In situ confirmation of permeability development in shearing bubble-bearing melts and implications for volcanic outgassing

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In situ confirmation of permeability development in

shearing bubble-bearing melts and implications for

volcanic outgassing

Alexandra Roma Larisa Kushnir, Caroline Martel, Rémi Champallier, Laurent

Arbaret

To cite this version:

Alexandra Roma Larisa Kushnir, Caroline Martel, Rémi Champallier, Laurent Arbaret.

In

situ confirmation of permeability development in shearing bubble-bearing melts and implications

for volcanic outgassing.

Earth and Planetary Science Letters, Elsevier, 2017, 458, pp.315-326.

In

situ confirmation

of

permeability

development

in

shearing

bubble-bearing

melts

and

implications

for

volcanic

outgassing

Alexandra

R.L. Kushnir

∗

,

Caroline Martel,

Rémi Champallier,

Laurent Arbaret

InstitutdesSciencesdelaTerred’Orléans(ISTO),UMR7327–CNRS/Universitéd’Orléans/BRGM,1A,RuedelaFérollerie,45071OrléansCedex2,France

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received5July2016

Receivedinrevisedform25October2016 Accepted25October2016

Availableonlinexxxx Editor:T.A.Mather

Keywords: ModeIfractures torsion magma outgassing experiments

The ferocity ofvolcaniceruptions – their penchantfor eithereffusive orexplosive behaviour– is to a large extent a matterof the easewith which volatiles are able to escape the volcanicsystem. Of particularimportanceare themechanismsbywhichpermeablenetworkswithinmagmaarefabricated and howthey permitgas escape, thereby diffusing possiblycalamitous explosions. Here, wepresent aseriesofexperimentsthatconfirmssample-scalefracturepropagationandpermeabilitydevelopment duringshearingviscousflowofinitiallyimpermeable,bubble-bearing(<0.20 bubblefraction)magmas underconditionspertinenttovolcanicconduits.Thesesamplesaredeformedintorsionatconstantshear strain ratesuntil anapplied differentialpore fluidpressureacrossthe sampleequilibrates,confirming permeability development insitu. Permeability develops atmoderate tohigh shear strain rates (

γ

˙>

2×10−4s−1).Atmoderateshearstrainrates(2×10−4s−1<

γ

˙<4.5×10−4s−1),permeabilityinitiates athighstrain(γ>3)viaenéchelonModeIfracturesproducedbyrepeatedfractureevents.Athighshear strainrates(

γ

˙>4.5_×10−4_s−1_{),permeabilitydevelopsshortlyaftertheonsetofinelasticdeformation} and is, again, established through a series of en échelon Mode I fractures. Critically, strain is not immediatelylocalized onMode I fractures, making themlong-lived and efficient outgassing channels that are ideallyoriented for directingvolatiles from the centralconduit upward and outwardtoward theconduitrim.Indeed,ModeIfracturearraysmayprovenecessaryfordissipatinggasoverpressuresin thecentral regionsofthemagmacolumn,whichareconsidered difficulttooutgas.Theseexperiments highlightmechanismsthatare likelyactivealongconduitmargins andconstrainpreviouslypostulated processesundertrulyapplicableconditions.

1. Introduction

The ease of gas escape from a volcanic system exerts a fun-damental control on eruption style (Eichelberger et al., 1986; Woodsand Koyaguchi, 1994). The effusion of silicic magmas oc-curs when magma is efficiently outgassed, curbing overpressure developmentandavoidingmagmafragmentation, whereas, explo-sive eruptions and attendant fragmentationoccur, in part, when magmais unable to sustain theshear stressesto which it is ex-posed. Thus, the conditions under which permeability develops withina risingand,therefore,deforming magmacolumnarealso conditionsunderwhichgasoverpressuredevelopment and explo-sivebehaviourmaybeavoided.

Porosity in magmas initially develops from decompression – (Sparks,1978) andthermally-induced(Lavalléeetal.,2015) vesic-ulation of isolated, pressurized bubbles, which supply the

buoy-*

Correspondingauthor.

E-mailaddress:[email protected](A.R.L. Kushnir).

antforces necessaryto drivemagma upward.Ultimately, gascan onlyescapethroughaconnectedporositynetworkthateventually leadstothesurface.Todothis,theisolatedbubblestructuremust be modified andbecome connectedby expansion- (Burgisserand Gardner, 2004) and shear-induced bubble coalescence (Okumura et al., 2008) and/or magma rupture (e.g. Stasiuk et al., 1996). Thesegasesthenneedtomakeuseofpre-existingpermeable net-works, like those found in edifice- and dome-forming rocks (e.g.

Eichelberger et al., 1986; Woods and Koyaguchi, 1994) or,when theseescaperoutesareinsufficient,bymagmafragmentation(e.g.

Kennedy etal.,2005).Thisinterconnected voidspacecanbe cre-atedovertime (Martel andIacono-Marziano,2015),often period-ically (Tuffen etal., 2003),and subsequentlydestroyed (Rust and Cashman,2004),makingpermeabilityinvolcanicsystemsdifficult toconstrain.

Fig. 1. Startingmaterial. (a) 2DgrainsizedistributionforthestartingHPG8powder.Wedefinedthegrainsizebythelengthofthelongestaxisofthepowdergrains.The powdergrainsizeis<90 μm,withadominantgrainsizeof2 μm. (b) 2Dbubbleradiusdistributionforthesynthesizedbubble-bearingmagma.Thepolydispersebubbles haveamaximumandpeakradiusof25 μm and2 μm,respectively. (c) SEMimageofPP506,aftersynthesis.Therosediagramgivestheorientations,θ,ofthesemi-major axesofthebubblesinthestartingmaterial,whereθisanglebetweenthebubblesemi-majoraxisandtheshearzoneboundary(thepermeablespacerinterface).Bubble/grain sizedistributionsandorientationsweredeterminedbyimageanalysis(usingImageJ)ofSEMimages.Wenotethat,assumingtheargonporefluidbehavesasanidealgas undertheexperimentalconditionsdescribedinthetext,theisobaricdecompressionofthesamplesledtoa4-foldincreaseintotalporosityandanincreaseinbubbleradius byafactorof1.6.

as tuffisite veins; e.g. Stasiuk et al., 1996; Tuffen et al., 2003; Castroetal., 2012). Thesefracturesact asefficienttransport net-worksforfluidflow,thoughrepeatedfractureeventsmaybe nec-essary to maintain permeability (e.g. Tuffen andDingwell, 2005; Castro et al., 2012; Shields et al., 2016). Indeed, low-frequency earthquakes at conduit margins suggest that the occurrence of suchfracture eventsisnotunusual(e.g.

Goto,

1999; Tuffenetal., 2003; Thomas and Neuberg, 2012). Unfortunately, shear-induced deformation along conduit walls may be relatively inefficient at outgassingtheconduitcentre(e.g.

Castro

etal.,2012; Gauntetal., 2014) andstrainlocalizationalongshearfracturesmayevenlimit furtheroutgassing,eventually shuttingoffthepermeablenetwork liningtheconduitrim(Okumuraetal.,2010).

Severalexperimentalstudieshaveinvestigatedpermeability de-velopment as magma is deformed in simple shear. Permeability development facilitated by shear-induced bubble coalescence in magmaswithmoderatetohighbubblefractions(

>

0.20)hasbeen demonstrated experimentally (e.g. Okumura etal., 2008). At low bubblefraction(

<

0.20),crystal-assistedstrainlocalizationcan re-sultin bubble coalescence,locally increasing strain rates and in-citingcataclasticbehaviourthat producesRiedelsheargeometries (Laumonier etal.,2011). Whileshear-induced bubblecoalescence and outgassing have been inferred in bubble-bearing phonolites containing less than 0.02 bubble fraction (Caricchi et al., 2011), outgassingintwo- andthree-phasemagmaswithlowbubble frac-tions (

<

0.20) appears to be most efficiently facilitated by the development of helical shear fractures (Cordonnier et al., 2012; Shieldsetal.,2014).

Shields

etal. (2014)demonstratedthatthese helicalfractureswerecomposed ofextension fractures(otherwise termed tensions gashes)oriented approximatelyperpendicular to the shear direction. Significantly, in the majority of these stud-ies,gasescapewasinferredpostmortem(thatis,post-experiment) by an overall reduction in bubble content (Pistone et al., 2012; Shields et al., 2014) and dissolved volatiles in the melt phase (Shields etal., 2014), makingit difficultto identifywhen andby what mechanisms permeability developed. In particular,

sample-scale permeabilitydevelopment inshearing viscousflow via frac-turedevelopmenthasnotyetbeenconfirmedinsitu.

The purpose of thisstudy is to beginto experimentally con-strain permeability-producing processes previously postulated to beactiveatconduitmargins.Wedemonstratethemechanismsby whichpermeabilitydevelopsinrhyoliticmagmasofrelativelylow bubble fraction under conditions pertinent to volcanic conduits. We characterize permeability development in situ during simple shearofaninitiallyimpermeable,haplogranitic,two-phase(bubble andmelt)magmaasafunctionofshearstrainrate.Further,we as-sociate permeabilitydevelopment withmicrostructureto identify what mechanisms may influence volcanic behaviour in a natural setting.

2. Methods

Bubble-bearing magma analogues were synthesized and de-formed in simple shear using an internally heated, gas-medium (argon) Paterson deformation apparatus equipped witha torsion motorandporefluidpressuresystem(PatersonandOlgaard,2000; AustralianScientificInstrumentsPtyLtd;atISTO,Orléans,France). Eachexperimentwas performedintwosteps:i)samplesynthesis andii)sampledeformation,detailedbelow.

2.1. Startingmaterialsynthesis

Fig. 2. SampleassemblyandPatersondeformationapparatus. (a) Sampleassembly configuration. (b) Schematicofthe Patersondeformationapparatusandthepore fluidpressuresystem,modifiedfromPaterson and Olgaard (2000).

1.5gofHPG8powderwasplacedbetweentwopermeableceramic spacers(Umicore Mulliteceramic;connected porosity,

φ

c

=

0

.

17;

permeability,k

=

2

.

7

×

10−16_m2_{) that were 15 mm in diameter}

andjacketedina 0.2mmthick iron sleeve (Fig. 2A). The sample was placed in the deformation apparatus and pressurized argon gaswas introduced into the interstitial spacebetweengrains via theporefluidsystem(Fig. 2B).

The gas was trapped as bubbles by sintering the powder. To facilitate quick synthesis, we chose to synthesize the magma at T

=

1150◦C usingaheatingrateof10◦C/min(Fig. 3A).Thesample waslocatedinanisothermalzone(

±

2◦C)andwasmonitored us-ingaN-typethermocoupleplaced3mmabovethesample.During bubblesynthesis, theconfiningpressure( Pc) andporefluid

pres-sure( Pf) were both equal to 310 MPa, resulting in an effective

pressure( Peff

=

Pc

−

Pf) equalto 0MPa (Fig. 3A). Thiseffective

pressureensured thatthesample’scylindricalgeometrywas pre-servedasthepowdersintered.

Giventhegrain size distributionofthe HPG8powder, we can constrainthecharacteristictimescaleforsinteringofdropletsofa highviscosityliquid(Wadsworthetal.,2014):

λ

s

=

R_Γηo,where R

istheparticleradius,

η

o isthemeltviscosity,and

Γ

isthesurface

tensionbetweenthemeltandgasphase.TheviscosityofHPG8at 1150◦Cisextrapolatedfrom

Hess

etal. (2001)andisfoundtobe

Table 1 Experimentlist. Experiment d (mm) l (mm) PCi (MPa) PCd (MPa) Pu (MPa) Pd (MPa) T (◦C) ˙ γ (s−1₎ γ η app (Pa s) k PP506 14.85 4.44 310 57 22 17 880 s.m. – – No PP545 16.56 4.63 314 59 26 21 880 9.9×10−5 _{6.9 1.2×10}10 _No PP511 15.12 3.69 320 58 26 21 880 2.2×10−4 _{7.1 2.0×10}10 _No PP512 14.42 3.98 312 58 26 21 880 1.8×10−4 _{2.9 2.1×10}10 _unclear PP509 15.08 4.40 307 58 26 21 880 4.5×10−4 _{3.4 2} .5×1010 _Yes PP444 16.10 4.59 306 57 31 26 880 4.5×10−4 _{1.6 2} .4×1010 _No PP443 15.67 3.55 309 56 33 28 870 5.7×10−4 _{0.2 – Yes} PP508 14.81 4.21 307 58 27 22 880 8.1×10−4 _{0.1 – Yes} PP439 14.57 7.17 298 56 17 23 880 1.0×10−4 _{– – No} – – – – – – – 3.0×10−4 _{– – –} – – – – – – – 6.0×10−4 _{– – –} d andl arethesamplediameterandlength,respectively,afterdeformation;PCiistheconfiningpressureduringstartingmaterialsynthesis(equaltotheporefluidpressure

duringsynthesis);PCd,Pu,andPdaretheconfining,upstreamporefluid,anddownstreamporefluidpressures,respectively,duringdeformation;T isthetemperatureat

whichdeformationoccurred;γ˙istheshearstrainrateatthesampleperiphery(s.m.denotesthestartingmaterialandwasnotdeformed);γ isthefinalstrainachieved duringtheexperimentbasedonsamplegeometry;ηappistheapparentviscosityofthesampleatγ=1;andk denoteswhetherpermeabilitywasestablishedduringthe

courseofdeformation.

107.0Pa s.Foramaximumgrainsizeof90 μm andassuming

Γ

=

0

.

3 N

/

m (Bagdassarovetal.,2000),

λ

sisapproximately25 min.

After one hour,the sample was isothermally decompressedto 60 MPa at an average rate of 5 MPa/min, while keeping Peff

=

0 MPa (Fig. 3A).Decompressionallowedbubbleexpansion, result-inginatwo-phasemagmacontainingpolydispersebubbleswitha peakandmaximumbubbleradiusof2 μm and25 μm,respectively (Fig. 1B).Thetimescaleofrelaxation,

λ

b,forthebubbleswas

calcu-lated:

λ

b

=

a_Γηo,wherea isthebubbleradius(Maderetal., 2013).

Foramaximumbubbleradiusof25 μm andusingameltviscosity of107.0Pa s,the relaxationtimescaleofthe bubbleswas 14 min. Thesamplewasallowedtoequilibratefor1 hat1150◦Ctoensure thatallbubblesattainedsphericalgeometries(Fig. 1C).

Following bubble entrapment and decompression-induced ex-pansion, the sample temperature was decreased to 880◦C at 10◦C/min (seebelow). Thepore fluid pressurewas isolated from theconfiningpressureandtheporefluidpressuresupstream( Pu)

and downstream ( Pd) of the sample were lowered to 25 and

20 MPa,respectively(Fig. 3A).Thesamplewasconfirmedtobe im-permeableifthesetwopressuresdidnotequilibrate;eachsample wasthenisobaricallyquenchedtoroomtemperatureat43◦C/min. X-ray computed tomography (XCT; Phoenix NanoTOM, ISTO, Or-léans, France) confirmed the absence of through-going cooling fractures and that the sample was homogeneously vesicular. All sampleswere

∼

15 mm in diameter,between 4and 7mm long, hadan average totalporosity of 0

.

14

±

0

.

01, anda bubble num-berdensityof0

.

002 μm−2 (asdeterminedby image analysis,see below).

2.2. Deformationinsimpleshear

After synthesis and XCT imaging, straight lines were scribed along thelength of thesample assembly jacketto act aspassive strainmarkers, aswell astoindicateifanystrainwas accommo-datedbyslipalongthespacerinterfacesduringdeformation.

Theviscosityofthemeltphaseat1150◦Cwastoolowfor de-formationtobereadilymeasuredinthePatersonapparatus, there-fore,weelectedtoperformalldeformationexperimentsat880◦C, wheretheviscosityofanhydrousHPG8is

∼

1011.0_{Pa s (Hessetal.,}

2001). Impermeablesampleswere putbackintothePaterson ap-paratus,placed underpressure such that Pc

=

Pf

=

60 MPa, and

heatedto 880◦C at10◦C/min (Fig. 3B). At 880◦C, the confining and pore fluid pressures were isolated from each other andthe pore fluid pressure was lowered such that Pf

=

25 MPa (except

in one experiment where Pf

=

40 MPa, see Supplementary

Ma-terial; Fig. 3B). Pu and Pd were then isolated from each other

andthe differential pressure (



P ) across the sample was set to

5 MPa(Fig. 3B). Thisserved to confirm that thesample was im-permeableandtheexperimentcontinuedundertheseconditions. Wenotethat becausetheporosityinallsampleswasinitially un-connected, the pressure in thebubbles was equal to the Pc (i.e.

∼

60MPa),thus,the Peff ofthesample was0MPaaslongasthe

sampleremainedimpermeable.

Samples were deformed inright-lateral simpleshear at shear strain rates,

γ

˙

,between9

.

9

×

10−5 _and8

_.

₁

_×

₁₀−4 _s−1 _{(Table 1).}

Deformationwasterminatedoncesamplesbecamepermeable (sig-nalledbytheequalizationofPu andPdacrossthesample;

Fig. 3

B)

oroncedeformationwasinexcessofatotalbulkshearstrain,

γ

,of

∼

7.Atthisviscosity,therelaxationtimescale(

λ

b)forbubbleswith

25 μm radiusis96days;noneofourexperimentsexceeded25 h, ensuring that the experiments were performed in the unsteady flowregime(Llewellinetal.,2002).Sincesampleswereisobarically quenchedonatimescale

 λ

b,weconcludethatthedeformation

microstructureswerepreservedformicrostructuralanalysis. Duringdeformation,thecentreofthesampleexperiencedzero torque and, therefore, zerostrain; both strain andstrain rate in-creasedradiallytowardthesampleexterior(PatersonandOlgaard, 2000). The torqueapplied to the sample was measured usingan internal loadcell withcalibratedlinearvariabledifferential trans-formers (LVDT). Measured torque was corrected for the strength oftheiron jacket(FrostandAshby,1982) and convertedtoshear stress:

τ

=

M4(3+

1

n)

πd3 ,where M isthetorque,d isthediameterof

the sample, andn is the stress exponent (Paterson andOlgaard, 2000). n is an unknown empirical parameter that is experimen-tally determined for a given sample by conducting a strain rate stepping experiment andcorresponds tothe slopeof thelog–log plotofradialdisplacementrate(

˙θ

)vs.M

:

n

=

_{d ln M}d ln˙θ (Patersonand Olgaard,2000). Apparentmelt viscosity,

η

app, during deformation

was calculated:

η

app

(

t

)

=

τ_{γ .}(_˙t) Therelativeviscosity,

η

rel,isgiven:

η

rel

(

t

)

=

ηapp(_ηot).

2.3. Microstructuralanalysis

Afterdeformation,all sampleswereimagedin3D intheiriron jacketsusingXCT.Tokeeptheimagesizemanageablefor process-ing,thevoxellengthwassetto15 μm (voxelvolume:3375 μm3); this did not provide enough resolution to image bubbles with semi-majoraxeslessthan

∼

15 μm.

Sam-Fig. 4. Log–logplotofradialdisplacementrate(˙θ)versustorque(M)(correctedfor thestrengthoftheironjacket).Solid,bluedotsrepresentthestrainratestepping experiment,PP439;open,orangedotsarethetorqueofallconstantshearstrainrate experimentsatγ=1 andnormalizedtoastandardsamplelengthanddiameter, afterChampallier et al. (2008).

ples were then placed in epoxy and polished to expose their longitudinaltangentialsurface,whichrepresentstheplaneof max-imumshearstrain(PatersonandOlgaard,2000).

Microstructuralimagingof the sampleswas carried out using a Mira3TESCAN scanning electron microscope (SEM; BRGM/Uni-versité d’Orléans/ISTO, Orléans, France). The total porosities, 2D bubblegeometries, and 2D bubble numberdensities were deter-minedforthestartingmaterialanddeformedsamplesby segment-ingSEMimagesusingimage-processingsoftware(ImageJ).Bubble geometrywas described by thesemi-major andsemi-minor axes ofthe best-fit ellipseof each bubble andthe angle betweenthe semi-majoraxisandthespacerinterface,

θ

(Fig. 1).

3. Results

3.1.Mechanicaldata

Weperformedseven constantstrain rateexperimentsandone strain rate stepping experiment (Table 1). Using the data pro-videdby the strain rate stepping experiment (PP439), we found a stress exponent,n, of 1.45(Fig. 4), consistent with shear thin-ningbehaviour (Arbaret etal., 2007). This value is confirmed by then-valuedeterminedusingtherecordedtorqueat

γ

∼

1 forall constantshearstrainrateexperimentsperformedunderthesame pressureandtemperatureconditionsandnormalizedtoastandard sample length and diameter, as described by Champallier et al. (2008)(Fig. 4).Weemphasizethatwechose

γ

∼

1 sinceall sam-ples exhibited steadystate behaviour up to this strain. However, thosesamplesdeformedat highshear strain rateexperienced an increasein shearstress withincreasing shear strain(strain hard-ening),thusthevalueofn givenheremaynotadequatelydescribe thedatabeyond

γ

∼

1.Similarly,wecannotbecertainofthe non-Newtonian behaviour of the magmas after

γ

∼

1. We note that strain hardening has beenobserved in simple shear deformation ofphonolitic magmas undersimilar conditions to thisstudyand hasbeenattributedtodeformation oftheiron jacket(Caricchiet al.,2011);weobservednowrinklingoftheironjacketduringour experimentsandhavenoreasontobelieve that thisbehaviouris anartefactofourexperimentalprotocol.

The apparent viscosities at

γ

∼

1 for all experiments ranged between2

.

5

×

1010 _{and 1}

_×

₁₀10_{Pa s (Table 1) and the relative}

viscosities were lessthan 0.6 forall experiments. Astress–strain

plotforallconstantstrain rateexperimentsispresentedin

Fig. 5

and theonset of permeabilitydevelopment is indicated foreach experiment(Fig. 5,inset).

Permeability developed in samples deformed at shear strain ratesgreaterthan

∼

2

×

10−4 s−1 (experimentsPP508,PP443,and PP509). At shearstrain ratesinexcess of 4

.

5

×

10−4s−1 (PP443, PP508),permeabilitydevelopedimmediatelyaftertheonsetof in-elastic deformation (Fig. 5, inset). PP508 experienced four stress drops before the pore fluid pressures equilibrated. We highlight that PP443 was performed at a temperature of 870◦C to en-sure that the melt viscosity was such that the glass transition couldbecrossed,inducingabrittleresponseinthesample.PP509

(

γ

˙

=

4

.

5

×

10−4_s−1

₎

_{strainhardened after}

_γ

_∼

_{1 and}

permeabil-itydevelopedinthecourseofstrainhardeningat

γ

∼

3

.

5 (Fig. 5, inset); the stress drop at the endof the experimentoccurred in conjunctionwiththeequilibrationoftheporefluidpressures(see Fig. SM.3 inSupplementary Material). Westress that we didnot observeanyperturbation insample temperaturewithoutgassing, asreportedby

Caricchi

etal. (2011).ExperimentPP444

(

γ

˙

=

4

.

5

×

10−4_s−1

₎

_{wasterminatedat}

_γ

_∼

₁

_.

_{6 toinvestigatethe}

microstruc-ture of the sample before strain hardening could begin. PP512

(

γ

˙

=

1

.

8

×

10−4 s−1

)

experiencedsignificant strainhardeningbut itisunclearfromtheporefluidpressuredata(seeSupplementary Material)ifthissample becamepermeablebefore theendof the experiment asthe jacket ruptured, ending the experiment. Sam-ples deformedatshearstrain rates

<

2

.

2

×

10−4_s−1 _(PP511and

PP545) did not exhibit significant strain hardening nor did they become permeable;theseexperiments were terminated at

γ

∼

7 (Fig. 5).WenotethatwhilePP511

(

γ

˙

=

2

.

2

×

10−4 _s−1

₎

_exhibited

an initial periodofstrain hardening,the sample strainweakened after

γ

∼

1

.

5 untiltheendoftheexperiment.Allporefluid pres-suredatacanbefoundinFig. SM.3oftheSupplementaryMaterial. 3.2. Samplemicrostructure

In all experiments, bubbles are deformed and their semi-major axes define the dominant sample foliation (see the Sup-plementary Material for the sample-wide microstructure of the deformedsamples).Calculated 2D bubbledensities areconsistent with the starting material (0

.

002 μm−2_{), with the exception of}

PP509

(

0

.

001 μm−2

)

, and we do not observe microstructure in-dicativeofbubblecoalescence.

Fiveofthedeformedsamples(PP508,PP443,PP444,PP509,and PP512)contain fractures andall samplesthat became permeable containenéchelonfracturearrays(Fig. 6).Thesefracturesare situ-atedaroundtheoutercircumferencesofthesampleswhereshear strainsare largest andfracturetips areoriented between34and 67◦ to theshearzone boundaries(Fig. 6). Athighstrain ratebut low strain (e.g. PP443), fractures nucleated atbubble–melt inter-facesandinthemiddleofthemeltphase(Fig. 7A).Atsmallstrain, these short fracturespropagated and interacted (Figs. 7A and B) andappeartohavebeguntocoalesceasthemeltbridgesbetween fracturesbegantothin(Fig. 7B).

Fig. 5. Mechanicaldata(shearstressversusshearstrain)forallconstantshearstrainrateexperiments.Theinsetshowsthe stressversusshearstraindataforsamples containingModeIfractures.Sigmoidalsymbols denotethe strainatwhichMode Ifracturesformed. Colouredcirclesdenotethestrainat whichthe samplesbecame permeable.

Fig. 7. SEMimagesofModeIfracturesindeformedproducts. (a) and (b) PP443,γ˙=5.7×10−4_s−1_{,γ=0.2. (a) ModeIfracturesnucleateatbubble–meltinterfaces(white}

arrow)andinthemeltphaseandopeninthedirectionoftheleastcompressivestress,σ3. (b) Adjacentmicrocracksbegintocoalesceasthemeltbridgesbegintothinand

rupture(whitearrows). (c) PP512,γ˙=1.8×10−4_s−1_{,γ=2.6.Fracturetipsareoffsetalongbubblemajor-axes(whitearrow);nosheardisplacementisobserved. (d) PP509,} ˙

γ=4.5×10−4_s−1_{,γ=2.7.Bubblesencroachonfractures,eventuallyleadingtobubblelossinthesurroundingmelt;seealsoSupplementaryMaterial.Theindicatedγ}

reflectthestraincalculatedfortheimagedplaneofthesample.

The microstructure of experiment PP545 could not be accu-rately determined asthe sample broke upon being taken out of thedeformationapparatus.Inspectionofspacerinterfacesshowed no slip along the spacer surfaces and the mechanical data were not suspect. The sample remainedimpermeable during deforma-tion(seeFig. SM.3GoftheSupplementaryMaterial).

4. Discussion

4.1.Dominantstructuralfeatures 4.1.1. Bubblesaspassivestrainmarkers

In all samples, the orientation of the semi-major axes of the elongated bubbles defines the global, shear-induced foliation. In steadyflow, these orientations record strain, even under the in-fluenceofarestoringsurfacetensionforce(Rustetal.,2003) and, critically,

Arbaret

etal. (2007)foundthat deformedbubblesacted as ideal passive strain markers in haplogranitic melts deformed under similar conditions as the present study. The accumulated strainrecordedbyarigidbodyrotatedinsimpleshearcanbe cal-culated:

γ

=

2

tan 2θ (Ramsay, 1980), where

θ

is theorientation of thebody’ssemi-major axiswithrespecttotheshearzone bound-ary.Ifweassumethatbubblesactasproxiesforthestrainellipse ofthe deforming system(thatis, they are passivelyrotating fea-tures), then, to a first order,

θ

is oriented at 45◦ to the shear zoneboundarywhendeformation commencesandapproaches0◦ with increasing strain (Fig. 8). We compare the weighted mean

of the bubble orientations and known bulk strains of the im-aged sections for each experiment with the strain predicted by the passiverotation of thestrain ellipse(Fig. 8). Despiteour ex-perimentshavingbeenperformedunderunsteadyflowconditions, the calculated shear strains are in agreement with those pre-dicted forthe rotation ofa rigid passivestrain markerin simple shear (Fig. 8). While the standard deviation in bubble orienta-tions suggests that, locally, strain and strain rate may have var-ied from the bulk behaviour of the sample, bubble orientations still reflect the total bulk strain expected, even in the presence of fractures(e.g.PP509,

Fig. 8

). Thus, we concludethat the frac-tures must have also behaved as passive structures after forma-tion.

4.1.2. Thedevelopmentandevolutionofafracturenetwork

Fig. 8. Bubbleorientationforallexperimentsversusshearstrain.Thesolidblack curverepresentstheorientationofthestrainellipsewithincreasingshearstrain:

γ= 2

tan 2θ (Ramsay, 1980).Filledcirclesaretheweightedmeanvaluesofbubble

orientationfortheexperimentsinthisstudy;verticallinesgiveorientationswithin onestandarddeviationofthemeanbubbleorientation.

purely extensional (Mode I) features and likely initiated at 45◦ tothe shearzone boundary (Ramsay, 1980). Ifthesefeatures are purelyextensional,theyopenedinthedirectionoftheleast com-pressive stress,

σ

3, propagated in the direction of the principal

compressivestress,

σ

1,anddidnotaccommodatesignificantstrain

untiltheywere passivelyrotatedandentrainedintotheshear di-rection(Ramsay,1980).

Whilewe donot consistentlyobservefracture tip orientations of 45◦ in all samples, these orientations are common in PP443 (Fig. 6) wherefracturesdevelopedshortlyafterdeformation com-menced.Inthat sample, we observetwo typesof fracture nucle-ation; fractures nucleated either within the melt phase (Fig. 7A) or at pore-melt interfaces (Figs. 7A and B). The latter bear a strong resemblance to pore-emanatingfractures, asdescribed by

Sammis and Ashby (1986). In that study, spherical voids locally perturbedthestress fieldsuch thatextension fracturesdeveloped during deformation and propagated in the direction of

σ

1 and

openedinthe directionof

σ

3.Whenunconfined ( Peff

=

0), these

fractures continued to propagate in

σ

1, eventually resulting in

sample-wideplanesoffailure.However,asconfiningpressurewas increased,thesefracturesbegantocoalesceatanangleto

σ

1

(usu-ally

∼

30◦), resultinginmacroscopicfailure inshear(Sammisand Ashby,1986).Inoursamples,weseenoevidenceto suggestthat the Mode Ifractures coalesced to give rise to shear fractureson thetimescalesofdeformation(Fig. 6),though,asawhole,theydo appeartohavelocalizedinabandinPP509.Ourobservationsare consistentwithModeIfracturedevelopmentwhen Peff

=

0 MPa.

As fracturesgrew andpropagated, dilating and creatingmore voidspace,theporefluid pressurewaslocallyreduced. The pres-sure gradient between the pores (60 MPa) and the propagating fractures (



60 MPa) promoted bubble evacuation into the frac-turesover time (Fig. 7D).In pyroclastic obsidians,fracture devel-opmentprovides lowpressure and/orhightemperaturesitesthat encouragediffusionofH2Othroughthemelt phaseandinto

frac-tures, resulting in gas escape andrecorded by dehydrated halos aroundhealedfractures(Cabreraetal.,2011).Weemphasizethat the pore fluid in our experiments is argon, which has a much lower solubility in silicate melts than H2O (Carroll and Stolper,

1993). Therefore, while diffusionis the dominantmechanism for H2Otransporttowardfracturesinnaturalrhyolites,diffusivemass

transport was not likely to have been operative in our system.

Volatile migration into fractures in our experiments was a slow and inefficientprocess andthe depletion in bubbles surrounding fractureslikelyresultedfromtheevacuationofbubblesintersected byfractures.

The deformedbubbles inPP509 actedas localstrain markers, mapping theinstantaneous shearstrain andshear strainrate be-tweenfractures(Fig. SM.4D).Thesevaluesindicatethatshearwas localizedinthecentreofthesample, andpeteredofftowardsthe spacers.Theresultantshearstrain rategradientacrossthesample gaverisetothesigmoidalshapeofthefractures(Lisle,2013);the sigmoidalfracture geometryresultedfromthe passiverotationof thecentresofthefracturesasdeformationcontinued, asopposed to beingcontrolled by the mechanical competence of the bridg-ing melt segments (see Fig. 2of Lisle,2013). As such, thestrain recorded by the central portion of these fractures can be used todeterminewhen,during deformation,theyformed.By compar-ing theinitialandfinalfractureorientations,wecancalculatethe strain accumulated during the passive rotation of these features (Ramsay,1980):

γ

=

cot

α

−

cot

α

,where

α

istheinitial orienta-tion ofthefractureand

α

 isthe orientationofthe fractureafter deformation.Inoursystem,weassume

α

=

45◦ and

α

isthe an-gle formed betweenthe spacer interface and the centres of the sigmoidal fractures. By calculating the strains recorded by these rotatedfeatures,wecanlocatetheirformationonthestress-strain curves(Fig. 5,inset).

At strain rates higher than 5

×

10−4 _s−1 _{(PP508, PP443)}

frac-turesformed shortlyafterdeformation began,suggestingthat the material was entirely brittle. At strain rates between

∼

2

×

10−4 and5

×

10−4 _s−1 _{(PP509andPP512),fractureformationoccurred}

after an initial deformation ofatleast

γ

∼

1 and was associated with strain hardening. Below

γ

∼

1, samples show little to no strainhardeningandthereisnoevidenceofModeIfracture devel-opment.Indeed,thefirstgeneration ofModeIfracturesinPP509 records a shear strain of

γ

∼

2, placing their formation around

γ

∼

1, wherethe sample began to exhibit strain hardening. This is reinforcedby thesingle tensiongashdeveloped inPP444: itis notsigmoidal,indicatingthatitwasnewlyformedjustpriortothe endofthatexperiment.

4.2. Fracture-inducedmechanicalresponseorexperimentalartefacts? Weobservedinstantaneous dropsinstressduringdeformation in twoexperiments(i.e. PP508andPP509;

Fig. 5

). Intorsion,the observation ofstress drops during deformation often reflects the development of a sample-scale helical fracture that results in a significantlossofcompetenceofthesample(Rybackietal.,2010). Further,theobservationofoscillatorystressdropsduring deforma-tionhasbeeninterpreted asreflectingfracture andhealingcycles inmagma(Pistoneetal.,2012).

InexperimentPP509,thedropinstress (Fig. 5) wasassociated withtheequilibrationofporefluidpressures,confirming thatthe formation of the Mode I fractures did not significantly alter the mechanicalbehaviourofthemagmas.Indeed,giventheorientation ofthesefeaturesandthelackofevidencethattheylocalizedshear strain upon formation,we wouldnot expect Mode Ifractures to decreasesamplecompetence.

system.Noslipalongspacerinterfaceswasrecordedbythescribed strainmarkers,leading ustosurmisethatslipoccurredalongthe upper(orlower)spacerandassemblyheadinterface(s)(see Sup-plementaryMaterial fora detaileddiscussion). We conclude that theperiodiclossesofstrengthobservedduring deformation were experimentalartefactsrelatedtoslipalongtheinterfacesbetween thespacers andsample assembly head,a consequence ofa high shearstrain ratethat overcame the friction along thesesurfaces. We,therefore,hazardcautionoftheinterpretationofthe mechan-icaldataforPP508.

4.3.Thebrittle–viscoustransition:tearingupmagma

While experiment PP443 behaved in a purely brittle manner, experiments PP509 and PP512 typify brittle–ductile shear zones (Ramsay,1980).Boththesesamplesdisplayedstrainhardening be-haviour, which may have been a symptom of local increases in viscosityduetobubble andvolatileloss(Schmockeretal., 2003; Shieldsetal.,2014),assuggestedbythedecrease inbubble den-sityobserved in PP509. In our experiments, oldergenerations of fractures are surrounded by bubble-depleted zones (Fig. SM.4D), whichis perhaps a resultofdifferential pressure-induced bubble evacuationintothefractures(seeSection4.1.2).Thismayhaveled to a local increase in the bulk viscosity ofthe magma, resulting instrain hardening. However,in PP512 –which experienced sig-nificantstrain hardening –we findno evidence ofbubble-bereft zonessurrounding the fractures. Therefore, aspiration of bubbles into these fractures was not the reason for the observed strain hardening.

In a silicate melt, non-Newtonian viscous flow precedes brit-tlefailure and,ultimately,fracture ofsilicic magmasoccurswhen thetensile strength ofthe magma is exceeded (Webb and Ding-well, 1990a). The relaxation timescale, tc, for a melt of given

viscosity is given by the Maxwell relationship: tc

=

Gη_∞o , where

G_∞, the unrelaxed elastic shear modulus, is 1010Pa for sil-icate melts (Webb and Dingwell, 1990b). The onset of non-Newtonian behaviour hasbeen observed to occur at strain rates three orders of magnitude less than the inverse of the struc-tural relaxation time of the liquid (Webb and Dingwell, 1990b). In our system, using a melt viscosity of 1011.0_{Pa s (Hess et al.,}

2001), the onset of non-Newtonian behaviour should occur at shear strain rates faster than 10−4 _s−1 _{andbrittle failure of the}

melt phase is expected at strain rates one order of magnitude above this (10−3_s−1_{). While our experiments appear}

consis-tent withnon-Newtonian shear thinning behaviour below

γ

∼

1 (Fig. 4; see Supplementary Material), this is very likely a result of the presence of highly deformed inviscid bubbles, which in-creasingly act to limit viscous dissipation in the suspension as bubbles become progressively more deformed (Rust and Manga, 2002).

We posit that the strain hardening of the samples likely re-flects the accumulation of stress within the melt and precedes eventual fracture. Indeed, changes in n suggest changes in de-formationmechanism(PatersonandOlgaard, 2000) and are con-sistent witha transition tomore brittle behaviour.We note that thedegreeofstrainhardeninginPP509issmallerthaninPP512, despitePP509 having been deformedata faster strain rate. Sev-eral generations of tension gash are present in PP509, reflecting multiple excursions across the viscous-brittle transition. Indeed, fracture development began shortly after

γ

∼

1, punctually re-leasinglocalbuild-upsinstressesandgloballyreducing thestrain hardeningofthesample.Further,weobservethattheModeI frac-turesinPP509 formaband acrossthe sample(Fig. 6). Thisband likely localized shear as the fractures became sigmoidal, muting thestrain hardening response of thesample during deformation.

Mode I fracture development at strain rates below those pre-dicted for pure melts may indicate strain rate heterogeneities in the sample, or that Mode I fracture development occurs during bubble-induced non-Newtonian flow and dominates in the more ductile endofthe brittle-ductile spectrum(Lavalléeet al., 2013). If the latter is true, then extension fracturesmay occur at rela-tively low strain ratesinthe conduitand beantecedent to shear fracturedevelopment.Weemphasizethat,atverylow strainrates (

<

2

×

10−4s−1), the rate of deformation was slow enough that themeltcouldrelaxandcontinuetoflowandnoModeIfractures developed; neither fracture nor outgassing occurred under these conditions.

4.4. Theefficacyofgasescape

We canqualitatively comparetheefficacyofgas egress across our samples (Fig. 9A). In the purely brittle case, PP443, several short fractures were created early during deformation (Figs. 5 and 6). None of these fractures extend across the whole sam-ple andgasflow was dependenton the interconnection ofthese short, shattered channels. In contrast, in samples where brittle andviscous processesworkedintandem (e.g.PP509 andPP512), fractures are well-developed and extend along the entire length of the sample. Despite takinglonger to form, these features are less tortuous and, therefore, more permeable than the fractures formed by purely brittle behaviour (Fig. 9A). Thus, at the onset of percolation, gas egress was most efficient at moderate strain rates (

∼

4

.

5

×

10−4 s−1; Fig. 9A). We emphasize that the defor-mation of PP443 was terminated upon gas percolation and, so, integrated over the same deformation timescale as PP509 (that is, to

γ

∼

3

.

5), the permeabilityof PP443 would be expected to be very high owing to the continued brecciation of the sample duringdeformation.However,giventherelativescaleofthese frac-tures, such a brecciated zone likely would not extend far into a volcanic conduit, limiting the region outgassed by these fea-tures.

5. Openingaclosedsystem:implicationsforthe

explosive–effusivetransitionofvolcaniceruptions

ModeIfracturesarenotararityinvolcanicsystems.Indeed, oc-currencesofModeIfractures,socalledtensiongashes,havebeen documented attrachybasaltic volcanic dyke margins (Petronis et al., 2013) and inobsidianflows (Shields etal.,2016).En échelon, elongate,fissure-likeporeshavealsobeeninterpretedasextension features reflecting thetransition fromviscous to brittle deforma-tion in extruding dacitic lava domes (Smithet al., 2001). Signif-icantly, variably-healed and ash-filled shear and extension frac-tureshavebeenidentified inrhyoliticsystemsatexposed conduit margins (Stasiuk et al., 1996; Tuffen andDingwell, 2005) and in ballisticbombs (Castroetal., 2012),suggestingthat fracture pro-cessesarecommonintheupperconduit.Indeed,ourexperiments demonstratethat theseprocessescan occur underconditions ap-propriateforeffusionintheupperconduitwheremeltviscosities are high(Goto, 1999) and shearstrain rates rangebetween10−2

and10−6_s−1_{(Tuffenetal.,2003).}

Dependingontheinitialwatercontentofarhyoliticmeltphase innature, thebubblefractionused inthisstudymaycorrespond to anywhere above 3500 m depth, for H2O contents less than

5 wt.% (Okumura et al., 2009 and references therein). Consider, for instance, two rhyolitic eruptions that show evidence of syn-eruptive magma fracture: the 19–21Ma eruption at Mule Creek (New Mexico, USA; Stasiuk et al., 1996) and the 2008 eruption of volcán Chaitén (Chile; Castro and Dingwell, 2009). In those systems, we estimate that the magmas had bubble fractions of

Fig. 9. (a) Downstreamporefluidpressure( Pd)equilibrationuponpermeabilitydevelopmentforPP509andPP443.Theinsetimagesarethefracturegeometriesforthetwo

experiments. (b) Schematicofthefracturenetworknearconduitmargins.ModeI(extension)fracturespropagateupwardfromtheconduitcentreandouttowardtheconduit margins.Atpercolation(theinitialdevelopmentofpermeability),gasegressismostefficientawayfromtheconduitedge,owingtowell-developed,largefractures.Despite highfracturedensitiesnearconduitmargins,gasflowisretardedbythetortuousinterconnectionsofsmallfractures.

Chaitén, respectively[we estimatedH2O saturation pressures

us-ing VolatileCalc (Newman and Lowenstern, 2002) and the pre-eruptivewatercontents andmagmatemperaturesfrom

Stasiuk

et al. (1996) andCastroandDingwell (2009); vesicularity was esti-matedfollowing

Jaupart

andTait (1990)andwecalculateddepths assuming lithostatic pressure]. These estimates assume equilib-rium dehydration and closed system degassing, which may not be an appropriate model when gas can be siphoned out of the magma along conduit marginsand into the surroundingcountry rock(Stasiuk et al., 1996). Thus, these calculationslikely overes-timate the vesicularities of these systems at any given depth. It is thereforereasonable that the fracture mechanisms highlighted in thisstudyare operative within the upperconduit, though we stress that several outgassing mechanisms are likely active con-currently.Whilebubblecoalescencemaydominateathighbubble fractions,asgascontinuestobelostfromthesystem,magma frac-ture will become increasingly important, further facilitating gas escape.

Inthe upper conduit,shear-induced fractures atconduit mar-ginsformefficientoutgassingpathways(Goto,1999; Gonnermann andManga, 2003) but, since shearfractures areprone to closure astheyaccommodatestrain(Okumuraetal.,2010) orheal(Tuffen and Dingwell, 2005), repeated fracture events may be needed

to maintain permeability. Critically, the application ofa constant shearstrainrateinourexperimentsappearstokeeplow-pressure extension zonesopen up tohigh strain (e.g. PP509). The passive nature oftheMode Ifracturesinthepresentstudysuggeststhat they remainideal, andlong-lived, outgassing channelsuntil they are rotatedinto the shearing direction. Furthermore,we demon-stratethat repeatedfractureeventsoccurundercontinuous shear, maintainingthe permeablenetworkasdeformation continues(as demonstratedinPP509).

6. Conclusions

Thedeformationmechanismsassociatedwithpermeability de-velopmentinmagma haveaprofound influenceon thelongevity andgeometryoftheseoutgassingnetworks. Wehighlightthe im-portanceofModeI(extension) fracturesaspassiveandrelatively long-lived features that assist outgassing at conduit margins. In our experiments,Mode I fractures formefficient outgassing net-works, at once creating low-tortuosity pathways across sample lengthsandlow-pressure voidspaces thatmay siphon surround-ingvolatilesoutofthemagma.Thesefractureslocalizelittlestrain and,therefore,havealimitedeffectonthe mechanicalbehaviour ofthe materialuntil they are rotatedinto thedirection ofshear, atwhichpoint,they maybeginto inducea strain weakening re-sponse. At high strain rates and low shear strain, in particular, fracturedensity ishighbutfractures are shortandgas escapeis inefficient, relyingon theinterconnection ofthinfracturesto de-liver gas across thesystem. While atlower strain ratesfractures takelongertodevelop,theyextendacrossthewholesample, cre-ating efficient networksfor gas escape. Repeated fracture events and relatively low strain localization ensure that these fracture networksencouragesustainedoutgassing.Critically, whenapplied toa volcanicsetting,the fracture networkgeometry createsfluid flowpathwaysthatextendfromthecentreofthevolcanicconduit, directinggasupwardandoutwardtowardtheconduitrim, modu-latinggasescapeandfavouringmagmaeffusion.

Acknowledgements

We wouldlike to extend our sincere thanks to T.Mather for hereditorialhandlingofthemanuscriptandF.Wadsworthandan anonymousreviewerfortheir insightfulcomments,whichgreatly improved the article. We would also like to thank A. Rust, Y. Lavallée, M. Violay, J.-L. Bourdier, J. Castro, J. Farquharson, J.K. Russell, and M.J. Heap for helpful discussions. Funding for re-searchcostswasprovidedbytheAgenceNationaledelaRecherche (ANR) project DOMERAPI (ANR-12-BS06-0012). Additional fund-ingforARLKwasprovidedbyaPostgraduateScholarship-Doctoral (CGSD3-444207-2013)providedbytheNaturalSciences and Engi-neeringResearchCouncilofCanada(NSERC).I.DiCarloisthanked forSEMassistance. S. JaniecandP. Benoistare acknowledgedfor thinsection preparation. We thank Q. Thibaultfor his dedicated guardianshipofthePatersonapparatus.

Appendix A. Supplementarymaterial

Supplementarymaterialrelatedtothisarticlecanbefound on-lineat

http://dx.doi.org/10.1016/j.epsl.2016.10.053

.

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