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Cold Regions Science and Technology 69 (2011) 156164

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Cold Regions Science and Technologyj o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / c o l d r e g i o n s

An explicit numerical model for the study of snow's response to explosive air blastD.A. Miller , R.G. Tichota, E.E. AdamsDepartment of Civil Engineering, Montana State University, Bozeman, MT, United States

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a b s t r a c tIn this paper, an analytic tool is used to examine the internal dynamic snow response during explosive events. An explicit nonlinear dynamic model (using ANSYS/AUTODYN) is presented where the explosion, shock propagation through air and snow response is simulated in a single analysis. This versatile approach handles the complex interactions from explosive events and solids, gases and liquids. Nonlinear interactions and responses are modeled during the detonation and subsequent propagation. The model predicts internal structural response during explosive events, including important parameters such as stress, strain, density changes, velocity and acceleration. Snow shock Hugoniots are used for volumetric constitutive relationships with the deviatoric relationships modeled as linear elastic. The analysis shows stress waves in the snow resulting from the explosive shock wave traveling over the surface. While the normal load transits the weak layer, a shear stress wave concentrated above the weak layer develops. The intensity at depth and lateral extent of the stress wave may be an important consideration for initiating avalanches with explosives. Examples with charges on and above the snow surface support the well known air burst advantage, but also show that the dynamic enhancement is not due to peak air pressure alone. Results for two explosive congurations support enhanced dynamic response with increased air pressure impulse, providing further insight into the suspended charge advantage. Charge size is briey examined with larger explosives providing an advantage in stress wave intensity and range. Various snowpack congurations and explosive charges with variable locations can be examined with this approach. The analytic approach provides a tool for future detailed examination of critical avalanche control parameters. 2011 Elsevier B.V. All rights reserved.

Article history: Received 19 November 2010 Accepted 6 August 2011 Keywords: Avalanche control Snow explosives Explicit model

1. Introduction Explosives are routinely used to initiate avalanches to stabilize snow on slopes. Many ski resorts and highway departments use this method as part of efforts to maintain public safety by reducing avalanche hazards. Understanding the dynamic response of a snowpack during shock wave interaction is important for effective use of avalanche control explosives. Currently, the probability of success in inducing an avalanche is based largely on the personnel experience in charge type, size, placement and timing coupled with historical performance of a particular slope. Unintended avalanche release, after explosive control efforts, has recently had a devastating toll. During the 2008/09 winter, 4 people were killed and another 18 buried within US ski resort boundaries by avalanches (Abromeit, 2010). Since 2009, avalanches within US resort boundaries have killed three additional people. Most of these incidents were classied post control release where the avalanche unexpectedly initiated after explosive control efforts failed to stabilize the slope. While we cannot yet identify all the causal mechanisms of these events, they have Corresponding author at: Department of Civil Engineering, Montana State University, PO Box, 173900, 205 Cobleigh Hall, Bozeman, MT 59717, United States. Tel.: + 1 406 994 6118. E-mail address: [email protected] (D.A. Miller). 0165-232X/$ see front matter 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.coldregions.2011.08.004

motivated new efforts looking at responses of snowpacks to explosive events. Historically, there has been signicant experimental investigation of explosives detonated on or above the snow surface (eg: Gubler, 1977; Ingram, 1962; Joachim, 1967; Wisotski and Snyer, 1966). These studies revealed the enhanced effectiveness of suspended explosives in inducing avalanches. As a result, suspended techniques are commonly practiced in the avalanche control industry. Buried explosives dedicate signicant energy to crater formation with local dissipation yielding little momentum transfer away from the crater (Johnson et al., 1994). Detonations on and above the surface are examined here, but the numerical techniques could accommodate analysis of buried explosives in snow covers. Detonations in the air produce a spherically expanding shock wave that decreases in intensity with distance from the blast due to geometric wave expansion and medium attenuation. As the wave travels over the snow surface, energy from the air shock is transmitted to the snowpack inducing shock in the pores and stress waves within the ice network. Within the snow, this produces a spherical shock that dissipates not only due to geometric expansion but also due to snow compaction. As detonation height above the snow is increased, the air pressure immediately beneath the blast decreases, but the air pressure at distances away from the blast will increase to a maximum value and then decrease as the explosive is raised further. Johnson et al. (1994) analyzed experimental air blast data from Ingram (1962) and Wisotski

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and Snyer (1966) (summarized in O'Keeffe (1965) and Mellor (1985)) and presented a scaled curve of maximum air pressure as a function of burst height and radius from the blast vertical axis. This curve identies the scaled burst height for maximum pressure at particular scaled distances. The data supports ~40% increase in overpressure as the detonation height is increased from the surface to the optimal height (for a particular range and net explosive weight). The maximum overpressure was relatively insensitive to scaled detonation heights above ~2 m/kg1/3. Gubler (1977) conducted eld experiments where charge mass, snowpack stratigraphy, explosive type, charge placement relative to the surface and ground type were considered. One signicant conclusion of Gubler's work is that 1 kg charges detonated from 1 to 2 m above the surface have enhanced results for releasing dry slab avalanches. Ueland (1992) used mining seismographs to measure the vertical response of snowpacks during explosive events. His work conrmed the air blast advantage over surface or buried charges, but also examined shock attenuation through the snowpack depth. He found snow hardness, more than density, was a signicant factor in shock attenuation. With the relationships of range, explosive weight and blast height established; what peak pressure at what range is required for avalanche release? Few data exist to answer this question, but Mellor (1973) suggests loading the anticipated avalanche release zone with at least 3.5 kPa, but detailed analysis or empirical data justifying this limit is lacking. A numerical approach that can predict internal snowpack responses would be valuable for investigating load distributions through the depth of the snowpack at various ranges from the blast center. Brown (1981) developed jump equations to describe the change in snow physical parameters across a shock wave. Of particular interest, he predicted the change in snow density across the shock. He found it difcult to validate his approach due to a shortage of good shock wave measurements in snow. Johnson (1991) developed a momentum model to predict shock wave attenuation in snow. He showed that snow attenuation was largely dependent upon the snow pressure density relationship. To predict the snow response to explosives, volumetric constitutive relationships must be used to describe snowpack compression during loading. Haehnel and Shoop (2004) present a capped DruckerPrager model simulating the loaddeformation characteristics of snow. Their model provides upper and lower bounds for the response of low density snow loaded at high strain rates, but was applied to tire movement through snow, not to explosive loading. Some experimental research has focused on snow response to explosives to better develop constitutive relationships. Furnish and Boslough (1996) conducted impact tests on snow samples and material simulators to experimentally derive shock Hugoniot states, reshock characteristics and release properties. They report reliable snow Hugoniot states, with snow density of 500 kg/m 3, at stresses up to ~4 GPa. Johnson and Solie (1993) conducted gas gun impact tests (with analysis) to determine the pressuredensity relationships for several initial snow densities with stresses up to 40 MPa. In all of the tests, snow had signicant shock attenuation. Johnson and Solie (1993, 1994) discuss snow's large load hysteresis due to its small volume recovery during unloading. This compaction characteristic is very important for understanding snow's response to explosives. In close proximity to the blast, the snow will compact to a critical density value before accepting signicant stress. The pressure required to compact snow to a nal density value increased with decreasing initial density. To initiate slab avalanche release, Heierli et al. (2008) present a two stage process for fracture and subsequent avalanche. In the rst stage, normal and shear stress combine in loading a preexisting aw. When the mechanical energy reaches a critical value for a particular crack nucleus, fracture progresses with a mixed mode anticrack. This failure mode is driven by a volumetric collapse of a layer containing the crack nucleus. Afte

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