Applicability of Diffusive model for mud-flows: an unsteady analysis

Simplified versions of the Shallow Water Equations, known as Kinematic and Diffusive models, are commonly applied to the analysis of debris- and mud- flow dynamics. For this reason, the study of their applicability conditions represents an important concern. The present work investigates on the applicability conditions of the Diffusive Wave Model (DWM) for the prediction of mud-flows of shear-thinning fluid represented by a power-law rheology. The study has been carried out through the numerical solution of the DWM and the Full Wave Model (FWM) in unsteady conditions with different hydrographs, i.e. characterized by different durations, assigned at the channel inlet. The analysis has considered different rheological indexes, several values of the Froude (F) and of the Kinematic Wave (K) numbers. Predictions of DWM and FDM have been compared considering the mean value of dimensionless errors on maximum flow depth,ε, and maximum discharge ε. Positive (negative) error leads to an overestimation (underestimation) of the maximum flow depth and flow discharge in the prediction of the DWM. In the present analysis the DWM is considered safely applicable in case of underestimation, i.e. for positive values of ε and ε. Negative errors are acceptable if their absolute value is smaller than 5%. For all the investigated values of the governing parameters, the performance of the DWM has been found to strongly depend on the value of the rheological index, getting worse as the fluid rheology becomes more shear-thinning. Regardless of the hydrograph duration, and for fixed power law exponent (n) and F number values, results indicate the existence of limiting values of the kinematic wave number and above which the DWM is applicable in terms of maximum depth and discharge, respectively. For K values smaller than and , the DWM applicability depends also on the hydrograph duration. In such conditions and for several values of the (F, n) pair, the threshold values of the hydrograph duration necessary for DWM applicability have been identified. The presented applicability criteria represent a useful guideline for the practical application of the DWM in assessing the hazard of a mud flood.