Modeling impacts of Cooperative Adaptive Cruise Control (CACC) on multi-lane freeway traffic can be challenging. It requires accurate description of the formation and disengagement of CACC vehicle strings when CACC vehicles are mixed with manually driven vehicles in the traffic stream. It also needs to depict the behaviors of CACC vehicles under the influence of CACC operation strategies such as the CACC vehicle managed lane (ML) and implementing the Vehicle Awareness Devices (VAD), which are intended to enhance the CACC string operations. To address these challenges, we extended a state of the art CACC modeling framework to incorporate new algorithms that are essential to describe the interactions among the CACC vehicles and manually driven vehicles in mixed traffic. The updated modeling framework adopts a new vehicle dispatching model to generate the high-volume traffic flow expected to exist due to the CACC string operation. The framework also includes new lane changing rules and automated speed control algorithms that ensure realistic CACC vehicle behaviors at freeway on/off-ramp areas where traffic disturbances might frequently interrupt the CACC string operations. With the model updates, we can further reproduce traffic flow dynamics under the influence of the CACC operation strategies. The modeling capability of the presented framework has been verified via case studies on a simple 4-lane freeway segment with an on-ramp and an off-ramp and a complex 18-kilometer freeway corridor. The case study results indicate that the presented modeling framework not only quantifies the mobility improvements for the study sites under different CACC market penetrations and CACC operation strategies, but also discloses the mechanism that governs the improvement. This study creates a methodology that can estimate detailed kinematics of connected automated vehicles under realistic traffic environments. Findings produced by the methodology are helpful for the future development, implementation and management of the advanced t...