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

The Introduction of IRC 59 provides key formulas, tables, and specifications for cement concrete mix design for road pavements, emphasizing gap-graded concrete. The design strength S at 28 days is calculated by:

S = s (1 - t.v/100)
where s = minimum specified strength, t = tolerance factor, v = coefficient of variation (Clause 2.4.2).

Table 2 lists tolerance factors t for different tolerance levels and sample sizes.

Mix proportions are based on the optimum void-filling principle (Clause 2.7), with volumes of coarse aggregate, finer aggregate, and cement paste calculated considering entrapped air and extra cement paste for workability. Key formulas include:

• Void content n = (1 - bulk density/(1000 × specific gravity)) × 100% (Clause 2.6.2)
• Weight of coarse aggregate Wa = V × da = (1 - v - v') × da (Eqn. 3)
• Weight of finer aggregate Wx = v5 × d5 (Eqn. 4)
• Weight of cement Wc = r × Wa (Eqn. 6)

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

Water-cement ratio selection is guided by 7-day cement strength and design strength curves (Fig. 1 and 2).

A worked example illustrates the procedure (Appendix).

Sources: Clause 2.4.2, Table 2, Clause 2.6.2, Clause 2.7, Table 4, Table 5, Fig. 1, Fig. 2

Key design stipulations from IRC 59 include the following:

• Design Strength of Concrete (S): The average strength to design for is given by the formula S = s (1 + t.v/100), where s is the minimum specified strength, t is a tolerance factor from Table 2, and v is the coefficient of variation (Clause 2.4.2).

• Tolerance Factors (t) Table:

• Mix Proportioning by Optimum Void-Filling Principle:

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

• Entrapped Air Content (Table 5):

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

• Worked Example Highlights:
  • Design strength calculated as 310 kg/cm² for 28 days.
  • Water-cement ratio selected as 0.50 from design curves.
  • Mix proportions per m³: Water = 158.85 kg, Cement = 317.7 kg, Fine Aggregate = 511.0 kg, Coarse Aggregate = 1424.0 kg.

These stipulations ensure concrete mix design meets strength, workability, and durability requirements with quality control accounted for (Clauses 2.4, 2.7, 3.15, and Appendix example).

Sources: Clause 2.4.2, Table 2, Clause 2.7.1, Table 4, Table 5, Clause 3.15, IRC 59 Appendix

Key tests for materials as per IRC 59 Clause 3.15 include:

• Specific Gravity:

  • Cement: IS 269-1967 (Ordinary, Rapid Hardening, Low Heat Portland Cement) with assumed value 3.15 if test not done.
  • Aggregates: IS 2386 Part III-1963 (Specific Gravity, Density, Voids, Absorption, Bulking).

• Bulk Density and Water Absorption: Bulk density of saturated surface-dry samples and water absorption per IS 2386 Part III-1963.

• Sieve Analysis: IS 2386 Part I-1963 for particle size distribution.

• Aggregate Grading: Prefer single-size coarse aggregate with gap grading principles (Clause 2.3).

• Design Strength of Concrete: Average design strength S at 28 days is calculated by

  [ S = s \left(1 + \frac{t v}{100} \right) ]

  where s = minimum specified strength, t = tolerance factor (from Table 2), v = coefficient of variation (%).

• Tolerance Factors (Table 2):

• Approximate Specific Gravity, Bulk Density, and Void Content of Aggregates (Table 4):

These tests and specifications ensure quality control and proper mix design for concrete used in pavements and other structures.

Sources: Clause 3.15, Clause 2.3, Clause 2.4, Table 2, Table 4

For aggregate grading in gap-graded concrete as per IRC 59, the key specification is to eliminate at least two, preferably three, successive sizes of aggregates from the continuous grading range to achieve compatible gradation (Clause 1.2.3). Table 1 provides suggested compatible gradation ranges for coarse and fine aggregates based on the maximum size of coarse aggregate. For example, for a maximum aggregate size of 63 mm, single-size coarse aggregates of 63-50 mm are used with 2 or 3 gaps, and compatible finer aggregates range from 20-10 mm or 10-4.75 mm, with corresponding sand zones (IS: 383) specified. Workability for gap-graded mixes should be low (slump 0-12 mm) to avoid segregation, and compaction must be by vibration only (Clause 1.2.5). Material tests and mix design parameters such as compressive strength, maximum aggregate size, and workability degree are also specified (Clause 2.1 and 2.2).

Sources: Clause 1.2.3, Clause 1.2.5, Clause 2.1, Clause 2.2, Table 1.2

The design strength of concrete in IRC 59 is governed by the equation S = s (1 + t.v/100), where S is the average design strength at 28 days, s is the specified minimum compressive or flexural strength, t is the tolerance factor from Table 2 depending on the tolerance level, and v is the coefficient of variation in percent (Clause 2.4.2). Table 2 provides values of t for different tolerance levels and sample sizes. For example, for a tolerance level of 1 in 15 and coefficient of variation 10%, the design compressive strength for 200 kg/cm² specified strength is 235 kg/cm² (Table 2). The water-cement ratio is selected based on the 7-day compressive strength of cement and desired 28-day concrete strength using curves in Fig. 1 (Clause 2.5). Approximate relationships between compressive and flexural strength are given in Fig. 2. Mix proportions are calculated by the optimum void-filling principle using bulk density, specific gravity, void content of aggregates (Table 4), entrapped air (Table 5), and extra cement paste for workability (Clauses 2.6 and 2.7). A worked example illustrates the full design procedure (Appendix).

Sources: Clause 2.4.2, Table 2, Clause 2.5, Fig. 1, Fig. 2, Table 4, Table 5, Clauses 2.6 and 2.7

The mix proportioning by the Optimum Void-Filling Principle in IRC 59 is based on gap-graded concrete where voids in coarse aggregate are filled by finer aggregate (usually sand), and voids in finer aggregate are filled by cement paste (Clause 2.6.1 and 2.7.1). The key formulas for quantities per 1 m³ of wet concrete are:

• Volume of single-size coarse aggregate: V = 1 - v - v'ₐ (where v = voids in coarse aggregate, v'ₐ = extra cement paste volume)
• Volume of finer aggregate: V_f = (v / 100) × V
• Volume of cement paste: V_c = (v_f / 100) × V_f (v_f = voids in finer aggregate)

Weights per m³ are:

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

Entrapped air volume and extra cement paste for workability are accounted for (Table 5 shows entrapped air % for max aggregate sizes). Extra cement paste volume v'ₐ is typically about 10-12% of total volume depending on workability and aggregate shape (Clause 2.7.4).

Key tables:

This method ensures the voids in coarser aggregates are optimally filled by finer aggregates and cement paste, minimizing water demand and improving workability and strength.

For detailed worked example and adjustments for workability, see Clauses 2.7.2 to 4.2.

Sources: Clause 2.6.1, Clause 2.7.1, Clause 2.7.2, Clause 2.7.3, Clause 2.7.4, Table 4, Table 5

Workability and compaction in IRC 59 are governed by the mix design based on the optimum void-filling principle and controlled water-cement ratio. Key points include:

• The volume of entrapped air (v_e) and extra cement paste (v_p) are critical for workability; for low workability (slump 0-25 mm), extra cement paste is about 10-12% of the wet concrete volume (Clause 2.7.4).
• Entrapped air volume depends on maximum aggregate size (Table 5): e.g., 1% for 40 mm aggregate.
• Mix proportions are calculated by:
  • Coarse aggregate weight W_a = (1 - v_e - v_p) × bulk density of coarse aggregate (Clause 2.7.2)
  • Fine aggregate weight W_x = voids in coarse aggregate × bulk density of fine aggregate
  • Cement and water quantities depend on water-cement ratio r and specific gravity of cement.
• Water-cement ratio is selected from design curves (Fig. 1) based on 7-day cement strength and desired 28-day concrete strength (Clause 2.5).

Tables for entrapped air and aggregate properties are:

Adjustments to extra cement paste are made based on observed slump changes (Clause 4.1). The mix design example in the Appendix illustrates these calculations in detail.

This approach ensures adequate compaction and workability while maintaining strength and durability.

Sources: Clause 2.7.2, Clause 2.7.3, Clause 2.7.4, Table 5, Table 4, Clause 2.5, Clause 4.1

The adjustment of mix proportions in IRC 59 is based on the optimum void-filling principle and involves the following key formulas and tables:

1. Void Content Calculation: [ n = \left(1 - \frac{d}{1000 \times s}\right) \times 100% ] where n = void content (%), d = bulk density (kg/m³), s = specific gravity (g/cm³) (Clause 2.6.2).

2. Mix Proportioning by Weight per m³ of Wet Concrete:

   • Coarse aggregate weight: ( W_a = V \times d_a = (1 - v - v') \times d_a )
   • Fine aggregate weight: ( W_x = v_a \times d_x )
   • Cement and water quantities calculated using water-cement ratio (r) and specific gravity of cement (Se) (Clause 2.7.2).

3. Entrapped Air Volume: Approximate entrapped air in non-air-entrained concrete varies with max aggregate size (Table 5):

4. Extra Cement Paste for Workability: Typically 10-12% of wet concrete volume, adjusted by ±1% depending on aggregate shape and grading gaps (Clause 2.7.4).

5. Adjustment for Slump Variation: For water-cement ratio 0.40–0.60, each 12 mm increase/decrease in slump changes extra cement paste by ±5% (Clause 4.1).

6. Design Strength Adjustment: Average design strength ( S = s (1 - t v / 100) ) where s = specified strength, t = tolerance factor from Table 2, v = coefficient of variation (Clause 2.4.2).

7. Table 4: Approximate Specific Gravity, Bulk Density, and Void Content of Aggregates:

These principles and tables guide the calculation and adjustment of mix proportions to achieve desired strength and workability in concrete mixes for road pavements.

Sources: Clause 2.6.2, Clause 2.7.2, Clause 2.7.3, Clause 2.7.4, Clause 4.1, Clause 2.4.2, Table 2, Table 4, Table 5

The IRC 59 provides a detailed worked-out example on cement concrete mix design based on the optimum void-filling principle (Clause 4.75). Key formulas for mix proportions per 1 m³ of wet concrete include:

• Volume of coarse aggregate: Wa = V.da = (1 - v - v') da
• Volume of finer aggregate (sand): Wx = v5.d
• Volume of cement paste: Wc = r.W (where r = water-cement ratio)

Entrapped air volume (Ve) and extra cement paste volume (Vp) are accounted for, with entrapped air values given in Table 5:

Extra cement paste volume (v's) depends on workability; typically about 10-12% of gross volume (Clause 2.7.4). Adjustments are made based on slump variations (Clause 4.1).

A worked example in the Appendix illustrates stepwise calculation of mix proportions, including design strength, water-cement ratio selection, and aggregate quantities. For instance, for 1 m³ wet concrete with 40 mm aggregate, entrapped air 0.01 m³, and extra cement paste 0.10 m³, the volume of coarse aggregate is 0.89 m³, and corresponding weights are calculated using bulk densities.

Mix proportions example:

This approach ensures optimized use of aggregates and cement paste for desired strength and workability (Clauses 2.7.1 to 4.2, Appendix).

Sources: Clause 2.7.2, Clause 2.7.3, Clause 2.7.4, Clause 4.1, Clause 4.2, Table 5, Appendix

The IRC 59 Appendix provides a detailed worked example of cement concrete mix design based on the optimum void-filling principle. Key formulas and tables include:

• Design strength calculation: S = s (1 - t.v/100), where s = minimum field strength, t = tolerance factor, v = coefficient of variation (Clause 2.4.2).

• Tolerance factors (t) for different tolerance levels and sample sizes are given in Table 2.

• Mix proportions by volume for 1 m³ wet concrete:

  • Volume of single-size coarse aggregate, Va = V - Ve - V'p (Eq. 3)
  • Volume of finer aggregate, Vf = (voids in coarse aggregate) × Va / 100 (Eq. 4)
  • Volume of cement paste, Vc = (voids in finer aggregate) × Vf / 100 + V'p (Eq. 5)

• Entrapped air volume percentages for different max aggregate sizes are in Table 5.

• Approximate specific gravity, bulk density, and void content for aggregates are in Table 4.

• Example mix proportions per m³ wet concrete and per 50 kg cement bag are calculated using these principles.

These details guide mix design for concrete pavements with specified strength, workability, and quality control (Clauses 2.3 to 4.2, Appendix).

Sources: Clause 2.4.2, Table 2, Clause 2.7.1, Table 4, Table 5, Clause 4.1, Appendix