The two numbers that are not the same
Most cube-result arguments on site are not disagreements about the concrete. They are disagreements about which number is being discussed. Two numbers matter, and they are not interchangeable.
| What it is | Who sets it | What it decides |
|---|---|---|
| Specified characteristic strength fck M30 → 30 N/mm² | The specification and the grade designation (IS 456, Table 2) | Acceptance. The gate the concrete is judged against under IS 456 Cl 16.1 and Table 11. |
| Target mean strength f′ck | The designer, from fck, the standard deviation and the grade factor (IS 456 Cl 9.2.2; IS 10262:2019 Cl 4.2) | Proportioning. The strength the mix is proportioned to produce, so that the production population clears fck. |
IS 456 Cl 9.2.2 states the design target as the characteristic strength plus 1.65 times the standard deviation. IS 10262:2019 Cl 4.2 states the same relation for mix proportioning, and adds a second route: the target may also be taken as fck plus a grade-based factor X from its Table 1, and whichever of the two is higher governs. For M30 that comparison is not academic — the two routes give different numbers, and the higher one is the one the mix is proportioned to.
Why the margin exists at all
A mix is not a single cube. It is a population: materials vary, moisture varies, the water that actually goes in the drum is not the water on the batching sheet, compaction and curing vary, and the test itself has a spread. The 1.65 s margin places fck near the lower 5% point of that population, so that a process whose mean is at the target still delivers a population in which roughly 95% of valid results clear the specified grade.
This is why the acceptance criterion uses 0.825 s and not 1.65 s. Table 11 judges the mean of a group of four non-overlapping consecutive test results, not a single result, and the standard deviation of a group mean is smaller than the standard deviation of an individual result by roughly a factor of two. The two numbers are the same idea measured at different points: the individual gate protects one batch; the group gate protects the population.
Worked example — M30, established σ = 5.0 N/mm²
Take M30 on a project that has established its standard deviation at 5.0 N/mm². The numbers below are arithmetic on that stated input; nothing is assumed beyond it.
| Quantity | Derivation | Value (N/mm²) |
|---|---|---|
| Specified characteristic strength | Grade M30 | 30.0 |
| Standard deviation s | Established for the project | 5.0 |
| Target, route 1 | fck + 1.65 s (IS 10262:2019 Cl 4.2) | 30 + 8.25 = 38.25 |
| Target, route 2 | fck + X, with X = 6.5 for M30 (IS 10262:2019 Table 1) | 30 + 6.5 = 36.5 |
| Design target | Whichever is higher | 38.25 |
| Acceptance gate, group mean | fck + 0.825 s, rounded off to the nearest 0.5 → 34.0; compare with fck + 3 = 33.0 and take the greater (IS 456 Table 11, col 2) | 34.0 |
| Acceptance gate, individual result | fck − 3 (IS 456 Table 11, col 3) | 27.0 |
So the mix was proportioned for a mean of 38.25 N/mm², and the concrete will be accepted with a group mean of 34.0. The margin between the two is 4.25 N/mm² — and that margin is the useful part of the design, because it is the band in which the process can drift before the acceptance decision is at risk.
| 28-day sample results | Group mean | Lowest individual | Table 11 outcome |
|---|---|---|---|
| 37.1 · 36.4 · 35.8 · 34.9 | 36.05 ≥ 34.0 | 34.9 ≥ 27.0 | Accepted — and 2.2 N/mm² below the design target, which is the signal. |
| 34.6 · 34.1 · 33.7 · 32.8 | 33.80 < 34.0 | 32.8 ≥ 27.0 | Not accepted — the group mean fails column 2, even though every individual result passes column 3. |
The first group would have raised no alarm on a site that only checks "is the cube above fck?" — 34.9 and 36.05 both clear 30 comfortably. But it was already 2.2 N/mm² under the design aim, and one group later the concrete failed. The early warning was in the distance from the target, not in the distance from fck.
The assumed standard deviation is a starting point, not a constant
Both codes carry a table of assumed standard deviations, and both treat it as a placeholder to be replaced as soon as real data exists. IS 10262:2019 Table 2 gives the assumed values for proportioning — 3.5 N/mm² for M10 and M15, 4.0 for M20 and M25, 5.0 for M30 to M60 and 6.0 for M65 to M80 — and Cl 4.2.1.3 requires the actual calculated standard deviation to be used as soon as sample results are available. IS 456 Cl 9.2.4.2 says the same for design mix, pointing at its own Table 8, which as amended by Amendment No. 4 carries the same 3.5 / 4.0 / 5.0 values for M10 to M60.
Two notes travel with those tables and both matter on site. First, the assumed values hold only while site control is good — proper cement storage, weigh batching, controlled water addition, and regular checks of grading, moisture, workability and strength. Where control deviates, both codes require the value to be increased by 1 N/mm², not left as it is. Second, a project with adequate past records for a similar grade may adopt a standard deviation different from the assumed one — a low one on a well-controlled plant, or a high one on a site that cannot hold its spread.
Either way, the standard deviation is a live number. Recalculating it after a change of mix design, a change of material source or a change of plant — as IS 456 Cl 9.2.4.1 requires — changes the target, changes the acceptance gate, and changes what the next cube result means.
What to do with a result below the target
Judge it against Table 11, and record it against the target separately
Two entries in the cube register: the acceptance decision under IS 456 Cl 16.1, and the distance from the design target. One is a compliance question; the other is a process question. Mixing them produces both false alarms and false comfort.
Look at groups, not at cubes
The unit of judgement is the group of four non-overlapping consecutive results. Plot the group means on a run chart and watch the trend. A run of means drifting towards the acceptance gate is the finding; a single low cube inside an otherwise healthy run usually is not.
Check the things that move a mean before you touch the mix
Aggregate moisture and the water that actually reached the drum, a change of cement or SCM source, admixture dosing and slump behaviour with time, compaction at the point of placing, curing in the first days, and the calibration of the testing machine and its cube preparation. Every one of these moves the mean of a group more cheaply than a redesign of the mix does.
Remember that a 7-day result is not an acceptance result
IS 456 Cl 15.1.1 allows optional 7-day testing, and it is useful for early warning. It is not a substitute: the 28-day strength alone is the criterion for acceptance or rejection. A good 7-day result does not accept a structure, and a poor one does not condemn it.
When the group fails, follow the code's route rather than a retest
IS 456 Cl 16.3 sends concrete that does not meet the strength requirement to Cl 17, where the engineer-in-charge may call for core testing under Cl 17.4 or a load test under Cl 17.6. Core results are read against Cl 17.4.3 — an average equivalent cube strength of at least 85% of the specified grade, with no individual core below 75%.
References & further reading
- IS 456:2000 — Plain and Reinforced Concrete — Code of Practice (Fourth Revision), Bureau of Indian Standards, as amended. Cl 9.2.2 design target mean strength; Cl 9.2.4 and 9.2.4.1 standard deviation and the 30-sample record; Cl 9.2.4.2 assumed standard deviation; Table 8 as amended by Amendment No. 4; Cl 15.1 and 15.1.1 specimen strength and the role of the 28-day result; Cl 15.2.2 sampling frequency; Cl 16.1 acceptance; Table 11 as amended by Amendments No. 1, 3 and 4; Cl 16.3 quantity represented; Cl 17.4.3 core acceptance.
- IS 10262:2019 (Second Revision) — Concrete Mix Proportioning — Guidelines, Bureau of Indian Standards. Cl 4.2 target strength for mix proportioning and the two routes to it; Cl 4.2.1 and 4.2.1.1 standard deviation from test results; Cl 4.2.1.2 computation; Cl 4.2.1.3 assumed standard deviation; Table 1 value of X; Table 2 assumed standard deviation.
- IS 516 — Hardened Concrete — Methods of Test, Bureau of Indian Standards. Applicable parts cover the making, curing and compressive testing of cube specimens and the preparation and testing of cores.
- IS 1199 — Fresh Concrete — Methods of Sampling, Testing and Analysis, Bureau of Indian Standards. Sampling of fresh concrete for the strength specimens.
Use the controlled copies of the standards and the project specification for contractual decisions. A project specification may impose requirements more stringent than the code minimum, and where it does, the specification governs.
Field-checklist blocks
A short questionnaire, an inspector's checklist, and three worked examples that show how the design target and the acceptance gate stay two separate numbers, and what each one decides on a cube register.
Questionnaire — asked when a 28-day result lands between fck and the design target
- What is fck for this grade, and what is the design target mean strength the mix was proportioned to? For M30 that is fck + 1.65σ under IS 456 Cl 9.2.2, which at σ = 5.0 gives 30 + 8.25 = 38.25 N/mm².
- Which route gave you the target, and did you take the higher one? IS 10262:2019 Cl 4.2 gives fck + 1.65σ or fck + X, and for M30 that is 38.25 against 36.5 with X = 6.5, so 38.25 governs.
- Is the σ you are using established or assumed, and when was it last recalculated? IS 456 Cl 9.2.4.1 wants a recalculation after a change of mix design, material source or plant, and where site control has deviated both codes want the assumed value increased by 1 N/mm².
- Is the acceptance decision being made against IS 456 Cl 16.1 and Table 11, rather than against the design target? For M30 at σ = 5.0 the group gate is 30 + 0.825 × 5.0 = 34.125, rounded off to the nearest 0.5 as 34.0, against fck + 3 = 33.0, so 34.0 governs; the individual floor is 30 − 3 = 27.0 N/mm².
- Are results being judged in groups of four non-overlapping consecutive samples, and is the group mean trend being watched rather than single cubes?
- Is this a 7-day result? IS 456 Cl 15.1.1 allows it for early warning only. The 28-day strength alone is the acceptance criterion.
- If a group has failed, does everyone know the route? IS 456 Cl 16.3 sends the concrete to Cl 17, where core testing under Cl 17.4 is read against Cl 17.4.3: at least 85% of the grade as an average equivalent cube strength and no core below 75%.
Inspector's checklist — what to verify on site
- Register header: grade, fck, the design target mean strength, the σ in use and where it came from, and the date it was last recalculated.
- Groups formed in sampling order, four non-overlapping consecutive results, with no regrouping to lift a mean.
- Group mean against the gate: for M30 at σ = 5.0, max(30 + 0.825 × 5.0 = 34.125 → 34.0, 30 + 3 = 33.0) = 34.0 N/mm².
- Every individual result against fck − 3, which for M30 is 27.0 N/mm², checked separately from the mean.
- Distance from the design target recorded next to the verdict: for M30 at σ = 5.0 the band between 38.25 and 34.0 is 4.25 N/mm² of drift you can absorb before acceptance is at risk.
- 7-day results flagged as warning only, kept out of the acceptance column.
- On failure, the Cl 16.3 and Cl 17 route prepared: quantity of concrete represented, and core acceptance at 85% and 75% of the grade ready to be applied.
What happens if… three worked examples
What happens. With fck = 30 N/mm² and σ = 5.0, the design target is 38.25 and the acceptance gate is 34.0. The result is 38.25 − 36 = 2.25 N/mm² below the design aim and comfortably above both the group gate and the 27.0 individual floor.
Likely outcome. The concrete is accepted. The 2.25 N/mm² gap is not a defect, it is the early warning: it tells you the process has moved 2.25 of the 4.25 N/mm² of available drift towards the gate. A site that checks only "is the cube above fck?" sees 36 against 30 and sees nothing wrong. The signal is the distance from the target, not the distance from fck.
What happens. The mean is (34.6 + 34.1 + 33.7 + 32.8) ÷ 4 = 33.80 N/mm², which is below the 34.0 gate, while the lowest individual, 32.8, is still above 27.0.
Likely outcome. The group is not accepted, even though every single cube would have passed on its own. Under IS 456 Cl 16.3 the concrete that this group represents goes to Cl 17, where the engineer-in-charge may call for core testing under Cl 17.4 or a load test under Cl 17.6, and core results are read against Cl 17.4.3. The 2.2 N/mm² that the previous group sat below the design target was the only warning this failure gave you.
What happens. The M30 mix was proportioned on an assumed σ of 5.0 N/mm², with a target of 38.25 and a gate of 34.0. Site control has also deviated, so the assumed value goes up by 1 N/mm² to 6.0, as both codes require. The target becomes 30 + 1.65 × 6.0 = 39.9 N/mm², and the gate becomes 30 + 0.825 × 6.0 = 34.95, rounded off to the nearest 0.5 as 35.0, against 33.0 from fck + 3, so 35.0 governs.
Likely outcome. The acceptance gate has moved 1.0 N/mm² upward and the design target has moved 1.65 N/mm² upward, and the individual floor is still 27.0. Concrete that passed at a group mean of 34.0 under the old σ now fails. Recalculating σ after a change of mix design, material source or plant, as IS 456 Cl 9.2.4.1 requires, changes the target, changes the gate and changes what the next cube result means, all at once.
Frequently asked questions
fck is the specified characteristic compressive strength named by the grade — the strength below which not more than 5% of valid test results are expected to fall. The target mean strength is a design and production aim, set higher than fck so that a well-run process still produces a population that satisfies fck. IS 456 Cl 9.2.2 states the target mean strength of the mix as the characteristic strength plus 1.65 times the standard deviation.
Yes. The acceptance decision is made under IS 456 Cl 16.1 against Table 11, not against the design target. The concrete complies when the mean of a group of four non-overlapping consecutive test results meets the Table 11 column 2 limit and every individual result meets the column 3 limit. A result below the target mean strength is a signal about the process, not a rejection of the concrete.
IS 10262:2019 Cl 4.2 sets the target mean strength as fck + 1.65 S, or fck + X, whichever is higher. With the assumed standard deviation of 5.0 N/mm² from Table 2, fck + 1.65 S gives 38.25 N/mm² for M30; the grade-based factor X from Table 1 gives 36.5 N/mm². The higher of the two governs, so the target for M30 is 38.25 N/mm².
Not on its own. One result below the target says the process is running under its design aim at that moment. A trend of results below the target is a different matter: the mean of successive groups of four is the right unit to look at, because it is the same unit Table 11 uses. Look at the trend first, and at the individual cube second.
When the group of four fails the Table 11 column 2 limit, or when an individual result falls below the column 3 limit. For M30 that is a group mean of at least fck + 0.825 S rounded off to the nearest 0.5 N/mm², or fck + 3 N/mm², whichever is greater, and every individual result at or above fck − 3 N/mm². IS 456 Cl 16.3 and Cl 17 then govern how the concrete is evaluated.
Yes. Both codes treat the assumed standard deviation as a starting point for first-time proportioning, not as a permanent value. IS 10262:2019 Cl 4.2.1.3 requires the actual calculated standard deviation to be used as soon as sample results are available, and IS 456 Cl 9.2.4.2 says the same for design mix. The assumed values assume good site control; where control deviates, the codes require the value to be increased by 1 N/mm².
Related articles
Acceptance Criteria for Concrete Strength — IS 456 Table 11
The group-of-four mean, the individual-result limit and the small-pour exception, in full.
IS 456 Cube Test Acceptance Explained — Cl 16 & Table 11
What a failing result means, and the route the code gives from there.
Amit Haridas
Founder & Proprietor, ConcreteInfo. 25+ years experience in construction QA/QC, concrete technology, RMC plant operations, consulting and technical training across India. For mix design review, strength-acceptance scope or an IS 456 audit, contact amit@concreteinfo.in.
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