A general two‐phase debris flow model

Abstract

[1] This paper presents a new, generalized two-phase debris flow model that includes many essential physical phenomena. The model employs the Mohr-Coulomb plasticity for the solid stress, and the fluid stress is modeled as a solid-volume-fraction-gradient-enhanced non-Newtonian viscous stress. The generalized interfacial momentum transfer includes viscous drag, buoyancy, and virtual mass. A new, generalized drag force is proposed that covers both solid-like and fluid-like contributions, and can be applied to drag ranging from linear to quadratic. Strong coupling between the solid-and the fluid-momentum transfer leads to simultaneous deformation, mixing, and separation of the phases. Inclusion of the non-Newtonian viscous stresses is important in several aspects. The evolution, advection, and diffusion of the solid-volume fraction plays an important role. The model, which includes three innovative, fundamentally new, and dominant physical aspects (enhanced viscous stress, virtual mass, generalized drag) constitutes the most generalized two-phase flow model to date, and can reproduce results from most previous simple models that consider single-and two-phase avalanches and debris flows as special cases. Numerical results indicate that the model can adequately describe the complex dynamics of subaerial two-phase debris flows, particle-laden and dispersive flows, sediment transport, and submarine debris flows and associated phenomena.

A multivariate generalized linear tsunami fragility model for Kesennuma City based on maximum flow depths, velocities and debris impact, with evaluation of predictive accuracy

“…Flow velocities, on the other hand, can be used as an IM but require detailed numerical simulations (Mader 2004). Recent advances in phase flow modeling also demonstrate flow height and velocity could better be obtained by applying sophisticated two-phase models such as those proposed by Pudasaini (2012Pudasaini ( , 2014. Scour is a complex process which depends on factors such as flow approach angle, number of waves, soil conditions (Chock et al 2011), which are typically not reported or straightforward to identify.…”

“…1-taken from FEMA (2008) and Chock et al (2011). Nevertheless, such dynamical quantities (flow depth and velocities) can better be obtained by applying a real two-phase mass flow model and unified simulation techniques as proposed in Pudasaini (2012Pudasaini ( , 2014. In addition, variables such as the Froude number (for example, as used in the scour depth estimation in Fig.…”

“…In this figure, h is the tsunami flow depth, u is the horizontal flow velocity, q s is the fluid density (accounting for sediment density), g is the acceleration of gravity, b is the breadth of the structure, C d is the drag coefficient, C m is the virtual mass coefficient, and u d is the velocity of the debris. u d must the relative velocity between the solid and the fluid with the virtual mass coefficient (Pudasaini 2012), k is the effective contact stiffness of the debris object and the impacted system as described in Chock et al (2011), m is the mass of the debris, z m is the scour depth, Fr is the Froude number (Hughes 1993), and K a the approach angle into account several important dynamical aspects of the flow including the gravity and pressure potential energies and the kinetic energy of the flow (Pudasaini and Dominik 2009). Moreover, the Froude number should also include the phase-Froude numbers for solid and fluid as proposed in Pudasaini (2012), which takes into account interactions between the solid and fluid components.…”

“…u d must the relative velocity between the solid and the fluid with the virtual mass coefficient (Pudasaini 2012), k is the effective contact stiffness of the debris object and the impacted system as described in Chock et al (2011), m is the mass of the debris, z m is the scour depth, Fr is the Froude number (Hughes 1993), and K a the approach angle into account several important dynamical aspects of the flow including the gravity and pressure potential energies and the kinetic energy of the flow (Pudasaini and Dominik 2009). Moreover, the Froude number should also include the phase-Froude numbers for solid and fluid as proposed in Pudasaini (2012), which takes into account interactions between the solid and fluid components. While flow depth has been found to be a good predictor of tsunami damage for low damage states (Charvet et al 2014a, b), it is clear that the contribution of such variables will be increasingly important in explaining higher damage states and should be included in the model in order to yield better results (Fig.…”

A depth-averaged debris-flow model that includes the effects of evolving dilatancy. II. Numerical predictions and experimental tests

“…Pitman & Le [4] developed a depth-averaged version of Jackson's [5] three-dimensional, two-phase granular-fluid equations, and various extensions of their model have been proposed (e.g. [6][7][8]). These models are expressed as hyperbolic systems of partial differential equations, yet they possess an unstable elliptic degeneracy associated with loss of hyperbolicity in particular flow regimes [6,9].…”