Numerical simulation of debris-flow behavior based on the SPH method incorporating the Herschel-Bulkley-Papanastasiou rheology model

Three-dimensional numerical simulation of mud flow from a tailing dam failure across complex terrain

“…Tailing fluid is similar to debris flow and is generally considered to be an incompressible and viscous fluid. Currently, most existing studies on debris flows and landslides assume that the mud-water mixture is a homogeneous non-Newtonian fluid with a constant density (Dai et al, 2014;Wang et al, 2016;Han et al, 2019). Several authors concluded that a fluid with solid concentrations above 10 % is a non-Newtonian fluid (Komatina and Jovanovic, 1997;Sloff, 1993), and their rheological properties can be described by the Bingham model Komatina and Jovanovic, 1997;Han et al, 2019) that can be represented by the following constitutive equation:…”

“…To overcome this inherent discontinuity issue, several regularized approaches have been proposed, where the infinite viscosity presented in the rigid zone can be approximated by a highly viscous fluid (Papanastasiou, 1987;Hannani et al, 2007;Frigaard and Nouar, 2005). The most popular regularization is the Bingham-Papanastasiou model (Papanastasiou, 1987), which is chosen as the constitutive equation of tailing fluid in the present work.…”

“…Since numerical modeling based on computational fluid dynamics (CFD) has the advantages of sophisticated theory and low cost, it is considered to be a more appropriate solution for analyzing geographic hazards such as water reservoir failures, landslides and debris flows (Dai et al, 2014;Issakhov and Imanberdiyeva, 2019;Han et al, 2019).…”

“…It can be numerically solved by different schemes such as smoothed particle hydrodynamics (SPH) , the finite volume method (FVM) (Medina et al, 2008;Li et al, 2013;Wang et al, 2020) and the finite difference method (FDM) (Wu et al, 2013). However, the shallow water equations are two-dimensional simplifications of Navier-Stokes equations, neglecting the observed nonlinear behavior through the mud depth (Han et al, 2019). For more reliable results, the 3-D Navier-Stokes equations are recommended to control the flow dynamic (Wang et al, 2016;Lee et al, 2010).…”

“…Unlike water, which is a Newtonian fluid, the tailing fluid formed by mixing tailings and water is in nature a non-Newtonian fluid (Henriquez and Simms, 2009) with complex rheological properties. In the early research, the Voellmy frictional model, the frictional model and the general two-phase model were used to describe the rheological behavior of a mixture of water-and clay-like tailing fluids and were successfully applied in 2-D shallow water equations, but these constitutive models may present difficulty in discretizing in the 3-D FVM scheme (Han et al, 2019). Currently, the Bingham model is considered a better way to describe the dynamic behavior of tailing fluids and easy to apply in a 3-D case (Mizani et al, 2013;Henriquez and Simms, 2009;Liao and Zhou, 2015;Gao and Fourie, 2015).…”