Modellingcohesioninsnowavalancheflow Perry BARTELT, Cesar VERA VALERO, Thomas FEISTL, Marc CHRISTEN, Yves BÜHLER, Othmar BUSER WSL Institute for Snow and Avalanche Research SLF, Davos Dorf, Switzerland Correspondence: Perry Bartelt <bartelt@slf.ch> ABSTRACT. Flowing snow is a cohesive granular material. Snow temperature and moisture content controlthestrengthofthecohesivebondingbetweengranulesandthereforetheoutcomeofgranular interactions.Strong,cohesiveinteractionsreducethefreemechanicalenergyintheavalanchecoreand therefore play a significant role in defining the avalanche flow regime. We introduce cohesion into avalanche dynamics model calculations by (1) treating cohesion as an additional internal binding energythatmustbeovercometoexpandtheavalancheflowvolume,(2)modifyingtheCoulombstress functiontoaccountfortheincreaseinshearbecauseofcohesiveinteractionsand(3)increasingthe activationenergytocontroltheonsetofavalanchefluidization.Themodifiedshearstressfunctionis based on force measurements in chute experiments with flowing snow. Example calculations are performedonidealandrealterraintodemonstratehowsnowcohesionmodifiesavalancheflowand runoutbehaviour. KEYWORDS: avalanches, snow, snow mechanics INTRODUCTION The cohesive properties of snow play an important role in the formation and movement of avalanches (Bozhinskiy and Losev, 1998). When the snow cover collapses and starts moving, it is the cohesive bonding of ice grains that facilitates the formation of hard, compact snow clods and granules that eventually compose the avalanche core (Fig. 1). The strength of the cohesive bonding is determined by the snow temperature and humidity, which therefore control the granule properties (Voytokskiy, 1977; Bartelt and McArdell, 2009) and subsequently the avalanche flow regime (Gauer and others, 2008; Issler and Gauer, 2008; Bartelt and others, 2012a; Naaim and others, 2013). Wet snow avalanches exhibit pronounced cohesive, visco-plas- tic-type flow behaviour (Fig. 1), in contrast to the non- cohesive and dispersive granular motion of dry snow avalanches, which are often accompanied by a powder cloud of suspended ice-dust. Although fundamental to a consistent understanding of avalanche motion, cohesion is rarely included in avalanche dynamics calculations (Naaim and others, 2003; Wang and others, 2004; Pudasaini and Hutter, 2007; Christen and others, 2010). In this paper we introduce one additional model par- ameter to account for cohesion in avalanche flow. The model is based on actual shear and normal stress measure- ments with both wet and dry snow performed on the Swiss Weissfluhjoch experimental chute (Platzer and others, 2007a,b). The model combines two classical definitions of cohesion (Rowlinson, 2002). Firstly, it acts as an additional shear stress in excess of the normal stress-dependent Coulomb shear resistance. This definition is common in soil mechanics applications, where cohesion is considered to arise in particle ensembles from either capillary stresses or discomfited granular geometries and packings (Mitchell, 1993). Cohesion then acts on the shearing processes in the avalanche core, especially in dense flows at low shear rates. Secondly, cohesion acts as an additional bonding potential to hinder volume expansion of the core. Cohesion therefore controls the avalanche flow density and thus, indirectly, the shear resistance and the flow height. These definitions of cohesion are based not only on the chute experiments, but also on the wide range of runout features found in avalanche deposits, especially in wet snow avalanche deposits, which often exhibit steep, cohesive side-walls and pile-ups (see Fig. 1) (Jomelli and Bertran, 2001; Miller and others, 2003; Bartelt and others, 2012b). In the next section we introduce the concept of a representative volume V � in the avalanche core � (Fig. 2). Model equations, presented in the following section, describe how the volume V � changes under the actions of the basal shear and normal forces. Only then is it possible to describe how cohesion modifies the shear resistance of the volume to changing boundary conditions, such as rough- ness. We then highlight some of the important character- istics of actual shear and normal stress measurements of both dry and wet snow flows. Of special importance is the slope, dS=dN, of the measured shear S versus pressure N diagrams, which often exhibit a sharp transition at low pressures, similar to yielding-type phenomena. This property has been observed in other experimental investigations with snow (Dent and Lang, 1983; Nishimura and Maeno, 1987; Nishimura, 1990; Salm, 1993; Bartelt and others, 2005). Therefore the relationship between S and N cannot be described by a simple Coulomb relation, as is typically assumed in avalanche models. To demonstrate how the model works, we simulate snow-chute experiments and investigate the role of cohesion in both theoretical and real case studies. The model describes cohesion in both dry and wet avalanche flows. AVALANCHEMASS,VOLUMEANDENERGY We consider the avalanche core � to consist of represen- tative volumes V � (Fig. 2). The height of the volume is the avalanche flow height h � . The volumes contain particulate snow mass in the form of granules or snow fragments. The amount of mass in the volume is M � . As we model the granular ensemble as a continuum, the self-weight of the Journal of Glaciology, Vol. 61, No. 229, 2015 doi: 10.3189/2015JoG14J126 837 https://doi.org/10.3189/2015JoG14J126 Published online by Cambridge University Press