A time-dependent Hoek-Brown strain-softening constitutive model was developed for underground coal-roof rock masses. The basic strain-softening model requires strength parameters ( $m$ and $s$ ) as functions of plastic strain and time. It is important to note that the material exhibits yielding before reaching peak strength at the crack/yield initiation point. The yielded elements show time-dependent (creep) behavior. During this process, the strength parameters decrease over time. Keeping this in mind, a mathematical exponential expression has been developed to estimate the peak strength parameter over time, considering an additional peak reduction parameter. The peak strength parameter at zero time is referred to as the ultimate peak strength parameter. The constitutive model comprises two sets of strength parameters: peak strength parameters ( $m_{rm}$ and $s_{rm}$ ), residual parameters ( $m_{\mathit{rmt}}$ and $s_{\mathit{rmt}}$ ), and the peak reduction parameter ( $\beta $ ). Deducing these parameters is practically impossible in the laboratory for large-scale coal masses. Therefore, instances of immediate failure, short-term stability, and long-term stability in field cases are used to deduce the strength parameters through a back analysis technique. In total, 34 Indian coal mine cases have been considered for assessing these parameters. The numerical models for all cases have been developed by incorporating the material properties, in-situ stress, and boundary conditions. This research introduces a novel method that employs numerical simulations using a viscoelastic-plastic model to capture the time-dependent behavior of rock, including the gradual reduction of its strength. The findings offer key insights into time-dependent roof rock behavior, supporting advanced stability strategies and collapse risk reduction.
