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Introduction

Concrete mix design is the process of selecting suitable quantities of cement, water, fine aggregate, coarse aggregate, chemical admixture and entrapped air to produce concrete with the required strength, durability and workability.

This article presents an illustrative M40 concrete mix design based on IS 10262:2019, Concrete Mix Proportioning—Guidelines, and the durability requirements of IS 456:2000.

The calculation is based on the following example:

• Grade of concrete: M40
• Exposure condition: Moderate
• Nominal maximum aggregate size: 20 mm
• Aggregate type: Angular crushed aggregate
• Fine aggregate: Grading Zone III
• Cement: OPC 43 grade
• Placement: Pumped concrete
• Required slump: 75 mm at the point of placement
• Chemical admixture: ECMAS HP 890
• Site control: Good
• No supplementary cementitious material is considered

This is a preliminary trial mix. The final mix must be confirmed through laboratory and field trials using the actual cement, aggregates, admixture, batching plant and placing conditions.

Applicable Codes and References

The following standards are used:

1. IS 10262:2019, Concrete Mix Proportioning—Guidelines.
2. IS 456:2000, Plain and Reinforced Concrete—Code of Practice.
3. IS 383:2016, Coarse and Fine Aggregate for Concrete—Specification.
4. IS 9103, Chemical Admixtures for Concrete.
5. IS 269:2015, Ordinary Portland Cement—Specification, as applicable to the cement manufacturer’s certificate.
6. ECMAS HP 890 product technical data sheet.

The following provisions of IS 10262:2019 are used:

• Clause 4.2 and Tables 1 and 2: Target mean strength
• Clause 5.1 and Figure 1: Selection of water-cement ratio
• Table 3: Entrapped air
• Clause 5.3 and Table 4: Water and admixture content
• Clause 5.4: Cement content
• Clause 5.5 and Table 5: Coarse aggregate proportion
• Clause 5.7: Absolute-volume method
• Clause 5.8: Trial mixes and reporting

Design Basis and Assumptions

The following data are adopted for this illustrative M40 mix design.

All aggregate quantities calculated below are initially reported on a saturated surface-dry, or SSD, basis.

The moisture correction must be performed again at the batching plant using actual moisture test results.

1. Determination of Target Mean Strength

According to IS 10262:2019, the target mean strength is calculated using the following two expressions. The greater value is adopted.

Target strength 1 = fck + 1.65S

Target strength 2 = fck + X

For M40 concrete, the assumed standard deviation S is 5.0 MPa and the value of X is 6.5 MPa.

Using the standard deviation

Target strength 1 = 40 + 1.65 × 5

Target strength 1 = 48.25 MPa

Using the grade factor

Target strength 2 = 40 + 6.5

Target strength 2 = 46.50 MPa

The greater value is adopted.

Adopted target mean strength = 48.25 MPa at 28 days

The value S = 5.0 MPa is an assumed standard deviation for this initial calculation. If at least 30 valid strength results are available for similar concrete, the actual standard deviation should be calculated and used.

2. Selection of Water-Cement Ratio

2.1 Strength requirement

For OPC 43 grade cement, Curve 2 of Figure 1 in IS 10262:2019 may be used when actual 28-day cement strength data is not available.

For a target concrete strength of 48.25 MPa, the preliminary free water-cement ratio read from the OPC 43 curve is approximately:

Strength-based free w/c ratio = 0.36

This is an approximate graphical value. The actual relationship between strength and free water-cement ratio depends on the cement, aggregates, admixture and other materials used. The final value must be confirmed by trial batches.

2.2 Durability requirement

For reinforced concrete under moderate exposure, IS 456:2000 gives the following durability limits:

The strength-based ratio is 0.36, and the maximum ratio for the adopted moderate exposure is 0.50.

Adopted w/c ratio = lower of 0.36 and 0.50

Adopted free water-cement ratio = 0.36

The adopted value also satisfies the stricter severe-exposure limit of 0.45. However, the design basis used in this example is moderate exposure.

Important note about admixture

A superplasticiser does not automatically justify subtracting a fixed value, such as 0.05, from the water-cement ratio.

The correct procedure is:

1. Select the preliminary water-cement ratio from strength and durability requirements.
2. Use the admixture to reduce water demand while maintaining the required slump.
3. Confirm the actual water reduction through trials.
4. Maintain the selected water-cement ratio unless the design is deliberately revised and rechecked.

For this example, a 20% reduction in water demand is assumed for the preliminary trial. This is not a guaranteed value for every cement or aggregate combination.

3. Selection of Water Content

IS 10262:2019 Table 4 gives a water content of 186 kg/m³ for 20 mm angular aggregate at 50 mm slump.

The selected slump is 75 mm. IS 10262:2019 permits an approximate 3% adjustment for every 25 mm change in slump.

Estimated water content at 75 mm slump:

Water at 75 mm slump = 186 × (1 + 3/100)

Water at 75 mm slump = 191.58 kg/m³

Therefore, before admixture reduction:

Estimated water content before admixture = 191.6 kg/m³

Water reduction using superplasticizer

Assume that ECMAS HP 890 provides a 20% reduction in water demand at the selected trial dosage.

Water after admixture reduction = 191.58 × (1 − 20/100)

Water after admixture reduction = 153.264 kg/m³

Adopt:

Design water content = 153.3 kg/m³

The 20% reduction must be confirmed using the actual cement and aggregates. If the trial does not achieve the required slump or workability retention, the water and admixture quantities must be adjusted.

4. Calculation of Cement Content

The cement content is calculated from the adopted water-cement ratio:

Cement content = Water content ÷ Water-cement ratio

Cement content = 153.264 ÷ 0.36

Cement content = 425.73 kg/m³

Adopt:

Cement content = 425.7 kg/m³, or approximately 426 kg/m³

Durability check

• Minimum cement content for moderate exposure = 300 kg/m³
• Calculated cement content = 425.7 kg/m³

Therefore:

425.7 kg/m³ > 300 kg/m³

The minimum cement-content requirement for moderate exposure is satisfied.

The calculated cement content is also below the 450 kg/m³ limit normally referenced under IS 456:2000 Clause 8.2.4.2. Project specifications or special durability requirements may impose a different limit and must be checked separately.

5. Chemical Admixture Content

Assume ECMAS HP 890 dosage of 1.1% by mass of cement.

Admixture content = 1.1/100 × 425.73

Admixture content = 4.68 kg/m³

Adopt:

ECMAS HP 890 = 4.7 kg/m³

The 1.1% dosage is an assumption for this worked example. It is not a fixed value required by IS 10262:2019. The final dosage must be established by trial batching and the manufacturer’s technical data.

Because the admixture is a liquid product, any water contribution from the admixture should be considered in the final batch calculation. The supplier’s current technical data sheet should be used for the final production mix.

6. Estimation of Coarse Aggregate Proportion

IS 10262:2019 Table 5 gives the following coarse aggregate volume fraction at a water-cement ratio of 0.50:

For 20 mm angular aggregate and Zone III fine aggregate:

Coarse aggregate fraction at w/c = 0.50 = 0.64

The value 0.62 applies to Zone II fine aggregate, not Zone III.

Adjustment for the adopted water-cement ratio

The adopted water-cement ratio is 0.36, which is 0.14 lower than 0.50.

IS 10262:2019 permits an increase of 0.01 in the coarse aggregate fraction for every 0.05 decrease in the water-cement ratio.

Increase in coarse aggregate fraction = (0.50 − 0.36) ÷ 0.05 × 0.01

Increase in coarse aggregate fraction = 0.028

Corrected coarse aggregate fraction = 0.64 + 0.028

Corrected coarse aggregate fraction = 0.668

Therefore, before the pump adjustment:

Corrected coarse aggregate fraction = 0.668

Adjustment for pump placement

For pumped concrete, the estimated coarse aggregate content may be reduced by up to 10% when necessary to improve pumpability.

For this preliminary pumpable trial, a 10% reduction is assumed:

Coarse aggregate fraction for pumping = 0.668 × (1 − 10/100)

Coarse aggregate fraction for pumping = 0.6012

The fine aggregate fraction is:

Fine aggregate fraction = 1 − 0.6012

Fine aggregate fraction = 0.3988

Therefore:

Adopted coarse aggregate fraction = 0.6012

Adopted fine aggregate fraction = 0.3988

The 10% pump adjustment is an assumed preliminary adjustment. It must be confirmed by trial batches. If the mix is sufficiently workable without this adjustment, the unadjusted value of 0.668 may be used and the aggregate quantities recalculated.

7. Absolute-Volume Calculation

The absolute-volume method is used to calculate the quantities of fine and coarse aggregate.

7.1 Absolute volume of cement

Volume of cement = 425.73 ÷ (3.16 × 1000)

Volume of cement = 0.134726 m³

7.2 Absolute volume of water

Volume of water = 153.264 ÷ (1.00 × 1000)

Volume of water = 0.153264 m³

7.3 Absolute volume of admixture

Volume of admixture = 4.68 ÷ (1.07 × 1000)

Volume of admixture = 0.004377 m³

7.4 Volume of entrapped air

For 20 mm aggregate, the adopted entrapped air content is 1%:

Volume of entrapped air = 1/100 × 1.00

Volume of entrapped air = 0.010000 m³

7.5 Volume of total aggregate

Volume of total aggregate = 1 − (volume of cement + volume of water + volume of admixture + volume of air)

Volume of total aggregate = 1 − (0.134726 + 0.153264 + 0.004377 + 0.010000)

Volume of total aggregate = 0.697634 m³

7.6 Mass of coarse aggregate

Mass of coarse aggregate = volume of total aggregate × coarse aggregate fraction × specific gravity of coarse aggregate × 1000

Mass of coarse aggregate = 0.697634 × 0.6012 × 2.66 × 1000

Mass of coarse aggregate = 1115.65 kg/m³

Adopt:

Coarse aggregate, SSD = 1116 kg/m³

7.7 Mass of fine aggregate

Mass of fine aggregate = volume of total aggregate × fine aggregate fraction × specific gravity of fine aggregate × 1000

Mass of fine aggregate = 0.697634 × 0.3988 × 2.72 × 1000

Mass of fine aggregate = 756.75 kg/m³

Adopt:

Fine aggregate, SSD = 757 kg/m³

8. Absolute-Volume Summary

The absolute-volume calculation confirms that the total volume is approximately 1.00 m³.

9. Preliminary M40 Mix Proportions per Cubic Metre

The calculated quantities are shown below. The first column gives the calculated value and the second gives a practical rounded value for the preliminary trial.

Mix ratio by mass

The mass ratio is calculated by dividing each aggregate quantity by the cement content.

Fine aggregate ratio = 756.75 ÷ 425.73 = 1.78

Coarse aggregate ratio = 1115.65 ÷ 425.73 = 2.62

Therefore, the approximate preliminary mass proportion is:

Cement : Fine aggregate : Coarse aggregate = 1 : 1.78 : 2.62

The adopted water-cement ratio is:

Free w/c ratio = 0.36

The admixture dosage is:

ECMAS HP 890 = 1.1% by mass of cement

This is a calculated starting point for trial batching. It should not be treated as a final approved site mix without test results.

10. Moisture Corrections at the Batching Plant

The aggregate quantities above are on an SSD basis. Actual aggregate stockpiles may be wet, saturated surface-dry, or partially dry.

If moisture content and absorption are expressed as percentages of oven-dry aggregate mass, the wet batch mass may be estimated from:

Wet batch mass = SSD mass × (100 + moisture content) ÷ (100 + absorption)

The free-water contribution from the aggregate is:

Free water from aggregate = SSD mass × (moisture content − absorption) ÷ (100 + absorption)

The water to be added at the mixer is:

Water to be added = design water − total free water contributed by aggregates

Moisture correction using the assumed data

For the assumed coarse aggregate condition, the aggregate is drier than SSD and requires approximately 5.55 kg of water to reach the SSD condition.

Approximate water to be added at the mixer:

Water to be added = 153.264 − (0 − 5.55)

Water to be added = 158.81 kg/m³

Thus, using only the assumed moisture values, the preliminary dry-aggregate batch would be approximately:

These values are examples only. Actual daily moisture test results must be used for production batching.

11. Trial Mix Procedure

The calculated mix proportions must be checked using trial batches before approval for construction.

Trial Mix 1

Prepare the calculated mix using the corrected aggregate moisture values and measure:

• Slump
• Slump retention
• Segregation
• Bleeding
• Finishability
• Air content
• Concrete temperature
• Density or yield
• Pumpability

If the measured workability is different from the specified value, adjust the water and/or admixture content while maintaining the selected free water-cement ratio.

Trial Mix 2

Recalculate the mix while maintaining the selected free water-cement ratio of 0.36. Check the fresh properties again using the same mixing sequence and equipment intended for the project.

Trial Mixes 3 and 4

Prepare additional trials with the water-cement ratio varied by approximately ±10% around the selected value, while recording all changes in material quantities.

The trial batches should be produced using the same cement, aggregate sources, moisture condition, batching plant, mixer, transport method and placing method intended for the project.

The final mix should be selected only after reviewing:

• 7-day compressive strength
• 28-day compressive strength
• Workability and slump retention
• Segregation and bleeding
• Pumpability
• Surface finish
• Density and yield
• Variability of test results

12. Important Limitations of the Calculation

This example is not a universal M40 nominal mix. The final proportions may change because of:

• Actual 28-day strength of the cement
• Aggregate grading and particle shape
• Fine aggregate grading zone
• Aggregate absorption and daily moisture
• Aggregate surface texture
• Temperature and transport time
• Required slump retention
• Actual admixture performance
• Pumping distance and line configuration
• Project-specific durability requirements

The final approved mix must be based on actual material test results and satisfactory trial-batch performance.

13. Final Result

For the stated assumptions, the preliminary M40 mix per cubic metre is:

Preliminary M40 trial mix per m³: 426 kg cement + 153 kg design water + 757 kg fine aggregate + 1116 kg coarse aggregate + 4.7 kg ECMAS HP 890, with a free w/c ratio of 0.36.

The final approved mix must be confirmed through laboratory trials, strength testing, workability checks and field verification using the actual project materials.

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