Application of a wide-ranging two-phase Debris Flow Model to the 2007 Crater Lake break-out lahar at Mt. Ruapehu, New Zealand

A variety of computational tools exist for portraying the dynamics of granular flow, but much additional research is still needed to produce accurate models that broadly satisfy important empirical data as well as theoretical aspects of this hazardous type of flow. Specifically, better information regarding their evolution in time, flow dynamics and run out distance would be helpful in forecasting the consequences of potentially hazardous events, development of hazard and risk maps, and designing of management policies in areas of potential natural disasters. Many existing models are: 1) empirical, 2) apply to dry flows like rock avalanches or dense pyroclastic flows, or 3) simulate very dilute water flows like floods. Although current models can replicate some specific scenarios of observed natural debris flows many fail to satisfy important aspects of the physics and dynamics of actual phenomena. Because water content plays a major role in the dynamics of debris flows we developed a new, more general, two-phase model that is valid for a broad range of water and solid mixtures. This model avoids some of the uncertainty involved in applying debris flow model parameters that are poorly constrained or theoretically unsatisfying. In this model mass and momentum are balanced for each phase; granular material in the flow is assumed to obey a Coulomb constitutive relationship and the fluid matrix is assumed to be inviscid. The Darcy-Weisbach formulation accounts for bed friction and a phenomenological drag coefficient reconciles momentum exchange between phases. The resulting depth averaged equations provide a system of 6 partial differential equations. The subsequent equations correspond to the Savage and Hutter model at the limit of no fluid, and to the typical shallow water solutions for pure water. The two-phase equations of this model operate within the familiar TITAN2D framework (Patra et al. 2005) that was developed to simulate dry granular flows in volcanic landscapes because this code is widely used in hazard assessment (see Murcia et al., 2010). This new model is capable of simulating particle volumetric fractions as dilute as 0.001 and as concentrated as 0.55. The model has been successfully tested on artificial topographic channels as well as on some volcano landscapes. The 2007 Crater Lake break-out lahar, Mt. Ruapehu, New Zealand, is a complex but well-characterized natural debris flow that follows an intricate course through a variety of topographic features. Detailed digital terrain data (DEM) and accurate flow observations allow us to test our computational model with an unusually high level of control for such a large natural flood wave. We compare model and actual data recorded at four Ruapehu observation stations located at runout distances of 2 km, 5 km, 7 km and 9 km. The specific flow data that we compare include: 1) arrival time of the flood front, 2) maximum flood depth, and 3) flow velocity. The computed values for these flow characteristics are all within about ± 10% of the observed figures.