A two-dimensional coupled energy-mass transfer model for simulating rain-on-snow load dynamics on roofs

Climate changes have led to an increase in the frequency and severity of rain-on-snow (ROS) events, risking structural safety with increasing roof snow loads. These events involve melting, freezing, and compaction induced by water infiltration in roof snowpacks. Existing models assume snow as a homogeneous medium with uniform ROS load distribution while ignoring critical phenomena like phase changes, heterogeneity, and evolution of snowpack's properties that alter water retention in snow. Although snow load is adjusted based on slope and roof geometry, these adjustments are not considered for ROS surcharge load. A two-dimensional coupled energy-mass (EM) transfer model using the Multi-point Flux Approximation method (MPFA) is employed to simulate ROS load on sloped roofs along with heat exchange, melting, refreezing, and compaction effects. Compared to simplified mass transfer models, the EM transfer model exhibits superior predictive capabilities when evaluated against experimental results. Although melting and compaction significantly increased the density, reducing porosity and permeability, the melted water accelerated saturation at the bottom boundary, enabling quicker outflow conditions. A non-uniform triangular water retention pattern at the lower roof edge was observed in both models, suggesting that heterogeneity has minimal impact on the water retention profile. Under the studied ROS load conditions, the ROS load at the roof edge is 1.6 times the overall ROS load due to non-uniform water retention. The study highlights the inadequacy of existing design code as the design ROS load is inapplicable to the studied ROS condition, despite localized loads being close to design ROS load (0.38 kN/m²).