The evolution of pore connectivity in volcanic rocks

HAL Id: hal-01452035

https://hal.archives-ouvertes.fr/hal-01452035

Submitted on 21 Aug 2020

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of

sci-entific research documents, whether they are

pub-lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diffusion de documents

scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

Distributed under a Creative Commons Attribution - NoDerivatives| 4.0 International

License

The evolution of pore connectivity in volcanic rocks

Mahieu Colombier, Fabian Wadsworth, Lucia Gurioli, Bettina Scheu, Ulrich

Kueppers, Andrea Di Muro, Donald B. Dingwell

To cite this version:

Mahieu Colombier, Fabian Wadsworth, Lucia Gurioli, Bettina Scheu, Ulrich Kueppers, et al.. The

evolution of pore connectivity in volcanic rocks. Earth and Planetary Science Letters, Elsevier, 2017,

462, pp.99-109. �10.1016/j.epsl.2017.01.011�. �hal-01452035�

Contents lists available atScienceDirect

Earth

and

Planetary

Science

Letters

www.elsevier.com/locate/epsl

The

evolution

of

pore

connectivity

in

volcanic

rocks

Mathieu Colombier

a

,

∗

,

Fabian

B. Wadsworth

a

,

Lucia Gurioli

b

,

Bettina Scheu

a

,

Ulrich Kueppers

a

,

Andrea Di Muro

c

,

Donald

B. Dingwell

a

a_{DepartmentofEarthandEnvironmentalSciences,Ludwig-Maximilians-UniversitätMünchen,Germany}

b_{UniversitéClermontAuvergne,CNRS,IRD,OPGC,LaboratoireMagmasetVolcans,F-63000Clermont-Ferrand,France}

c_{InstitutdePhysiqueduGlobedeParis,ObservatoireVolcanologiqueduPitondelaFournaise(OVPF),SorbonneParisCité,UMR7154CNRS,UniversitéParis}

Diderot,France

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory: Received24June2016

Receivedinrevisedform10January2017 Accepted15January2017

Availableonline30January2017 Editor:T.A.Mather

Keywords: connectivity permeability percolationthreshold eruptivestyle vesiculation densification

Poreconnectivityisameasureofthefractionofporespace(vesicles,voidsorcracks)inamaterialthat isinterconnectedonthesystemlengthscale.Poreconnectivityisfundamentallyrelatedtopermeability, which has been shown to control magma outgassing and the explosive potential of magma during ascent inthe shallowestpart ofthe crust. Here, wecompilea databaseofconnectivity and porosity frompublishedsourcesandsupplementthiswithadditionalmeasurements,usingnaturalvolcanicrocks produced in a broad range of eruptive styles and with a range of bulk composition. The database comprises2715pairsofconnectivityC andporosityφvaluesforrocksfrom35volcanoesaswellas116 productsofexperimentalwork.For535volcanicrock samples,thepermeabilityk wasalsomeasured. Data from experimental studies constrain the general features ofthe relationshipbetween C and φ associatedwithbothvesiculationanddensificationprocesses,whichcanthenbeusedtointerpretnatural data.Toafirstorder,weshowthatasuiteofrocksoriginatingfromeffusiveeruptivebehaviourcanbe distinguishedfromrocksoriginatingfromexplosiveeruptivebehaviourusingC andφ.Weobservethat onthisbasis,aparticularlycleardistinctioncanbemadebetweenscoriaformedinfire-fountainsand thatformedinStrombolianactivity.Withincreasingφ,theonsetofconnectivityoccursatthepercolation threshold φc whichinturn canbehugely variable.We demonstratethat C isanexcellentmetric for

constrainingφcinsuitesofporousrocksformedinacommonprocessanddiscusstherangeofφcvalues

recordedinvolcanicrocks.Thepercolationthresholdiskeytounderstandingtheonsetofpermeability, outgassingandcompactioninshallowmagmas.Weshowthatthisthresholdisdramaticallydifferentin rocksformedduringdensificationprocessesthaninrocksformedinvesiculatingprocessesandpropose thatthisvalueisthebiggestfactorincontrollingtheevolutionofpermeabilityatporositiesaboveφc.

©2017TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

Volcanic eruption style is controlled dominantly by the effi-ciency with which exsolved volatiles can outgas from the sys-tematshallowlevels(e.g.,RustandCashman,2004; Gonnermann

and Manga, 2012). This is governed by the development and

longevityofpermeability(e.g.,Blower,2001).Theexplosive poten-tial,drivenby apressurizinggasphase,canbereducedif perme-abilityis quickly established andremains high (e.g.,Eichelberger etal., 1986; Klug and Cashman, 1996). Understanding the time-dependence of permeability evolution in shallow magmatic sys-temsshould help to refinemodels of a wide range ofmagmatic

*

Correspondingauthor.

E-mailaddress:mathieu.colombier@min.uni-muenchen.de(M. Colombier).

processes, includingheat transfer (e.g.,Connor et al., 1997), vol-canic welding (e.g., Wadsworth et al., 2014; Heap et al., 2015), fragmentationlikelihood(e.g.Muelleretal.,2008)andvolcanicgas flux(e.g.,ofSO2;EdmondsandHerd,2007).Inallthesecases,the

evolutionofgaspermeabilityisstronglycoupledtothe evolution ofthebulkporosityofthesystembyconstitutivelawsthatdepend on the geometry ofthe pore space (e.g., Saarand Manga, 1999; Blower, 2001; Wadsworth et al., 2016a, 2016b). Metrics for the geometry of pore space, including inter-pore aperture size, pore networkanisotropyandtortuosityor,inthecaseofawelding sce-nario, initial particle size and shape, have all been found to be usefulinscalingmodelsofpermeabilitywithporosity(e.g.,Blower, 2001; Le Pennec et al., 2001; Bernard et al., 2007; Yokoyama and Takeuchi, 2009; Wright et al., 2009; Degruyter et al., 2010; WrightandCashman,2014;Wadsworthetal.,2016a,2016b). http://dx.doi.org/10.1016/j.epsl.2017.01.011

0012-821X/©2017TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Pore connectivity, the fraction of total porosity that is con-nected, directly records the onset ofpermeability (e.g., Rust and Cashman, 2011). These two properties, connectivity and perme-ability, are different since permeability is a vector quantity and is dependent on several pore properties such as tortuosity and anisotropy whereas connectivity is a scalar quantity and is only afunction oftheextent ofcoalescenceorcracksize andnumber densityin thesystem. Connectivity is thus a relativelyaccessible variableasitdoesnotrequirequantificationofanisotropyinorder tobeobtained.

In the simplestview ofmagma ascent, volatiles exsolve from the melt,and leadto bubble nucleation,growth andcoalescence (e.g., Gonnermann and Manga, 2007). At a critical percolation porosity (the percolation threshold

φc

), bubble coalescence be-comessystem-spanningleadingtothedevelopmentofconnectivity (e.g.Blower, 2001). In volcanicrocks, porosity is oftencomposed dominantlyorevencompletelyofconnectedporosity(i.e.,isolated porosityofzero)reflectingextensivecoalescenceormicrocracking (e.g.,Robertetal.,2008; Kennedyetal.,2010).Ifcontinuedvolatile exsolutioninto thiscoalescing pore network issufficiently vigor-ous,orascentissufficientlyrapid,thenthegaspressurerisesand canresultinfragmentation(e.g.,NamikiandManga,2008).

The traditional view espoused above is ubiquitouslycast asa systeminwhichporosity,andconnectivityincrease duringascent untilfragmentation.However,amorenuancedviewacknowledges that magma with a highly connected pore phase is unstable if thegaspressuredoesnotbalance themagmastaticpressure.This canbethecasewhenconnectivityextendsoverlargelength-scales wherethe porepressurecan dropdueto outgassingthrough the system. Magmas forwhichthisis thecase willdensify eitherby compaction(Michautetal.,2009) orbysurfacetensionatmelt–gas interfaces(Wadsworthetal., 2014, 2016a;Kennedy etal., 2016), decreasingporositybacktowardathreshold

φc

.

Inadditiontonucleatingandgrowingbubbles,magmaporosity can be formed by cracks (e.g. Lavallée etal., 2008) or by crack-fillinggranularmagmasuchastuffisite(e.g.Kendricketal.,2016) thatpossiblyrepresentsintra-conduitfragmentationeventsinthe absenceofexplosiveeruption(e.g.GonnermannandManga,2003; Castroetal., 2012). Inthecaseofcracks, connectivitycan be in-creasedrapidlywithlittlechangeinporosity.Crackdevelopmentis ubiquitousinshallowdome-forminglavas(e.g.,Calderetal.,2015). Inthecaseoftheformationofgranularmaterials,theinter-particle connectivityistypicallyhigh(Wadsworthetal.,2016a).

We have collated literature data in order to explore a con-nectivity metric for porosity that has been used to elucidate the development of permeability (Farquharson et al., 2015). We show that while vesiculation will increase porosity

φ

and in-crease connectivity at

φ > φc

(e.g., Blower, 2001), crack-closure, viscous compaction of bubbly magma, gas-resorption, and vol-canic welding all conspire to decrease porosity andconnectivity toward a low

φc

. We highlight that the

φc

intercepted during porosityincreaseneednotbe thesamevalueasthatwhichis in-tersectedduring porosity-decreasingprocesses.Thisisinherentin theconceptofapermeabilityhysteresis(RustandCashman,2004; Michautetal.,2009).Wepropose thatpore-connectivityisuseful fordistinguishingglobalcomposition-dependent characteristics of magmaporositydevelopmentanddestructionandweexplorethe efficacyofthismetricforunderstandingtheevolutionoferuption style.

2. Methodology

2.1. Definitionsandmeasuringtechniques

In most previous studies dealing with the evolution of pore connectivitywithporosity,theresultshavebeenpresentedby

vi-sualizingtheconnectedporosity

φ

asafunctionofthebulk poros-ity

φ

(Klug et al., 2002; Formenti and Druitt, 2003; Bouvet de Maisonneuve et al., 2009; Shea et al., 2012). The interpretation of such correlation plots is difficult because the trends are not easy to discriminate and interpret when data plot close to the equiline. A moreintuitive wayto makeuse oftheseresultsis to plotporeconnectivityasafunctionofbulk porosity,an approach that hasbeenadoptedinonlyvery fewstudiesto date(Shimano andNakada, 2006; Nakamura etal., 2008; Okumura etal., 2013; Farquharsonetal.,2015; Colombieretal.,2017).Weusethe com-mondefinitionofconnectivityC where

C

=

φ



φ

(1)

In this study, and in the case of

∼

99% of the values in the databaseherecompiled,wemeasure

φ

 byapycnometrymethod. With thistechnique, pore clustersconnected tothe exterior of a rock sample are considered connected porosity. However, these pores do not necessarily contribute to fluid transport and per-meability. A subset of the data represent a

φ

 determined us-ing water impregnation (Kato, 1987; Nakamura et al., 2008) or by X-ray tomographicimagingtechniques (Okumura etal., 2008; Songetal., 2001).The poreconnectivitycan alsobequalitatively estimated from the Euler characteristic which is calculated by countingthe numbersofconnections andisolatedobjects (Vogel, 2002). Finally, it can also be retrieved using skeleton analysis whichreliesonthequantificationofnumberandgeometryofthe disconnectedporemedialaxis(Lindquistetal.,1996).Whilethese different definitions of connectivity yield similar results and are usedsynonymouslyinthisstudy,somediscrepanciesarelikelyand shouldbeconsidered.

2.2. Compilationoftheconnectivitydatabase

Wecompiledalargedatabaseofporosityandconnectivity com-prising bulk-rock composition and measurement techniques for naturaland experimental datafromstudies published in thelast 30 years as well as unpublished data for erupted volcanic ma-terials measured herein. The compiled database results in 2715 pairsofconnectivityandporosityvaluesfornaturalvolcanicrocks across35volcanoescovering abroadrangeoferuptivestylesand compositions and 116 pairs from 7 experimental studies. This databaseincludesrhyolitic(Kato,1987; Klugetal.,2002; Rustand Cashman, 2004; Mueller, 2007; Nakamuraetal., 2008; Bouvet de Maisonneuveetal.,2009; Alfanoetal.,2012; Nguyenetal.,2014), dacitic (Rust et al., 1999; Mueller, 2007; Wright et al., 2007; Nguyen et al., 2014; Heap et al., 2015), phonolitic and trachytic (Sheaetal.,2012; Colombier etal.,2017),andesitic(Formentiand Druitt,2003; Mueller,2007; Platzetal.,2007; Bernardetal.,2007; Giachetti et al., 2010; Farquharson et al., 2015), and basaltic to basaltic andesitic (Rust et al., 1999; Song et al., 2001; Mueller, 2007; Kawabata et al., 2015) volcanic rocks from a wide range of sites, as well asnaturally welded deposits (Klug et al., 2002;

Michol et al., 2008; Wright and Cashman, 2014; Heap et al.,

2015). It should be noted that more than 90% of the data for the trachytes arise from analysis of rocks of a single eruption (Colombieretal.,2017).Thedatabasealsocomprisesexperimental products fromboth vesiculation (Okumuraet al., 2008; Takeuchi et al., 2009) and densification experiments (Robert et al., 2008; Okumuraet al.,2013; Vasseur etal., 2013; Kennedyetal., 2016; Vasseuretal.,2016).

We complement the above database with unpublished mea-surementsofbasalticscoriafromtheChisnyAD 381BP(Morandi et al., 2016) lava fountaining eruption (Piton de la Fournaise; DynVolc database),Stromboli 2011and 2013eruptions (DynVolc

database), and of andesitic pumices from Montagne Pelée vol-cano. Where measurements were made by the authors, helium-pycnometers at LMU (Ludwig-Maximilians-Universität) and LMV (LaboratoireMagmasetVolcans)wereused(Quantachrome Ultra-pyc 1200eand Micromeritics Accupyc 1340, respectively). In the supplementaryfile,we provideSupplementaryTable1withalist of all the contributions to the database specifying the publica-tiontitle,theeruptiondateandstyleorthetype ofexperimental study, the number of samples analyzed, the technique used to measure connectivity, the porosity and connectivity ranges and, ifavailable, the sample permeability range.We also provide the completedatabase(SupplementaryTable2)withporosity, connec-tivityand ifavailable permeability datafor each dataset,aswell asthe sample type, chemistry, eruption and eruptive style asso-ciated for natural volcanic rocks or the type of experiments for experimentaldata.

2.3.Potentialweaknessesintheconnectivitydatabase

ThedatabaseincludesdatawithC

>

1.Sincesuchconnectivity valuesaboveunityareunphysical,wehavetoconsiderthe poten-tial sources of errors on the measurements. Key to the accurate measurementoftotalporosity isknowledgeofthedensityofthe solid,pore-free phase(s) inthe volcanicrock.A firstweakness in thedatacompiled herearisesfromthevalue chosenforthesolid densityinthecalculationoftheporosity.Indeed,insome studies onlythesolid-densityofonerepresentativeclastismeasured and thisdensityvalue isusedtocompute totalporosityfora suiteof samples.Thiscarrieswithittheimplicitassumptionthatthesolid densitydoesnot vary fromclast-to-clast. However, heterogeneity inthephenocrystassemblage betweenclastsorvariationsinbulk composition may be common. This can lead to unphysical con-nectivityvalues greaterthan 1.Toaddress thisissue,Wright and Cashman (2014)demonstratethatarangeofsoliddensitycouldbe plausibleforweldeddepositsanddiscussdifferencethatmayarise duetochemicalvariations.However,inmoststudiestherock pop-ulationstudiedaremorehomogeneouswithlittlevariationsofthe soliddensity.Thiswasthecaseforexampleforabreadcrustbomb populationfromSoufrièreHillsvolcano(Giachettietal.,2010) and weldedblockandashflowsdepositsfromMountMeagervolcano (Micholetal., 2008) inwhichthesoliddensityofalargenumber ofrocksweremeasuredandshowedverysmallstandarddeviation. In this case, the potential source of error on connectivity arises onlyfromdeterminationofbothbulkandconnectedporosities.In afewstudies,theseerrorsarequotedbytheauthorsandallowus todeterminetheerroronconnectivity(FormentiandDruitt,2003; Micholetal.,2008; Giachettietal.,2010; Sheaetal.,2012).

Anotherdrawback to consider is that the connectivity that is measurableontypically-sizedrocksample (typicallyontheorder of

∼

10−5 to 10−7 m3) may not scale to volcanic length-scales. Thatis,connectivityofporenetworksextends overfinite lengths andporosity that is system spanning in the laboratory may not be systemspanning innature. Nevertheless,these measurements remaininformativewhen interpretinglaboratory-scale permeabil-ity measurements on which most permeability scaling laws are based.

3. Results

ConnectivityC co-varieswith

φ

inatrendthatdependonthe processinvolvedincontrolling changesin

φ

.Inwhat follows,we presentsubsetsof thecompileddatabaseto analyzethesetrends for(1)experimental ornaturaldataforwhich themechanismby whichconnectivity was createdor destroyed isknown,and then (2) data from natural rocks of a wide range of bulk chemistry. Byadoptingthistwo-stageanalysisweaimtodiscriminatetrends

that can inform usaboutthe processes by which connectivity is typicallyestablishedordestroyedinmagmasthatcometobe de-positedasvolcanicrocks.

3.1. Contrastingvesiculationanddensificationtrends

Here we constrain the trends in which

φ

was an increasing function of time in experiments in which samples were vesicu-lated to different total

φ

. In these experimental data, the onset of non-zero C occurred at

φc

,which is the point at which bub-blecoalescencespannedthemeasuredsampleorconnectedtothe outside. Wetermthesetrends“vesiculating”torefertoanytrend in which bubble nucleation, growth, coalescence and forced gas percolation, orall ofthese dominatethemechanism bywhich

φ

increases.Wedistinguishvesiculatingtrends fromthose inwhich experimentalworkshowedthat

φ

decreasedwithtime,whichwe term“densifying”.

Fig. 1a showsthe relationshipbetweenC and

φ

for vesiculat-ing trends for a range of materials. First, the post-experimental resultsareshownforsamplesformedinvesiculationexperiments (Okumuraetal., 2008; Takeuchietal., 2009) performedwithand withoutsyn-vesiculation shearstress imposed onthe samples.In the former case, a qualitative estimate of the minimum thresh-old

φc

is

∼

0.21,whereasinthelattercase,0

.

42

< φc

<

0

.

6.These experiments confirm that forthe vesiculating trend, the positive correlation ofC with

φ

can beused toestimate a wide rangeof

φc

whichwillbediscussedlater(seeSection4.2).

We compare the experimental results with those from sam-ples for which

φ

is known to have been a positive function of time. Breadcrust bombsamples fromSoufrière Hills (Giachetti et al., 2010), Unzen (Mueller, 2007) and Guagua Pichincha (Wright etal., 2007) volcanoesare shown. Thesetrends arecharacterized by post-fragmentation vesiculation of the bomb-cores while the bomb-rindsremainedlessporousduetofastquenchingand solid-ification.Asaresult,therindsrecord0

≤ φ ≤

0

.

25 andthevesicles inside are completely isolated with C

=

0, whereas their associ-atedcoresrecordhigherporosity0

.

2

≤ φ ≤

0

.

7 andcorresponding 0

.

65

≤

C

≤

0

.

95.Notethat inthecaseofUnzenandGuagua Pich-inchavolcanoes(Mueller,2007; Wrightetal.,2007) therindswere not measured. The

φc

at which connectivity onset can be esti-mated is likely to be in the range of the porosity of the rinds, thatis0

≤ φ

c

≤

0

.

25.Finally,wecomparethesedatawithrhyolitic

pumices that contain vesicles with no diagnostic sign of shear-deformation orpost-vesiculationcollapseandwhichare reported to record coalescence features (Klug et al., 2002; Mueller, 2007; Bouvet de Maisonneuve etal., 2009; Nguyen et al., 2014). These pumices show a wide range of C from 0

.

25 to

∼

1 over a small range of porosity 0

.

63

≤ φ ≤

0

.

85. Qualitative estimatesof what thevalueof

φ

wouldbeatC

=

0,mightsuggestahigh

φc

of

>

0.5.

Fig. 1bshowsdatafromnaturalvolcanicrocksthat canbe in-terpreted to be the result of densification mechanisms in what was initially a granular material and evolvedto be non-granular and dense (Klug et al., 2002; Michol et al., 2008; Wright and

Cashman, 2014; Heap et al., 2015) and experimental data from

densifying systems (Robert et al., 2008; Okumura et al., 2013;

Vasseuretal., 2013,2016;Kennedyetal., 2016).The compaction experiments from Robert et al. (2008) and the sintering exper-iments from Vasseur et al. (2013, 2016) were performed using initially granular materials. Robert et al. (2008) used a rhyolitic volcanic ash with a high initial porosity (

φi

≈

0

.

8) as starting material, whereas Vasseur et al.(2013, 2016) used angular glass fragments with an initial porosity of

φi

≈

0

.

4. In these experi-ments

φ

decreased with time while the material maintained a high connectivity around C

∼

1. Only at the late stages of com-paction orsintering, withcontinueddensification did C decrease toward a low

φc

that can be qualitatively assessed to be on the

Fig. 1. ThecovarianceofC withφforsystemsthataredominantlyrecording(a)vesiculationand(b)densification.In(a)weshownaturaldatafromsamplesofbreadcrust bombrinds(bluecrosses;Giachettietal.,2010)andbreadcrustbombcores(bluesquares;Mueller,2007; Wrightetal.,2007; Giachettietal.,2010)fromSoufrièreHills volcano,GuaguaPichinchavolcanoandUnzenvolcanoaswellasnaturalpumicedataforwhichthereisnosignofsheardeformation(greycircles;Klugetal.,2002; Mueller, 2007; Bouvet deMaisonneuveetal.,2009; Nguyenetal.,2014).Additionallywegiveresultsofvesiculationexperimentswithshearstressesappliedduringvesiculation(red triangles;Okumuraetal.,2008)andwithoutshearstresses(blackandwhitediamonds;Okumuraetal.,2008; Takeuchietal.,2009).(b)Weshowtheresultsofdensification experimentsconsistingofsinteringofglassbeads(greysquares;Vasseuretal.,2013,2016),compactionofsinteredrhyoliticash(blackopencircles;Robertetal.,2008)and compactionofrhyoliticmeltbygasescape(blackcrosses;Okumuraetal.,2013).Weadditionallyshowdatafromnaturalsamplesfromweldeddeposits(bluecircles;Klug etal.,2002; Micholetal.,2008;WrightandCashman,2014;Heapetal.,2015).ThegreyfieldscorrespondtounphysicalvaluesofconnectivitywithC>1.Whenquotedin theoriginalstudy,theuncertaintiesonconnectivityandporosityarerepresented.(Forinterpretationofthereferencestocolourinthisfigurelegend,thereaderisreferred tothewebversionofthisarticle.)

order of

φc

≈

0

.

05. The experimental results of Okumura et al.

(2013) demonstrate a similar evolution of

φ

and C down to a

similar

φc

. However, in this study (Okumura et al., 2013) the compaction was a result of gas escape after an initial vesicula-tion andcoalescence process. In Kennedy etal. (2016), the den-sification was a consequence of surface tension processes and also led to a decrease of C with

φ

. The natural datasets se-lected to demonstratethe densification trendare those fromthe Wineglass Tuff(CraterLake; Klug etal., 2002), weldedblock and ash flow deposits (Mount Meager volcano; Michol et al., 2008; Heap etal., 2015), and the Shevlin Park Tuff(Wright and Cash-man, 2014). We see that these naturaldatasets follow a similar relationship between

φ

and C as the experimental densification trendwithadramaticdropofporosityandalesspronouncedand morescattereddecreaseofconnectivity.

3.2. Trendsassociatedwithbulkcomposition

InFig. 2wepresentcompileddatasetsfornaturalvolcanicrocks groupedbybulkchemicalcomposition.Furtherdistinctionismade betweenvesicularrockseruptedduringexplosiveactivity(pumice orscoriaandbreadcrustbombs) andvolcanicrocks derived from effusiveeruptionssuch aslavas, domelavas sampledinsitu orin block and ash flow deposits where these distinctions are made inthe studies originatingthe data andnot here. Some problems withthissimpleseparationmightbeencounteredwithtransitional orcomplex eruption styles. Forthe rocks fromexplosive basaltic

eruptions, we further differentiate between those from Strombo-lianeruptionsandthosefromHawaiianfirefountainactivity.

The first observationwe make isthat C is highformost vol-canicrocksindependentoferuptivestyle.Abroadrangeof connec-tivity is nevertheless observed for rhyolitic pumices and basaltic scoria(Figs.2aandb).Weemphasizethatsimilarpatternscanbe discernedacrossallcompositions;namelythatrocksformedin ex-plosiveeruptionstendtohavearelationshipbetweenC and

φ

that isdistinctfromrocksformedineffusiveactivity.DuetothehighC inallrocks,itisdifficulttodiscernwhat

φc

isforeach rocktype exceptfortherinds ofthebreadcrustbombs(Fig. 1).However, it isclearthattheminimum

φ

forrocksformedinexplosiveactivity isgreaterthantheminimum

φ

foundforrocksformedineffusive activity. Thedacitic,andesiticandtrachyticrocks formedby effu-siveactivityrecordlow-

φ

trendsthatshowhowC isanincreasing functionof

φ

.

AnotherfeatureisthatthescoriafromHawaiian fire fountain-ingandfromStrombolianactivityhaveasimilarrangeofporosity buttheformerhaveamuchbroaderrangeofconnectivityandat loweraveragevalues.

The globaltrends recordedin Fig. 2 are lessdiagnostic ofthe mechanismofformation,thanthetargetedandexperimentaldata presentedinFig. 1.

3.3. Connectivityandpermeability

The onset of system-spanning connectivity at

φc

is the onset ofnon-zeropermeabilityk.ThevariableC doesnotinclude

infor-Fig. 2. ThecovarianceofC withφforallnaturalrocksclassifiedbybulkrockcomposition.(a)Rhyolitesdifferentiatedintopumices(blueopencircles)andeffusiverocks(blue squares).(b)Basaltsdividedintoscoriathatareformedinfirefountainactivity(blackcross),scoriaformedinStrombolianactivity(redopencircles)andlavas(redsquares). (c)Dacitesdividedintopumices(orangeopencircles),breadcrustbombs(blackcross)andeffusiverocksfromdomes,lavasorblockandashflowdeposits(orangesquares). (d)Andesitesdividedintopumices(greenopencircles),breadcrustbombcoresandrinds(blackcross)andeffusiverocksfromdomes,lavasandblockandashflows(green squares).(e)Trachytesdividedintopumices(purpleopencircles)ordomerocks(purplesquares).(f)Alldatacoarselyseparatedintorocksformedduringexplosiveeruptions (greycircles)androcksformedbyeffusiveeruptions(blackopensquares).BCBandBAFarebreadcrustbombsandrocksfromblockandashflowdeposits,respectively.The greyfieldscorrespondtounphysicalvaluesofconnectivitywithC>1.DetailsoncompileddataareavailableinSupplementary Table2.Whenquotedintheoriginalstudy, theuncertaintiesonconnectivityandporosityarerepresented.(Forinterpretationofthereferencestocolourinthisfigurelegend,thereaderisreferredtothewebversion ofthisarticle.)

mationaboutanisotropy.Furthermore,k dependsstronglyonpore aperture size andtortuosity (e.g.Blower, 2001;Saar andManga, 1999)whilst C doesnot.Therefore,typically,onlythevariationof k with

φ

are constrainedandnotthevariations ofC with

φ

. No-tably, as shown in Figs. 1 and 2, for most vesiculating systems, thereis an extended region of

φ > φc

where0

<

C

<

1, demon-stratingthatusingabulkmetric

φ

includesporesthatareisolated andnotcontributingto permeableflow whichconfuses interpre-tations of model constraints. To solve this issue, often only the connectedporosityisusedwhenexploringrelationships with per-meability(Wrightetal.,2009; Farquharsonetal.,2015).

We comparein thissection theevolution of connectivity and permeabilitywithporositytoassessif,despitethesediscrepancies, thesepropertiesstill providesimilar informationaboutthe vesic-ulationanddensificationprocesses.For535volcanicrocksamples, parametersk,

φ

andC areavailable.Fig. 3showshowaplotofthe

covarianceofC and

φ

compareswiththemoretypicalk–

φ

plotfor thesamedatasets.

Rocksproducedineffusiveeventsrecordsimilarcharacteristics usingeithermetricC ork (Figs. 3aandb).Twokeyfeaturesare(1) thesteep increase ofconnectivityandpermeabilitywithporosity uptoaporosity thresholdofaround0.2forandesitesanddacites and(2)thelowerconnectivityandpermeabilityforrhyolitesata givenporositycomparedtolessevolvedrocksproducedineffusive events.

Vesicular rocks produced in explosive events (pumice, bread-crust bombs and scoria) also show similar patterns when either C or k arecomparedrelativeto

φ

(Figs. 3candd).In bothcases, theandesitesandtrachyticpumicesandthebasalticscoriaplotat a higher C and k at a given

φ

than dacitic and rhyolitic bread-crust bombsandpumices. However, whenonly consideringk, all dacitic and rhyolitic breadcrust bombs and pumices cluster

ap-Fig. 3. Comparisonbetweentheevolutionofboth(a,c)connectivityand(b,d)permeabilitywithporosityforrocksfrom(a–b)effusiveand(c–d)explosiveeruptions.The upperandlowerboundsonpermeabilityaregiven(afterMuelleretal.,2005)andarek=1×10−17_φ3.8_andk=1×10−17_φ3_{,respectivelyforrocksformedbyeffusive}

eruptions;ork=8×10−15_{(φ− φ}

c)2andk=1×10−16(φ− φc)2,respectivelyforrocksformedbyexplosiveeruptions,whereacommonφcisestimatedat0.3(Muelleret

al.,2005).MicrovesicularpumicesfromtheKosPlateautuff(bluetriangles;Bouvet deMaisonneuveetal.,2009)aredifferentiatedfromtheotherrhyoliticpumices(blue circles).ThegreyfieldscorrespondtounphysicalvaluesofconnectivitywithC>1.DetailsoncompileddataareavailableinSupplementary Table2.(Forinterpretationof thereferencestocolourinthisfigurelegend,thereaderisreferredtothewebversionofthisarticle.)

proximatelywith10−15

<

k

<

10−11m2 regardlessofcomposition andnotrendisobserved(Fig. 3d). Notealsothatthe majorityof thesevesicular rocks fall within the wide empirical bounds pro-vided by Mueller et al. (2005) for explosive volcanic rocks for which

φc

≡

0

.

3.If we instead compare how C varies with

φ

for thesesamedata(Fig. 3c), basaltic,andesitic,trachytic anddacitic vesicularrocks clusterwithmoderateto highC ,butthe rhyolitic pumices demonstrate that low C is achieved at mid to high

φ

. Thissuggeststhatforsomeoftherhyoliticpumicesuites

φc

>

0

.

3. Theseobservationsareconsistentwithhighexperimentally deter-mined

φc

forsome vesiculatingsystems(Fig. 1)andwithfindings ofotherworkers(RustandCashman,2011andreferencestherein) anddemonstratethatauniversal

φc

constrainedonthebasisofk (Muelleretal.,2005) maynotbeappropriate.

Another important detail can be seen when considering the relationship betweenconnectivity andpermeability(Fig. 4). Con-ceptually,asC

→

0 at

φ

→ φ

c permeabilitymustalsotendtozero.

ButasC

→

1 thereisnostrictlimiton

φ

ork,bothofwhichcan increasewhileconnectivityremainsatunity.Therefore,C contains themostusefulinformationabouttheevolutionk intheregionof

φ

∼ φ

c. This is demonstrated in Fig. 4 where we show that for

all compositions there is a clustering of k values around C

=

1 butanon-lineartail aswe trackfromC

=

1 downto C

<

1. Un-fortunately, there is little data in the region of low C for which permeability data also exist and as such we cannot observe the expectedlimitasC andk approachzero.Italsoappearsthatrocks formedinexplosiveeruptionshaveagenerallyhigherk foragiven C thanrocks producedin effusiveeruptions,whichlikelyreflects fundamental differencesin thepore geometries generallyformed in those two eruption styles, as has been previously suggested (Muelleretal.,2005).

4. Extendeddiscussion

4.1. Granularandnon-granularmaterials:Insightsfromexperimental work

Wehighlightthat asubsetofdensificationtrendsinFig. 1 de-rivefrominitiallygranularmaterials,whilethevesiculationtrends arefornon-granularporousmedia.Herewediscussthedifferences onemightexpectfromthisgeometricdistinction.

First,forthedensificationdatapresentedinFig. 1(Robertetal., 2008; Vasseur etal., 2013, 2016), theevolution of C with

φ

ap-pearstoafirstordertobeindependentofthedensification mech-anismoverawiderangeofconditions.ForthedatafromRobertet al. (2008),granularvolcanicashwaspartiallysinteredbeforebeing drilled to a cylindricalcore, thena uniaxial loadwas applied re-sultinginarangeofstrainratesathightemperatureintheviscous regime such that densification proceeded before quenching. The data fromVasseuretal.(2013,2016) were producedusing gran-ularcrushedsyntheticglassshardsloadedincruciblesand densi-ficationproceededundersurfacetensionattheparticleinterfaces, no applied loadwas used. InOkumura etal. (2013),the densifi-cationarisesfromshear-inducedoutgassingofahighlyconnected porenetwork.InKennedyetal. (2016),surfacetension-driven re-traction ofbubblewallsledtothedensificationofcrystal-bearing pumices. Despite these large differences in densification mecha-nism,C and

φ

varyconsistentlysuchthatweconcludethatinthe viscous regimedensificationtrendsproduceasimilarevolutionof connectivity.

On the other hand,examination of the data for the vesicula-tion trend presented in Fig. 1 shows that the same mechanism-invarianceofthetrendofC with

φ

cannotholdhere.Asan exam-ple,theincreaseinC from

φc

occursatamuchlowerwindowof

Fig. 4. Thevariationofconnectivity C with permeabilityk for (a)rhyolites, (b) dacites,and(c)andesites,separatedintoclassesofrocksproducedineffusive ac-tivityandrocksproducedinexplosiveactivity.Thegreyfieldscorrespondto un-physicalvaluesofconnectivitywithC>1.BCBandBAFarebreadcrustbombsand rocksfromblockandashflowdeposits,respectively.Detailsoncompileddataare availableinSupplementaryTable2.

φ

forexperimentsinwhich vesiculation was coincidentwith ap-pliedshearstressthanforvesiculationexperimentsintheabsence ofshearstress(Okumuraetal.,2008; Takeuchi etal.,2009).This indicatesthat bubblegrowth-driven coalescenceisstrongly influ-encedbyshearstrainwhereasthedeformationofinitiallygranular materialsislessinfluencedbydeformation(Fig. 5).

4.2.Thepercolationthreshold

φc

inmagmas

Inpercolationtheory,acommonmethodforpredicted

φc

isto createnumerically generated porous networksfrom distributions ofdiscs (2D) orspheres (3D). These are strictly geometrical, and not dynamic considerations of

φc

. These techniques predict that monodisperse spheres, distributed randomly in a volume where

Fig. 5. Effectofshear-deformationon(a)theconnectivityand(b)permeabilitywith

porosityfornaturalrhyoliticanddaciticpumicesandexperimentalproducts.The greyfieldcorrespondstounphysicalvaluesofconnectivitywithC>1.

they can also overlap, achieve system-spanning connectivity at

φc

∼

0

.

3 when the spheres are considered to be the pore-phase (e.g., Rintoul, 2000). Treating the spheres as the pore phase in this way can be thought of as being most similar to the vesic-ulating case. Contrastingly, if the spheres are considered to be the non-pore phase (the solid in the caseof rock or the liquid-crystalsuspensioninthecaseofmagma),then

φc

isonlyrecorded whentheoverlappingspheresoccludeasystem-spanning connec-tion atmuch lower

φ

. Typically,in thiscase,

φc

≈

0

.

03 (Rintoul, 2000; Wadsworth etal., 2016a,2016b). This second case, where thespheresarethenon-porematrixmaterialisbroadlyanalogous to thevolcanic welding scenario. Wefind it informativeto high-light howthese

φc

constraints forspherepopulations are altered by simple variablesin both cases;(1) wherethe spheres arethe pores and(2)wherethespheres areparticles. Incase(1)

φc

isa strong function of the polydispersivity ofthe spheres sizes used inthegeometricalsimulation(e.g.,Blower,2001),whereasincase (2)

φc

isaweak functionof polydispersivity(Rintoul, 2000). This isfurtherdemonstratedinFig. 1,where

φc

coversawiderangeof valuesforthevesiculatingcase(case1),whereas

φc

isubiquitously consistent with the

φc

=

0

.

03 prediction for the granular case (case2).MicrovesicularrhyoliticpumicesfromtheKosPlateautuff (Bouvet deMaisonneuve et al., 2009) contain two vesicle popu-lationsattributedtotwo distinctnucleation events.Consequently, thesepumicesapparentlyrecordamorecomplexapproachtothe percolationthreshold(Fig. 3).

Innaturalmagmas,theintersectionofthepercolationthreshold as

φ

increasesordecreasesisoftencomplicatedbydynamic pro-cesses that may invalidate thenumerical geometrical approaches outlinedabove. Someoftheseare discussedbrieflyhere. Variable

φc

havebeen discussedinnumerical,experimental or permeabil-itystudies (RustandCashman, 2011 andliterature therein) with referencetodynamicscenarios.First,crystallinityhasbeenshown to haltdensification processesata

φ

greater than

φc

that would

havebeenpredictedongeometricalgroundsalone,duetocrystal– crystalinteractions (Kennedy etal., 2016).Theseinteractions pro-duce a rigid framework and thus an elevated yield stress in the systemthatneeds tobe overcomefordensification toproceedto

φc

.Insomeofthesecases,however,thesystemisstillpercolating (i.e.permeable)evenwhenchangesin

φ

havestopped.

Additional, first-order effects controlling

φc

and the onset of connectivityforvesicularmagmasarethepresenceornotof shear-deformation(Okumuraetal.,2008; Takeuchietal.,2009; Burgisser andGardner,2004; RustandCashman,2011),themeltcrystallinity and the modality of the vesicle size distribution in vesiculating systems (Blower, 2001). Shear-stress and the resulting deforma-tion will favour the onset of connectivity and permeability at a lower

φc

asshownbydecompressionandvesiculationexperiments (Figs. 1 and 5;Okumuraetal.,2008, 2013;Takeuchietal.,2009; NamikiandManga,2008).Tubepumices,generallytheproductof large shearstrain (Dingwell etal., 2016), are consistentwith ex-perimentalworkforwhichvesiculationwascoincidentwithshear deformation (Fig. 5). Contrastingly,isotropicpumicematerials are moreconsistent withexperimentswhere vesiculationhappens in theabsence ofsheardeformation (Figs. 1 and5). Itis clearfrom bothnaturalandexperimental datasetsthat

φc

issignificantly re-ducedinthepresenceofshearing,consistentwithpreviousstudies (Okumuraetal.,2008; BurgisserandGardner,2004).

The differences in

φc

between vesicular rocks might be also related to differences in crystallinity.The role of crystals on the connectivity and percolationthreshold is complex. First, because bubblescannot occupythecrystal-phase, foragivenporosity,the additionofcrystalsreducesthe spacebetweenbubbles, therefore enhancingcoalescenceatlower porosities(Blower,2001).Second, thecrystalsare barrierstosimpleflow patternsandsothey pro-motebubbledeformation enhancingthelikelihoodofcoalescence (Oppenheimeretal.,2015).Inboth cases,theaddition ofcrystals appearsto inducea shiftof

φc

tolower porosity.Inversely,

φc

in crystalpoorpumicesmightbe quitehigh(Nakamuraetal.,2008;

Rust and Cashman, 2011). Even though our database lacks

sig-nificant crystallinity data to establish definitive implications for the percolation threshold, we stress that rhyolitic pumices with a potentially high

φc

also havelow melt crystallinity(

<

20vol%;

Bouvet deMaisonneuveetal.,2009; Alfanoetal.,2012).Inversely, andesiticbread crust bombs have a very low percolation thresh-oldassociatedwithahighmeltcrystallinityofmorethan50vol% (Giachettietal.,2010).

4.3. Distinguishingbetweeneruptivestyles

Wepropose thatconnectivitycanbe ausefultoolto discrimi-natebetweendifferentkindsofvolcanicactivity.Thebestexample isthebasalticscoriafromHawaiian (firefountaining)and Strom-bolian activity that have very distinct features when plotted to-getheronaC –

φ

plot.Althoughthesescoriahaveasimilarporosity range,thescoriafromfirefountaininghaveonaveragesignificantly lowerandbroadervaluesofconnectivitycomparedtoscoriafrom Strombolianactivity(Fig. 2b).The broadrangeofconnectivityfor scoriafromfirefountainingcanbeinterpretedsimplybyvariations intime available before quenchingdueto differencesin location and residence time in the fountain, as suggested by other au-thorsforHawaiianactivityinHawaii(ManganandCashman,1996; Stovalletal.,2012);Etna(Polaccietal.,2006),Villarrica(Gurioliet al.,2008) andAl-Madinah,SaudiArabia(Kawabataetal.,2015).

On the contrary, several factors can explain the higher con-nectivityobservedforStrombolianactivitysuchashigheraverage crystallinity,andmoreimportantdegassing priorto theeruption. Notethatthevariationsintimeavailablebeforequenchingarealso observed for the connectivity of the breadcrust bombs (Fig. 1a)

which islow in therinds (fast quenching) andhighinthe cores (slowquenching).

4.4. Theformationofeffusiverocks:developmentofcrack-networks andhysteresis

WecanseefromFigs. 2 and3thatfortheandesitic,daciticand rhyolitic rocks produced in effusive eruptions,there is an appar-ently low

φc

that isinconsistent withexperimental ornumerical data for vesiculating systems and these data are not associated with samples that were initially granular. Therefore, we invoke heretwopossibilitiesfortheadditionalmechanismthatproduces largeC atlow

φ

.

First,weproposethatbrittledeformationandtheonsetofcrack networkdevelopmentcanleadtothisincreaseofC atlow

φ

.This isconsistentwithexperimental workthatdemonstratesthat even small shear strain inhigh viscositysystems, such asandesitic to rhyoliticmagmas,canresultinbrittledeformation(Lavalléeetal., 2008; Cordonnier et al., 2009; Kendrick et al., 2013). This is an additionalprocessthatimplicatespotentialvariabilityinthevalue of

φc

.Mostsimply,crackswillforminmagmawhentheproductof thelocalshearstrainrate

ε

˙

andtheliquidrelaxationtime

λ

,which is

ε

˙

λ

,approachesunity(DingwellandWebb,1989).Whenthe sys-temonlyconsistsofliquid(puremelt)thenthismightoccurasthe bulk shearstrain rateincreasessuch that

ε

˙

λ

approaches1. How-ever, when the system suspends crystals, for example, the local strainrateislargerbetweenthecrystals,resultingincrack forma-tion in the liquid when the bulk shear strain rate is

ε

˙

λ

<

1. In thiscase,Cordonnieretal. (2012)showedthat

ε

˙

cλ

∝

1

− (φ

x/φM

)

where

ε

˙

c isthebulkshearstrainraterequiredtocracktheliquid

betweenthecrystals,

φx

isthecrystalvolumefraction,and

φM

is the maximumpacking ofthose crystals.Cracks additionallyform asmagmascool.Ifcracksdevelopandspanthesystembeing mea-sured,thenC canincreasetolargevaluesatlow

φ

,evenwhen

φ

is lessthanthepredicted

φc

forthatvesiculatingsystem.Ifthisisthe mechanismthat isdrivingthe developmentoflarge C at anoma-louslylow

φ

fortheandesitic,daciticandrhyoliticlavaspresented inFigs. 2 and3thennotonlyiscrackdevelopmentubiquitousin theselava-formingsystems,butalsosystem-spanningcrack devel-opmentoccurswhile

φ

islow.

Anotherpossibleexplanationisacyclewith(i)anearly coales-cence eventincreasing porosityandconnectivityandthecreation of a permeable pore space and(ii) gas escape through this per-meable porous network leading to compaction and reduction of C and

φ

.During this compaction, cracks or crystalscould act to maintainarelativelyhighconnectivity(Kennedyetal.,2016).This successionofcoalescenceandgasescapewouldresultina hystere-sis inthetime-dependence oftherelationship betweenC and

φ

.

Okumura et al. (2013) experimentally obtained thistype of hys-teresis with an initial coalescence stage at a low

φc

by shearing followedbygasescapeandcompaction(Fig. 1).

These two possibilities are illustrated for rhyolites in Fig. 6

whichis aconceptualdrawing illustratingthetemporal evolution of porosity andconnectivity for different processes andshowing the associated textures. The different connectivity paths in this conceptualmodelwereconstructedbasedondirectmeasurements or on constraints of the percolation threshold from experimen-talstudies ofvesiculationanddensificationofrhyoliticmelts.The percolation threshold in the case of vesiculation in the absence of cracking and shear-deformation is typically high (path A–B in

Fig. 6a; Takeuchietal., 2009) andcouldoccurina widerangeof porositybetween0.4andthemaximumface-centred cubicpacking of bubbles of

π

/

3

√

2

≈

0

.

74. In the case of vesiculation experi-ments inthe presenceof shearing(path C–Ein Fig. 6a), the per-colationthresholdwassignificantlylowerwith

φc

∼

0

.

2 (Okumura etal., 2008) and theconnectivityincreases steeplywithporosity.

Fig. 6. Differentpathsofconnectivitywithporosityfordifferentprocessesinrhyoliticmagma.(a)Themap ofC withφ wheretheshadedareasfortherhyoliticrocks fromeffusiveandthosefromexplosiveeruptionsforreference(seeFig. 2)andthetrendsforcracking,vesiculationanddensificationofrhyoliticmeltsarereported.(b–c) Representativebinaryimagesofexperimentalsamplesproducedunderdifferentconditionsin(b)non-granularsystems,and(c)granularsystems.Inallcasestheblack representstheporephase.In(a),theletteredpointsrefertotheimagesin(b)and(c)andappearattherespectivemeasuredφandC .Thepathbetweentheoriginand pointArepresentsthevesiculationofanisolatednetworkofbubbles.ThepaththroughBrepresentsvesiculationandcoalescencewithoutsheardeformation(isotropic).The pathC–Erepresentsvesiculationinthepresenceofsheardeformation(anisotropic;Okumuraetal.,2008).ThepathF–Grepresentscracksconnectingisolated,elongated bubbleswithapercolationthresholdatφc∼0.14 (Kushniretal.,2016).ThepathtopointIisthatfordensificationundersurfacetensionofnaturalnon-granularsamples

(Kennedyetal.,2016).ThepathJ–Listherepresentationofviscoussinteringofporousrhyoliticashundercompactiveappliedstress(Robertetal.,2008).PathM–Oisfor viscoussinteringofglassfragmentsundersurfacetension(Vasseuretal.,2016).ThedashedlinecorrespondstothepathF–Gforwhichtherearenodirectmeasurementsof connectivityandwasdrawnfromtheexperimentalconstraintsontheinitialporosityandthepercolationthresholdonly(Kushniretal.,2016).Otherwisepathsaredrawn connectingmeasureddatapoints.Thedarksolidlinecorrespondstothetrendofcompactionbygasescapeafterinitialvesiculationinthepresenceofshear-deformation (Okumuraetal.,2013).

The percolationthreshold in the presence ofcracks can be even lowerandtheconnectivitycanincreasedramaticallywithonly mi-norchangesinporosity.Inthecasepresentedhere(pathsF–G–H inFig. 6a), cracks connect apopulation ofinitially isolated, elon-gated bubbles formed in torsion experiments on bubble-bearing silicatemelts(Kushniretal.,2016).Inthiscase,theinitial poros-ity before the crack formation was approximately

φ

∼

0

.

14 and the percolationthreshold must therefore alsobe

φc

∼

0

.

14. Tex-tures similar to those of these experiments can be observed in dense effusive rhyolites froma rhyolitic dome at Novarupta vol-cano(Adamsetal.,2006; Nguyenetal.,2014).Allofthesecracking andvesiculationprocessescould befollowedbydensificationdue to gas escape leading to a hysteresis. The path terminating at L (Fig. 6a)representsa densification by gas escapeprocess follow-ing a vesiculation event(Okumura etal., 2013). In thiscase, the outgassingwas accompanied by shearing andcompaction. In the caseofgasescapeundersurfacetension(Kennedyetal.,2016),the densificationcanreducesignificantlyconnectivityatahigh poros-ity (path terminating at I in Fig. 6a). We also include in Fig. 6

the caseof granular densification by welding ofporous rhyolitic ashunder compaction(path J–L; Robertet al., 2008) and sinter-ing of dense angular glass fragments (path M–O; Vasseur et al., 2016),thatleadtoreductionofporosityandconnectivity.This pro-cessisimportantintuffisiteveinsandcouldbeimplicatedinthe formationofeffusivelavasthatrepresentdensifiedpyroclastic ma-terial(e.g.,Castroetal.,2014).Thismodelimpliesthatinformation aboutthe textureofa rhyolitecan provideinsights intothe con-nectivitypathandassociateddominantprocess.However,mostof thesepossible paths crossthe field of measured

φ

andC values foreffusiverocksandsimilartexturescouldbeobservedforrocks formedin differentprocesses makinginterpretations difficult un-lesssampleswitharangeof

φ

arecollectedthatcanbeattributed toa single mechanism. Furthermore,itmust benoted thatother cracking,vesiculationanddensificationpaths are possiblebutwe onlyreportedherethetrendsconstrainedbyexperimentalstudies tocomparewiththerangeofnaturaldata.

5. Conclusions

Wepresenthereadatabaseofporeconnectivity C and poros-ity

φ

datafornaturalvolcanicrocks(n

=

2715) andexperimental products (n

=

116) from published sources and additional mea-surements. When available, permeability data was also included for comparison(n

=

535). Analysis ofthese data lead to the fol-lowingbroadconclusions:

•

Connectivity can be used to distinguish between subsets of volcanic materials including effusive and explosive products, products of fire fountaining andStrombolian basaltic activity andbulk chemical differences, when large datasets are mea-suredorcompiled.

•

Connectivitycanbeusedtoidentifythepercolationthreshold porosityasitcanbe constrainedinsamplesbelowandabove thisthreshold,wherepermeabilitycannot.

•

Poreconnectivitydevelopsbyvesiculationandbubble growth-drivencoalescenceorbycrackingorcombinationsofboth pro-cesses.Pore connectivity decreasesby densification processes includingcompaction,sinteringorwelding.Thetrendof con-nectivitywithporosityisdistinctfortheseporosity-increasing andporosity-decreasingprocesses.

•

Connectivitypotentiallycontains importantinformationabout permeability at porosities close to the percolation threshold where0

<

C

<

1.

Our work shows that a valuable frontier to pursue would be the systematic measurement of suites of rocks or experimental samples in the range where connectivity is less than unity but greater thanzero.It isinthisrangethat theco-variationof con-nectivity withporosity is directlyinformative ofthe evolution of permeability. That is, near to the percolation threshold, connec-tivity is an underutilized metric. Specifically this constraint for a range of processes could be achieved using tomographic tech-niques and targeted experimental work spanning the evolution from non-percolating to percolating systems during both vesicu-lation anddensification processes.Key first order implications of

suchconstraintswouldbeassociatedwithknowinghowandwhen permeability is established or shuts off in volcanic interiors or deposits.Inturn,thiswouldpermitustoknowunderwhat condi-tionsavolcanomaystarttobuildfluidoverpressureleadingtoan eruptionandwhenthevolcanomayeffectivelydissipate overpres-sure.

Acknowledgements

B.S. and M.C. acknowledge the PROCOPE grant (grant no. 57130387),fundedandimplementedby theDeutscher Akademis-cher Austauschdienst (DAAD) in Germany, and the Ministry of Foreign and European Affairs (MAE) and the Ministry of Higher EducationandResearch(MENESR)inFrance.D.B.D.acknowledges the supportof theERC Advanced Grant(EVOKES — no. 247076). This research was partially financed by the French Government Laboratory of Excellence (initiative no. ANR-10-LABX-0006), the Région Auvergne, andthe European Regional Development Fund. Work was also supported by the Laboratory of Excellence Cler-Volc(contributionnumber236).WealsothanktheeditorTamsin Matherwhohelpedtoreinforcetheclarityandimplicationsofthe manuscript.Thispaperhasbenefitedfromconstructivereviewsby twoanonymousreviewers.WethankH.M.N.Wright,J.Vasseur,K.J. Russel,S.J.Cronin,F.AlfanoandT.Platzforprovidingrawdata.We arethankfultoJérémieVasseurforthehelpfuldiscussions.

Appendix A. Supplementarymaterial

Supplementarymaterialrelatedtothisarticlecanbefound on-lineathttp://dx.doi.org/10.1016/j.epsl.2017.01.011.

References

Adams,N.K.,Houghton,B.F.,Fagents,S.A.,Hildreth,W.,2006.Thetransitionfrom explosive to effusive eruptive regime: the example of the 1912 Novarupta eruption,Alaska.Bull.Geol.Soc.Am. 118,620–634.http://dx.doi.org/10.1130/ B25768.1.

Alfano,F.,Bonadonna,C., Gurioli,L., 2012.Insights intoeruptiondynamicsfrom texturalanalysis:thecaseoftheMay,2008,Chaiténeruption.Bull.Volcanol. 74, 2095–2108.http://dx.doi.org/10.1007/s00445-012-0648-3.

Bernard,M.L., Zamora, M., Géraud, Y.,Boudon,G., 2007. Transportproperties of pyroclastic rocksfrom Montagne Pelée volcano(Martinique, LesserAntilles). J. Geophys.Res.,SolidEarth 112,1–16.http://dx.doi.org/10.1029/2006JB004385. Blower,J.,2001.Factorscontrollingpermeability–porosityrelationshipsinmagma.

Bull.Volcanol. 63,497–504.http://dx.doi.org/10.1007/s004450100172. BouvetdeMaisonneuve,C.,Bachmann,O.,Burgisser,A.,2009.Characterizationof

juvenilepyroclastsfrom theKosPlateau Tuff(Aegean Arc):insights intothe eruptive dynamicsof alargerhyolitic eruption. Bull. Volcanol. 71, 643–658.

http://dx.doi.org/10.1007/s00445-008-0250-x.

Burgisser,A.,Gardner,J.E.,2004.Experimentalconstraintsondegassingand per-meabilityinvolcanicconduitflow.Bull.Volcanol. 67,42–56.http://dx.doi.org/ 10.1007/s00445-004-0359-5.

Calder,E.S.,etal.,2015.Lavadomeeruptions.In:EncyclopediaofVolcanoes,2nd ed.AcademicPress,SanDiego.

Castro,J.M.,Cordonnier,B.,Tuffen,H.,Tobin,M.J.,Puskar,L.,Martin,M.C.,Bechtel, H.A.,2012.Theroleofmelt-fracturedegassingindefusingexplosiverhyolite eruptions at volcánChaitén. EarthPlanet. Sci.Lett. 333–334, 63–69. http:// dx.doi.org/10.1016/j.epsl.2012.04.024.

Castro, J.M.,Bindeman, I.N., Tuffen, H.,Ian Schipper, C., 2014. Explosiveorigin ofsilicic lava:textural and δD–H2Oevidence for pyroclastic degassing

dur-ing rhyolite effusion. Earth Planet. Sci. Lett. 405, 52–61. http://dx.doi.org/ 10.1016/j.epsl.2014.08.012.

Colombier,M.,Gurioli,L.,Druitt,T.H.,Shea,T.,Boivin,P.,Miallier,D.,Cluzel,N.,2017. Texturalevolutionofmagmaduringthe9.4katrachyticexplosiveeruptionat KilianVolcano,ChaînedesPuys,France.Bull.Volcanol. 79,17.http://dx.doi.org/ 10.1007/s00445-017-1099-7.

Connor,C.B.,Lichtner,P.C.,Conway,F.M.,Hill,B.E.,Ovsyannikov,A.A.,Federchenko, I., Doubik, Y., Shapar, N., Taran, Y.A., Lichtner,P.C., 1997. Cooling ofan ig-neousdike20yr afterintrusion.Geology 25(8), 711–714.http://dx.doi.org/ 10.1130/0091-7613(1997)025<0711.

Cordonnier,B.,Hess,K.,Lavallee,Y.,Dingwell,D.B.,2009.Rheologicalpropertiesof domelavas:casestudyofUnzenvolcano.EarthPlanet.Sci.Lett. 279,263–272.

http://dx.doi.org/10.1016/j.epsl.2009.01.014.

Cordonnier,B.,Caricchi,L.,Pistone,M.,Castro,J.,Hess,K.,Gottschaller,S.,Manga, M.,Dingwell,D.B.,2012.Theviscous-brittletransitionofcrystal-bearingsilicic melt: directobservationofmagmaruptureandhealing.Geology,5–8.http:// dx.doi.org/10.1130/G3914.1.

Degruyter,W.,Burgisser,A.,Bachmann,O.,Malaspinas,O.,2010.SynchrotronX-ray microtomographyandlatticeBoltzmannsimulationsofgasflowthrough vol-canicpumices.Geosphere 6,470–481.http://dx.doi.org/10.1130/GES00555.1.

Dingwell,D.B., Webb,S.L., 1989.Structural relaxation insilicatemelts and non-Newtonian melt rheology ingeologic processes. Phys. Chem.Miner. 16 (5), 508–516.

Dingwell,D.B.,Lavallée,Y.,Hess,K.,Flaws,A.,Marti,J., Nichols,A.R.L.,Gilg,H.A., Schillinger,B.,2016.Eruptiveshearingoftubepumice:pureandsimple.Solid Earth 7,1383–1393.http://dx.doi.org/10.5194/se-7-1383-2016.

Edmonds,M.,Herd,R.A.,2007.Avolcanicdegassingeventattheexplosive–effusive transition.Geophys.Res.Lett. 34,1–6.http://dx.doi.org/10.1029/2007GL031379.

Eichelberger,J.C.,Carrigan,C.R.,Westrich,H.R.,Price,R.H.,1986.Non-explosive sili-cicvolcanism.Nature 323(6089),598–602.

Farquharson, J., Heap, M.J.,Varley, N.R.,Baud, P., Reuschlé, T., 2015. Permeabil-ityand porosityrelationships ofedifice-formingandesites:acombinedfield andlaboratorystudy.J.Volcanol.Geotherm.Res. 297,52–68.http://dx.doi.org/ 10.1016/j.jvolgeores.2015.03.016.

Formenti, Y., Druitt, T.H., 2003. Vesicle connectivity in pyroclasts and impli-cations for the fluidisation of fountain-collapse pyroclastic flows, Montser-rat (West Indies). Earth Planet. Sci. Lett. 214, 561–574. http://dx.doi.org/ 10.1016/S0012-821X(03)00386-8.

Giachetti,T.,Druitt,T.H.,Burgisser,A.,Arbaret,L.,Galven,C.,2010.Bubble nucle-ation,growthandcoalescenceduringthe1997vulcanianexplosionsofSoufrière Hills Volcano, Montserrat. J. Volcanol. Geotherm. Res. 193,215–231. http:// dx.doi.org/10.1016/j.jvolgeores.2010.04.001.

Gonnermann,H.M.,Manga,M.,2003.Explosivevolcanismmaynotbeaninevitable consequence of magma fragmentation. Nature 426, 8–11. http://dx.doi.org/ 10.1038/nature02159.1.

Gonnermann, H.M., Manga, M., 2007. The fluid mechanics inside a volcano.

http://dx.doi.org/10.1146/annurev.fluid.39.050905.110207.

Gonnermann,H.M.,Manga,M., 2012.Dynamicsofmagmaascentinthevolcanic conduit.In:ModelingVolcanicProcesses:ThePhysicsandMathematicsof Vol-canism.CambridgeUniversityPress,pp. 55–84.

Gurioli,L.,Harris,A.J.L.,Houghton,B.F.,Polacci,M.,Ripepe,M.,2008.Texturaland geophysicalcharacterizationofexplosivebasalticactivityatVillarricavolcano. J. Geophys.Res. 113,1–16.http://dx.doi.org/10.1029/2007JB005328.

Heap, M.J., Farquharson,J.I., Wadsworth, F.B., Kolzenburg, S., Russell, J.K., 2015. Timescales for permeability reduction and strength recovery in densifying magma. EarthPlanet.Sci.Lett. 429, 223–233.http://dx.doi.org/10.1016/j.epsl. 2015.07.053.

Kato,Y.,1987.Woody pumicegeneratedwithsubmarineeruption.Chishitsugaku Zasshi 93,11–20.

Kawabata,E.,Cronin,S.J.,Bebbington,M.S.,Moufti,M.R.H.,El-Masry,N.,Wang,T., 2015.Identifyingmultiple eruptionphasesfromacompoundtephrablanket: anexampleoftheAD1256Al-Madinaheruption,SaudiArabia.Bull.Volcanol. 77.

http://dx.doi.org/10.1007/s00445-014-0890-y.

Kendrick,J.E.,Lavallée,Y.,Hess,K.,Heap,M.J.,Gaunt,H.E.,Meredith,P.G.,Dingwell, D.B., 2013. Tracking the permeableporous networkduring strain-dependent magmatic flow. J. Volcanol. Geotherm. Res. 260, 117–126. http://dx.doi.org/ 10.1016/j.jvolgeores.2013.05.012.

Kendrick,J.E.,Lavallée,Y.,Varley,N.R.,Wadsworth,F.B.,Lamb,O.D.,Vasseur,J.,2016. Blowingoffsteam:tuffisiteformationasaregulatorforlavadomeeruptions. Front.EarthSci. 4,1–15.http://dx.doi.org/10.3389/feart.2016.00041.

Kennedy,B.M.,Jellinek,A.M.,Russell,J.K.,Nichols,A.R.L.,Vigouroux,N.,2010. Time-andtemperature-dependentconduitwallporosity:akeycontrolondegassing andexplosivityatTaraweravolcano,NewZealand.EarthPlanet.Sci.Lett. 299, 126–137.http://dx.doi.org/10.1016/j.epsl.2010.08.028.

Kennedy,B.M.,Wadsworth,F.B.,Vasseur,J.,Schipper,C.I.,Jellinek,A.M.,Von Aulock, F.W.,Hess,K.,Russell,J.K.,Lavallée,Y.,Nichols,A.R.L.,Dingwell,D.B.,2016. Sur-facetensiondriven processesdensifyandretainpermeabilityinmagmaand lava.EarthPlanet.Sci.Lett. 433,116–124.http://dx.doi.org/10.1016/j.epsl.2015. 10.031.

Klug,C.,Cashman, K.V.,1996.Permeabilitydevelopmentinvesiculatingmagmas: implicationsforfragmentation.Bull.Volcanol. 58,87–100.

Klug, C., Cashman, K.,Bacon,C., 2002. Structureand physical characteristicsof pumicefromtheclimacticeruptionofMountMazama (CraterLake),Oregon. Bull.Volcanol. 64,486–501.http://dx.doi.org/10.1007/s00445-002-0230-5. Kushnir, A.R.L.,Martel, C., Bourdier,J., Heap,M.J.,Reuschlé,T., Erdmann, S.,

Ko-morowski, J.,Cholik, N., 2016. Probingpermeability andmicrostructure: un-ravelling the role ofalow-permeability dome onthe explosivity ofMerapi (Indonesia).J. Volcanol.Geotherm. Res. 316,56–71.http://dx.doi.org/10.1016/ j.jvolgeores.2016.02.012.

Lavallée,Y.,Meredith,P.G.,Dingwell,D.B.,Hess,K.,Wassermann,J.,Cordonnier,B., Gerik,A.,Kruhl,J.H.,2008.Seismogeniclavasandexplosiveeruptionforecasting. Nature 453,507–510.http://dx.doi.org/10.1038/nature06980.

LePennec,J.L.,Hermitte,D.,Isya,D.,Pezard,P.,Coulon,C.,Cochemé,J.-J.,Mulyadi, E.,Ollagnier,F.,Revest,C.,2001.Electricalconductivityandpore-spacetopology

ofMerapilavas:implicationforthedegassingofporphyriticandesitemagmas. Geophys.Res.Lett. 28(22),4283–4286.

Lindquist,W.B.,Lee,S.-M.,Coker,D.A.,Jones,K.W.,Spanne,P.,1996. Medialaxis analysisofvoidstructureinthree-dimensionaltomographicimagesofporous media.J.Geophys.Res. 101,8297.http://dx.doi.org/10.1029/95JB03039.

Mangan,M.T.,Cashman,K.V.,1996.Thestructureofbasalticscoriaandreticuliteand inferencesforvesiculation,foamformation,andfragmentationinlavafountains. J.Volcanol.Geotherm.Res. 0273,1–18.

Michaut,C.,Bercovici,D.,Sparks,R.S.J.,2009.Ascent andcompactionofgasrich magmaandtheeffectsofhystereticpermeability.EarthPlanet.Sci.Lett. 282, 258–267.http://dx.doi.org/10.1016/j.epsl.2009.03.026.

Michol,K.A.,Russell,J.K.,Andrews,G.D.M.,2008.Weldedblockandashflow de-positsfromMount Meager,BritishColumbia, Canada. J.Volcanol. Geotherm. Res. 169,121–144.http://dx.doi.org/10.1016/j.jvolgeores.2007.08.010.

Morandi,A.,DiMuro,A.,Principe,C., Michon,L.,Leroi, G.,Norelli,F.,Bachèlery, P.,2016.Pre-historic(<5kiloyear)explosiveactivityatPitondelaFournaise volcano.In:ActiveVolcanoesoftheSouthwestIndianOcean.Springer,Berlin, Heidelberg,pp. 107–138.

Mueller,S.,2007.PermeabilityandPorosityasConstraintsontheExplosiveEruption ofMagma:LaboratoryExperimentsandFieldInvestigations.PhDthesis.

Mueller, S., Melnik, O., Spieler, O., Scheu, B., Dingwell, D.B., 2005. Permeabil-ityand degassingofdomelavasundergoing rapiddecompression:an exper-imentaldetermination. Bull.Volcanol. 67, 526–538.http://dx.doi.org/10.1007/ s00445-004-0392-4.

Mueller, S., Scheu, B., Spieler, O., Dingwell, D.B., 2008. Permeability control on magma fragmentation. Geology 36, 399–402. http://dx.doi.org/10.1130/ G24605A.1.

Nakamura,M.,Otaki,K.,Takeuchi,S.,2008.Permeabilityandpore-connectivity vari-ationofpumicesfromasinglepyroclasticfloweruption:implicationsfor par-tialfragmentation.J.Volcanol.Geotherm.Res. 176,302–314.http://dx.doi.org/ 10.1016/j.jvolgeores.2008.04.011.

Namiki,A.,Manga,M.,2008.Transitionbetweenfragmentationandpermeable out-gassingoflowviscositymagmas.J.Volcanol.Geotherm.Res. 169,48–60.http:// dx.doi.org/10.1016/j.jvolgeores.2007.07.020.

Nguyen,C.T.,Gonnermann,H.M.,Houghton,B.F.,2014.Explosivetoeffusive transi-tionduringthelargestvolcaniceruptionofthe20thcentury(Novarupta1912, Alaska).Geology 42,703–706.http://dx.doi.org/10.1130/G35593.1.

Okumura, S., Nakamura,M., Tsuchiyama, A., Nakano, T., Uesugi, K., 2008. Evo-lutionofbubblemicrostructure inshearedrhyolite: formationofa channel-likebubblenetwork.J.Geophys.Res.,SolidEarth 113,1–18.http://dx.doi.org/ 10.1029/2007JB005362.

Okumura,S.,Nakamura,M.,Uesugi,K.,Nakano,T., Fujioka,T.,2013.Coupled ef-fectofmagmadegassingandrheologyonsilicicvolcanism.EarthPlanet.Sci. Lett. 362,163–170.http://dx.doi.org/10.1016/j.epsl.2012.11.056.

Oppenheimer, J., Rust, A.C., Cashman, K.V., Sandnes, B., 2015. Gas migration regimesandoutgassinginparticle-richsuspensions.Front.Phys. 3,1–13.http:// dx.doi.org/10.3389/fphy.2015.00060.

Platz,T.,Cronin,S.J.,Cashman, K.V., Stewart,R.B., Smith, I.E.M.,2007. Transition fromeffusivetoexplosivephasesinandesiteeruptions–acase-studyfromthe AD1655eruptionofMt.Taranaki,NewZealand.J.Volcanol.Geotherm.Res. 161, 15–34.http://dx.doi.org/10.1016/j.jvolgeores.2006.11.005.

Polacci,M.,Baker,D.R.,Mancini,L.,Tromba,G.,Zanini,F.,2006.Three-dimensional investigation of volcanic textures by X-ray microtomography and implica-tions for conduit processes. Geophys. Res. Lett. 33, 3–7. http://dx.doi.org/ 10.1029/2006GL026241.

Rintoul,M.D.,2000.Precisedeterminationofthevoidpercolationthresholdfortwo distributionsofoverlappingspheres.Phys.Rev.E 62(1),68.

Robert,G., Russell,J.K.,Giordano,D., 2008. Rheologyofporousvolcanic materi-als:high-temperatureexperimentationundercontrolledwaterpressure.Chem. Geol. 256,215–229.http://dx.doi.org/10.1016/j.chemgeo.2008.06.028.

Rust, A.C.,Cashman, K.V., 2004.Permeability ofvesicularsilicicmagma: inertial and hysteresis effects. EarthPlanet. Sci.Lett. 228, 93–107. http://dx.doi.org/ 10.1016/j.epsl.2004.09.025.

Rust,A.C.,Cashman,K.V.,2011.Permeabilitycontrolsonexpansionandsize distri-butionsofpyroclasts.J.Geophys.Res.,SolidEarth 116,1–17.http://dx.doi.org/ 10.1029/2011JB008494.

Rust,A.C.,Russell,J.K.,Knight,R.J.,1999.Dielectricconstantasapredictorof poros-ityindryvolcanicrocks.J.Volcanol.Geotherm.Res. 91,79–96.http://dx.doi.org/ 10.1016/S0377-0273(99)00055-4.

Saar,M.O.,Manga,M.,1999.Permeability–porosityrelationshipinvesicularbasalts. Geophys.Res.Lett. 26(1),111–114.

Shea,T.,Gurioli,L.,Houghton,B.F.,2012.Transitionsbetweenfallphasesand py-roclasticdensitycurrentsduringtheAD79eruptionat Vesuvius:building a transientconduitmodelfromthetexturalandvolatilerecord.Bull.Volcanol. 74, 2363–2381.http://dx.doi.org/10.1007/s00445-012-0668-z.

Shimano,T.,Nakada,S.,2006.Vesiculationpathofascendingmagmainthe1983 and the 2000 eruptions of Miyakejima volcano, Japan. Bull. Volcanol. 68, 549–566.http://dx.doi.org/10.1007/s00445-005-0029-2.

Song,S.R.,Jones,K.W.,Lindquist,W.B.,Dowd,B.A.,Sahagian,D.L.,2001.Synchrotron X-raycomputed microtomography:studiesonvesiculated basalticrocks.Bull. Volcanol. 63,252–263.http://dx.doi.org/10.1007/s004450100141.

Stovall, W.K., Houghton, B.F., Hammer, J.E., Fagents, S.A., Swanson, D.A., 2012. Vesiculation of high fountaining Hawaiian eruptions: episodes 15 and 16 of 1959 K¯ılauea Iki. Bull. Volcanol., 441–455. http://dx.doi.org/10.1007/ s00445-011-0531-7.

Takeuchi,S.,Tomiya,A.,Shinohara,H.,2009.Degassing conditionsforpermeable silicicmagmas: implications from decompression experimentswith constant rates.EarthPlanet.Sci.Lett. 283,101–110.http://dx.doi.org/10.1016/j.epsl.2009. 04.001.

Vasseur,J.,Wadsworth,F.B.,Lavallée,Y.,Hess,K.U.,Dingwell,D.B.,2013.Volcanic sintering:timescales ofviscousdensificationandstrengthrecovery.Geophys. Res.Lett. 40,5658–5664.http://dx.doi.org/10.1002/2013GL058105.

Vasseur,J.,Wadsworth,F.B.,Lavallée,Y.,Dingwell,D.B.,2016.Dynamicelastic mod-uliduringisotropicdensificationofinitiallygranularmedia.Geophys.J.Int. 204, 1721–1728.http://dx.doi.org/10.1093/gji/ggv550.

Vogel,H.-J.,2002.Topologicalcharacterizationofporousmedia.In:Morphologyof CondensedMatter.In:LectureNotesinPhysics,vol. 600,pp. 75–92.

Wadsworth,F.B.,Vasseur, J.,Von Aulock,F.W.,Hess,K.-U., Scheu,B., Lavallée,Y., Dingwell,D.B.,2014.Nonisothermalviscoussinteringofvolcanicash.J. Geo-phys.Res.,SolidEarth.http://dx.doi.org/10.1002/2014JB011453.

Wadsworth,F.B.,Vasseur,J., Llewellin,E.W., Schauroth,J., Dobson,K.J.,Scheu,B., Dingwell,D.B.,2016a.Sinteringofviscousdropletsundersurfacetension.Proc. R.Soc.A 472(2188),20150780.

Wadsworth, F.B.,Vasseur, J., Scheu,B., Kendrick, J.E.,Lavallée, Y.,Dingwell, D.B., 2016b.Universalscalingoffluidpermeabilityduringvolcanicweldingand sed-imentdiagenesis.Geology 44,219–222.http://dx.doi.org/10.1130/G37559.1. Wright,H.M.,Cashman,K.V.,2014.Compactionandgaslossinweldedpyroclastic

depositsasrevealedbyporosity,permeability,andelectricalconductivity mea-surementsoftheShevlinParkTuff.Geol.Soc.Am.Bull. 126,234–247.http:// dx.doi.org/10.1130/b30668.1.

Wright,H.M.N.,Cashman,K.V.,Rosi,M.,Cioni,R.,2007.Breadcrustbombsas indica-torsofvulcanianeruptiondynamicsatGuaguaPichinchavolcano,Ecuador.Bull. Volcanol. 69,281–300.http://dx.doi.org/10.1007/s00445-006-0073-6.

Wright,H.M.N.,Cashman,K.V.,Gottesfeld,E.H.,Roberts,J.J.,2009.Porestructureof volcanicclasts:measurementsofpermeabilityandelectricalconductivity.Earth Planet.Sci.Lett. 280,93–104.http://dx.doi.org/10.1016/j.epsl.2009.01.023. Yokoyama, T., Takeuchi, S., 2009. Porosimetry of vesicular volcanic products

by a water-expulsion method and the relationship of pore characteristics to permeability. J. Geophys. Res., Solid Earth 114. http://dx.doi.org/10.1029/ 2008JB005758.