The standard deviation is a statistical technique used to assess the consistency and reliability of compressive strength results in a batch of concrete. Its purpose is to control the variability in test results for the same batch of concrete by measuring the degree of dispersion or variation from the mean, average, or expected value.
This method involves a series of statistical analyses such as correlation analysis, hypothesis testing, analysis of variance, and regression analysis to compare two or more sets of compressive strength data. Essentially, the standard deviation indicates the extent to which the results deviate from the expected value, providing insight into the range of dispersion or variation in the data.
In short, the standard deviation is a statistical tool that helps determine the degree of variability in compressive strength results for a batch of concrete, and it is an essential factor in quality control and ensuring consistency in construction projects.
Calculation of Standard Deviation for Concrete
There are two different methods that can be used for calculating the standard deviation of compressive strength when it comes to concrete. These methods provide slightly different results and may be more appropriate for certain situations depending on the specific needs and context.
It’s important to understand the differences between these methods in order to choose the appropriate one for your needs. Both methods involve calculating the standard deviation of a set of concrete samples, which can help provide insight into the quality and consistency of the concrete being used.
By understanding the nuances and variations of these two methods, one can make an informed decision about which method to use for their specific application. This can lead to more accurate and reliable results when it comes to testing the strength of concrete and ensuring its overall quality.
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1. Assumed Standard Deviation
According to IS-456 Table 8 (Clauses 3.2.1.2), a minimum of 30 cube test samples is required to derive the standard deviation for a particular grade of concrete. However, there may be cases where enough test results are not available for a specific grade of concrete. In such situations, the standard deviation value can be assumed based on the table provided by IS-456.
This means that if there are not enough test results available, the value of standard deviation can be estimated using the values provided in the table. It is important to note that these values are based on past data and may not be a perfect representation of the actual standard deviation for a particular grade of concrete. Therefore, it is always better to have a sufficient number of test results to derive an accurate value for the standard deviation.
Table 1: Assumed Standard Deviation
| Sl.No | Grade of Concrete | Characteristic compressive strength (N/mm2) | Assumed standard deviation (N/mm2) |
| 1 | M10 | 10 | 3.5 |
| 2 | M15 | 15 | |
| 3 | M20 | 20 | 4 |
| 4 | M25 | 25 | |
| 5 | M30 | 30 | 6 |
| 6 | M35 | 35 | |
| 7 | M40 | 40 | |
| 8 | M45 | 45 | |
| 9 | M50 | 50 | |
| 10 | M55 | 55 |
The minimum number of test results should be obtained before calculating and using the standard deviation. It is important to note that the values mentioned are contingent on proper site control measures being in place. These include appropriate storage of cement, the use of weigh batching for all materials, controlled addition of water, and regular checking of all elements, such as aggregate grading and moisture content. It is also crucial to regularly assess workability and strength. By following these procedures, the derived standard deviation will be more accurate and reliable.
2. Derived Standard Deviation
When there are more than 30 test results available, the standard deviation of the test results is calculated using a specific method.
The standard deviation (phi) in the context of concrete strength testing is a measure of the variability or spread of test results around the average strength of concrete (µ). A lower value of standard deviation indicates excellent quality control at the construction site, where most of the test results are expected to be close to the mean value. On the other hand, if quality control is unsatisfactory, the test results may deviate significantly from the mean value, resulting in a higher standard deviation. In simpler terms, a higher standard deviation implies more variability in test results and lower quality control, while a lower standard deviation suggests less variability and better quality control.
Fig 1: Variation Curve for Standard Deviation
As per the guidelines provided by IS-456 Table No-11, there are permissible deviations allowed in the mean of compressive strength for concrete. These allowable deviations are prescribed in the table and are to be adhered to. The table provides specific values that can be considered acceptable for the mean compressive strength of concrete, and any deviation from these values may not be permissible. It is important to follow these guidelines to ensure that the concrete used in construction projects meets the required quality standards. Adhering to the permissible deviations in the mean compressive strength of concrete as prescribed in the IS-456 Table No-11 helps to ensure the reliability and durability of the concrete structures.
Table 2: Characteristic Compressive Strength Compliance Requirement
| Specified Grade | Mean of Group of 4 Non-Overlapping Consecutive test results in N/mm2 | Individual Test Results in N/mm2 |
| M-15 | fck + 0.825 x derived standard deviation or fck + 3 N/mm2 (Whichever is greater) | Greater than or equal to – fck-3 N/mm2 |
| M-20 and above | fck + 0.825 x derived standard deviation or fck + 4 N/mm2 (Whichever is greater) | Greater than or equal to – fck-4 N/mm2 |
Example Calculation of Standard Deviation for M60 grade Concrete with 33 cubes.
A concrete slab with a volume of 400 cubic meters was poured, and 33 cubes were cast for a compressive strength test that lasted 28 days. The strength of the concrete was measured by testing the cubes, and the results were used to calculate the standard deviation for the 33 tests.
Table 3: Test Result of Concrete Cubes
| SL No | Weight of the cube in Kg | Max Load in KN | Density in Kg/Cum | Compressive Strength in Mpa | Remarks |
| 1 | 8.626 | 1366 | 3594.2 | 60.71 | Pass |
| 2 | 8.724 | 1543 | 3635.0 | 68.57 | Pass |
| 3 | 8.942 | 1795 | 3725.8 | 79.77 | Pass |
| 4 | 8.850 | 1646 | 3687.5 | 73.15 | Pass |
| 5 | 8.466 | 1226 | 3527.5 | 54.48 | Fail |
| 6 | 8.752 | 1291 | 3646.7 | 57.37 | Fail |
| 7 | 8.806 | 1457 | 3669.2 | 64.75 | Pass |
| 8 | 8.606 | 1285 | 3585.8 | 57.11 | Fail |
| 9 | 8.708 | 1465 | 3628.3 | 64.71 | Pass |
| 10 | 8.696 | 1387 | 3623.3 | 61.64 | Pass |
| 11 | 8.848 | 1476 | 3686.7 | 65.60 | Pass |
| 12 | 8.752 | 1529 | 3646.7 | 67.95 | Pass |
| 13 | 8.450 | 1564 | 3520.8 | 69.51 | Pass |
| 14 | 8.708 | 1703 | 3628.3 | 75.68 | Pass |
| 15 | 8.602 | 1478 | 3584.2 | 65.68 | Pass |
| 16 | 8.762 | 1539 | 3650.8 | 68.40 | Pass |
| 17 | 8.468 | 1475 | 3528.3 | 65.55 | Pass |
| 18 | 8.862 | 1386 | 3692.5 | 61.60 | Pass |
| 19 | 8.728 | 1507 | 3636.7 | 66.97 | Pass |
| 20 | 8.480 | 1550 | 3533.3 | 68.88 | Pass |
| 21 | 8.708 | 1738 | 3628.3 | 77.24 | Pass |
| 22 | 8.712 | 1463 | 3630.0 | 65.02 | Pass |
| 23 | 8.562 | 1327 | 3567.5 | 58.97 | Fail |
| 24 | 8.370 | 1529 | 3487.5 | 67.99 | Pass |
| 25 | 8.592 | 1388 | 3580.0 | 61.68 | Pass |
| 26 | 8.622 | 1383 | 3592.5 | 61.46 | Pass |
| 27 | 8.732 | 1245 | 3638.3 | 55.39 | Fail |
| 28 | 8.776 | 1482 | 3656.7 | 65.86 | Pass |
| 29 | 8.724 | 1367 | 3635.0 | 60.75 | Pass |
| 30 | 8.628 | 1590 | 3595.0 | 70.66 | Pass |
| 31 | 8.604 | 1394.7 | 3585.0 | 61.98 | Pass |
| 32 | 8.566 | 1406.1 | 3569.2 | 62.49 | Pass |
| 33 | 8.578 | 1387.2 | 3574.2 | 61.65 | Pass |
| Total | 2149.22 | ||||
| Average | 65.12 |
The given data presents the calculation of the standard deviation for concrete of grade above M-20. The sum of the squared deviations from the mean (x-µ)2 is 1132.55, and the resulting standard deviation is found to be 5.94 N/mm2 using the formula SD = SqRt (sum of squared deviations/degrees of freedom).
According to the IS-456 standard, for concrete of grade above M-20, the characteristic strength can be calculated by adding 0.825 times the derived standard deviation to the mean strength. The value obtained is 64.90 N/mm2 by using the calculated standard deviation of 5.94 N/mm2. Alternatively, the characteristic strength can be found by adding 4 N/mm2 to the mean strength of 60 N/mm2. The higher value of the two is considered to be the characteristic strength, which is 64.90 N/mm2 in this case.
The average/mean value of the compressive strength for the given data is 65.12 N/mm2, which is found to be higher than the standard deviation of 5.94 N/mm2. Therefore, it can be concluded that the compressive strength of the concrete has a mean value of 65.12 N/mm2 and a standard deviation of 5.94 N/mm2, and the characteristic strength is 64.90 N/mm2 as per the IS-456 standard.
Conclusion
Table-3 displays the test results of five concrete cubes, and it can be observed that their values are below 60 N/mm2. This indicates that the cubes have failed to meet the required standard. However, it is important to note that the standard deviation calculation shows that the concrete member as a whole can still be considered acceptable. Therefore, non-destructive tests are not required to be conducted.
1. What is Standard Deviation for Compressive Strength of Concrete?
The variability in the compressive strength results of a concrete batch is measured by the standard deviation. It provides an indication of the reliability between different results and represents the extent to which the results are dispersed or vary from the mean or expected value. In simpler terms, the standard deviation is a measure of the range of variation in compressive strength results.
2. What is the importance of Standard Deviation for concrete?
Concrete is a commonly used building material that undergoes various stages, including storing, mixing, transportation, and testing. During these stages, poor handling of concrete can result in deviations in its compressive strength. These deviations are accounted for by the standard deviation of concrete.
The compressive strength of concrete is an essential factor that determines its quality and durability. Therefore, any deviations in its strength due to poor handling must be taken into consideration. The standard deviation of concrete provides a measure of the variations or deviations in the compressive strength results caused by poor handling of concrete during its various stages.
Several factors can contribute to poor handling of concrete, such as improper mixing, incorrect proportions of materials, inadequate curing, and poor transportation. These factors can affect the quality of concrete and result in deviations in its compressive strength. To ensure the quality and durability of concrete, it is essential to consider the standard deviation of concrete while testing its compressive strength.