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This is a practical paper which consists of investigating fracture behavior in asphalt concrete using an intrinsic cohesive zone model ͑CZM͒. The separation and traction response along the cohesive zone ahead of a crack tip is governed by an exponential cohesive law specifically tailored to describe cracking in asphalt pavement materials by means of softening associated with the cohesive law. Finite-element implementation of the CZM is accomplished by means of a user subroutine using the user element capability of the ABAQUS software, which is verified by simulation of the double cantilever beam test and by comparison to closed-form solutions. The cohesive parameters of finite material strength and cohesive fracture energy are calibrated in conjunction with the single-edge notched beam ͓SE͑B͔͒ test. The CZM is then extended to simulate mixed-mode crack propagation in the SE͑B͒ test. Cohesive elements are inserted over an area to allow cracks to propagate in any direction. It is shown that the simulated crack trajectory compares favorably with that of experimental results.

Dynamic stress intensity factors (DSIFs) are important fracture parameters in understanding and predicting dynamic fracture behavior of a cracked body. To evaluate DSIFs for both homogeneous and non-homogeneous materials, the interaction integral (conservation integral) originally proposed to evaluate SIFs for a static homogeneous medium is extended to incorporate dynamic effects and material non-homogeneity, and is implemented in conjunction with the finite element method (FEM). The technique is implemented and verified using benchmark problems. Then, various homogeneous and non-homogeneous cracked bodies under dynamic loading are employed to investigate dynamic fracture behavior such as the variation of DSIFs for different material property profiles, the relation between initiation time and the domain size (for integral evaluation), and the contribution of each distinct term in the interaction integral.

Asphalt paving layers, particularly the surface course, exhibit vertically graded material properties. This grading is caused primarily by temperature gradients and aging related stiffness gradients. Most conventional existing analysis models do not directly account for the continuous grading of properties in flexible pavement layers. As a result, conventional analysis methods may lead to inaccurate prediction of pavement responses and distress under traffic and environmental loading. In this paper, a theoretical formulation for the graded finite element method is provided followed by an implementation using the user material subroutine ͑UMAT͒ capability of the finite element software ABAQUS. Numerical examples using the UMAT are provided to illustrate the benefits of using graded elements in pavement analysis.

A B S T R A C T Recent work with fracture characterization of asphalt concrete has shown that a cohesive zone model (CZM) provides insight into the fracture process of the materials. However, a current approach to estimate fracture energy, i.e., in terms of area of force versus crack mouth opening displacement (CMOD), for asphalt concrete overpredicts its magnitude. Therefore, the δ 25 parameter, which was inspired by the δ 5 concept of Schwalbe and co-workers, is proposed as an operational definition of a crack tip opening displacement (CTOD). The δ 25 measurement is incorporated into an experimental study of validation of its usefulness with asphalt concrete, and is utilized to estimate fracture energy. The work presented herein validates the δ 25 parameter for asphalt concrete, describes the experimental techniques for utilizing the δ 25 parameter, and presents three-dimensional (3D) CZM simulations with a specially tailored cohesive relation. The integration of the δ 25 parameter and new cohesive model has provided further insight into the fracture process of asphalt concrete with relatively good agreement between experimental results and numerical simulations.