Enhancing the Energy Line Principle: A Force-Based Perspective for Simulating Gravitational Hazard Runout Zones

Accurately identifying hazard-prone areas is critical for mitigating risks from gravitational natural hazards such as landslides and rockfalls. Although many models exist to simulate these rapid mass movements, there are often trade-offs between simplicity, robustness and precision. This study builds upon the well-established energy line principle by reinterpreting the energy line angle as a kinetic friction coefficient, enabling the derivation of equations of motion that describe the forces driving mass movements. Using the Lagrange formalism for a sliding friction block, the equations of motion are developed and solved numerically with an Euler-based algorithm applied to digital terrain models. This force-based perspective retains the energy line principle’s simplicity and robustness while offering improved accuracy. In this study, the method is evaluated using two case studies with 36 documented landslide and 6 rockfall events in northern Italy. The results were compared with those of a traditional energy-based approach  as well as with documented past events. The refined model produces smaller, more differentiated runout zones, achieving 41% resp. 11% higher true positive and 65% resp. 16% lower false positive rates compared to the energy-based approach for reproducing the past rockfall and landslide events. These findings demonstrate that the developed approach enhances accuracy without increasing computational complexity. This enhancement has the potential to extend the application of the energy line principle beyond preliminary analyses, enabling more detailed and reliable hazard mapping at larger spatial scales.