We build a hydro-mechanical coupled model that is a multi-layered geological structure. We use joint elements to represent a normal fault extending from the top of a reservoir into a basement formation. Two sets of injection scenarios are considered. The first one simulates three different injection rates (constant injection rate, increasing injection rate, and decreasing injection rate) with the same total injection volume. The second volume’s set of simulations account for the influences of the variation total injection volume on fault stability. The model captures the spatiotemporal evolution of pore pressure and stress fields along the fault. Results indicate that joint damage occurs at high initial injection rate, implying an early onset of fault reactivation. Injection volume also has a significant impact on initiation of the first joint element to damage and the period needed to reach complete damage. Transient fault slip is captured by the progressive damage initiation and propagation in joint elements. This study expects to provide insights into the correlation between fluid injection and fault instabilities and contribute to the optimized design of injection activities to minimize fault reactivation potential.