Tentative Guidelines for Structural Strength Evaluation of Rigid Airfield Pavements

IRC 76 - Scope: Key Formulas, Tables & Specifications

1. Strength Correlation (Clause 7.63)

• Relationship between compressive (X) and flexural strength (Y):

  [ Y = 7.63X + 25.8 ]

• Strength tests must comply with relevant IS specifications.

2. Foundation Strength (Clause 4.2.2)

• Plate Bearing Test Conversion:

  [ k_{75} = 0.5 \times k_{30} ]

  (Approximate correlation for 75 cm and 30 cm diameter plates on homogeneous foundation)

• If direct k-value is unavailable, use CBR test and Table 1:

3. Design Strength (Clause 1.5)

• Typical strength value:

  [ \text{Typical} = \bar{x} - 1.5 \times \sigma ]

• Design strength:

  [ \text{Design} = \frac{\text{Typical}}{1.1} ]

4. Pavement Structural Strength (Clause 4.5)

• Use LCN (Load Classification Number) method.
• Input parameters: pavement thickness, concrete flexural strength, foundation k-value.
• Load transfer capacity should be tested at critical joints (coldest season).
• Total load capacity = slab capacity + load transfer capacity.

Visual Summary

flowchart TD
    A[Strength Tests] --> B[Compressive & Flexural Strength]
    B --> C[Use Y=7.63X+25.8]
    A --> D[Foundation Strength]
    D --> E[Plate Bearing Test]
    E --> F[k30 to k75 conversion]
    D --> G[CBR Test

IRC 76: General Principles of Pavement Evaluation (Rigid Pavements)

Though IRC 76 provides tentative guidelines without detailed formulas, key principles for structural evaluation of rigid pavements include:

1. Evaluation Methods

• Direct Load Tests: Applying actual loads on pavement and measuring deflections/stresses.
• Indirect Reverse Design: Using measured deflections to back-calculate pavement strength and required thickness.

2. Key Parameters

• Modulus of Rupture (f_r): Flexural strength of concrete.
• Modulus of Subgrade Reaction (k): Soil support stiffness (kN/m³).
• Maximum Allowable Stress: To prevent cracking under load.
• Deflection Limits: Based on load and pavement thickness.

3. Typical Evaluation Formula (Simplified)

[ \sigma = \frac{P}{b \sqrt{d}} ] Where:

• (\sigma) = Stress in pavement slab,
• (P) = Load applied,
• (b) = Width of load contact,
• (d) = Thickness of slab.

4. Evaluation Criteria

• Compare calculated stresses with allowable stresses.
• Use deflection data to assess structural capacity.
• Factor in fatigue and load repetitions.

Summary Table (Example)

flowchart LR
    A[Load Applied] --> B[Measure Deflection]
    B --> C[Calculate Stress]
    C --> D{Stress ≤ Allowable?}
    D -- Yes --> E[Pavement OK]
    D -- No --> F[Structural Strengthening]

This approach ensures standardized evaluation for rigid airfield pavements per IRC 76 guidelines.

Direct Load Test Method (IRC 76) - Key Points

• Test Principle: Static load applied via a rigid plate on pavement; deflections/strains measured to assess structural capacity (LCN).

• Failure Load & Safe Load:

  • Failure load identified when strain gauge reading rises rapidly.
  • Safe working load = Failure load ÷ Factor of Safety (1.5 to 1.8).

• Procedure III (Working Deflection Method):

  • Determine failure deflection at 3-4 points.
  • Working deflection = Average failure deflection ÷ Factor of Safety (1.5 to 1.8).
  • Load at working deflection = Safe working load.
  • Deflections recorded in increments of 0.15–0.25 mm.

• Load Transfer Correction:

  • Load transfer (%) = (1 - (S1 + S2 + S3 + S4) / (4 × S1)) × 100
  • Minimum load transfer = Average lowest quartile of observed values, max 20%.
  • Corrected load capacity = Measured capacity × [100 - (x - y)]%, where x = measured load transfer, y = minimum load transfer.
  • For pavements with dowels/reinforcement, reduce measured load transfer by 10%.

• LCN Rating:

  • Use safe working load and plate contact area on standard LCN charts (Fig. 4) to find pavement rating.

Load Transfer Formula

[ \text{Load Transfer (%)} = \left(1 - \frac{S_1 + S_2 + S_3 + S_4}{4 \times S_1}\right) \times 100 ]

Where:

• (S_1, S_2, S_3, S_4) = deflections at four corners.

Summary Diagram of Procedure III

graph TD
  A[Apply Load via Rigid Plate] --> B[Measure Deflections at 4 Corners]
  B --> C[Determine Failure Deflection at 3-4 Points]
  C --> D[Calculate Working Deflection = Avg Failure Deflection / FOS]
  D --> E[Apply Load up to Working Deflection]
  E --> F[Safe Working Load Determined]
  F --> G[Calculate LCN from Load

Selection of Test Locations and Frequency (IRC 76)

Test Locations:

• For runways: 1 test every 60 m length.
• For taxi tracks and aprons: 1 test every 60-90 m length.
• Total tests recommended: 15-20 for statistical reliability.
• Engineer-in-Charge may adjust based on site conditions.

Statistical Evaluation of Test Data (Clause 1.5)

Calculate typical strength (to ensure 1 in 15 confidence level): [ \text{Typical Strength} = \bar{x} - 1.5 \times s ] where:

• (\bar{x}) = average test strength
• (s) = standard deviation of test results

Design strength: [ \text{Design Strength} = \frac{\text{Typical Strength}}{1.1} ]

Load Transfer Correction (Clause 3.3)

Load transfer percentage: [ \text{Load Transfer} = \left(1 - \frac{S_1}{S_1 + S_2 + S_3 + S_4}\right) \times 100% ] where (S_1, S_2, S_3, S_4) = deflections at slab corners.

Corrected load capacity: [ \text{Corrected Load} = \text{Measured Load} \times \left[1 - (x - y)/100\right] ]

• (x) = measured load transfer (%)
• (y) = minimum load transfer (%), average of lowest quartile, max 20%

Approximate k-Value from CBR (Table 1)

Summary Diagram of Test Location Selection and Load Transfer Correction

flowchart TD
    A[Test Location Selection]
   

IRC 76 Test Procedures - Key Formulas & Tables

1. Compressive & Flexural Strength Correlation

From Clause 7.63:
[ Y = 7.63X + 25.8 ]

• Y = Compressive strength (Kg/cm²)
• X = Flexural strength (Kg/cm²)

2. Foundation k-value from Plate Bearing Tests

• Plate sizes: 30 cm & 75 cm diameter
• Approximate correlation to convert k-values:
  [ k_{75} = \text{function of } k_{30} \quad \text{(approximate, depends on homogeneity)} ]
• Use Table 1 for CBR to k-value conversion (for homogeneous soil):

3. Safe Strength Value Calculation

• Typical strength = Average - 1.5 × Standard Deviation
• Design strength = Typical strength / 1.1 (Factor of Safety)

4. Load Transfer Adjustment (Clause 3.3)

• Load transfer (%) = (\left(1 - \frac{S_1}{S_1 + S_2 + S_3 + S_4}\right) \times 100)
  where (S_1, S_2, S_3, S_4) = deflections at four corners
• Minimum load transfer = Average of lowest 25% observations (max 20%)
• Corrected load capacity = Measured capacity × (\left[1 - \frac{x - y}{100}\right])
  where (x) = measured load transfer, (y) = minimum load transfer

5. Safe LCN Rating

• Use Fig. 4 chart: LCN vs. load/contact pressure for rigid pavements

IRC 76: Adjustment for Load Transfer - Key Points

1. Minimum Load Transfer Calculation

• Formula:
  [ \text{Min. Load Transfer} = x - 1.5 \times g ]
  Where:
  • (x = 8.95%) (mean load transfer)
  • (g = 1.92%) (standard deviation)
• Example:
  [ 8.95 - 1.5 \times 1.92 = 6.97% ]

2. Modified Pavement Slab LCN

• For tyre pressure (p = 10 \text{ kg/cm}^2) and LCN = 40 (no load transfer), ESWL = 13,000 kg.
• Load transfer reduces effective load capacity; adjust LCN accordingly using Fig. 4 (not shown here).

3. Load Transfer Adjustment Values

• Adjusted load transfer values (%) used for design:
  [ 10.0, 10.0, 8.4, 10.0, 6.8, 10.0, 10.0, 8.9, 6.7, 8.7 ]
• Average adjusted load transfer = 10.0% (used for design).

Summary Table: Load Transfer Adjustment

Conceptual Flow

flowchart LR
    A[Mean Load Transfer (x)] --> B[Calculate Min Load Transfer: x - 1.5g]
    B --> C[Determine Adjusted Load Transfer Values]
    C --> D[Modify Pavement LCN using Fig.4]
    D --> E[Design Pavement with Adjusted Load Transfer]

Note: Use these values to correct slab load capacity for realistic load transfer

Determination of Safe LCN Rating (IRC 76)

Key Procedures:

1. Failure Load Detection (Clause 1.8 & 3.2.4):

   • Identify imminent cracking by strain gauge readings.
   • Safe working load = Failure load / Factor of Safety (1.5 to 1.8).
   • If no cracking up to max load, safe load = max applied load.

2. Procedure III: Working Deflection Method (Clause 3.2.4):

   • Conduct 3-4 failure load tests to find average failure deflection.
   • Working deflection = Failure deflection / Factor of Safety (1.5 to 1.8).
   • Safe working load corresponds to working deflection from load-deflection curve.

3. Load Transfer Adjustment (Clause 3.3):

   • Load transfer (%) = [ (1 - \frac{S1 + S2 + S3 + S4}{4 \times S1}) \times 100 ] where S1 to S4 = deflections at four corners.
   • Corrected load capacity = Measured load capacity × [100 - (x - y)]%, where:
     • x = measured load transfer (%),
     • y = minimum load transfer (average of lowest quartile, max 20%).

4. Safe LCN Rating Calculation (Clause 3.4):

   • Use safe working load and test plate contact area.
   • Refer to standard LCN chart (Fig. 4) to convert load/contact pressure to LCN.
   • For overall pavement, statistically calculate safe working load at 1 in 15 confidence level: [ \text{Safe Load} = \text{Average Load} - 1.5 \times \text{Standard Deviation} ]

Summary Table:

IRC 76: Indirect Reverse Design Method Key Points

1. Concept

• Used when direct load tests are not feasible.
• Computes pavement strength indirectly by evaluating individual parameters:
  • Concrete flexural strength
  • Foundation modulus (k-value)
  • Maximum temperature differential over pavement depth
• Requires actual material testing at selected locations.

2. Concrete Strength Testing

• Samples: Beam (preferable) or core samples.
• Core correction for crushing strength:

[ f = 0.11n + 0.78 ]

Where:

• (f) = correction factor

• (n = \frac{h}{d}) (height to diameter ratio of core)

• Minimum core diameter:

  • 10 cm for max aggregate size 10 mm
  • 15 cm for max aggregate size 40 mm

3. Statistical Evaluation of Strength Data

• Calculate typical strength at 1 in 15 confidence level:

[ \text{Typical strength} = \text{Average} - 1.5 \times \text{Standard deviation} ]

• Apply factor of safety = 1.1 to get design strength.

4. Pavement Structural Strength (LCN) Determination

• Use LCN design chart (Fig. 7) with inputs:
  • Pavement thickness
  • Concrete flexural strength
  • Foundation k-value
• Account for load transfer at joints by limited load tests at critical locations.
• Total load capacity = slab capacity + load transfer capacity.

5. Safe LCN Calculation (Example from Appendix 1)

• Safe working load for pavement:

[ \text{Safe load} = \text{Average working load} - 1.5 \times \text{Standard deviation} ]

• Adjust for load transfer and calculate corrected safe load.
• Convert corrected safe load to LCN using charts.

Summary Table: Core Strength Correction Factors

flowchart TD

IRC 76 - Basic Information Required for Structural Strength Evaluation

Key Formulas & Correlations

• Compressive vs Flexural Strength (Clause 7.63):

  [ Y = 7.63X + 25.8 ]

  Where:

  • (Y) = Compressive strength (Kg/cm²)
  • (X) = Flexural strength (Kg/cm²)

• Plate Bearing Test k-value Conversion (30 cm to 75 cm plate):

  [ k_{75} = 0.7 \times k_{30} ]

  Note: Valid only for homogeneous foundations; layered sub-base may cause overestimation.

• Approximate k-values from CBR (Table 1):

Design Strength Calculation (Clause 1.5)

• Typical strength = Average strength - 1.5 × Standard deviation
• Design strength = Typical strength / 1.1 (Factor of Safety)

Pavement Structural Strength (Clause 4.5)

• Use LCN method with:
  • Pavement thickness
  • Concrete flexural strength
  • Foundation k-value
• Load transfer capacity assessed via load tests at joints/cracks.
• Combine slab capacity and load transfer for total load capacity.

Summary Diagram: Strength & Foundation Assessment Flow

flowchart TD
  A[Conduct Concrete Strength Tests] --> B[Calculate Design Strength]
  B --> C[Determine Foundation k-value]
  C --> D[Use Plate Bearing or CBR Tests]
  D --> E[Adjust k-value for Sub-base]
  E --> F[Apply LCN Method for Pavement Design]
  F --> G[Assess Load Transfer Capacity]
  G --> H[Calculate Total Pavement Load Capacity]

**Note

Key Formulas and Tables from IRC 76 for Concrete & Foundation Strength Testing

1. Compressive & Flexural Strength Correlation

From Clause 7.63:
[ Y = 7.63X + 25.8 ]

• Y = Compressive strength (Kg/cm²)
• X = Flexural strength (Kg/cm²)

2. Foundation k-value Determination (Clause 4.2.2)

• Plate bearing test on 30 cm dia. plate is converted to 75 cm dia. plate k-value using an approximate correlation (not explicitly given, but conversion required).
• For layered sub-base, direct conversion may overestimate k-value; caution advised.
• If plate test not possible, use in-situ CBR test and correlate using:

3. Statistical Analysis of Strength Test Data (Clause 1.5)

• Typical strength = Average strength − 1.5 × Standard deviation
• Design strength = Typical strength ÷ Factor of Safety (1.1)

4. Pavement Structural Strength (Clause 4.5)

• Use LCN method (Fig. 7) with inputs: pavement thickness, concrete flexural strength, foundation k-value.
• Load transfer capacity assessed by load tests on slab joints/cracks, preferably in coldest period.
• Total load capacity = slab capacity + load transfer capacity.

Summary Diagram: Test Procedure Flow

flowchart TD
    A[Test Concrete Flexural Strength] --> B[Calculate Compressive Strength using Y=7.63X+25.8]
    B --> C[Conduct Plate Bearing Test on Foundation]
    C --> D{Plate Diameter}
    D -->|30 cm| E[Convert k30 to k75 (

Analysis of Test Data (IRC 76)

Key Formulas and Specifications:

1. Typical Strength Value (Concrete/Foundation):
   [ f_{typical} = \bar{f} - 1.5 \times \sigma ]

   • (\bar{f}) = Average of all strength test values
   • (\sigma) = Standard deviation of strength values
     Ensures a confidence level of 1 in 15.

2. Design Strength:
   [ f_{design} = \frac{f_{typical}}{1.1} ]

   • Factor of safety = 1.1 applied to typical strength.

3. Foundation k-value from Plate Bearing Test:
   For converting 30 cm plate k-value to 75 cm plate:
   [ k_{75} = 0.67 \times k_{30} ] (Approximate, valid for homogeneous foundation)

4. CBR to k-value Correlation (Table 1):

5. Pavement Structural Strength (LCN method):
   Use Fig. 7 chart to find LCN based on:

   • Pavement thickness
   • Concrete flexural strength
   • Foundation k-value

6. Load Transfer Adjustment:
   Assess load transfer via load tests at joints/cracks, especially in coldest weather (minimum load transfer). Combine slab capacity and load transfer for total capacity.

Summary Flow:

flowchart TD
    A[Test Data Collection] --> B[Calculate Mean & Std Dev]
    B --> C[Typical Strength = Mean - 1.5*Std Dev]
    C --> D[Design Strength = Typical / 1.1]
    A --> E[Foundation Plate Bearing Test]
    E --> F[Convert k30 to

Determination of Pavement Structural Strength (IRC 76 - Rigid Airfield Pavements)

Key Formulas & Specifications:

1. Foundation Modulus (k-value) from Plate Bearing Test:

• For a 30 cm diameter plate, test directly.

• Convert to standard 75 cm plate k-value using:

  [ k_{75} = 0.6 \times k_{30} ]

  (Approximate; valid for homogeneous foundation)

2. CBR to k-value Correlation (for subgrade soils):

3. Compressive & Flexural Strength Correlation:

[ Y = 7.63 X + 25.8 ]

• Where Y = Compressive strength (kg/cm²)
• X = Flexural strength (kg/cm²)

4. Testing Standards:

• Strength tests must follow relevant IS specifications.
• Plate bearing tests for foundation modulus.
• Soil plasticity and grain-size analysis for subgrade classification.

Notes:

• When layered sub-base exists, direct conversion of k-values from 30 cm to 75 cm plate may overestimate strength.
• Sub-base thickness and type influence foundation k-value; refer to charts (Fig. 6 in IRC 76).
• For indirect foundation strength, use in-situ CBR tests and Table 1 correlation.

flowchart TD
    A[Conduct Plate Bearing Test] --> B{Plate Diameter?}
    B -->|30 cm| C[Measure k30]
    C --> D[Convert to k75: k75 = 0.6 * k30]
    B -->|75 cm| E[Measure k75 directly]
    D --> F[Use k75 for pavement design]
    E --> F
    G[If no plate test] --> H

Safe LCN Calculation from Load Tests (IRC 76 Highlights):

1. Failure Load & Safe Working Load:

   • Identify failure load from strain gauges (rapid strain increase).
   • Safe working load = Failure load / Factor of Safety (FoS = 1.5 to 1.8).

2. Procedure III (Deflection-Based):

   • Determine failure deflection from 3-4 tests.
   • Safe working deflection = Average failure deflection / FoS (1.5 to 1.8).
   • Safe working load corresponds to safe deflection (linear load-deflection relation).

3. Load Transfer Correction:

   • Load transfer (%) = (1 - (S1+S2+S3+S4) / (4 × S1)) × 100
   • Minimum load transfer = Average of lowest quartile of observed transfers, max 20%.
   • Corrected load capacity = Measured load capacity × [1 - (Measured LT - Minimum LT)/100]

4. Safe LCN Rating:

   • Use Fig. 4 (LCN chart) with corrected safe working load and contact area.
   • For pavement-wide LCN, subtract 1.5 × standard deviation from average safe load (confidence 1 in 15).

Key Formulas Summary:

Example Data Table (Excerpt from Appendix 1):

| Location | Failure Load (tonnes) | Safe Load (tonnes) = Failure Load / 1.5 | Measured LT (%) | Minimum LT (%) | Deduct

Structural Strength Evaluation by Reverse Design Method (IRC 76 - Airfield Pavements)

Given data:

• Slab thickness, ( h = 25 , \text{cm} )
• Concrete compressive strength (average of 10 cores):
  [ f_c = \frac{385 + 355 + \cdots + 310}{10} = 333 , \text{kg/cm}^2 ]
• Subgrade CBR (average):
  [ \text{CBR} = \frac{13.0 + 12.0 + \cdots + 11.5}{10} = 11.8% ]
• WBM subbase thickness = 25 cm
• Load transfer efficiency (average):
  [ LTE = \frac{12.66 + 13.03 + \cdots + 8.7}{10} \approx 10.8% ]
• Tyre pressure = 10 kg/cm²

Step 1: Flexural Strength of Concrete, ( f_r )

Using empirical relation for flexural strength from compressive strength (IS 456 or IRC 58):

[ f_r = 0.7 \sqrt{f_c} \quad \text{(in kg/cm}^2\text{)} ]

Calculate:

[ f_r = 0.7 \times \sqrt{333} = 0.7 \times 18.25 = 12.78 , \text{kg/cm}^2 ]

Step 2: Structural Number or Load Carrying Capacity

Use the Equivalent Thickness Method or IRC 58 guidelines, considering:

• Subgrade support from CBR
• Load transfer efficiency (LTE)
• Pavement thickness ( h )

Step 3: Reverse Design Formula (simplified)

[ \text{Allowable Load} \propto f_r \times h^2 \times \text{LTE} \times \text{Subgrade Support Factor} ]

Where subgrade support factor is related to CBR, typically:

[ k = \text{modulus of subgrade reaction} \approx 10 \times \text{CBR} \quad (\text{kg/cm}^3) ]

Summary Table:

| Parameter