# Uncertainty Quantification of Fatigue Life for Cement-Stabilized Cold Recycled Mixtures Using Probabilistic Programming

## TL;DR

This paper introduces a new method using probabilistic programming to quantify uncertainty in the fatigue life of pavement materials.

## Contribution

A novel uncertainty quantification method using PyMC3 for cement-stabilized cold recycled mixtures is proposed.

## Key findings

- The method achieved R² values above 0.96 for fatigue life predictions.
- Maximum and average errors in coefficient determination were under 11% and 7%, respectively.
- The predicted fatigue life closely matched test data and aligned with prior findings.

## Abstract

The assessment of fatigue life is important for the design of pavement materials because fatigue cracks are one of the most common types of failure in pavement structures. The fatigue test is commonly used to determine the fatigue life. However, there are lots of uncertainties, such as the construction environment and personal operations, during the fatigue test due to the complexity of the pavement materials. Determining the fatigue life of pavement materials under uncertainty is a challenging task. In this study, considering cement-stabilized cold recycled mixtures (CSCRMs) as an example, an uncertainty quantification (UQ) method based on PyMC3, a novel and powerful probabilistic programming package, was developed to address the uncertainty in fatigue behavior based on fatigue tests. Probabilistic programming was employed to characterize the uncertainty of fatigue life based on fatigue test data and the fatigue life formula. The uncertainty of fatigue life was quantified by determining the unknown coefficient of the fatigue life formula. Two independent datasets for the CSCRM were used to illustrate and verify the developed method. The coefficients of determination (R2) for the prediction results of fatigue life were higher than 0.96, based on the obtained formula and test data. The maximum and average errors of the coefficients determined using the fatigue equation were less than 11% and 7%, respectively. The verification demonstrates that the predicted fatigue life closely agrees with the test data, and the determined coefficients of the fatigue equation are in excellent agreement with prior findings. The developed method avoided complex statistical computations and references. The UQ can evaluate the fatigue life and its uncertainty and significantly enhance the understanding of the fatigue behavior of the CSCRM.