Verification of a 2D finite element debris flow model using Bingham and cross rheological formulations

Abstract

We propose a vertically-averaged 2D debris flow model based on the non-Newtonian Bingham and Cross rheological formulations. In the Cross model, fluid viscosity changes continuously through the range of shear rates. The 2D model is based on the shallow water equations, where the internal friction losses are implemented using the Cross constitutive relations. The numerical method is based on a four-step, selective lumping, explicit time stepping scheme. We present preliminary tests for one dimensional and two dimensional dam break problems. Model results show very good agreement with experimental data and analytical solutions in one dimensional cases. For the flow early stages, the numerical solution agrees better with the experimental data than with the analytical solution. However, in final stages, the numerical solution predicts that the fluid front advances more rapidly than the analytical solution and measured fluid front. The proposed 2D debris flow model provides very stable results even in the range of very low shear rates, where other discontinuous constitutive relations that use the yield stress may become unstable.

A Modular, Non-Newtonian, Model, Library Framework (DebrisLib) for Post-Wildfire Flood Risk Management

“…These physics-based numerical models simulate advection with constitutive laws of fluid mechanics in one-and two-dimensions. Savage and Hutter 40 (1989) provided the foundation for predicting non-Newtonian flow using Saint-Venant based shallow-water equations which have been commonly applied for numerical modelling of rapid mass movements over irregular geometry (e.g., Chen and Lee, 2000;Iverson and Denlinger, 2001;Pudasaini et al, 2005;Naef et al, 2006;Martinez et al, 2007;Pastor et al, 2009;Luna et al, 2012).…”

Prediction of debris flows in the Korean Oship River based on climate change scenarios

“…McDougall et al (2003) developed a depth-averaged model to simulate slope failures, and Calligaris et al (2008) simulated the debris flow in the Italian Alps using a numerical computer program. Martinez et al (2008) analyzed debris flow using the Non-Newtonian Bingham model with the shallow water wave equation and compared these results with the ones obtained by the finite element method. Nakataini et al (2008) developed a computer program that can consider check dams with the one-dimensional depth-averaged model using the erosion/deposition model developed by Takahashi et al (1992), and applied it to Cipanas, Indonesia.…”