What is Compressive Strength of Concrete?
Simply, the compressive strength can be defined as the capacity of concrete to withstand loads before failure. Of the many tests applied to concrete, the compressive strength test is the most important, as it gives an idea about the characteristics of the concrete.
Since you are reading about target mean strength in this article, I guess you are aware of characteristic compressive strength. In case you do not know the difference, read about characteristic compressive strength vs target mean strength.
Concept of Concrete Target Mean Strength
Target mean strength is the average strength that we target when designing a concrete mix. This value is higher than the characteristic strength that the structural designer uses in structural design.
This means that if the structural drawings mention a concrete grade of 25 MPa [we call it concrete characteristic strength], the concrete mix design will not target exactly 25 MPa. Instead, it will target a higher value [we call it target mean strength]. Why?
Because in concrete production and casting on site, there are multiple sources of variability that may cause a reduction in the compressive strength of concrete. Therefore, we add a statistical margin from the beginning to account for this expected variation. This margin is not an additional structural factor of safety.
Target Mean Strength Formula
The basic margin that we add to the characteristic strength is 1.65 multiplied by the standard deviation of concrete strength test results.
f’ck = fck + 1.65S
| Symbol | Meaning | Unit |
|---|---|---|
| f’ck | Target mean compressive strength at 28 days | MPa or N/mm2 |
| fck | Characteristic compressive strength at 28 days | MPa or N/mm2 |
| S | Standard deviation of compressive strength results | MPa or N/mm2 |
| 1.65 | Statistical factor corresponding to the 5% lower fractile | No unit |
Look at the previous figure. What you see is the curve that we usually obtain for compressive strength results. Assume we have 40 specimens from the same concrete mix.
When we plot the results for the 40 specimens, we obtain the bell curve. The mean value on the curve is the target mean strength that we design the mix for. Therefore, the basic thing here that is essential to determine the target mean strength is the standard deviation.
Current IS 10262 Check
Under IS 10262:2019, calculate the target mean strength using both of the following equations. Then, use whichever value is higher:
or
f’ck = fck + X
Use whichever is higher. The value of X depends on the grade of concrete according to the standard.
The second equation provides a minimum margin. As a result, a very small standard deviation cannot reduce the design target below the minimum margin required for that grade.
Worked Examples
Example 1: M25 Concrete
For M25 concrete, take fck = 25 MPa, S = 4 MPa, and X = 5.5 MPa.
| Check | Calculation | Result |
|---|---|---|
| Statistical margin | 25 + (1.65 x 4) | 31.60 MPa |
| Minimum margin | 25 + 5.5 | 30.50 MPa |
| Adopted target | Higher of the two results | 31.60 MPa |
Example 2: M30 Concrete
If I told you we need to design a concrete mix with 30 MPa characteristic strength and we have the standard deviation of results as 6 MPa, what is the target mean strength?
Target mean strength = fck + 1.65S = 30 + (1.65 x 6) = 39.9 MPa.
If the code also specifies a minimum-margin equation, calculate it as well and use the higher result.
How Standard Deviation Affects Target Strength
Standard deviation describes the variation between test results. Therefore, a larger standard deviation means that the concrete production is less consistent and a larger margin is required. On the other hand, a smaller standard deviation indicates better control.
| Characteristic strength | Standard deviation | fck + 1.65S |
|---|---|---|
| 30 MPa | 3 MPa | 34.95 MPa |
| 30 MPa | 4 MPa | 36.60 MPa |
| 30 MPa | 5 MPa | 38.25 MPa |
| 30 MPa | 6 MPa | 39.90 MPa |
However, calculate the standard deviation using eligible results and the procedure in the code you are following. Do not combine unrelated mixes or different production conditions just to obtain a lower value.
Target Mean Strength Is Not an Acceptance Limit
Target mean strength is an input for proportioning the concrete mix. It is not the pass or fail value for every cube or cylinder. Concrete acceptance depends on the sampling and acceptance criteria specified by the applicable code and project specification.
In addition, achieving the target strength does not by itself prove that the concrete is durable. The mix must still satisfy requirements for exposure, water-to-cement ratio, cementitious content, workability, compaction, and curing.
Summary
To calculate concrete target mean strength, start with the characteristic strength and add a margin for production variation. Under IS 10262:2019, calculate f’ck = fck + 1.65S and f’ck = fck + X, then use the higher value. Finally, remember that this is a mix-design target, not the acceptance limit for an individual test result.
References
- Bureau of Indian Standards, concrete mix-proportioning example applying the IS 10262 target-strength equations
- American Concrete Institute, Expect Compressive
- The Concrete Society, Characteristic Strength
Read Also:
Characteristic Compressive Strength vs Target Mean Strength