Concrete has become an indispensable construction material in the modern world. In the context of highway engineering and infrastructure development, Pavement Quality Concrete (PQC) forms the rigid backbone of our transportation networks. According to the present state-of-the-art, concrete has bypassed the stage of being a mere four-component system consisting of cement, water, coarse aggregate, and fine aggregate. Today, it can be a judicious combination of ingredients from more than ten distinct materials.
In the recent past, alongside the basic four ingredients, supplementary materials like fly ash, ground granulated blast furnace slag (GGBFS), silica fume, rice husk ash, metakaolin, superplasticizers, and various fibers are generally used in concrete. With this added complexity, having a standardized approach to mix proportioning is absolutely essential.
The objective of designing concrete mixes is to arrive at the most economical and practical combinations and proportions of different ingredients. This ensures the production of concrete that will meet the strict performance requirements under specified conditions of use.
Reference: IRC 44:2017 – Guideline for Cement Concrete Mix Design For Pavements
1. The Core Principles of Concrete Mix Design
Before diving into the mathematics, it is vital to understand the underlying philosophy of mix design. The basic principle of concrete mix design is to select the proportion of all the ingredients on the basis of their absolute volume, ensuring that the total absolute volume of the compacted concrete is 1 m3.
The basic principles which underline the proportioning of mixes are Abram’s law for strength development and Lyse’s rule for making a mix with adequate workability for placement in a dense state. This enables the strength development as contemplated.
While compressive strength is often taken as an index of acceptability from a practical point of view, it does not necessarily satisfy the requirements of durability unless examined under specific contexts. Therefore, mix proportioning is generally carried out for a particular compressive strength or flexural strength requirement. This ensures that the fresh concrete possesses adequate workability for placement without segregation and bleeding, while ultimately attaining a dense state.
An integral part of concrete mix proportioning is the preparation of trial mixes and effecting adjustments to such trials. This strikes a delicate balance between the requirements of placement (workability), strength, and durability. Ultimately, as a guarantor of quality in construction, the contractor should carry out the mix proportioning, and the Engineer-in-Charge must approve the finalized mix.
2. Decoding the Materials for PQC
A successful mix design begins with selecting high-quality materials. Here are the parameters and limits set for the ingredients used in pavement concrete.
2.1 Cement
Any of the following types of cement capable of achieving the design strength may be used, subject to the condition that they satisfy their respective Indian Standard specifications:
- Ordinary Portland Cement (OPC), 43 Grade & 53 Grade.
- Portland-Pozzolana Cement (PPC).
- Portland Slag Cement (PSC).
- Composite Cement.
Crucially, the minimum 28-day compressive strength of the chosen cement should not be less than 43 MPa.
2.2 Aggregates
Aggregates form the bulk of the concrete matrix and heavily influence its mechanical properties. Aggregates for pavement concrete shall comply with IS:383.
Coarse Aggregates:
- They must consist of clean, hard, strong, dense, non-porous, and durable pieces of crushed stone or crushed gravel.
- They shall be devoid of pieces of disintegrated stone, soft, flaky, elongated, very angular, or splintery pieces.
- The combined flakiness and elongation index shall not be more than 35 per cent.
- The Aggregate Impact Value (AIV) shall not be more than 30 per cent.
- The maximum size of coarse aggregate shall not exceed 31.5 mm in PQC.
- No aggregate which has water absorption more than 2 per cent shall be used in the concrete mix. If aggregates of 2 per cent absorption are unavailable, a higher value subject to a maximum of 3 per cent may be allowed, provided other engineering properties are satisfied.
Fine Aggregates:
- Fine aggregates shall be free from soft particles, clay, shale, loam, cemented particles, mica, and organic matter.
- Fine aggregates possessing water absorption of more than 3 per cent shall not be used.
- The fine aggregate shall not contain material passing the 75-micron IS sieve (wet sieving) exceeding 3 per cent by weight for natural sand, 12 per cent for crushed stone sand, or 8 per cent for a blend of both.
- The use of crushed stone sand is permitted in PQC.
Combined Gradation: It is highly recommended to achieve a specific combined grading of fine and coarse aggregates. Graded coarse aggregates or single-sized coarse aggregates of nominal size shall be mixed in suitable proportions with fine aggregate to achieve the combined grading requirement.
2.3 Mineral and Chemical Admixtures
Admixtures are heavily utilized to tweak the fresh and hardened properties of the concrete.
- Chemical Admixtures: Retarders, plasticizers, and superplasticizers conforming to IS:9103 may be used up to 0.5 per cent, 1 per cent, and 2 per cent by mass of cementitious materials, respectively. However, the dosages of polycarboxylate-based admixture shall not exceed 1.0 per cent. In freezing weather, the use of an air-entraining admixture is recommended to counter the freezing and thawing effect.
- Pozzolanas (Mineral Admixtures): Fly ash may be used as a partial replacement for Portland cement up to a maximum dosage of 25 per cent by mass of cementitious materials. Silica fume is usually used in proportions of 5 to 10 per cent and is generally advantageous for higher grades of concrete (M50 and above). Metakaolin may be used up to 20 per cent. Ground granulated blast furnace slag (GGBFS) may be mixed up to 50 per cent by weight of cementitious material.
2.4 Water and Fibers
Potable water is generally considered satisfactory for mixing and curing. It shall be clean and free from injurious amounts of oil, salt, acid, vegetable matter, or other harmful substances. Additionally, fibers (carbon, steel, or polymeric synthetic) may be added to concrete for special applications to enhance properties.
3. Data Required for Mix Proportioning
Before attempting calculations, you must gather all the necessary input parameters. The following data are required for the mix proportioning of a particular grade of concrete:
- Grade designation (required compressive or flexural strength)
- Type of cement
- Maximum nominal size of aggregate
- Minimum cement/cementitious materials content and maximum water-cement ratio
- Workability required at the time of placement (slump)
- Degree of site control (or established standard deviation)
- Type and properties of fine and coarse aggregates
- Details of chemical and mineral admixtures (if any)
4. The Step-by-Step PQC Mix Design Process
Step 1: Determine the Target Strength
To ensure that not more than 5 per cent of test results fall below the characteristic strength, the concrete mix is designed for a higher target mean compressive strength or flexural strength.
Based on Flexural Strength: Calculate using both equations and select the higher value:
f’cr = fcr + 1.65 x Sf
OR
f’cr = fcr + 0.55
(Where f’cr is target mean flexural strength, fcr is characteristic flexural strength, and Sf is the standard deviation).
Based on Compressive Strength: Calculate using both equations and select the higher value:
f’ck = fck + 1.65 x Sc
OR
f’ck = fck + X
(Where X is a margin value depending on the grade, e.g., 6.5 for M40, 8.0 for M65).
Where sufficient test results for a particular grade of concrete are not available, assumed standard deviation values can be utilized for proportioning the mix in the first instance. For example, the assumed standard deviation for M40 compressive strength is 5.0 N/mm2, and for 4.5 N/mm2 flexural strength, it is 0.40 N/mm2.
Step 2: Estimate Air Content
Even without air-entraining agents, concrete naturally entraps some air. The absolute volume of air has been considered as 1.5 per cent for 9.5 mm, 1.0 per cent for 19 mm, and 0.8 per cent for 31.5 mm maximum size of aggregate.
Step 3: Select the Water-Cement Ratio
The preliminary free water-cement ratio (by mass) corresponding to the design strength at 28 days can be selected from established relationships or standard tables. For instance, to achieve a target flexural strength of 5.0 N/mm2 using OPC-43, the approximate w/c ratio is 0.34.
Crucially, the maximum water-cement ratio shall be restricted to 0.40 for the respective grade as per IRC:15 specifications. If supplementary cementitious materials are used, this becomes the water-cementitious materials ratio (w/cm).
Step 4: Determine Water Content and Admixture Dosage
The quantity of approximate mixing water per unit volume of concrete for saturated surface dry (SSD) aggregate is standardized for a 50 mm slump.
For angular coarse aggregate, the suggestive water content is 165 kg/m3 for a 31.5 mm aggregate, and 186 kg/m3 for a 19 mm aggregate.
This suggested water content may be reduced by approximately 10 kg for sub-angular aggregates, 15 kg for gravel with some crushed particles, and 20 kg for rounded gravel.
Furthermore, water-reducing admixtures or superplasticizing admixtures usually decrease water content by 5 to 10 per cent, and by 20 per cent and above, respectively, at appropriate dosages.
Step 5: Calculate Cementitious Material Content
The cement and supplementary cementitious material content per unit volume is calculated from the free water-cement ratio and the determined quantity of water.
This calculated value must be checked against regulatory limits. The minimum cement/cementitious material content shall be 360 kg/m3, and the maximum cement content (not including mineral admixtures) shall be 450 kg/m3. If the calculated amount is lower than the stipulated minimum, the greater of the two values shall be adopted.
Step 6: Estimate Coarse and Fine Aggregate Proportions
Aggregates of essentially the same nominal maximum size, type, and grading will produce concrete of satisfactory workability when a given volume of coarse aggregate is used per unit volume of concrete.
For a water-cement ratio of 0.50, the volume of coarse aggregate per unit volume of total aggregate for a 31.5 mm aggregate is 0.68 for Zone III sand, 0.65 for Zone II sand, and 0.63 for Zone I sand.
This baseline must be adjusted for different w/c ratios: the proportion of the volume of coarse aggregates is increased at the rate of 0.01 m3 for every decrease in water-cement ratio by 0.05, and decreased at the same rate for every increase in water-cement ratio by 0.05.
Step 7: Absolute Volume Mix Calculations
With all ingredients estimated except the aggregate masses, absolute volume calculations are performed. The volumes of cementitious material, water, and chemical admixture are determined by dividing their mass by their respective specific gravity and multiplying by 1/1000.
Subtracting the summation of these volumes (along with entrapped air) from 1 m3 yields the total absolute volume available for aggregates. This remaining volume is divided into coarse and fine fractions based on the ratios calculated in Step 6. The final masses are determined by multiplying these absolute volumes by their respective specific gravities and 1000.
5. Comprehensive Example: Mix Proportioning Based on Flexural Strength
To truly understand the process, let’s walk through a real-world example of designing a concrete mix for a 4.5 N/mm2 Flexural Strength pavement.
5.1 Stipulations and Data
- Target Grade: 4.5 N/mm2 Flexural Strength
- Cement: OPC 43 grade (Specific Gravity: 3.15)
- Maximum Nominal Size of Aggregate: 31.5 mm
- Aggregates: Crushed angular coarse aggregate (Specific Gravity: 2.74, Water absorption: 0.5%). Fine aggregate (Specific Gravity: 2.62, Water absorption: 1.0%, Zone II grading). Both have nil surface moisture.
- Minimum Cement Content: 360 kg/m3
- Maximum w/c ratio: 0.40
- Target Slump: 25 ± 10 mm
- Admixture: Superplasticizer
5.2 Step-by-Step Calculation
1. Design Flexural Strength: We use the standard deviation for 4.5 N/mm2, which is 0.40 N/mm2.
- Equation 1: 4.5 + 1.65 x 0.40 = 5.16 N/mm2
- Equation 2: 4.5 + 0.55 = 5.05 N/mm2
Target strength is the higher value: 5.16 N/mm2.
2. Approximate Air Content: For 31.5 mm aggregate, entrapped air is 0.8 per cent.
3. Selection of Water-Cement Ratio: For a target strength of 5.16 N/mm2 using OPC-43, the interpolated w/c ratio is 0.32. This is safely lower than the maximum 0.40.
4. Selection of Water Content: The base water content for a 31.5 mm aggregate at a 50 mm slump is 165 kg/m3.
We adjust this for our 25 mm target slump: 165 x (97/100) = 160 kg/m3 (approx).
Since we are using a superplasticizer, we can assume a 20 per cent water reduction.
Reduced water content = 160 x 0.80 = 128 kg/m3.
5. Calculation of Cement Content: Cement content = 128 / 0.32 = 400 kg/m3.
This satisfies the requirement since 400 kg/m3 is between the minimum (360) and maximum (450) limits.
6. Proportion of Aggregate Volumes: For a 31.5 mm aggregate with Zone II sand at a 0.50 w/c ratio, the coarse aggregate volume is 0.65.
We adjust this for our 0.32 w/c ratio.
The difference is (0.50 – 0.32) / 0.05 = 3.6 units of 0.01.
Adjusted coarse aggregate ratio = 0.65 + 0.036 = 0.686.
Fine aggregate ratio = 1 – 0.686 = 0.314.
7. Mix Calculations (Absolute Volume):
- Volume of concrete = 1 – 0.008 = 0.992 m3
- Volume of cement = (400 / 3.15) x (1 / 1000) = 0.127 m3
- Volume of water = (128 / 1) x (1 / 1000) = 0.128 m3
- Volume of admixture (at 1.0% dosage, SG 1.2) = (4.0 / 1.2) x (1 / 1000) = 0.0033 m3
- Remaining volume for aggregates = 0.992 – (0.127 + 0.128 + 0.0033) = 0.7337 m3
Now, calculate aggregate masses:
- Mass of coarse aggregate = 0.7337 x 0.686 x 2.74 x 1000 = 1379 kg/m3
- Mass of fine aggregate = 0.7337 x 0.314 x 2.62 x 1000 = 604 kg/m3
5.3 Final SSD Mix Proportions (Trial 1)
- Cement: 400 kg/m3
- Water: 128 kg/m3
- Fine Aggregate: 604 kg/m3
- Coarse Aggregate: 1379 kg/m3
- Chemical Admixture: 4.0 kg/m3
- w/c ratio: 0.32
6. Adjusting for Aggregate Moisture Conditions
The quantities calculated above assume the aggregates are in a Saturated Surface Dry (SSD) condition. However, at the construction site, aggregates are rarely in perfect SSD condition.
They might be bone dry or completely wet due to rain.
Adjustments for Dry Aggregates:
If aggregates are dry, they will absorb mixing water, ruining your w/c ratio and dropping the slump.
- The quantities of both coarse and fine aggregates shall be divided by 1 plus their respective water absorptions to find the dry mass.
- The mixing water content must be increased by an amount equal to the difference in mass of the aggregate in SSD condition and the dry condition.
(In our example, dry sand requires 6 kg extra water, and dry coarse aggregate requires 7 kg extra water, bringing the total mixing water to 141 kg/m3).
Adjustments for Wet Aggregates:
Wet aggregates contribute surface moisture to the mix, which will increase the w/c ratio and potentially cause bleeding or segregation.
- Determine the dry mass by dividing the SSD mass by 1 plus the water absorption.
- Multiply this dry mass by 1 plus the total moisture content to get the mass of the wet aggregate.
- The surface moisture is the wet mass minus the SSD mass.
- The required batching water content shall be reduced by an amount equal to the mass of surface moisture present in the aggregates.
7. The Crucial Final Step: Trial Mixes
Theoretical calculations are only the starting point. The calculated mix proportions must be checked by means of trial batches.
- Trial Mix 1: Batch the concrete as calculated and measure its workability.
Observe the mix carefully for freedom from segregation and bleeding, and note its finishing properties. - Adjustments: If the measured workability is different from the stipulated value, the water and/or admixture content shall be adjusted suitably.
With this adjustment, the mix proportion is recalculated while keeping the free w/c ratio at the pre-selected value.
This becomes Trial Mix No. 2. - Bracketing: Make two more trial mixes (No. 3 and 4) keeping the water content the same as Trial Mix No. 2, but varying the free water-cement ratio by ± 10 per cent of the preselected value.
Mixes 2 through 4 provide sufficient information, including the relationship between compressive strength and water-cement ratio, from which the final field proportions can be confidently selected.
Remember, the concrete for field trials shall be produced by the actual methods of concrete production intended for the site.
For the recommended mix proportions, the yield of the mix shall be checked, and the proportions adjusted proportionately to ensure the mix yields exactly 1 m3 of concrete.
Furthermore, if the concrete is produced at a Ready Mixed Concrete (RMC) plant, it is generally designed for a higher slump initially to account for transit loss over long distances.
Conclusion
Designing Pavement Quality Concrete is a rigorous scientific process that demands a deep understanding of materials, precise mathematics, and practical testing.
By following the IRC:44-2017 guidelines detailed above (i.e carefully selecting materials, accurately calculating absolute volumes, and conducting thorough trial mixes) engineers can ensure the construction of durable, high-performance rigid pavements that will withstand the test of time and traffic.
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Frequently Asked Questions (FAQs) on PQC Mix Design
Q1: What is the maximum allowable size of coarse aggregate in Pavement Quality Concrete (PQC)?
A: According to the IRC:44-2017 guidelines, the maximum size of coarse aggregate shall not exceed 31.5 mm in standard PQC. For high-strength concrete (M65 and above), a smaller maximum size like 19 mm, 12.5 mm, or 9.5 mm is suggested depending on the specific grade.
Q2: What is the minimum cement content and maximum water-cement ratio for standard PQC?
A: To ensure adequate strength and durability, the minimum cementitious material content must be 360 kg/m³. Additionally, the maximum water-cement ratio is strictly restricted to 0.40 for standard pavement grades. The maximum cement content, excluding mineral admixtures, is 450 kg/m³.
Q3: Can mineral admixtures like fly ash or slag be used in PQC? A: Yes, mineral admixtures are highly recommended and permitted. Fly ash can be used as a partial replacement for Portland cement up to a maximum dosage of 25% by mass of cementitious materials. Ground Granulated Blast Furnace Slag (GGBFS) can be used up to 50% by weight of the cementitious material.
Q4: Is crushed stone sand allowed as a fine aggregate in pavement concrete?
A: Yes, the use of crushed stone sand is permitted in PQC. However, to maintain the quality of the mix, its percentage of fines passing the 75-micron sieve (wet sieving) must not exceed 12% by weight.
Q5: Why are trial mixes necessary if I have already calculated the mix proportions? A: Theoretical calculations only provide a starting point. Trial mixes are essential to verify that the calculated proportions actually meet the practical requirements for placement, such as workability, freedom from segregation, and proper finishing properties. If the fresh concrete does not behave as expected, the water or chemical admixture content must be adjusted in subsequent trials before field application.
Q6: What is Pervious Concrete, and how does its mix design differ from normal PQC?
A: Pervious concrete is a zero-slump, open-graded material with sufficient interconnected voids (typically 15% to 35%) that allows water to readily pass through. Unlike normal concrete, the conventional water-cement ratio versus compressive strength relationship does not apply. Instead, its mix proportioning focuses on establishing the minimum paste volume necessary to bind aggregate particles together while maintaining the critical void structure for drainage.