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Connected and automated vehicles (CAVs) and human-driven vehicles (HVs) are expected to coexist in the near future. CAV-dedicated lanes and phases have been explored to handle the uncertainty in the driving behavior of HVs in the mixed traffic environment. However, CAV-dedicated phases could significantly sacrifice HV benefits. This study proposes a shared-phase-dedicated-lane (SPDL)-based traffic control model at isolated intersections under the mixed traffic environment. Left-turn and through CAVs share CAV-dedicated lanes and cross the intersection during the shared phases with HVs. A three-level optimization model is developed. At the upper level, a standard NEMA (National Electrical Manufacturers Association) ring barrier structure is used for the signal optimization and barrier durations are optimized by dynamic programming to minimize the total vehicle delay. At the middle level, phase sequence and phase durations are optimized by enumeration for the given barrier from the upper level and the minimum vehicle delay is fed to the upper level. At the lower level, CAV platooning in the buffer zone and trajectory planning in the passing zone are conducted based on the signal timings of the barrier from the middle level and the travel time of CAVs is fed to the middle level. A rolling-horizon scheme is further designed for the dynamical implementation of the proposed model with time-varying traffic conditions. Numerical studies validate the advantages of the SPDL-based control over the blue-phase based control in previous studies in terms of average vehicle delay and intersection capacity. Further, the SPDL-based model is extended to serve as an alternative approach without the buffer zone.