Effects of granular collisions on the rapid coarse-grained materials flow

Abstract

A continuum model to predict the mobility of landslides is developed according to the formulation by Savage and Hutter as well as the main ‘microscopic aspects’ affecting the rapid sliding of granular masses. Conservation of mass and momentum equations, describing the geometry and velocity evolution during the motion, are re-written by considering the effects of collisions between solid grains (‘granular temperature’ and ‘dispersive pressures’) typically occurring within a basal thin ‘shear’ layer, causing a ‘fluidification’ effect and corresponding energy dissipations. To this purpose, a ‘frictional−collisional’ rheological law allowing to simulate the energy dissipation related to grain inelastic collisions and friction, simultaneously acting within the basal ‘shear layer’, is developed and applied. The interstitial pressures, and their possible increment along curved paths related to centrifugal force, and the mass variation due to erosion/deposition processes are also considered. The numerical simulation of a documented experimental test is finally carried out.

Grain‐energy release governs mobility of debris flow due to solid–liquid mass release

“…This implies that existing quasi‐single‐phase models (e.g. Takahashi et al ., 1992; Iverson, 1997; McDougall and Hungr, 2005; Medina et al ., 2008; Armanini et al ., 2009; Rosatti and Begnudelli, 2013; Iverson and George, 2014; Lucas et al ., 2014; Frank et al ., 2015; Cuomo et al ., 2016; Xia et al ., 2018; Federico and Cesali, 2019; Gregoretti et al ., 2019), two‐phase models that presume a single grain size (e.g. Pitman and Le, 2005; Pelanti et al ., 2008; Pailha and Pouliquen, 2009; Pudasaini, 2012; Kowalski and McElwaine, 2013; Bouchut et al ., 2015), and energy balance‐based models (Wang et al ., 2010; Bouchut et al ., 2015) may need to be enhanced for more accurate resolution of debris flows.…”

“…The present model is constructed according to continuum mechanics principles, in which inter‐phase interaction is explicitly taken into account, unlike single‐phase flow models (e.g. Takahashi et al ., 1992; Iverson, 1997; McDougall and Hungr, 2005; Medina et al ., 2008; Armanini et al ., 2009; Rosatti and Begnudelli, 2013; Iverson and George, 2014; Lucas et al ., 2014; Frank et al ., 2015; Cuomo et al ., 2016; Xia et al ., 2018; Federico and Cesali, 2019; Gregoretti et al ., 2019). Unlike existing two‐phase flow models (Pitman and Le, 2005; Pelanti et al ., 2008; Pailha and Pouliquen, 2009; Pudasaini, 2012; Kowalski and McElwaine, 2013; Bouchut et al ., 2015), the present model incorporates multiple grain sizes (noting the typically broad distribution of grain size, which directly affects debris flow mobility – Johnson et al ., 2012; de Haas et al ., 2015; Kaitna et al ., 2016), mass exchange with the bed (that may affect mobility – Iverson, 1997; Hungr and Evans, 2004; Mangeney et al ., 2007; Iverson et al ., 2011; Lube et al ., 2012), and stresses due to strong liquid and solid fluctuations.…”

“…The last several decades have witnessed the development and application of many numerical models of debris flows, the majority being based on depth‐averaged single‐phase flow formulations (e.g. Takahashi et al ., 1992; Iverson, 1997; McDougall and Hungr, 2005; Medina et al ., 2008; Armanini et al ., 2009; Rosatti and Begnudelli, 2013; Iverson and George, 2014; Lucas et al ., 2014; Frank et al ., 2015; Cuomo et al ., 2016; Xia et al ., 2018; Federico and Cesali, 2019; Gregoretti et al ., 2019). Notably, a single‐phase flow model based on energy conservation was proposed by Wang et al .…”