SPRUT Technical Note: Individual Test Result for Concrete IS 456:2000 (EN)

Point of View 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, f ck , where the probability of occurrence of strength lower than that corresponding to f ck is always 5% (or 1 in 20) and this value is independent of standard deviation. 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. 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 So the subject matter of this paper is statistical in nature than technical, since many items such as the actual The Indian Concrete Journal APRIL 2012 26

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Point of View Table 1a. Failure rate for ‘Individual test result’ criterion before Amendment No. 3 to IS 456:2000 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 statement The 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: Table 1b .Failure rate for ‘Individual test result’ criterion after Amendment No. 3 to IS 456:2000 “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):

ITRf1 = Factor in ‘ITR’ criterion of IS 456:2000 before Amendment No 3=4 MPa since ITR criterion for acceptability was f ck -4 MPa for grade M20 and above ITRf2 = Factor in ‘ITR’ criterion of IS 456:2000 after Amendment No 3=3 MPa since ITR criterion for acceptability was f ck -3 MPa for Grade M15, Grade M20 and above SD = Standard Deviation, MPa; z = X-coordinate of ‘standard normal distribution’ curve = ( x – μ ) / σ = ( f c – fm ) / SD = ( ( f ck –ITRf ) – f m ) / SD where f m = f ck + 1.65 * SD A FL = Fraction of the area to the left of f c considering the total area under curve as 1 %A FL = %age of the area to the left of f c considering the total area under curve as 100 = Percentage of specimens with value less than f c Failure Rate = For each one of the specimens having strength less than f c , the possible number of specimens having strength more than f c 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.

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 27 APRIL 2012 The Indian Concrete Journal SD ITRf1 z A FL %A FL Failure Rate = 1/ A FL 2 4 -3.65 0.00013 0.013 7627 2.5 4 -3.25 0.00058 0.058 1733 3 4 -2.98 0.00143 0.143 701 3.5 4 -2.79 0.00261 0.261 383 4 4 -2.65 0.00402 0.402 248 4.5 4 -2.54 0.00556 0.556 180 5 4 -2.45 0.00714 0.714 140 5.5 4 -2.38 0.00872 0.872 115 6 4 -2.32 0.01026 1.026 97 6.5 4 -2.27 0.01174 1.174 85 7 4 -2.22 0.01316 1.316 76 7.5 4 -2.18 0.01451 1.451 69 8 4 -2.15 0.01578 1.578 63 SD ITRf2 z A FL %A FL Failure rate = 1/ A FL 2 3 -3.15 0.00082 0.082 1225 2.5 3 -2.85 0.00219 0.219 457 3 3 -2.65 0.00402 0.402 248 3.5 3 -2.51 0.00609 0.609 164 4 3 -2.40 0.0082 0.820 122 4.5 3 -2.32 0.01026 1.026 97 5 3 -2.25 0.01222 1.222 82 5.5 3 -2.20 0.01407 1.407 71 6 3 -2.15 0.01578 1.578 63 6.5 3 -2.11 0.01736 1.736 58 7 3 -2.08 0.01883 1.883 53 7.5 3 -2.05 0.02018 2.018 50 8 3 -2.03 0.02143 2.143 47

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Point of View 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 = 4 MPa 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 456:2000 The 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: Acceptability of data for ‘Itr’ criterion In the present case of M30 grade concrete, fc individual ≥ 30 – 3 fc individual ≥ 27 MPa fc individual ≥ f ck – 3 for concrete of M15.

It is worthwhile to recognise here that, for given f ck , i.e., grade of concrete, there could be different values of Standard Deviation, SD pop , then for each pair of fck and SD pop , 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. fc individual ≥ f ck – 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 f ck , 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 f ck -4 to f ck -3 for concrete of M20 and 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:

Check for acceptability It 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.' fc individual ≥ f ck – 3 The Indian Concrete Journal APRIL 2012 28

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Point of View Test data set A (i) 35, (ii) 33, (iii) 33, (iv) 34 MPa 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’, f ck , denoted by the number describing the Grade of concrete. 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.

In the present case, the M30 Grade concrete has the ‘characteristic strength’, f ck of 30 MPa and it is seen that each of the test results has to be more than or equal to 27 MPa. Test data set B (i) 35, (ii) 27, (iii) 40, (iv) 34 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 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. Statistical basis of ‘ITR’ criterion It 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 – f ck and SD. The f ck and ‘mean population’ f m , are related through SD by following relation:

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 f m = f ck + 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 :

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. 1. Abscissa, x-axis, represents the compressive strength, f c 2. Ordinate, y-axis, represents the frequency of occurrence of f c 3.

Total area of curve is equal to unity Test data Set E (i) 38, (ii) 28, (iii) 29, (iv) 44 MPa 4. 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 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. 5. Any fraction of the area represents the corresponding fraction of total number of 29 APRIL 2012 The Indian Concrete Journal

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