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Abrupt maneuvers by surrounding vehicles (SVs) can typically lead to safety concerns and affect the task efficiency of the ego vehicle (EV), especially with model uncertainties stemming from environmental disturbances. This paper presents a real-time fail-operational controller that ensures the asymptotic convergence of an uncertain EV to a safe state, while preserving task efficiency in dynamic environments. An incremental Bayesian learning approach is developed to facilitate online learning and inference of changing environmental disturbances. Leveraging disturbance quantification and constraint transformation, we develop a stochastic fail-operational barrier based on the control barrier function (CBF). With this development, the uncertain EV is able to converge asymptotically from an unsafe state to a defined safe state with probabilistic stability. Subsequently, the stochastic fail-operational barrier is integrated into an efficient fail-operational controller based on quadratic programming (QP). This controller is tailored for the EV operating under control constraints in the presence of environmental disturbances, with both safety and efficiency objectives taken into consideration. We validate the proposed framework in connected cruise control (CCC) tasks, where SVs perform aggressive driving maneuvers. The simulation results demonstrate that our method empowers the EV to swiftly return to a safe state while upholding task efficiency in real time, even under time-varying environmental disturbances.