Concrete bridge piers are critical components of bridge structures and their performance under seismic loading is of utmost importance. Traditional reinforced concrete bridge piers have shown limitations in terms of residual deformations and seismic resilience. This has led researchers to explore alternative reinforcement materials, such as Shape Memory Alloy (SMA) coupled with steel reinforcing bars, which have demonstrated promising attributes like energy dissipation as well as self-centering capacity. This study aims to fill this gap by evaluating the performance of concrete bridge piers with SMA-Steel coupled (SMASC) reinforcing bars under various intensities of vertical gravity loads and the action of pulse-like ground motion components, throughout a probabilistic framework. To this end, a group of bridge piers with different reinforcement types, including pure steel and SMASC are considered. These piers are subjected to 55 near-fault (NF) pulse-like records as well as 32 far-fault (FF) ground motions, throughout the Incremental Dynamic Analysis (IDA). The influence of distinct frequency components is analyzed by decomposing NF records into low-frequency pulses and high-frequency residual components. Also, the role of pulse to the 1st modal period of the piers (Tp/T1) is investigated by evaluating the piers’ response under the action of NF records, which were clustered into four groups. Results were assessed by evaluating the intensity measure and capacity of the studied piers at the desired performance objectives according to the FHWA manual. Moreover, the mean annual frequencies of exceeding performance limit states and the confidence levels of meeting performance objectives are studied. The results of the study indicate that the dominance of the component of NF ground motions depends on factors such as the intensity of gravity loads, ground motion characteristics, and the Tp/T1 ratio. The components of NF records within certain clusters of the Tp/T1 ratio are necessary for accurate response assessment, while FF records can be used for conservative design purposes, depending on the level of ground motion intensity and the intensity of applied gravity load. The SMASC-reinforced piers with specific λ factors (i.e. λ = 0.5 or λ = 1.0) and low intensity of gravity loads lead to a higher (1.6 times higher) mean annual frequency of exceeding a limit state, compared to pure steel rebars. Also, the confidence levels for meeting performance objectives vary depending on the ground motions, but, as gravity load intensity increases, confidence levels decrease, particularly for piers with a λ factor of 0.5.