Bi-Linear Laws Govern the Impacts of Debris Flows, Debris Avalanches, and Rock Avalanches on Flexible Barrier

Geophysical mass flows impacting flexible barriers can create complex flow patterns and multiway solid-fluid-structure interactions, wherein estimates of impact loads rely predominantly on analytical or simplified solutions. However, an examination of the fundamental relations, applicability, and underlying mechanisms of these solutions has been so far elusive. Here, using a coupled continuum-discrete method, we systematically examine the physical laws of multiphase, multiway interactions between geophysical flows of variable natures, and a permeable flexible ring net barrier system. This model well captures the essential physics observed in experiments and field investigations. Our results reveal for the first time that unified bi-linear laws underpin widely used analytical and simplified solutions, with inflection points caused by the transitions from trapezoid-shaped to triangle-shaped dead zones. Specifically, the peak impact load increases bi-linearly with increasing Froude number, peak cable force, or maximum barrier deformation. Flow materials (wet vs. dry) and impact dynamics (slow vs. fast) jointly drive the patterns of identified bi-linear correlations. These findings offer a physics-based, significant improvement over existing solutions to impact problems for geophysical flows.