Development of double-tangent method to determine transition points of three-stage permanent deformation of asphalt mixture

The three-stage behavior is the most significant feature of permanent deformation of asphalt mixture under repeated loading, and the transition points, which refer to the dividing points of different stages, are commonly used as vital parameters to evaluate the rutting resistance. This study aims to propose a novel calculation method for transition points, which are with clear physical significance and independent of human factors. First, the effects of human factors on transition points of existing methods are assessed. As revealed from the research, the thresholds significantly impact the three-stage model method, while the termination condition and the iteration cycle significantly impact the two-step secant method and secant method with other steps, respectively. Subsequently, a three-step algorithm termed as a double-tangent method is proposed, and the physical significances of the transition points are clarified. The transition points obtained by the proposed method are proved to be of clear physical significance and independent of human factors. The slopes of the tangent line at the transition points equal to the strain rate value when the average strain rate equals to the instantaneous strain rate. Lastly, the differences of transition points and slopes between the proposed double-tangent method and existing methods are studied.