Fibonacci-Like Propagation Graph for Infiltration and Internal Erosion in Heterogeneous Layered Soils

Simone Cammarasana, Marianna Miola 

Infiltration and internal erosion in heterogeneous layered soils involve coupled flow, pressure build-up, and material degradation across preferential subsurface pathways. High-fidelity Richards-type simulators are physically detailed but can be too expensive for rapid scenario screening and Monte Carlo uncertainty propagation when hydraulic parameters are poorly constrained. We introduce a deterministic reduced-order model in which subsurface pathways are encoded by a Fibonacci graph T. The model propagates wetting, pressure, and erosion-propensity indicators through a geotechnically parameterised recurrence, augmented for wetting-front benchmarking by a local reservoir state and an interface-aware hydraulic-contrast correction. Synthetic forcing experiments, uncertainty propagation, and topology ablations show that the Fibonacci graph provides an intermediate-complexity propagation structure between a one-dimensional Chain and a Binary Tree. Direct HYDRUS-1D benchmarks on representative van Genuchten-Mualem homogeneous sand and sand-over-clay profiles show that the interface-aware Fibonacci ROM reproduces the main HYDRUS wetting-front progression with errors on the order of one aggregated depth level. The results support the model as a rapid screening tool for infiltration and pressure-threshold indicators in layered soils.