Understanding Concrete Strength Variation through Standard Deviation

Concrete is a crucial construction material, and assessing its compressive strength is vital. The standard deviation method gauges the consistency of compressive strength results within a concrete batch. This statistical approach helps control variations in test results for a specific concrete batch.

Explaining Standard Deviation

In simpler terms, standard deviation illustrates the spread or diversity of results from the mean or expected value. It uses statistical analyses like correlation, hypothesis testing, analysis of variance, and regression analysis to compare compressive strength series for concrete batches.

Two Methods of Calculating Standard Deviation

1. Assumed Standard Deviation

If there are insufficient test results, an assumed standard deviation is used. Once a minimum of 30 cube test samples is available, the derived standard deviation is calculated based on the IS-456 Table 8. The assumed standard deviation values are determined according to the concrete grade.

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

…

…

…

…

Note: Values are site-control-dependent, emphasizing proper storage, batching, water addition, and regular quality checks.

2. Derived Standard Deviation

When more than 30 test results are available, the standard deviation is derived using the formula: $ϕ=n−∑(x−μ)2 $
Where:

$ϕ$: Standard Deviation

$μ$: Average Strength of Concrete

$n$: Number of Samples

$x$: Crushing value of concrete in N/mm2

A lower standard deviation indicates better quality control, aligning test results closely with the mean value.

Understanding Standard Deviation Variation

Fig 1: Variation Curve for Standard Deviation

The permissible deviation in mean compressive strength, as outlined in IS-456 Table No-11, is crucial for compliance.

Mean of Group of 4 Non-Overlapping Consecutive Test Results (N/mm2)

Individual Test Results (N/mm2)

M-15

$fck+0.825×Derived Standard Deviation$

$≥fck−3N/mm2$

M-20 and above

$fck+0.825×Derived Standard Deviation$

$≥fck−4N/mm2$

Example Calculation for M60 Grade Concrete

A concrete slab of 400Cum was poured, and 33 cubes were cast for a 28-day compressive test. The standard deviation for these 33 cubes is calculated below.

$fck+0.825×Derived Standard Deviation=60+0.825×5.94=64.90N/mm2$

$fck+4N/mm2=60+4=64N/mm2$

The higher value is considered, leading to a Standard Deviation of $64.90N/mm2$.

Considering the average compressive strength of $65.12N/mm2$ from Table-3, it surpasses the standard deviation $64.90N/mm2$.

Conclusion

Despite five cubes having results below $60N/mm2$, the standard deviation calculation suggests concrete approval, and non-destructive tests are not mandated. This highlights the importance of statistical methods in ensuring concrete quality.