Discrete blasts in granular material yield two-stage process of cavitation and granular fountaining

Authors


Abstract

A discrete blast within granular material, such as a single subterranean explosion within a debris-filled diatreme structure, is typically considered to produce a single uprush of material. Our experiments demonstrate that apparent “debris jet deposits” can be formed by a two-stage process of cavitation and subsequent granular fountaining. Bench-scale experiments reported here demonstrate that for a range of overpressures and depths, individual, discrete, buried gas blasts open space and expel particles from the blast site in two largely decoupled stages. Expanding gas initially pierces material nearest the blast source to open a cavity above it; then a fountain of grains rises from the source into the cavity. This staged motion dynamically segregates source grains from host-material grains, and the rates of cavity opening versus fountain rise show a power law decay relationship with initial pressure. Our experimental analysis has implications for maar-diatreme systems, field-scale detonation experiments, and underground nuclear testing.

1 Introduction

A “debris jet” in volcanology can be defined as an explosion-generated upward moving low-density mixture of pyroclastic debris and gases, propelled into a preexisting, nonfluidized, and nonconsolidated mass [Ross et al., 2008b]. They have been specifically inferred from deposits of maar-diatreme volcanic systems; the material mobilized by debris jets is inferred to have penetrated through the overlying material, and the jet either breaches or fails to breach the surface of the system [Lorenz and Kurszlaukis, 2007; Ross et al., 2008a, 2008b; Taddeucci et al., 2009; Lefebvre et al., 2013]. In such maar-diatreme systems, debris jet(s) directly and characteristically shape the diatreme-structure infill through the initial explosive expansion followed by within-cavity sedimentation plus or minus surface eruptive effects [White and Ross, 2011]. Gases rapidly expand and propagate upward toward the surface during any discrete explosion at depth within a granular host; these overpressurized gases may be carrying particles generated at the explosion site (e.g., bomb casings and “active” phreatomagmatic particles [Büttner et al., 2002]) and particles entrained from the granular host surrounding the site.

Discrete explosions can form craters, and there are known relationships between explosion energy and crater size [e.g., Sato and Taniguchi, 1997; Goto et al., 2001; Valentine et al., 2012]. Less well known is how particles, both juvenile and accidental, become entrained in such explosions and how preserved subcrater structures reflect the dynamics of discrete explosions and particle entrainment during discontinuous volcanic eruptions [e.g., White and Ross, 2011; Ross et al., 2013]. The bench-scale blast experiments here, although designed primarily to study the “debris jet” phenomenon, yield new information related to crater formation, debris jet formation, diatreme formation, particle entrainment, and sedimentation from blasts within any particulate material. We focus here on describing and quantifying an unanticipated phenomenon clearly observed in the experiments, which we call dynamic segregation. It segregates blast-source material into a granular fountain, which forms after and enters into the cavity opened within the host granular material by the blast.

2 Methods

In our experiments, we use a setup based on the one described by Ross et al. [2008b], but our new setup allows the variation of blast depth within the granular system and the recording of the pressure and force history during the experimental runs. A variable, initial pressure-dependent volume of compressed argon gas was rapidly released (300 ms), at a range of overpressures (0.5–2 MPa), through an orifice of constant radius and volume, into the base of a crucible filled with very well sorted 300 µm red glass beads. The orifice is smaller in diameter than the crucible, and for the red beads in the crucible to be driven upward, they must couple with the expanding gas. Upon release into the crucible, the compressed gas in our experiments begins to expand, entrains a proportion of the red beads, then further expands upward into an overlying mass of very well sorted (300 µm) white glass beads. For the purpose of examining particle transport and emplacement, the red beads in the crucible, which separate the orifice from the overlying granular mass, represent primary “juvenile” pyroclastic particles of a volcanic explosion that originate and are entrained at the explosion source. Experiments were filmed through a vertical glass window with a high-speed (1000 fps) high-resolution (1 Mpx/frame) camera imaging an area of 400 × 500 mm at 5 px/mm2. We also recorded several time-dependent physical parameters including the vertical force applied to the setup by the accelerating mass of particles, the driving pressure beyond the valve, and the pressure fluctuations both in the crucible and in the overlying stratigraphy, with sensors aligned vertically upward from the opening of the crucible behind the overlying granular material. (see Figure S1 in the supporting information for a depiction of the experimental setup.)

3 Experimental Results

To facilitate description, we highlight key terms here in a generalized description of a run. A blast is the rapid expansion of compressed gas released into the base of a crucible filled with red beads that are a proxy for juvenile grains from the explosion source. The crucible lies within a granular mass of white beads, which enclose and overlie the crucible. Lines of blue beads at the inner wall of the rig help visualize behavior of layers, strata, in the bead mass. The explosion opens a cavity by the process of cavitation as expanding gas pushes the bead mass aside and upward. The cavity begins growing below the surface of the bead mass but domes the overlying beads upward, above the surrounding bead surface. Fully developed, a cavity has a domed roof, and walls where the white bead mass has been pushed aside. Cavity collapse takes place as walls flow inward and the roof breaks up or falls downward. A granular fountain is the ~ cylindrical uprush of red beads from the crucible, sometimes followed by opening of a secondary cavity in the granular mass. An eruption takes place when the dome bursts and material rising through the cavity is expelled to the bead-mass surface.

During almost all experimental runs here, the argon jet initially penetrated the mass of red beads in the crucible and expanded to open a cavity in the overlying white bead mass (Figure 1, t = 130 ms). The expanding overpressurized gas opens the cavity into an inverse teardrop shape, with space for this expansion made by doming of the white bead mass's surface (Figure 1). The pressure peak reading in Figure 2 (t = 50 ms, red line) records the maximum driving pressure as the compressed gas begins explosive expansion into the granular mass. This part of the run we refer to as the “cavitation phase.”

Figure 1.

Images from Run 18 video (16 cm crucible depth and 2 MPa initial pressure). Top left numbers in each frame give time after initiation in milliseconds. SIKA 1 (purple circle) and SIKA 2 (blue circle) are pressure sensors located behind the white bead mass. Thick, black, horizontal line indicates width and level of crucible top. At 0 ms the valve opens and compressed argon gas is released. The granular fountain, containing the majority of the red beads, emerges at 185 ms, after the driving pressure values have dropped to nearly zero, implying that expansion of the compressed gas has already taken place. Much of the crucible's red bead fountain is “captured” to form a vertical, roughly cylindrical structure, beginning at 330 ms, through zipping. Note that the crater initially visible is the result of a previous, shallow blast.

Figure 2.

Driving pressures and force record for Run 18 illustrated in Figure 1. Pressure peaks for each sensor match observed time at which the opening cavity's front passed the sensors, first behind the crucible, then opening upward past SIKA 1 and then 2. Pressure and force curves, beyond the initial sharp declines, record only system resonance.

Before surface doming has concluded, the gas cavity begins to close from the base by lateral inflow of the granular walls (Figure 1, t = 287 ms onward) or breaks down at the top by outward expansion and breakdown of the attenuating dome (Figure 3, t = 211 ms onward). This continues while material from the roof of the dome, and beads of the cavity walls, begins descending into the space generated by the expanding gas.

Figure 3.

Run 22 (8 cm crucible depth and 1.5 MPa initial pressure), an eruption produced after a previous, deeper blast, deposits from which are visible before this run. Cavity opening is visible from 105 ms onward. The granular fountain, which transports most of the red beads out of the crucible, is visible from 285 ms onward. This run's dome bursted and collapsed outward, rather than inward, reflecting the shallow blast depth and high initial pressure. Thick, black, horizontal line indicates width and level of crucible top.

The force peak reading in Figure 2 (t = 70 ms, green line) records the maximum unloading of the mass on the crucible, denoting the maximum acceleration of the red bead mass and the point at which the entirety of the red bead mass within the crucible has begun moving up into the overlying granular system. Note that at this point in the runs cavity growth has just commenced, and only a minority of the red beads from the crucible are seen moving upward.

As the cavity begins to collapse, most of the red bead mass contained initially within the crucible rises in a granular fountain upward from the base of the white bead stratigraphy, along with a small volume of entrained white beads. The fountain then begins to spread within the collapsing cavity (Figures 1 and 3). This fountaining is almost always observed in runs at initial compressed gas pressures of 0.5 MPa or more across all depths, and regardless of whether or not the run produced an eruption. Less pronounced upward red bead flow is mentioned briefly in Ross et al. [2008b], whose authors referred to it as the “flat bottom effect”—an inward lateral flow of material.

Cavity collapse involves gravity-driven sedimentation of the roof with downward and inward flows of the cavity walls in a zipping motion that can capture a still rising granular fountaining mass as a vertical, thin structure [Ross et al., 2008b] and leaves a crater at the bead mass surface (Figures 1 and 3). Together, cavitation, fountaining, and collapse form what has been described as a “debris jet” deposit [White and Ross, 2011]. This deposit, a vertical, thin structure—produced in each of these experimental runs—is comparable to those in natural maar-diatremes [Ross et al., 2008a, 2008b; White and Ross, 2011; Lefebvre et al., 2013].

Experimental runs 18, 22, 17, and 20 are included as high-speed Movies S1–S4, respectively, wherein across a range of conditions, the separation of cavity opening from the granular fountain of beads from the crucible is clearly visible. Run 23 (Movie S5) shows additional evidence for the initial piercing jet feature of the runs during the gas-expansion cavitation phase.

4 Discussion

The compressed argon gas released during these runs expands too quickly to flow through interconnected pores between beads and instead pushes aside and upward a mass of overlying white beads, even at the lowest initial pressures used. Beads move in two stages (Figure 4):

  1. First, the argon gas jet penetrates the crucible red bead mass above the orifice, where the vertical driving pressure and gas flow velocity will inevitably be highest, before expanding to open the cavity in the white bead host. This expanding jet carries few red beads, in contrast to behavior documented by Ross et al. [2008a, 2008b] in which most red beads apparently were entrained at this stage and accumulated at the walls and roof of the cavity.

  2. Next, the bulk of red beads leaves the crucible as a granular fountain upward into the open cavity. The fountain is largely driven by secondary expansion of gas from the same release of compressed gas that opened the cavity. Upon release, some gas spreads out at the base of the crucible because it was not accommodated in the piercing central jet and could not simply escape through the open porosity of the overlying beads. After the opening of the cavity by the initial piercing gas jet, the pressure gradients within the granular system change, and the horizontally dispersed gas pressed into the crucible beads reexpands back toward the center of the cavity. The merging of the inward flowing gas with its disrupted granular host is additionally driven by gravitational flow of the beads, and we also infer that there is some elastic deformation of the beads themselves, with recovery also aiding the inward drive of the gas bead mass. The inward flowing mass converges to form a fountain, which carries the majority of the red bead mass upward into the center of the cavity. On a scale of milliseconds, fountaining begins distinctly later than cavitation.

Figure 4.

Run 17 (8 cm crucible depth and 2 MPa initial pressure), with schematic, unscaled, illustration of the dynamic segregation effect. Yellow arrows represent the cavity-forming piercing gas; the green arrows represent the rest of the gas escaping. Thick, black, horizontal line indicates width and level of crucible top.

Velocity calculations obtained from particle image velocimetry (PIV) are detailed in Figure 5a for the central piercing, for the cavity-opening jet, and for the red bead granular fountain. The higher the ratio between the two velocities, the more strongly separated in time the rise of the granular fountain is from initial opening of the cavity. Thus, it can be said that this ratio represents a dynamic segregation of particles in the overlying mass (α) from those of the fountaining mass (β). It is clear in Figure 5a that this dynamic segregation effect is more pronounced at shallow depths: The velocity ratios for each depth are distinct across all overpressures, with the ratio value increasing greatly with the decrease in blast depth. For each blast depth, the velocity ratio increases in an approximately linear fashion with increasing initial overpressures.

Figure 5.

(a) Initial pressure plotted against velocity ratio. Velocities in m/s were derived by particle image velocimetry (PIV): {α}, the average velocity of the cavity roof mass, and {β}, the average velocity of fountaining red bead mass. We plot the ratio α/β, which quantitatively represents the degree of dynamic segregation in a run: The higher the ratio, the more unevenly distributed the momentum from the gas-release blast. (b) Differential of (velocity ratio/initial pressure) plotted against crucible depth relates the velocity ratio (α/β) and initial overpressure (PI) trends as seen above, to the crucible “blast” depth.

The rates of change between the velocity ratio and the initial overpressures for each depth are represented in Figure 5a; Figure 5b plots the relationship between the differential functions of the velocity ratio (α/β) and initial overpressure (PI) trends, and the blast depth (D). The approximate relationship is represented as

display math

This suggests that with increased depth, there is a power law decay in magnitude of this segregation effect, with a blast-depth constant of 0.0133. At sufficient blast depth, the magnitude of dynamic segregation for a given pressure will approach zero, and the effect will not occur. The overlying preexisting mass load (and in nature, lithostatic pressure) is higher at increased depths, and even with increased initial overpressures, formation of a penetrating jet is impeded. When no penetrating jet forms, the momentum is spread through the crucible and the base of the overlying mass more evenly at depth, and the dynamic segregation effect is reduced or eliminated, as may have been the case for the Ross et al. [2008a, 2008b] experiments.

(See Table S1 for specific velocimetric data for individual runs; Figure S2 depicts the PIV velocity calculation methodology used to obtain this data.)

5 Conclusions

Though not direct analogs for active particles, the red beads are an excellent proxy for the passive particles that comprise the bulk of ejecta transported in subterranean explosions, including “juvenile” phreatomagmatic particles [Büttner et al., 2002]. Significantly, they act as tracer particles for explosion-adjacent material. Our experiments indicate that subterranean explosions in granular materials do not only open a cavity, which may open to a surface crater, but may also generate a granular fountain that focuses transport of material from the explosion site upward into the cavity and potentially to the ground surface. Also, in these experiments the deposition of the majority of the red bead mass, representing at-source particles, to form a cylindrical deposit was controlled by interaction of the granular fountain with cavity closure. The fountain results from a dynamic segregation effect showing a power law decay with depth/pressure and will not form at depth.

As Ross et al. [2008b] note, volcanic vents generally narrow with depth. We suggest that an explosion within debris, filling such a tapering vent structure, could generate a granular fountain into the opened cavity by the process of dynamic segregation described here. If the blast-adjacent particles were fountaining juvenile magmatic ones in a maar-diatreme system, their limited dispersion followed by capture (deposition) in a narrow subvertical column would mean that they were minimally cooled and hence prone to potential welding or other thermal effects.

According to Nordyke [1961], during the gas-venting stage of a subterranean nuclear explosion, “the surface layers experience a much longer period of acceleration than the deep layers,” i.e., a form of dynamic segregation. In addition, final crater morphology may be affected by deposition from a granular fountain. Field-scale experiments in both 2012 and 2013 at Buffalo produced some craters with pronounced mounds inside the crater, which reflect concentrated fallback that might be ascribed to collapse of a granular fountain, though videos do not reveal details in the center of the fallback zone [Valentine et al., 2012; Ross et al., 2013]. The apparent roles of dynamic segregation in both nuclear-explosion and field-scale volcanological experiments illustrate the breadth in scale and intensity of explosions in granular material that may be affected by the dynamic segregation effect described here.

Acknowledgments

R.G.A's travel to Germany was funded by the University of Otago, New Zealand, and from assistance from a subcontract to J.D.L.W from GNS Science, New Zealand.

The Editor thanks James Russell and an anonymous reviewer for their assistance in evaluating this paper.

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