A Python-based framework for probabilistic rockfall trajectory analysis

Rockfall events pose significant hazards to infrastructure and human safety in mountainous regions. This paper presents a comprehensive Python-based probabilistic rockfall simulation framework (PRSM) developed for 2D trajectory analysis of falling rocks. The model integrates projectile motion physics, impact mechanics with normal and tangential restitution coefficients, rolling behavior with friction angle, and stochastic variations in rock properties and initial conditions. The framework employs an algorithm to simulate rockfall trajectories, velocities, and energies. Statistical outputs including probability density functions, velocity and energy envelopes, and shape factors. The model's flexibility allows for user-defined slope geometries and rock characteristics, making it applicable to various geological settings. Validation against analytical solutions and comparison with established software demonstrate the model's accuracy and reliability. In addition, a comprehensive sensitivity analysis demonstrated that slope geometry and the normal restitution coefficient are the dominant controls on rockfall runout, velocity, and kinetic energy, whereas shape factor and rolling parameters exert secondary influences through impact energy dissipation mechanisms. The open-source nature of the implementation provides a transparent and customizable tool for rockfall hazard assessment.