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Formula & How to Use The Pavement Temperature Calculator

Core Formulas

The calculator uses the BELLS empirical models to predict the temperature at a specific depth (Td) within an asphalt layer.

  • BELLS2 (LTPP Protocol):
    Td = 2.78 + 0.912·IR + {log₁₀(d)−1.25}·{−0.428·IR + 0.553·T₁₋day + 2.63·sin(hr−15.5)} + 0.027·IR·sin(hr−13.5)
  • BELLS3 (Routine Testing):
    Td = 0.95 + 0.892·IR + {log₁₀(d)−1.25}·{−0.448·IR + 0.621·T₁₋day + 1.83·sin(hr−15.5)} + 0.042·IR·sin(hr−13.5)
  • Asphalt Temperature Adjustment Factor (ATAF):
    ATAF = 10(Slope · (Tᵣ − Td))

Example Calculation

Given routine testing (BELLS3) with an IR surface temperature of 35°C, a previous day average air temp of 25°C, at a depth of 50 mm, measured at 2:00 PM (14.0 hours). Using a default slope of -0.021 and reference temp of 21°C:

  1. The BELLS3 formula calculates the temperature at depth (Td) to be approximately 33.56°C.
  2. The ATAF is then calculated: 10(-0.021 * (21 - 33.56))1.84.
  3. This means a modulus measured at 33.56°C should be multiplied by 1.84 to adjust it to the standard 21°C reference.

How to Use

  1. Enter Surface & Air Temps: Input the pavement surface temperature measured by an IR sensor and the average air temperature from the previous day, both in °C.
  2. Provide Depth & Time: Enter the depth below the surface (in mm) and the time of day in 24-hour decimal format (e.g., 3:30 PM is 15.5).
  3. Select Model: Choose BELLS3 for routine testing (e.g., FWD with minimal shading) or BELLS2 for LTPP protocol (5-6 minutes of shading).
  4. Set Adjustment Parameters: Confirm the reference temperature (typically 21°C) and the asphalt modulus vs. temperature slope (default -0.021).
  5. Click "Calculate": The tool computes the pavement temperature at depth and the corresponding Asphalt Temperature Adjustment Factor (ATAF).

Tips for Accurate Pavement Temperature Prediction

  • Choose the Right Model: The primary difference between BELLS2 and BELLS3 is the duration of surface shading before IR measurement. BELLS3 is more common for routine FWD testing.
  • Accurate IR Readings: Ensure your infrared thermometer is calibrated and used correctly. Inaccurate surface temperature is the largest source of error.
  • Verify Modulus Slope: The default slope of -0.021 is a general average. If you have lab data for your specific asphalt mix, use that value for a much more accurate ATAF.
  • Understand Depth Impact: Temperature fluctuations are greatest near the surface. At deeper points (e.g., >150mm), the temperature becomes more stable and less influenced by daily swings.
  • Use Decimal Hours: Convert time to a decimal format for the 'hr' input. For example, 9:45 AM should be entered as 9.75.

About The Pavement Temperature Calculator

The Pavement Temperature Calculator is a specialized engineering tool designed for pavement engineers, technicians, and researchers to accurately predict the temperature within an asphalt layer at a specific depth. It also calculates the Asphalt Temperature Adjustment Factor (ATAF), which is crucial for standardizing pavement modulus data. The calculator is based on the well-established BELLS empirical models (BELLS2 and BELLS3), which were developed as part of the Strategic Highway Research Program (SHRP) and the Long-Term Pavement Performance (LTPP) program. These models are the industry standard for estimating in-situ pavement temperatures from easily obtainable surface measurements.

The primary benefit of the Pavement Temperature Calculator is its ability to normalize pavement structural data. The stiffness (or modulus) of asphalt concrete is highly dependent on its temperature—it is stiffer when cold and softer when hot. When conducting tests like the Falling Weight Deflectometer (FWD) to assess a pavement's structural capacity, the measured modulus will vary significantly throughout the day. To make meaningful comparisons of data collected at different times and temperatures, it must be adjusted to a standard reference temperature. This is where the ATAF becomes indispensable. Our Pavement Temperature Calculator computes this factor, allowing for reliable pavement analysis and management.

The tool provides two distinct models. The BELLS2 model is intended for use under LTPP data collection protocols, where the pavement surface is shaded for five to six minutes before the IR temperature is taken. This shading causes some surface cooling. The BELLS3 model, however, is calibrated for more routine testing scenarios where shading is minimal (one minute or less), making it more suitable for typical FWD operations. The formulas incorporate variables for surface temperature, previous day's air temperature, depth, and time of day to capture the complex thermal dynamics of the pavement structure. For more detailed information on the LTPP program, the Federal Highway Administration (FHWA) provides extensive resources. The fundamental principles of asphalt properties are also well-documented on platforms like Wikipedia's article on Asphalt Concrete.

Ultimately, the Pavement Temperature Calculator serves as an essential utility for anyone involved in pavement evaluation. By removing the guesswork from temperature correction, it enhances the accuracy and consistency of structural analysis. This leads to better decision-making in pavement rehabilitation, maintenance, and overall asset management. Using the Pavement Temperature Calculator ensures that your pavement data is comparable and reliable, regardless of the ambient conditions during testing.

Key Features:

  • Dual Model Support: Implements both BELLS2 (LTPP Protocol) and BELLS3 (Routine Testing) models.
  • In-Depth Temperature Prediction: Calculates the pavement temperature at any specified depth.
  • Modulus Adjustment Factor (ATAF): Automatically computes the ATAF to normalize pavement stiffness data.
  • User-Friendly Interface: Requires common field measurements for straightforward calculations.
  • Based on Industry Standards: Utilizes validated formulas from the LTPP program, trusted by transportation agencies worldwide.

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Frequently Asked Questions

What is the difference between the BELLS2 and BELLS3 models?

BELLS2 is for LTPP testing where the pavement is shaded for 5-6 minutes before taking an IR temperature reading, causing cooling. BELLS3 is for routine testing (like FWD) with minimal shading (less than 1 minute), which results in a warmer surface temperature reading. Choose the model that matches your field procedure.

Why is it important to adjust the asphalt modulus for temperature?

Asphalt is a viscoelastic material, meaning its stiffness (modulus) changes significantly with temperature. To compare pavement structural capacity measured on different days or times, the modulus values must be adjusted to a single, standard reference temperature. The ATAF allows for this normalization.

What should I do if I don't know the specific modulus slope for my asphalt mix?

The default value of -0.021 log(MPa)/°C is a widely accepted average based on extensive LTPP research. While using a mix-specific value from laboratory testing is always more accurate, the default value provides a reasonable estimate for most standard asphalt mixes.