Predicting explosive eruptions remains an outstanding challenge. Knowledge of the controlling parameters and their relative importance is crucial to deepen our understanding of conduit flow dynamics and accurately model the processes involved. This experimental study sheds light on one important parameter—outgassing—and evaluates its influence on magma fragmentation behavior. We perform fragmentation experiments based on the shock tube theory at room temperature on natural pyroclastic material with a connected porosity ranging from 15% to 78%. For each sample series, we determine the initial pressure (P) required to initiate magma fragmentation (fragmentation threshold, Pth). Furthermore, we measure the permeability of each sample for P < Pth and the fragmentation speed for P > Pth. A significant loss of initial pressure, caused by outgassing in samples with permeability ≥1e–12 m2, is observed within the fragmentation time scale (a few milliseconds). The samples are classified into: (a) dome/conduit wall rocks and (b) pumice/scoria. Substantial outgassing during fragmentation leads to higher fragmentation thresholds. Experimental fragmentation speeds are significantly higher than the modeled fragmentation speeds for high-permeability dome/conduit wall rocks, but lower for high-permeability pumices. Experimental fragmentation speeds for low-permeability dome/conduit wall rocks and low-permeability pumice/scoria are as expected. We also find that low-porosity, low-permeability, altered dome/conduit wall rocks fragment at significantly higher speeds than expected. Because fragmentation threshold and fragmentation speed are among the determining parameters for the initiation, sustainment and cessation of an eruption, outgassing should be considered in the modeling of magma fragmentation dynamics.
 The fragmentation of highly viscous bubbly magma lies at the heart of explosive eruption dynamics because it is the ultimate process by which magma breaks up into fragments to form a gas-pyroclast mixture from a volcanic conduit or lava dome. Therefore, parameters controlling fragmentation also control transitions between effusive and explosive eruption regimes. The brittle failure of magma may occur due to (1) the rapid decompression of a bubbly magma by dome collapse or landslide and the overcoming of the tensile strength of the melt [Dingwell, 1996]; (2) high magma acceleration in the volcanic conduit causing an increase in strain rate [Papale, 1999]; (3) the vesiculation of magma until a critical bubble-to-melt volume ratio is reached, followed by a disruption causing bubbles to burst [Sparks, 1978]; or (4) the contact of magma with external water producing phreatomagmatic eruptions. To better understand the fragmentation process triggered by sudden decompression events, shock tube experiments have been performed on natural porous volcanic rocks [e.g., Alidibirov and Dingwell, 1996a; Spieler et al., 2004b; Scheu et al., 2006, 2008].
 The term “fragmentation” refers commonly to magma fragmentation, the magma being a three-phase medium consisting of melt, crystals, and volatiles, with a given porosity and permeability. As mentioned above, there are several processes proposed for magma fragmentation, but our study focuses on the fragmentation of highly viscous bubbly magma by rapid decompression where bubble nucleation and growth are not considered [Dingwell, 1996]. This fragmentation process occurs so rapidly that the magma behaves in a brittle way, just as a solid [Alidibirov, 1994]. Ichihara and Rubin  have explored magma brittleness in detail and their study suggests that for the short time scales of our experiments, highly viscous magma (≥109 Pa s) would behave in a brittle manner. Therefore, it is relevant to investigate controlling parameters for this type of magma fragmentation process such as fragmentation speed and permeability, using volcanic rocks at room temperature [Mueller et al., 2005; Scheu et al., 2006; Mueller et al., 2008; Scheu et al., 2008].
 In the fragmentation of highly viscous bubbly magma, the initial pressure (P) required to initiate and sustain fragmentation (fragmentation threshold) is mainly controlled by the fractional connected porosity (Ф). This initial pressure corresponds to the pressure of the compressed gas inside the bubbles contained in the magma. The energy stored in the compressed gas per unit volume of magma for initial pressures much greater than atmospheric pressure represents the main energy source for the fragmentation process, and is expressed by Alidibirov  as
where γ is the specific heat capacity ratio for magma and gas [Woods, 1995]. We use γ = 1.67 because we assume a “reversible” adiabatic fragmentation process, meaning that there is no heat transfer between the pyroclasts and the expanding gas. Therefore, a state of thermal disequilibrium prevails. In other words, we assume that the fragmentation process is isentropic (no change in entropy). The time scale for gas expansion as the fragmentation front passes is very short relative to the heat transfer time scale between pyroclast and gas [Koyaguchi et al., 2008], which justifies the assumption of isentropic conditions. Based on equation (1), high-porosity magma requires a lower initial pressure to fragment because more energy is available for fragmentation.
 Fragmentation criteria have been defined empirically [Spieler et al., 2004b] and theoretically [McBirney and Murase, 1970; Alidibirov and Dingwell, 1996a; Zhang, 1999; Spieler et al., 2004b; Koyaguchi et al., 2008; Fowler et al., 2010]. Mueller et al.  found an empirical relationship relating permeability, a measure of how easily a fluid can flow through porous media, to the energy required to fragment dome rocks and explosive activity products at threshold overpressures. The fragmentation process itself is thought to consist of bubbles bursting layer by layer before bubble expansion can occur [McBirney and Murase, 1970; Alidibirov and Dingwell, 1996a, 2000; Scheu et al., 2006]. In addition, initial pressure and connected porosity have been shown experimentally to be the main controlling parameters on the speed at which the fragmentation surface propagates through highly viscous bubbly magma (dubbed the fragmentation speed) [Spieler et al., 2004a; Scheu et al., 2006].
Spieler et al. [2004b] postulated, however, that high permeability resulted in higher fragmentation thresholds, based on experimental results on Campi Flegrei samples of 82% and 85% connected porosity. Mueller et al.  have shown that permeability is highly variable even within rocks of similar porosity and suggested that, above a critical permeability value (k) of 1e–12 m2, the fragmentation threshold of magma is higher. Numerical models have considered the effect of gas loss from magma in the volcanic conduit [e.g., Jaupart and Allègre, 1991; Woods and Koyaguchi, 1994; Melnik et al., 2005], but these models account for permeability only as a parameter conducive to effusive volcanism. Burgisser and Gardner  have investigated experimentally and empirically the role of magma ascent rate, bubble growth, and coalescence in the transition between explosive and effusive eruptive regimes, where escape of gas from the magma prevents fragmentation. Klug and Cashman  and Rust and Cashman  have discussed in detail the development of permeability, its effect on the conditions leading to magma fragmentation, and the resulting pyroclast size distribution, but, as in Burgisser and Gardner , not the effect of permeability on the actual fragmentation process for fragmentation threshold or speed.
 In this study, we revisit the influence of permeable gas flow on the fragmentation threshold, but focus our interest on the influence of permeable gas flow on fragmentation speed. We refer to permeable gas flow/gas loss observed within the time scale of magma fragmentation as outgassing. We expect that outgassing due to high permeability hinders the build up of overpressure in highly viscous bubbly magma during rapid decompression and reduces the energy available for fragmentation. The overpressure is the pressure difference between the pressure in the gas phase and the pressure in the solid phase or magma once decompression begins [Fowler et al., 2010]. We perform shock tube experiments on natural volcanic rock samples of dome/conduit wall rocks and pumice/scoria over a wide range of connected porosity and permeability and detect significant outgassing of samples. The model of Koyaguchi et al.  is used to calculate fragmentation speeds to compare with our experimental fragmentation speeds and investigate the effect of outgassing on magma fragmentation speed.
2 Sample Material
 Pumice, scoria, and mostly blocks from preexisting lava domes or possibly volcanic conduit walls were collected in volcanoclastic deposits from Lipari, Aeolian Islands, Italy and from volcanoes along the Ring of Fire: Colima, Mexico; Augustine, Alaska, USA; Bezymianny, Russia; Krakatau and Kelut, Java, Indonesia (Table 1). Field samples were large enough to drill at least five cylinders that were 60 mm high and of 25 mm diameter. The connected porosity of the cylindrical samples was measured with a Helium Pycnometer (Accupyc 1330, Micromeritics) and spans a wide range from 15 to 78% (Table 1). We will refer to each sample set by the name of the sample set, and we sometimes add the sample's average connected porosity for clarity. The samples collected were as fresh as possible, with little to no alteration and a groundmass containing glass (Figure 1). Groundmass compositions range from rhyolite through basaltic andesite. Colima-C6 is one exception where the sample had a slightly reddish tint and its groundmass consisted of feldspar microlites, oxides and < l% glass. Plagioclase phenocrysts had altered rims and amphibole phenocrysts showed corona textures. It is also worth noting that this sample contained fine-grained enclaves up to 1 cm in size. Colima-D2 and Bezymianny-D2 show pronounced tortuous elongated voids, possibly as a result of shear within a dome or conduit wall.
Table 1. Description of the Samples Collected: Provenance, Bulk and Glass Composition, Average Connected Porosity, Closed Porosity, Formation Factor, Electrical Tortuosity, and Permeability
Bulk and Glass Composition
Average Connected Porosity (Fraction Void Space Φ)
1999 block-and-ash flow deposits in San Antonio valley
andesitic, <<1% visible glass
andesitic, rhyolitic groundmass
1913 lahar in Cordoban valley
Augustine, Aleutian Islands
1986 pyroclastic flow deposit
andesitic, rhyolitic groundmass
1956 pyroclastic flow deposit from directed blast
andesitic, rhyolitic groundmass
2000 block-and-ash flow deposit
andesitic, rhyolitic groundmass
Anak Krakatau, Indonesia
1999 pyroclastic deposit from Strombolian eruption
basaltic-andesite, andesitic groundmass
1990 pyroclastic flow deposit from subplinian eruption
basaltic-andesite, dacitic groundmass
Lipari, Aeolian Islands
Pumice from 500-600 AD Monte Pilato eruption
rhyolitic, rhyolitic groundmass
 The experimental cylinders were usually drilled in the elongation direction of the fabric formed by vesicles, crystals and/or compositional banding. However, for Colima-C6 and Krakatau-D4, the cylinders were drilled perpendicular to the observed fabric due to the shape of the samples. Bezymianny-C3 I and Bezymianny-C3 II were drilled from the same block, but the former sample set was drilled perpendicular to the fabric, and the latter, parallel to the fabric. The orientation of the drilled samples relative to the rock fabric can have an effect on the permeability of the samples during experiments due to permeability anisotropy.
 A shock-tube apparatus is used to perform fragmentation experiments by rapid decompression at room temperature and pressures up to 30 MPa (Figure 2) [Alidibirov and Dingwell, 1996a, 1996b; Spieler et al., 2004a, 2004b; Scheu et al., 2006]. The experimental setup consists of a steel autoclave fixed to the bottom of a tank (height = 3 m, diameter = 0.4 m), the latter of which operates at atmospheric conditions. The sample cylinders are glued with Crystal Bond glue into a steel sample holder and tightly inserted in the autoclave. The autoclave and the tank are separated by a series of copper or aluminum diaphragms that rupture for specific initial pressures. The autoclave is slowly pressurized with argon gas to the desired initial pressure; in this study, the maximum initial pressure is 30 MPa. Following the sudden rupture of the diaphragms, a shock wave propagates into the air of the large tank, the argon gas expands up into the large tank, the autoclave decompresses rapidly, and a rarefaction wave is generated. A fragmentation front (or surface), defined as the boundary between the intact porous rock and the gas-pyroclast mixture, travels down the sample cylinder for P > Pth. As long as the overpressure, defined as the pressure difference between the pressure in the gas phase and the pressure in the solid phase, is higher than the tensile strength of the solid phase, fragmentation continues. Two dynamic pressure transducers track the pressure release at the top and at the bottom of the sample cylinder. The sudden pressure drop at the top of the sample cylinder is considered as the start of the fragmentation process for P > Pth, and the sudden pressure drop at the bottom of the sample cylinder, as the end of the fragmentation process. The very short delay between the start of decompression of the autoclave and the start of fragmentation is neglected. We are also aware that, once the fragmentation front has reached the bottom of the sample cylinder, the fragmentation process may continue. Further desintegration of individual fragments can occur as long as the fragments are in a decompressive regime [McGuinness et al., 2012].
3.1 Types of Experiments
 The shock tube apparatus allows us to (1) determine the fragmentation threshold of each sample set, (2) estimate permeability for most sample cylinders used in fragmentation experiments, and (3) measure the fragmentation speed for initial pressures greater than the fragmentation threshold. All experiments are performed at room temperature.
 First, a series of experiments is performed for each sample set in order to obtain a fragmentation threshold. The fragmentation threshold was previously defined as the initial pressure at which a sample completely fragments [Spieler et al., 2004b] and was set to a fragmentation speed value of 0 m/s. However, it is possible to calculate a fragmentation speed when the sample completely fragments, not to mention that the fragmentation threshold is likely to be at a pressure value slightly lower than the pressure at which a sample completely fragmented during an experiment. For this reason, we follow the modified fragmentation threshold definition used in [Scheu et al. 2006 and Alatorre-Ibargüengoitia et al. 2011]. The fragmentation threshold is a pressure range that includes both fragmentation initiation and complete fragmentation. The initiation of fragmentation represents the breaking away of the top few millimeters of the sample cylinder and the complete fragmentation means that the whole sample cylinder fragments, indicating that the initial pressure was sufficient to sustain the fragmentation process. Partial fragmentation occurs when the fragmentation process cannot be sustained for the whole length of the sample cylinder, and part of the sample cylinder remains intact and glued inside the sample holder. For each sample set, we average the initial pressure where fragmentation initiation is observed and the initial pressure at which complete fragmentation occurs. Threshold values for a given sample set are averaged.
 Before each fragmentation experiment, we estimate permeability by measuring the pressure decay at the top and bottom of sample cylinders for initial pressures of 2 MPa for samples with >40% connected porosity, and 4 MPa for samples with <40% connected porosity. We use the same experimental apparatus for permeability measurements as for fragmentation experiments. Therefore, we ensure highest reliability of the data because each sample remains glued in the same sample holder for all measurements and experiments performed on any given sample. In our measurements, a steady (or quasi-steady) state of the gas flow cannot be achieved due the absence of a compressed gas volume below the sample cylinder in the fragmentation apparatus. For this reason, we use a modified version of the original code [Mueller et al., 2005] that accounts for the shorter time scale of our experiments and the fact that a steady gas flow through our samples cannot be achieved. The code includes a modified nonlinear correction coefficient. Each permeability measurement results in two pressure decay curves that are subsequently modeled with this modified code. Our permeability values are similar to the values from Mueller et al. , again attesting to the reliability of our method.
 Multiple experiments with initial pressures up to 30 MPa produce a fragmentation speed profile for each sample set to demonstrate the relationship between initial pressure, connected porosity, fragmentation threshold, and speed of fragmentation. The number of experiments for each sample set is limited by the number of sample cylinders available. The fragmentation speed is calculated by dividing the cylinder length by the time interval, representing the time between the pressure drop of upper and lower pressure transducers. Estimating the permeability of all sample cylinders before speed experiments has not been done in previous studies. This simple permeability test allows us to interpret our results with respect to permeability.
4 Experimental Results
4.1 Fragmentation Threshold
 Most fragmentation thresholds from this study (Figure 3 and Table 2) fit well the trend from previously measured data at room temperature [Scheu et al., 2006; Mueller et al., 2008]. The fragmentation threshold relation was calculated based on the fragmentation threshold criterion of Koyaguchi et al.  for the no-bubble-expansion case. The model is based on the Griffith theory for crack propagation through elastic media and involves the propagation of a crack from the inner bubble wall to the outer bubble wall, considering the tensile strength of the solid phase and tangential stress at the outer bubble wall. The criterion is defined as
Table 2. Fragmentation Threshold Values for All Sample Series Investigated for Their Fragmentation Speed. The Threshold Values for Colima-P4 and Kelut-R5 are Missing Due to the Small Number of Sample Cylinders. However, Because Colima-P4 has a High Permeability, and the Same Origin and Connected Porosity as Colima-P3, its Threshold Value Should Lie Close to Colima-P3's Threshold Valuea
a“+” and “–” represent the wide spread in threshold values for the two high-k dome/conduit wall rocks sample series. An uncertainty of 0.5 MPa is comprised within the symbols of Figure 3. The average % represents the pressure range in which fragmentation initiation (PFI) occurs relative to the fragmentation threshold. Calculations were made for each threshold experiment and all % were then averaged for one sample series.
Bezymianny C3 l
Bezymianny C3 ll
S is the effective tensile strength (Table 3) and was obtained from the least-squares analysis of the best fit for the above relationship between fragmentation threshold and connected porosity [Koyaguchi et al., 2008]. Their analysis used data from room temperature experiments on samples from Mt. Unzen, Japan [Scheu et al., 2006] and Soufrière Hills, Montserrat [Kennedy et al., 2005; Scheu, 2005]. Colima-D2, Bezymianny-D2, and Colima-P3 plot significantly above the trend, whereas the rest of the data follows the trend more closely. Note that the threshold value for Lipari-F was determined by Mueller et al. . Based on data from this study (Table 2), fragmentation initiation occurs at initial pressures between 5 and 10% below Pth, but even up to ~35% below Pth for dome/conduit wall rocks with k ≥ 1e–11 m2. Moreover, the spread in fragmentation threshold values is wide for Colima-D2 and Bezymianny-D2 in comparison to the other sample series: up to 4.2 MPa above and 2.3 MPa below the average fragmentation threshold.
Table 3. Parameters Used in the Calculations of Fragmentation Speeds Based on the Koyaguchi et al.  Model
Density of solid phase [kg/m3]
Specific gas constant [J/kg∙K]
Ratio specific heats for gas phase
Effective tensile strength [Pa]
 Our permeability data (Figure 4) are plotted along with data from Mueller et al.  on a graph differentiating effusive (dome/conduit wall rocks) from explosive (pumice/scoria) activity products. Our data fall within these two classification fields, which justifies the separation of our data into two subsets: (1) dome/conduit wall rocks and (2) pumice/scoria. The Colima-D2 k-value is an average of 4 k-values, representing a subgroup of the 12 fragmented sample cylinders. Colima-D2 k-values are estimated for 8 of the 12 fragmented sample cylinders because, although a permeability test had not been performed prior to these fragmentation experiments, we consider these experiments worth including in our study. We find justified to attribute a minimum k-value of 1e–12 m2 to these cylinders based on the fact that the k-values for the other four fragmented sample cylinders as well as for three additional sample cylinders (Table 1) are all above 1e–12 m2.
 Permeability measurements had previously been performed on 1 to 3 samples per sample set by Mueller et al.  (Table 1). These experiments were done using a shock-tube–like apparatus, where a volume of compressed gas below the pressurized sample flowed through the sample when decompression occurred, as described by Mueller et al. . The permeability values obtained in our study are consistent with permeability values obtained by Mueller et al. , except for Augustine-P1, where our values are consistently about one order of magnitude lower, possibly due to some degree of heterogeneity in the sample. Permeability values are again verified by measurements performed on the exact same samples as Mueller et al. , with a similar setup except for the shorter autoclave and absence of a gas volume below the sample. In addition, permeability measurements performed by R. Leonhardt, now at the Conrad Observatory in Vienna, on five of our samples with a steady state permeameter confirm our permeability values.
 In an attempt to explain the scatter in fragmentation thresholds (Figure 3), we plot, as in Mueller et al. , the fragmentation threshold energy density (Eth) as a function of permeability (Figure 5). The power law best fit from Mueller et al.  as well as the Eth values were adjusted by a factor of 1/(γ − 1) to account for the assumption of adiabatic conditions instead of isothermal conditions. We use equation (1) to define the fragmentation threshold energy density:
 γ = 1.67 because our experiments are performed using Argon gas and we assume adiabatic conditions. Kelut-C15 is omitted from the graph because the sample cylinder was only partially fragmented during the threshold experiment at 3 MPa. The threshold experiment could not be repeated due to the limited number of cylinders. Indeed, the scatter from Figure 3 is significantly reduced (Figure 5) and our results support the conclusion from Mueller et al.  that the fragmentation initiation of high permeability rocks requires more energy (Eth) than that of low-permeability rocks (Figure 5). Consequently, this means that, for a given connected porosity, the fragmentation threshold (Pth) of high-permeability rocks is increased (equation (3)) relative to that of low-permeability rocks. The fragmentation thresholds of Colima-D2, Bezymianny-D2, and Colima-P3 attest to this observation (Figure 3).
4.3 Fragmentation Speed
 Three representative fragmentation speed profiles are illustrated in Figure 6 to give the reader a sense of how initial pressure and connected porosity affect the fragmentation speed. Profiles demonstrate the nonlinear, logarithmic relation between initial pressure and fragmentation speed [Scheu et al., 2006]. Experimental fragmentation speeds are calculated for experiments where the pressure decay curves clearly indicate a sharp decrease of the initial pressure at the bottom of the sample (Figure 7). We compare our experimental fragmentation speeds (X) with fragmentation speeds computed using the model by Koyaguchi et al. . The fragmentation criterion appropriate for P ≥ Pth is defined as
where Δpf is the gas overpressure in the sample at the fragmentation front and P is the initial pressure. Equation (3) is the simplified form of equation (4) because at the fragmentation threshold for the no-bubble-expansion case, Δpf = Pg = Pth, where Pg is the gas pressure. Furthermore, a relationship between overpressure and fragmentation speed, modified from Koyaguchi and Mitani , was derived for the adiabatic no-bubble-expansion case [Koyaguchi et al., 2008]. The relationship assumes [Koyaguchi and Mitani, 2005; Koyaguchi et al., 2008] (a) the fragmentation front travels at a constant speed; (b) the fragmentation front is a discontinuous boundary between bubbly magma and gas-pyroclast mixture across which mass, momentum and energy are conserved; (c) the dynamics of the gas-pyroclast mixture follow the shock tube theory for inviscid fluid; and (d) gas expansion occurs under isentropic conditions. This relationship is defined as
 We combined equations (4) and (5) to obtain the calculated fragmentation speeds (U). γ is the ratio of specific heats for the gas phase. a is the sound speed in the gas-pyroclast mixture and is defined as where Pg is the gas pressure, equal to the initial pressure P in the no-bubble-expansion case, ρ is the density of the gas-pyroclast mixture, n is the gas mass fraction, Rg is the gas constant and T is the gas temperature. For the details of the conservation laws across the fragmentation front, we refer to Koyaguchi and Mitani . The fragmentation criterion was developed and tested using fragmentation threshold and fragmentation speed data obtained from experiments performed in the same conditions as experiments from the present study.
 Our calculations consider the parameters of each experiment, such as connected porosity, cylinder length, cylinder radius and initial pressure, and a few other constant parameters (Table 3), as to produce the most realistic fragmentation speed values possible. The complete set of experimental fragmentation speed data from this study is plotted against the calculated, or “expected”, fragmentation speeds (Figure 8). Although a large part of the data fits the model, several experimental fragmentation speeds lie significantly below and above calculated fragmentation speeds. This scatter confirms our suspicion that fragmentation speed does not only depend on initial pressure and connected porosity, and opens the door to other potential parameters, such as outgassing.
4.4 Outgassing During Fragmentation Events
 Experiments performed to test the fragmentation threshold reveal that outgassing can occur within the time scale of the fragmentation experiments. Initial pressure reduction due to outgassing can be recorded by the lower-pressure transducer at the bottom of sample cylinders during fragmentation speed experiments and that within the time scale of fragmentation of ~1–3 ms (Figure 7). This pressure loss is observed especially during the Bezymianny-D2 and Colima-D2 experiments. These sample series have k > ~1e–12 m2, which is the permeability defined by Mueller et al.  to have a significant effect on fragmentation. Figure 7 shows examples of the end-member cases using the contrasting Bezyminany-D2 and Krakatau-D4 sample sets. The pressure loss is directly associated to gas loss and is defined as the difference between the initial pressure P, recorded by both the upper- and lower-pressure transducers, and the pressure recorded by the lower-pressure transducer before it rapidly decays as the fragmentation front reaches the bottom of the sample cylinder. In the absence of gas loss, the initial pressure recorded by the lower-pressure transducer stays constant until the abrupt pressure drop. The pressure loss that occurs just before the abrupt pressure drop is associated with the passing of the fragmentation front at the bottom of the sample cylinder and is neglected here. This late-stage pressure loss represents gas loss at the scale of the fragmentation layer, which is observed in all of our fragmentation experiments. During the fragmentation of BEZ-D2 with Φ = 45.4%, k = 1.1e–11 m2, and P = 9 MPa, a pressure loss of 0.7 MPa is measured (Figure 7a). Some experiments at low initial pressures (usually <10 MPa) show a high and constant rate in pressure loss (Figure 7b), reducing significantly the energy available for fragmentation. During the fragmentation of BEZ-D2 with Φ = 45.8%, k = 2.0e–11 m2, and P = 10 MPa, a pressure loss of 2.35 MPa is measured. On the other hand, some experiments show very little to no loss of initial pressure. During the fragmentation of KRA-D4 with Φ = 44.2%, k = 5.5e–14 m2, and P = 10 MPa, no significant pressure loss is measured (Figure 7c).
4.5 Effect of Outgassing on Fragmentation Speed
 Each sample cylinder is identified as either having low or high permeability, with 1e–12 m2 being the cut-off permeability. The fragmentation speed data are divided into two subsets: (a) dome/conduit wall rocks, with average connected porosity 15.6–45.6% (Figure 9a), and (b) pumice/scoria, with average connected porosity 44.7–76.2% (Figure 9b). For each subset, black symbols correspond to low-permeability samples, and white symbols, to high-permeability samples. We suspected these two subsets to show differing behaviors. Figure 9 compares experimental fragmentation speeds (X) with calculated fragmentation speeds (U) for all fragmentation speed experiments in the form of ratios (X/U) and allows us to interpret these ratios relative to the P/Pth ratios. Because connected porosity does not appear in Figure 9, a direct comparison between sample sets would be inaccurate. The main purpose of this figure is to determine whether we detect an influence of permeability on fragmentation speed, and if so, whether there is a positive or negative correlation. As one might intuitively expect, the model reproduces well the low permeability data and X/U ratios for highly permeable pumice are mostly below the X/U = 1 line (Figure 9). The relatively small scatter for the low-k data points represents both a “natural” deviation resulting from the use of natural samples, and the accuracy of the model for low permeability samples. On the other hand, the scatter is significantly larger for the high permeability data, with experimental fragmentation speeds up to twice as high as calculated fragmentation speeds (Figure 9a). As a general trend, highly permeable dome/conduit wall rocks are associated with X/U ratios >1. However, in experiments where P ≈ Pth, we obtain several fragmentation speeds below the X/U = 1 line. Colima-C6 experiments exhibit unusual fragmentation behavior. This sample set produces fragmentation speeds up to four times higher than expected, even though its permeability is relatively low (~1e–13 m2). These findings support the hypothesis that high permeability, and possibly an additional factor in the case of Colima-C6 discussed in a later section, influence fragmentation speed, adding a degree of difficulty in the prediction of fragmentation speeds.
5 Implications for the Fragmentation Process
 Our results support previous studies by showing that connected porosity is the dominant parameter controlling the fragmentation of highly viscous magma. However, Bezymianny-D2, Colima-D2, and Colima-P3 represent such examples where connected porosity alone cannot explain the fragmentation threshold. All three sample sets prove to be highly permeable. Regardless of high or low permeability, pressure loss begins with the start of decompression. For low-permeability samples, pressure loss is negligible and can hardly be measured with the pressure drop curves (Figure 7c). For samples with permeability above a cut-off permeability of 1e–12 m2, pressure loss is substantial enough (Figures 7a and 7b) to rapidly reduce the initial pressure and to hinder fragmentation initiation. In such cases, higher initial pressures are required to initiate and achieve complete fragmentation. Therefore, it is reasonable to state that high permeability affects magma fragmentation dynamics and results in higher fragmentation thresholds.
5.1 Outgassing: Speeding Up or Slowing Down Fragmentation?
 As shown above, gas escape through highly permeable rocks, to which we also refer as outgassing, can occur within the time scale of fragmentation (~1–3 ms), or even faster, and thereby affect the fragmentation process. We now analyze the effect of outgassing on the fragmentation speed. At first glance, there is scatter on either side of the 1:1 correlation dashed line, and no obvious trend can be observed (Figure 8). However, the separation of the samples into the two subsets (a) dome/conduit wall rocks and (b) pumice/scoria reveals two distinct trends (Figures 9 and 10). Figure 9 allows us to interpret our fragmentation speed data with respect to initial pressure, which is normalized to the fragmentation threshold of each sample set. When comparing our experimental fragmentation speeds with the calculated fragmentation speeds, we can say that high permeability influences the speed of fragmentation of porous volcanic rocks, but its effect varies depending on the rock type:
5.1.1 Dome/Conduit Wall Rocks
 Outgassing in highly permeable dome/conduit wall rocks correlates with increased fragmentation speeds (Figure 9a). However, at P/Pth~ 1, we observe a large variability in the X/U ratios. Explanations for the high ratios are that (a) P/Pth is in some cases higher than that plotted in Figure 9 due to the variability in fragmentation thresholds within a sample set (Table 2) or (b) the sample cylinders contained inhomogeneities such as large cavities or fractures which weakened the sample cylinder. In contrast, several low X/U ratios suggest that high permeability may often correlate with reduced fragmentation speeds when the initial pressure is too close to the fragmentation threshold (P/Pth ~ 1) and that pressure loss is substantial, as shown on Figure 7b. Fragmentation speeds for two low-k dome/conduit wall rock sample cylinders are also below the X/U = 1 line. The lowest X/U ratio corresponds to an experiment where the initial pressure probably equaled the threshold value for this specific sample cylinder and the fragmentation speed was for this reason very low. The second X/U ratio corresponds to a sample cylinder that went through repeated experiments to evaluate its fragmentation threshold. Repeated experiments at P close to Pth could in some instances create small fractures and increase the permeability. However, as a general trend, low-k dome/conduit wall rocks behave as predicted, high-k dome/conduit wall rocks fragment at higher speeds than would be expected, and it remains a challenge to predict the fragmentation speed for high-k dome/conduit wall rocks around initial pressures close to the fragmentation threshold.
 Outgassing in highly permeable pumice results in reduced fragmentation speeds for the complete range of initial pressures tested in this study, except for one data point that lies above the X/U = 1 line (Figure 9b, white star). The fragmentation behavior of this rock type is more predictable.
 We did consider the possible effect of isolated porosity on the fragmentation process in that it could slightly reduce the strength of the sample. However, we could not detect any influence in our experiments. The low percentage of isolated porosity compared to the connected porosity (Table 1) most likely explains this lack of influence of the isolated porosity on the fragmentation process.
 High-k dome/conduit wall rocks behave differently from high-k pumice when fragmented under high pressures. Based on our evidence, we suggest that outgassing slows down the fragmentation process in the case of highly permeable pumice, but speeds up the fragmentation process in the case of highly permeable dome/conduit wall rocks at least for initial pressures well above threshold.
 Linear trends fitting fragmentation energy density data to fragmentation speeds allow us to describe empirically these differing fragmentation behaviors and support our interpretations for these two subsets (Figure 10 and Table 4). Fragmentation speeds for initial pressures below the fragmentation threshold are not included in the comparison of the calculated and experimental linear fits to avoid skewing the fit. The linear fits to the Colima-C6 (15.6%) (Figure 10a) and pumice (k > 1e–12 m2) (Figure 10b) data clearly stand out. The linear fit to the dome/conduit wall rocks (k > 1e–12 m2) data lies significantly away from calculated fragmentation speeds (Figure 10a). Both the low-k pumice/scoria and dome/conduit wall rocks behave as defined by the Koyaguchi et al.  model. As a side note, the experimental fragmentation speeds for Bezymianny-C3 I and Bezymianny-C3 II are comparable despite the fact that the two sample series were drilled perpendicularly to each other. This is most likely because the permeability values for both sample series lie mostly below 1e–12 m2.
Table 4. Parameters m and b for the Linear Fits to the Energy Density Data. m Represents the Slope, b, the y-Intercept
Low-k dome/conduit wall rocks
High-k dome/conduit wall rocks
5.2 Gas Flow Dynamics Considerations
 To quantify the importance of outgassing during fragmentation speed experiments, we estimate the magnitude of pressure loss, following the method described in the results section for Figure 7. Interestingly, high-k dome/conduit wall rocks experience a higher gas pressure loss than the high-k pumices for any given permeability above k ~ 1e–12 m2 (Figure 11). Permeability is influenced by textural properties, such as bubble size, bubble aperture size, bubble shape, bubble size distributions, tortuosity of the pathways, and/or the presence of crystals [e.g., Kozeny, 1927; Carman, 1956; Dullien, 1992; Saar and Manga, 1999; Wright et al., 2009]. The high-k dome/conduit wall rocks have a bubble network that can be approximated by the capillary tube [e.g., Kozeny, 1927; Carman, 1956] and/or fracture flow model [e.g., Lamb, 1945; Langlois, 1964]. Bezymianny-D2 and Colima-D2 represent low-tortuosity examples where bubbles have most likely partly collapsed due to shear deformation within a conduit or a dome, and where permeability has increased also due to the shear deformation [e.g., D'Oriano et al., 2005; Saar and Manga, 1999; Wright et al., 2009]. On the other hand, the high-k pumices have a bubble network that can be better approximated by the fully penetrable-sphere percolation theory model [e.g., Sahimi, 1994; Saar and Manga, 1999]. Colima-P3, Colima-P4, and Kelut-C15 have experienced bubble expansion and coalescence, but little shear deformation. Their bubble network is more tortuous than the bubble network from dome/conduit wall rocks. The length and curvature of paths followed by the gas during outgassing must differ substantially for the two types of bubble networks. We therefore suggest that differences in bubble network textures between high permeability effusive (dome/conduit wall rocks) and high permeability explosive (pumice) volcanic rocks could be linked to differences in fragmentation speed.
 The flow of fluid through porous media can be characterized based on the relative influence of viscous (friction along walls) and inertial forces (such as turbulence) acting upon this flow. A flow dominated by viscous forces can be described by Darcy's law, which predicts the fluid flow rate for a given pressure gradient, dynamic fluid viscosity, permeability, sample length, and cross-sectional area. The fluid flow rate varies proportionally to changes in pressure gradient, which is valid for very low Reynolds numbers. For very large Reynolds numbers and Forchheimer numbers greater than 1, inertial forces become dominant over viscous forces, and the flow is non-Darcian (turbulent) [Ruth and Ma, 1992]. In a non-Darcian flow, flow rates vary nonlinearly to changes in pressure gradient [Forchheimer, 1901; Bear, 1972]. The Forchheimer number considers both the flow velocity and the structure of the porous network and is therefore an accurate means to distinguish Darcian from non-Darcian flow [Ruth and Ma, 1992].
 We propose that the observed differences in bubble network textures (or structure) play a significant role in the efficiency of outgassing at high initial pressures above Pth. Degruyter et al.  have shown, using a numerical model, that variations in the textural properties of magma have an important effect on outgassing dynamics in the context of eruptive style transitions. We suggest that textural variations could explain differences in fragmentation speed between high-k dome/conduit wall rocks and high-k pumice. When our high-permeability rocks are submitted to high pressure fragmentation experiments where P > Pth, we can assume that gas flow rates, as in permeability measurements from Rust and Cashman , correlate nonlinearly with pressure gradients due to the large inertial effects. We could also expect that the effect would be similar for dome/conduit wall rocks and pumices. Yet, highly permeable dome/conduit wall rocks outgas more quickly than highly permeable pumice (Figure 11). We argue that gas flow rates through the highly permeable pumice decrease more significantly with high pressure gradients than through the highly permeable dome/conduit wall rocks because of greater tortuosity of the flow paths and/or other textural differences such as bubble aperture size.
 Both the velocity of the gas, which is directly related to the pressure gradient, and the bubble network texture (or structure) determine whether a flow behaves in a Darcian or non-Darcian manner [Bear, 1972; Ruth and Ma, 1992; Rust and Cashman, 2004]. Gas flow through tortuous paths is associated with increased inertial effects, leads to non-Darcian flow, and dissipates energy viscously [Ruth and Ma, 1992]. Moreover, gas flow velocity is a determinant parameter in the generation of turbulence, an inertial effect that occurs at Forchheimer numbers greater than 1. Highly permeable dome/conduit wall rocks have a bubble network that can be compared to a straight tube model, and highly permeable pumice, to a bent tube model. It has been shown that turbulence occurs in the straight tube model for much higher Reynolds numbers and gas flow velocities than in the bent tube model [Ruth and Ma, 1992]. Gas flow disturbances most certainly occur in highly permeable dome/conduit wall rocks, only to a lesser extent. Rust and Cashman  found experimentally that both viscous and inertial effects increased resistance to the gas flow in the case of helical pore samples in comparison to straight tube samples. These observations support that at high pressure gradients, gas flow rates increase, but the rate of increase most likely differs for the two bubble network textures, which would explain the observed differences in gas pressure loss rates between dome/conduit wall rocks and pumice (Figure 11).
 The positive correlation between pressure loss rates and fragmentation speeds in the case of high-k dome/conduit wall rocks has been established. We suggest that very rapid gas escape in high-k dome/conduit wall rocks could possibly contribute to, and accelerate, the layer-by-layer fragmentation process. Following is our reasoning for such a statement. Gas flowing at subsonic speeds decelerates when it reaches a larger cross-sectional area and gas flowing at supersonic speeds accelerates when it reaches a larger cross-sectional area [Liepmann and Roshko, 1957, p. 52]. In the case of high-k dome/conduit wall rocks, the gas flow has the potential to reach supersonic speeds inside the sample cylinder, and when the cross-sectional area suddenly increases at the top of the sample cylinder, the gas flow rate could further increase. As a consequence, fragmented material gets moved away from the sample cylinder at a higher velocity and the overpressure inside the sample cylinder rebuilds more quickly [Fowler et al., 2010, Figure 4]. This explanation could also apply in the case where the gas flows at subsonic speeds, because gas flow rates would nevertheless be higher than for high-k pumice. An additional effect of outgassing on the fragmentation process is that it can reduce the suction (described in Fowler et al. ) that acts upon a fragmented layer as the created and expanding void has to be filled and the fragmented layer moves away from the sample cylinder. Whether the gas flow reaches supersonic speeds or not, the fact remains that (a) the experimental fragmentation speeds and pressure loss rates in the high-k dome/conduit wall rocks are higher than in the high-k pumice and (b) more efficient outgassing in high-k dome/conduit wall rocks than in high-k pumice could have a significant suction reduction effect, allowing us to suggest that higher gas flow rates accelerate the fragmentation process.
5.3 Fragmentation of Altered Dome Material
 Interestingly, low connected porosity and low permeability of Colima-C6 cannot explain why fragmentation speeds are high for relatively low energy inputs and clearly above the general trend (see Figure 10). Another parameter is required to explain higher fragmentation speeds. It is worth noting that its fragmentation threshold, although close to the fragmentation criterion, plots in the lower range of experimental threshold values for its connected porosity value (Figure 3). This andesitic sample has a groundmass that contains plagioclase microlites of no preferred orientation, oxides, and very small amounts of glass (<1%). Edges from phenocrysts are diffuse due to the growth of microlites and chloritization of the groundmass, and represent evidence of possibly thermal and hydrothermal alteration. As mentioned before, this sample was extruded and most likely remained part of the dome for a relatively long time before tumbling down the volcano. Continuous viscous deformation within the dome may cause outgassing, explaining low permeability and reduced connected porosity. This sample does not represent fresh material, but an altered version of the fresh material (Colima-D2) with the glassy groundmass being almost fully crystallized. Alteration may influence the rock strength in at least two ways: (1) circulation of hydrothermal fluids through the fresh material could lead to the sealing of fractures due to crystallization, resulting in a strengthening of the rock, whereas (2) alteration of the groundmass and phenocrysts would result in a lower yield strength and significant weakening of the dome rocks, leading to a low fragmentation threshold. Accordingly, the effective tensile strength of the material's solid phase (S) in equation (2) would have to be adjusted in order to adequately model the fragmentation of these altered rocks. For Colima-C6 only signs pointing to a weakening of the rock were found, such as alteration of the groundmass and phenocrysts. Thus the tensile strength (S) would have to be reduced to account for the weakened rock. As a result, more energy would be available for the fragmentation of the rock, which in turn would have an impact on the ejection velocity of the particles [Alatorre-Ibargüengoitia et al., 2010, 2011]. Our observations are based on one sample set only, but represent nevertheless strong evidence for the more energetic fragmentation of weakened dome rocks.
 We suggest that altered, almost fully crystallized, low-permeability and low-porosity dome rocks may represent weak zones within the dome that could fragment at relatively high speeds for low initial pressures. Similarly to the fragmentation scenario described in Scheu et al. , the fragmentation of weaker zones could in turn reduce the overburden and cause the fragmentation of the more permeable dome rocks that require higher initial pressures. Further studies are required to support these findings.
6 Concluding Remarks
 Our study focused on testing the influence of outgassing on the magma fragmentation speed.
 A number of additional studies could contribute greatly to the understanding of all the processes that are involved. Our interpretations are based on a rather qualitative analysis of the fluid dynamics associated with outgassing that occurs during magma fragmentation and a few points would be worth exploring in more detail:
 (a) The determination of the Forchheimer number for each of our sample sets as was performed by Rust and Cashman  could confirm our interpretations regarding gas flow rates inside sample cylinders at high pressures.
 (b) Although the two basic types of textures that we present in our study are sufficient to explain the differences in fragmentation speeds observed, a detailed description and quantification of the bubble network of each sample set could shed light on the complexity of gas flow paths and on the main factors responsible for differences in gas flow rates. This would allow us to refine the interpretations of our results. This would require a high resolution three-dimensional characterization to detect the possibly very narrow apertures between bubbles.
 (c) Our suggestions that outgassing reduces the suction force between the sample cylinder and the fragmented layer at the fragmentation front and that the gas flow may reach supersonic speeds should be tested numerically.
 (d) Grain size distribution analyses of the pyroclasts resulting from fragmentation speed experiments with high-k dome/conduit wall rocks and high-k pumice could help to constrain the thickness of the fragmentation layer as well as the steepness of the pressure gradient at the scale of the fragmentation layer.
 In summary, our experimental results support the results from Mueller et al.  that permeability and porosity control the amount of energy available for fragmentation. The amount required is determined by the properties of the rock to be fragmented. Permeability higher than 1e–12 m2 results in higher fragmentation thresholds. In addition, outgassing during the fragmentation process significantly affects fragmentation speed. Highly permeable dome/conduit wall rocks fragment with increased speeds whereas high-k pumices fragment with decreased speeds. Fragmentation speeds for initial pressures close to the fragmentation threshold are more difficult to predict in the case of highly permeable dome/conduit wall rocks, but our results suggest that the speeds are mostly reduced. In order to explain our findings regarding the high-k experiments at high initial pressures, we suggest that inertial effects during outgassing affect the permeable gas flow rates within the bubbly magma, which in turn affects the pressure gradient at the scale of the fragmentation layer and the removal of the fragmented material. The result is the deceleration or acceleration of the fragmentation process depending on the bubble network texture of the rocks. The alteration of dome/conduit wall rocks may also lead to increased fragmentation speeds by reducing the amount of energy consumed by fragmentation. Our findings apply to the fragmentation of highly viscous bubbly magma (not considering bubble nucleation and growth) that occurs during rapid decompression events associated with dome collapses, landslides, and Vulcanian eruptions.
 The effect of outgassing on conduit flow dynamics has been included in many numerical models as a process conducive to effusive eruptions. One assumption was that outgassing is not significant within the time scale of the magma fragmentation process [e.g., Jaupart and Allegre, 1991; Melnik et al., 2005]. Our results clearly show that this is not always the case. Significant outgassing can occur within time scales of a few milliseconds and should be taken into consideration when attempting to understand the migration of a fragmentation front through permeable magma in a volcanic conduit or lava dome. The amount of material that is erupted during a single eruptive event is in part controlled by the migration of this fragmentation front. The speed at which this front migrates will influence the duration and style of the eruption. Numerical and theoretical models may need to include outgassing and dome rock weakening to reproduce more closely observed explosive eruptions and forecast future eruptions.
 The authors wish to thank Miguel Alatorre for his helpful and inspiring comments, Ulrich Kueppers for his help in the laboratory and at the microprobe, and Simon Kremers for his assistance in the field. Detailed comments by the Associate Editor Micol Todesco and two anonymous reviewers have greatly helped to improve the manuscript. Financial support to D.R. was provided jointly by the German Ministry of Education and Research (BMBF) and the German Research Foundation (DFG) (PTJ MGS/03G0584ASUNDAARC-DEVACOM), the Fonds de recherche du Québec-Nature et technologies (FRQNT) and the IDK 31 THESIS program funded by the Elite Network of Bavaria (ENB). D.B.D. wishes to acknowledge the support of the research professorship of the Bundesexzellenzinitiative (LMUexcellent) and the ERC advanced grant 247076 EVOKES. D.B.D. and B.S. also wish to acknowledge the support of the Collaborative project of the Seventh Framework Program (282759 VUELCO).