Tentative Guidelines for Design of Gap-Graded Cement Concrete Mixes for Road Pavements
1976 Edition

The initial section of IRC 59 presents essential formulas, charts, and specifications pertinent to the design of cement concrete mixes for road pavement, placing special emphasis on gap-graded concrete. The 28-day design strength S is computed using:

S = s (1 - t.v/100)

where s is the minimum required strength, t is the tolerance factor, and v is the coefficient of variation (Clause 2.4.2).

Tolerance factors for various sample sizes and tolerance levels are tabulated in Table 2.

Mix proportions follow the optimum void-filling concept (Clause 2.7), calculating volumes of coarse aggregate, fine aggregate, and cement paste while accounting for entrapped air and supplementary cement paste for workability. Key equations include:

• Void content n = (1 - bulk density / (1000 × specific gravity)) × 100% (Clause 2.6.2)
• Coarse aggregate weight Wa = V × da = (1 - v - v') × da (Equation 3)
• Fine aggregate weight Wx = v5 × d5 (Equation 4)
• Cement weight Wc = r × Wa (Equation 6)

Tables 4 and 5 provide typical values for specific gravity, bulk density, void content, and entrapped air in aggregates.

Water-cement ratio is selected based on cement strength at 7 days and desired design strength curves (Figures 1 and 2).

An example demonstrating the design process is included in the Appendix.

This section outlines critical design criteria as per IRC 59:

• Design Strength (S): Calculated by S = s (1 + t.v/100), with s as the minimum strength, t as the tolerance factor from Table 2, and v the coefficient of variation (Clause 2.4.2).

• Tolerance Factors (Table 2):

• Mix Proportioning Using Optimum Void-Filling:

  • Volume of single-size coarse aggregate V_a = (1 - v - v')
  • Volume of fine aggregate V_x = voids present in coarse aggregate
  • Volume of cement paste V_c = voids within fine aggregate
  • Water-cement ratio (r) to determine quantities of water and cement (Clauses 2.7.1 & 2.7.2).

• Entrapped Air Content (Table 5):

• Typical Specific Gravity, Bulk Density, and Void Content (Table 4):

• Example highlights include a design strength of 310 kg/cm² at 28 days, water-cement ratio set at 0.50, and mix proportions per cubic meter of water = 158.85 kg, cement = 317.7 kg, fine aggregate = 511.0 kg, coarse aggregate = 1424.0 kg.

These requirements ensure that the concrete mix achieves necessary strength, workability, and durability with proper quality control.

According to Clause 3.15 of IRC 59, the following tests are mandatory:

• Specific Gravity:

  • Cement: Tested per IS 269-1967; default value 3.15 if testing is not conducted.
  • Aggregates: Evaluated as per IS 2386 Part III-1963 including specific gravity, density, voids, absorption, and bulking.

• Bulk Density and Water Absorption: Determined on saturated surface-dry samples following IS 2386 Part III-1963.

• Particle Size Distribution: Conducted using sieve analysis according to IS 2386 Part I-1963.

• Aggregate Grading: Preference for single-size coarse aggregates adhering to gap grading guidelines (Clause 2.3).

• Concrete Design Strength: Calculated average strength S at 28 days using the relationship S = s(1 + t.v/100), where s is minimum specified strength, t is tolerance factor, and v is coefficient of variation.

• Tolerance Factors: Provided in Table 2 for varying tolerance levels and sample sizes.

• Typical Aggregate Properties: Specific gravity, bulk density, and void content as detailed in Table 4.

These tests ensure adherence to quality standards and facilitate accurate mix design for concrete pavements.

For gap-graded concrete, IRC 59 mandates omitting at least two, preferably three, consecutive aggregate sizes from a continuous gradation to obtain compatible aggregate distribution (Clause 1.2.3). Table 1 outlines suitable gradation ranges of coarse and fine aggregates dependent on the maximum coarse aggregate size. For instance, with a maximum size of 63 mm, single-size coarse aggregates between 63-50 mm are combined with finer aggregates in the ranges of 20-10 mm or 10-4.75 mm, associated with designated sand zones per IS 383. To prevent segregation, the concrete’s workability should be minimal, with slump limited to 0-12 mm, and compaction must be achieved exclusively through vibration (Clause 1.2.5). Additional parameters such as compressive strength targets, maximum aggregate size, and workability levels are specified in Clauses 2.1 and 2.2.

The concrete’s design strength in IRC 59 is determined by the formula S = s (1 + t.v/100), where S represents the mean design strength at 28 days, s is the minimum specified compressive or flexural strength, t is the tolerance factor sourced from Table 2, and v denotes the coefficient of variation expressed as a percentage (Clause 2.4.2). Table 2 provides values for t corresponding to various tolerance levels and sample quantities. For example, at a tolerance level of 1 in 15 and a coefficient of variation of 10%, the design strength for a specified strength of 200 kg/cm² is computed as 235 kg/cm². The water-cement ratio is selected based on 7-day cement compressive strength and target 28-day concrete strength, utilizing curves provided in Figure 1 (Clause 2.5). Approximate correlations between compressive and flexural strengths are illustrated in Figure 2. Mix proportions are derived employing the optimum void-filling method, factoring in bulk density, specific gravity, aggregate void content (Table 4), entrapped air (Table 5), and supplementary cement paste for workability (Clauses 2.6 and 2.7). An example demonstrating the entire design process is included in the Appendix.

IRC 59’s mix proportioning method based on the Optimum Void-Filling Principle involves filling voids in the coarse aggregate with finer aggregate (typically sand), and subsequently filling voids in the finer aggregate with cement paste (Clauses 2.6.1 and 2.7.1). The calculations per cubic meter of fresh concrete are as follows:

• Volume of single-size coarse aggregate: V = 1 - v - v', where v is the void content in coarse aggregate and v' is the volume of additional cement paste.
• Volume of fine aggregate: V_f = (v / 100) × V
• Volume of cement paste: V_c = (v_f / 100) × V_f, where v_f is the void content in finer aggregate.

Weights per cubic meter are computed using:

• Coarse aggregate weight: W_a = V × d_a = (1 - v - v') × d_a
• Fine aggregate weight: W_f = V_f × d_f = v × d_f
• Cement weight: W_c = V_c × S_e (specific gravity of cement)
• Water weight: W_w = r × W_c (r is the water-to-cement ratio by mass)

Entrapped air volume and additional cement paste for achieving workability are considered. Table 5 lists entrapped air percentages relative to maximum aggregate sizes. The supplementary cement paste volume v' typically ranges from 10-12%, adjusted depending on workability requirements and aggregate morphology (Clause 2.7.4).

Tables summarizing entrapped air and aggregate properties are provided to guide these calculations, ensuring optimized filling of voids to reduce water demand and enhance concrete performance.

The mix design in IRC 59 emphasizes workability and compaction controlled by the optimum void-filling concept and regulated water-cement ratio. Important considerations include:

• Entrapped air volume (v_e) and additional cement paste volume (v_p) are pivotal for adequate workability; for low slump concrete (0-25 mm), extra cement paste accounts for approximately 10-12% of the concrete volume (Clause 2.7.4).
• Entrapped air varies with maximum aggregate size, as detailed in Table 5, e.g., 1% air content for 40 mm aggregates.
• Mix weights are calculated as follows:
  • Coarse aggregate: W_a = (1 - v_e - v_p) × bulk density of coarse aggregate
  • Fine aggregate: W_x = voids in coarse aggregate × bulk density of fine aggregate
  • Cement and water quantities depend on selected water-cement ratio and cement specific gravity.
• Water-cement ratio is determined from design curves (Figure 1) based on 7-day cement strength and desired 28-day concrete strength (Clause 2.5).

Adjustments to extra cement paste volume are made according to observed slump variations (Clause 4.1). The example in the Appendix elaborates these calculations in detail, ensuring concrete achieves the necessary workability and compaction for performance and durability.

Modifications in mix proportions per IRC 59 adhere to the optimum void-filling principle through the following steps:

1. Void content (n) is calculated as: n = (1 - d / (1000 × s)) × 100% where d is bulk density (kg/m³), s is specific gravity (g/cm³) (Clause 2.6.2).

2. Mix weights per cubic meter of fresh concrete are computed as:

   • Coarse aggregate: W_a = V × d_a = (1 - v - v') × d_a
   • Fine aggregate: W_x = v_a × d_x
   • Cement and water amounts derived using the water-cement ratio (r) and cement’s specific gravity (S_e) (Clause 2.7.2).

3. Entrapped air volumes vary with maximum aggregate size (Table 5):

4. Additional cement paste volume is usually 10-12% of the total volume, adjusted ±1% based on aggregate form and grading gaps (Clause 2.7.4).

5. Slump variations affect extra cement paste volume by ±5% for each 12 mm change within water-cement ratio range 0.40–0.60 (Clause 4.1).

6. Design strength adjustment uses the formula S = s (1 - t.v /100) with parameters as defined earlier.

7. Typical aggregate properties are summarized in Table 4.

These procedures ensure that mix proportions are fine-tuned to attain the desired concrete strength and workability for road pavement applications.

IRC 59 includes a step-by-step demonstration for designing a cement concrete mix based on the optimum void-filling principle (Clause 4.75). Key calculation steps per cubic meter of fresh concrete involve:

• Coarse aggregate volume: Wa = V × da = (1 - v - v') × da
• Fine aggregate volume: Wx = v5 × d
• Cement paste volume: Wc = r × W (r is water-cement ratio)

Entrapped air volume (Ve) and additional cement paste volume (Vp) are factored in, with entrapped air values from Table 5:

Additional cement paste volume averages 10-12% of total concrete volume and is adjusted based on workability demands (Clause 2.7.4), with further modifications tied to slump changes (Clause 4.1).

The example in the Appendix details the stepwise computation, including selection of design strength, determination of water-cement ratio, and calculation of aggregate weights. For a 1 m³ mix with 40 mm aggregate size, entrapped air volume of 0.01 m³, and additional cement paste volume of 0.10 m³, the coarse aggregate occupies 0.89 m³, and weights are derived using bulk density figures.

Example mix proportions per cubic meter:

This methodology optimizes the use of aggregates and cement paste to meet performance criteria.

The Appendix provides an in-depth worked example illustrating the mix design process for gap-graded cement concrete based on the optimum void-filling principle. It includes:

• Calculation of design strength using S = s (1 - t.v/100), with s as minimum field strength, t the tolerance factor, and v the coefficient of variation (Clause 2.4.2).

• Tolerance factors for various tolerance levels and sample sizes detailed in Table 2.

• Mix volume proportions per cubic meter of fresh concrete:

  • Coarse aggregate volume Va = V - Ve - V'p (Equation 3)
  • Fine aggregate volume Vf = (voids in coarse aggregate) × Va / 100 (Equation 4)
  • Cement paste volume Vc = (voids in finer aggregate) × Vf / 100 + V'p (Equation 5)

• Entrapped air volumes for different maximum aggregate sizes are listed in Table 5.

• Typical aggregate properties such as specific gravity, bulk density, and void content are shown in Table 4.

• Calculated mix proportions for 1 cubic meter and per 50 kg cement bag are tabulated.

These comprehensive details assist engineers in designing concrete mixes that fulfill the strength, workability, and durability requirements for road pavement construction.