = For each one of the specimens having strength less than fc, the possible number of specimens having strength more than fc Higher numerical value in last column under ‘Failure Rate = 1/ AFL’ in above table’ means stricter quality control , but lower possibility of actual occurrence on site or higher difficulty achieving this in practice. It may be noted here that it is not always possibility, beyond a limit, to suggest specific steps for improvement in quality control measures to get the change of ‘Failure Rate’ from lower value to higher value, in case of concrete production.

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Concrete properties for examining the test samples The above test samples are to be examined against the following concrete:

Grade of concrete = M30

Standard deviation of 28 day compressive strengths of concrete = 5 MPa.

Target mean compressive strengths of concrete at 28 day

= fm= fck + 1.65 * SD= 30 + 1.65 * 5 = 38.25

MPa= Population mean

strength of the concrete mix= µ

Now, the task is to decide whether the given data of four consecutive test results, in each of data sets given under 'Typical test data sets', is acceptable as representative of the above concrete, as per provisions in IS 456:2000, from consideration of ‘Individual Test Result’ (ITR).

acceptance criteria for ‘individual test’ result in IS 456:2000The number of cube specimens for getting any sample considered for computations for acceptability of concrete is 3 and this ‘Individual Test Result’ has to checked as per the Column 3 of Table 11 of IS 456 2000.6 The value of each test result of the test samples, was to be checked before Amendment No. 3 against the following criteria:

fcindividual ≥ fck – 3 for concrete of M15.

fcindividual ≥ fck – 4 for concrete of M20 and above grades.

It may be noted here that SD of concrete under consideration was not used here; only the numerical value of fck, representing the grade of concrete, is used for computing the numerical value of the criterion on ‘Individual Test Result’ (ITR).

However, there was, later on, an Amendment No. 3 to IS 456 dated August 2007, to modify the Table 11 on ITR acceptance from fck-4 to fck-3 for concrete of M20 and

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above grades. Thus, for concretes of M15, M20 and above grades, the value of each test result of the test samples should satisfy the following condition:

fcindividual ≥ fck – 3

acceptability of data for ‘ITr’ criterionIn the present case of M30 grade concrete,

fcindividual ≥ 30 – 3

fcindividual ≥ 27 MPa

It is worthwhile to recognise here that, for given fck , i.e., grade of concrete, there could be different values of Standard Deviation, SDpop , then for each pair of fck and SDpop , there is only one average compressive strength computable as per the Codal provision given in Column 2 of Table 11 of IS 456:2000. However, for checking against ‘Individual Test Result’ (ITR) criterion, SD of concrete is not required. If we recognise that SD represents the degree of quality control on the site, then by not considering SD, the ‘ITR’ criterion is applicable to the given concrete grade produced under any quality control.

Check for acceptabilityIt is clear from earlier paragraph that each of ‘Individual Test Result’ in any data set should be equal or more 'than 27 MPa. It is important to note here the numerical value used 27 is less the number 30 representing the grade of concrete.'

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Test data set A (i) 35, (ii) 33, (iii) 33, (iv) 34 MPa

Each of the above test results is more than 27 MPa and hence, this concrete is acceptable from ‘Individual Test Result’ criterion. However, the concrete test data has to be scrutinised against other criteria of the Code also for deciding about the concrete itself.

Test data set B (i) 35, (ii) 27, (iii) 40, (iv) 34 MPa

Three of the above test results are more than 27 MPa and one test result is equal to 27 MPa. Hence, this concrete is still acceptable from ‘Individual Test Result’ criterion. However, the concrete test data has to be scrutinised against other criteria of the Code also for deciding about the concrete itself.

Test data set C (i) 35, (ii) 25, (iii) 41, (iv) 34 MPa

Three of the above test results are more than 27 MPa, but, one test result is less than 27 MPa. Hence, this concrete is not acceptable from ‘Individual Test Result’ criterion. Hence, the concrete test data need not be scrutinised against other criteria of the code and we can now declare that the concrete as unacceptable as a whole.

Test data set D (i) 38, (ii) 26, (iii) 27, (iv) 44 MPa

Among the above four consecutive test results, two are more than 27 MPa, and, one test result is equal to 27 MPa. But, there is a test value of 26 MPa, which is 1 MPa less than 27 MPa. Hence, the concrete represented by the above four samples test values is not acceptable from ‘Individual Test Result’ criterion. Therefore, the concrete test data need not be scrutinised against other criteria of the Code and it is possible to decide about the unacceptability of the concrete itself, immediately after checking against the ITR criterion.

Test data Set E (i) 38, (ii) 28, (iii) 29, (iv) 44 MPa

All of the above test results are more than 27 MPa. Hence, this concrete is acceptable from ‘Individual Test Result’ criterion. However, the concrete test data has to be scrutinised against other criteria of the Code also for deciding about the concrete itself.

The above mentioned conclusions on non-acceptability of some of the concretes are valid even when we observe that some of the four test values are numerically more than the ‘characteristic strength’, fck, denoted by the number describing the Grade of concrete.

In the present case, the M30 Grade concrete has the ‘characteristic strength’, fck of 30 MPa and it is seen that each of the test results has to be more than or equal to 27 MPa.

It should be recognised here that after checking the individual value in any concrete sample (consisting of four test results), the sample average needs to be checked against the criterion given in Column 2 of Table 11 of IS 456:2000.6

Statistical basis of ‘ITr’ criterionIt is interesting to note that the ‘ITR’ criterion does not use SD characteristic of concrete, but, the other criterion of ‘average of four consecutive tests’ needs SD characteristic of concrete for acceptability. It would be now worthwhile to consider the statistical aspect of ‘ITR’. For this purpose, we should consider the ND curve which represents the strength variations of the concrete defined by two parameters – fck and SD. The fck and ‘mean population’ fm, are related through SD by following relation:

fm = fck + 1.65 * SD

The actual population of normal distribution of compressive strengths of the concrete considered in this paper is given in Figure 2. The main features of the ND curve are :

Abscissa, x-axis, represents the compressive strength, fc

Ordinate, y-axis, represents the frequency of occurrence of fc

Total area of curve is equal to unity

Actually, ND curve is a kind of conventional histogram where the interval of strengths on the x-axis is very small so that a continuous curve can be drawn.7

Any fraction of the area represents the corresponding fraction of total number of

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specimens. If Area, A, is taken as 100% of specimens, then, fraction of area, Af, is equal to percentage of specimens given by 100*(Af/A)

Mean is a point on the x-axis having maximum frequency and dividing the area into two exact halves.

The curve is symmetrical about the centrally located ‘mean’.

The curve is defined by the equation:

where, σ = Standard Deviation of the all data points = SDpop = Standard Deviation for the ‘population’

μ = Mean value of all the data points = Xbar-pop = Average value for the ‘population’

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It can be proved that the integration of the equation of the curve given above is equal to unity.

9. The spread of the curve is related to SD; a lower SD means narrower distribution of strengths and a higher peak in the middle.

10. fck is a point on x-axis such that 5% of the area of curve lies to left side and remaining 95% area lies towards right. This indicates that an fck is a specific point where 5% of the test results can be less than this value and 95% of the test results can be more than this value. Thus, if fck is considered, there is a 1 in 20 chance that the strength from tests will be less than this. The point, fck , is situated at a distance of 1.65*SD from mean value, fm , situated at the middle of the ND curve.

11. A ‘Standard Normal Distribution’ is a normal distribution with mean 0 and standard deviation 1. The abscissa of this curve is given by the following equation:

z = ( x – μ ) / σ = ( fc – Xbar-pop ) / SDpop where fc is any strength on x-axis

(i) Areas under this curve can be found using a ‘standard normal table’ from many textbooks and handbooks

(ii) The 68% of the observations fall between -1 and 1 (within 1 standard deviation of the mean of 0). In the present case of M30 with SD of 4, 68% of the strengths can be expected to lie between (38.25-5) and (38.25+5) i.e., 33.25 and 43.25.

(iii) 95% fall between -2 and 2 (within 2 standard deviations of the mean). In the present case of M30 with SD of 4, 95% of the strengths can be expected to lie between (38.25-2*5) and (38.25+2*5) i.e., 28.25 and 48.25.

(iv) 99.7% fall between -3 and 3 (within 3 standard deviations of the mean). In the present case of M30 with SD of 4, 95% of the strengths can be expected to lie between (38.25-3*5) and (38.25+3*5) i.e., 23.25 and 53.25.

(v) We may note here that the above mentioned ranges may look sometimes too wide for M30 grade concrete and seems to indicate inconsistency or lack of control in quality management. But, once, the concrete is

(Continued on page 35)

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accepted to be represented by ND curve, the above ranges are part of the distribution of strengths of the concrete and general quality control is assumed to correspond to SD of 4 in the present case. Therefore, it could be natural that when four samples (each sample is itself the mean of 3 cube strengths) are taken as required by IS 456:2000, it could be that this data set may itself show large variation, as in the case of Data Set D where the range is 26 to 44 MPa.

(vi) Though no naturally measured variable has this ‘Standard Normal Distribution’, all normal distributions are equivalent to this distribution where the unit of measurement ox x-axis is changed to measure in terms of standard deviations from the mean and this new x-ordinate is marked as z. Therefore, this ‘standard normal distribution’ is used to handle problems involving any normal distribution.

(vii) For any value of z, the standard tables supply the area under the curve over the region to the left of z. We may note that this area denotes the relative frequency occurrence of a value less than z.

(viii) For example, for fck, the characteristic strength, which is situated at a distance of 1.65*SDpop, the value of z for this point is

fck = Xbar-pop – 1.65 * SDpop

Z = ( fc – Xbar-pop ) / SDpop

= ( fck – Xbar-pop ) / SDpop

= 1.65

Corresponding to a measurement value of z = 1.65, the fraction of the area to the left of this point is an area of 0.049471 (from Standard Table) which is approximately 5%. Thus, it can be said that 5% the fc values can be expected to fall below fck, which alternately confirms that 95% the fc values are expected to exceed fck.

The above procedure can be used to estimate the percentage of fc values to fall below at any z. This will give us a technique to know the probability of occurrence of ITR value suggested in the Code.

estimation of probability of strength to be less than ‘ITr’ According to the ‘ITR’ criterion, the minimum strength of concrete in a test sample must be equal to or more than fck – 3.

Assuming the minimum fc to be fck – 3, we can write,

fc = fck – 3

But, fck = fm - 1.65 * SDpop , therefore,

fc = fm - 1.65 * SDpop – 3 = Xbar-pop - 1.65 * SDpop – 3

We may note here that

Xbar-pop = fm = µ = Population mean

Therefore, the value of z on ‘standard normal distribution’ curve as discussed earlier is computed as:

Z = ( fc – Xbar-pop ) / SDpop

= (Xbar-pop - 1.65 * SDpop – 3 – Xbar-pop ) / SDpop

= - 1.65 – (3 / SDpop )

The above equation shows that the ITR criterion gives a different probability of fc values falling below (fck – 3) for the same grade of concrete depending upon the standard

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deviation of the concrete itself. However, the failure rate of this must be less that of fck itself which has a failure rate of about 5% as seen earlier. The data regarding the area falling to the right of the minimum ‘ITR’ value for any grade of concrete, but, with different SD values, is given in Tables 1a and 1b, and Figure 3. It is seen that the probability of getting strength lower than strength of ITR criterion increases with increase in SD and hence, lower value of SD is always preferable. When the SD is normally adopted/observed SD of 5 MPa gives a failure rate of 1 in 140, which has less probability of occurrence than that of fck, where the probability is 1 in 20 only, before Amendment No 3 to IS 456:2000 (Table 1a). But after considering the Amendment No 3 to IS 456:2000 (Table 1b), for a SD of 5 MPa, the failure rate becomes 1 in 82, which has less probability of occurrence than that of fck, where the probability is 1 in 20 only. Thus, the data from the Tables 1a and 1b, represented in Figure 3, it is seen that the failure rates have increased at each SD. Probably, the amended clause demands a higher level of quality control.

Concluding remarksConcrete is a heterogeneous material and hence, each portion of its total volume can have a different strength. Therefore, compressive strength of concrete is treated mathematically as a ‘random variable’. However, the concrete strength of a given grade follows generally a ‘Normal Distribution Curve’ and hence, the concrete can be characterised by statistical parameters for the purpose of quality control, mix design, quality control, and evaluation of sample test results for conformity to acceptance criteria of BIS Codes.

Practically every structural concrete, for the purpose of quality checking, according to IS 456:2000, should be always defined by two parameters: (a) its grade (numerically equal to its characteristic strength, fck) and (b) its standard deviation, SD. But, for checking against ‘Individual Test Result’ criterion, SD is not required even though the probability of the ITR value being not reached depends upon SD itself. As the SD increases (meaning that with lower quality control systems), the probability of the ITR value occurring is more. Hence, it is always necessary to maintain the stricter quality control so that the SD anticipated is never exceeded in actual concrete mixes.

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Based on the provision in IS 456:2000 regarding ‘Individual Test Result’ criterion, the mixtures represented by the data sets A, B, and E discussed in this paper, are acceptable, but the data sets C and D are not acceptable.

As ‘Individual Test Result’ criterion is independent of SD, this criterion is applicable to concretes produced under any quality control system. This is the present position of the criterion in IS 456:2000. However, it may be rational to connect this to SD of the concrete also so that the rejection or acceptance of concrete remains at same level in terms of statistical nature of concrete. The degree of quality control may be also made part of the criterion of ‘ITR’ in the code. Or as defined in case of characteristic strength, fck, the ITR may be specified with certain degree of acceptability of failure which is 1 in 20 for the fck.

The ‘Individual Test Result’ criterion, when analysed statistically, indicates that for a typical SD of 5 MPa, before the Amendment No. 3 of IS 456:2000, the probability of strength falling below ITR criterion is 1 in 140 which reduces to as less as 1 in 700 for a SD of 3 MPa, and further down to a failure rate of 1 in 7627 when the SD falls to 2 MPa. However, after the Amendment No. 3, the above numerical values gets lowered; 140 changes to 82, 700 changes to 248, 7627 changes to 1225. Thus, the rate of occurrence of ITR lower than the specified minimum ITR increases (Tables 1a and 1b). It is interesting to note that these failure rates computed statistically are independent of the grade of the concrete itself.

In contrast to characteristic strength, fck , the ‘ITR’ criterion gives a probability of failure depending upon the SD itself. So perhaps a case exists for specifying an ‘ITR’ value containing SD also. Because, the statistical nature of strengths of concretes is generally accepted.

Towards above, ACI 214 criterion on minimum strength test value of 1 in 100 failure can be considered in Indian context and incorporated suitably in the IS 456. Under Criterion No 3 under paragraph 4.3.3 of ACI 214R, it is stated that “The minimum required average strength is established so that non-conformance of an individual, random test is anticipated no more often than 1 in 100 times in either case”.

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It is pertinent to observe that slightest changes in acceptance criteria can have severe financial and practical ramifications in the field. Therefore, discussions among the experienced engineers is necessary in trying to arrive at consensus for evolving practical guidelines. BIS as a body can plan a programme to collect different view points on the ITR to bring about meaningful and practically acceptable modifications to the provisions in IS 456.

There is a need for special consideration to be given for practising engineers’ concern related to ‘minimum acceptance value’ and ‘strength for structural design’, while fixing lower bound values of concrete strength in the form of ITR. Though the mean strength and standard deviation define a concrete represented by the Normal Distribution Curve, mean strength, fm, (with 50% probability of occurrence as seen from the ND curve) is taken for laboratory design of concrete mix (often called as ‘Target Mean Strength’) and the Characteristic Strength, fck, (a 95% probability value from ND Curve) for structural design. The minimum acceptable strength value on site should also be taken logically from ND curve. This is the ITR value of the IS 456 and this definitely should have rationally probability much lower than both fm and fck. Considering this, a probability of 99% (i.e, 1 in 100 failure) value (mentioned in Criterion No 3 under paragraph 4.3.3 of ACI 214R) or much more stricter than this can be suggested for the ITR which represents the ‘minimum acceptance value’. Instead of mentioning openly probability value for defining the ITR, another suggestion could be (fck-SD) as ITR which means a value of (fm-2.65*SD) since the fck is at a distance of 1.65 from the fm (on the ND curve). The data in Table 1 shows that, this could mean a failure rate of more than 1 in 700 which may seem to be a little stiff criterion.

acknowledgementsThe topic of this paper was earlier presented at DST sponsored ‘National workshop on utilisation of fly ash (UFA 11)’, June 10-11, 2011, organised by SVNIT, Surat. The technical discussions occurred during this Workshop were utilised in the preparation of this paper. The authors wish to acknowledge here the contributions made by Dr C.S. Viswanatha, Chairman, Civil - Aid Technoclinic Pvt. Ltd., Bangalore. He felt that the topic discussed here is of high practical importance. He

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encouraged the authors to write this paper and did the early scrutiny of the draft of the paper.

referencesNeville A.M. (1995). Properties of concrete Fourth edition. By A.M. Neville. Addison-Wesley Longman Ltd., USA p. 844.

Cook James E. (1989), Research and application of High-strength concrete- 10,000 psi concrete, Concrete International, October, pp 67-75.

Mehta, P.K. and Monteiro, P.J.M., (2005). Concrete: Microstructure, Properties and Materials. Third Ed., New York: McGraw-Hill

ACI, (2002), ACI Committee 214, Evaluation of Strength Test Results of Concrete, ACI214R-02, American Concrete Institute, Detroit, 20 p.

BIS (1999), SP 23(S&T): 1982. Handbook on concrete mixes, Fifth reprint, Bureau of Indian Standards, 1999.

______Indian standard code for plain and reinforced concrete-code of practice, IS : 456:2000, 4th Revision, Bureau of Indian Standards, New Delhi.

Benjamin Jack R. and Cornell C. Allin, Probability, Statistics. And Decision Making For Civil Engineers, McGraw Hill Book Company, New York, 1970. 683 p

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N.P. Rajamane holds a B.E. (Civil) First Class with Distinction, from Karnataka University and M.Tech. from IIT Madras. He is former Head, Advanced Materials Lab, CSIR, SERC, Chennai. At present, he is Head, Centre for Advanced Concrete Research, SRM University, Kattankulathur, Tamil Nadu. He is the recipient of “Outstanding Concrete Technologist for 2008” by Indian Concrete Institute. He has patents on building blocks from lateritic soil and

natural rubber latex modified cement concrete. He has about 300 technical publications related to his research interests of high performance concrete, geopolymer concrete, lightweight concrete, concrete chemicals, repair materials, nanotechnology and mineral admixtures.

Dr. M.C. Nataraja holds a PhD from Indian Institute of Technology, Kharagpur. He is a Professor in the Department of Civil Engineering at Sri Jayachamarajendra College of Engineering, Mysore. He has research experience of 25 years and has published over 100 technical papers in national and international journals and conferences. His areas of interest are SFRC, concrete mix design

and controlled low strength materials. He is in the international technical committee of PROTECT in connection with international conferences.

Dr. T.P. Ganesan holds a PhD from Indian Institute of Technology Madras, Chennai. He is Pro-Vice Chancellor (Planning and Development) of SRM University, Tamil Nadu. He has published several technical papers in national and international journals and conferences, besides authoring books in the field of model analysis

of structures. His wide areas of interest/expertise in civil engineering include masonry structures, preparation of laboratory models and testing for special structures, experimental stress analysis, analysis and design of structures, modern building materials, low cost housing and repairs and renovation of buildings.