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The timescales and consequences of solid-state sintering in volcanic systems Ryan, Amy Grace 2020

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THE TIMESCALES AND CONSEQUENCES OFSOLID-STATE SINTERING IN VOLCANIC SYSTEMSbyAmy Grace RyanB.A., Colorado College, 2010M.Sc., The University of British Columbia, 2014A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Geological Sciences)The University of British Columbia(Vancouver)August 2020c© Amy Grace Ryan, 2020The following individuals certify that they have read, and recommend to the Faculty of Grad-uate and Postdoctoral Studies for acceptance, the thesis entitled:THE TIMESCALES AND CONSEQUENCES OF SOLID-STATE SIN-TERING IN VOLCANIC SYSTEMSsubmitted by Amy Grace Ryan in partial fulfillment of the requirements for the degree ofDoctor of Philosophy in Geological Sciences.Examining Committee:James Kelly Russell, Earth, Ocean and Atmospheric Sciences, University of British ColumbiaSupervisorLori Kennedy, Earth, Ocean and Atmospheric Sciences, University of British ColumbiaSupervisory Committee MemberErik Eberhardt, Earth, Ocean and Atmospheric Sciences, University of British ColumbiaSupervisory Committee MemberMichael Bostock, Earth, Ocean and Atmospheric Sciences, University of British ColumbiaUniversity ExaminerChad Sinclair, Materials Engineering, University of British ColumbiaUniversity ExaminerJames Watkins, Earth Sciences, University of OregonExternal ExamineriiAbstractThe permeability of rocks controls the movement of fluids and distribution of porepressure in Earth’s crust. In volcanic systems the eruptive behavior of silicate magmas isgoverned by the volume and pressure state of magmatic gases. Reductions in permeabilitycan promote explosivity. At the elevated pressure-temperature conditions endemic to volcanicsystems, permeable pathways are ephemeral and can be destroyed by densification processes.The prediction of the intensity and timing of explosive eruptions depends on understandingthe mechanisms that create and destroy permeable pathways, and their operational timescales.Solid-state sintering is a diffusion-driven process that converts unconsolidated, crystalline ag-gregates into dense, low-permeability composites. Elevated temperatures and pressures andsubstantial dwell times facilitate densification and lithification by solid-state sintering. How-ever, solid-state sintering has largely been discounted in volcanic systems because densificationtimescales were assumed to be long. In this dissertation I show, for the first time, that solid-statesintering occurs in volcanic settings and on timescales short enough to influence volcanic activ-ity. I use the chemistry, mineral contents, physical properties and microstructures of volcanicshear zones exhumed during two dome-building eruptions to show that they were densifiedand lithified within the volcanic conduit as a result of solid-state sintering. Reconstructions ofeach of the eruptions indicate sintering occurred on the timescale of magma ascent (months toyears). I also use hot pressing experiments conducted at volcanic temperature-pressure con-ditions to further constrain the timescale of densification by solid-state sintering: the exper-iments produce dense, low-permeability rocks over periods of hours to days, and reproducethe dominant textures and properties of naturally-sintered volcanic rocks. The experimentaldataset is the basis of a quantitative model that predicts the time-dependent evolution of ma-terial density as a result of solid-state sintering. Overall, I identify solid-state sintering as aviable, unrecognized mechanism driving rapid permeability loss and material strengthening involcanic settings. Densification and lithification as a result of solid-state sintering hinder fluidflow and modulate eruptive behavior, including promoting cyclical explosivity. Finally, mywork challenges the perception that crystal-rich aggregates in volcanic settings are persistentlypermeable and weak areas.iiiLay SummaryWhether volcanoes will erupt explosively depends on the behavior of gases trapped inthe subsurface. If gas pressures are high within a volcano, the surrounding magma and rockscan break, causing explosive eruption. Alternatively, if gases vent to the surface through inter-connected void spaces, explosive behavior is avoided. Void spaces in volcanoes are ephemeral– numerous processes can close them. Identifying processes that reduce void space, and theiroperational timescales, is necessary to understand eruption dynamics. Solid-state sintering isone such process, used in manufacturing to produce dense ceramics. Here I test whether solid-state sintering operates in volcanoes by studying volcanic rocks and conducting hot-pressingexperiments. The rocks and experimental products have textures and properties indicative ofsolid-state sintering. The experiments also show that solid-state sintering causes rapid voidspace closure. Based on these results solid-state sintering is a newly recognized process thatcan modulate eruptive behavior, including promoting cyclical explosivity.ivPrefaceThis dissertation comprises an introduction, four research chapters, a conclusion andfour appendices. The research chapters are presented in manuscript format: three have beenpublished in peer-reviewed international geoscience journals, one has been accepted pend-ing revisions. As they are stand-alone manuscripts, each contains some repeated backgroundinformation. The appendices contain the corresponding supplementary information for eachpublished/accepted manuscript.I am the 1st author on all manuscripts, and the material contained in all manuscriptsprincipally derives from my own research, analysis of data and interpretation of results. Myco-authors, including my supervisor J.K. Russell, have helped with data collection and anal-ysis, and, given their diverse backgrounds, have provided additional context and framing forthe implications outlined within each manuscript. Below I describe the contributions of eachauthor.• A version of chapter 2 has been published: Ryan, A., Friedlander, E.A., Russell, J.K.,Heap, M.J. and Kennedy, L.A. (2018a) Hot pressing in conduit faults during lava domeextrusion: Insights from Mount St. Helens 2004-2008. Earth and Planetary ScienceLetters, 482, 171-180.E.A. Friedlander conducted the field work and collected samples. I measured sam-ple physical properties, developed the solid-state sintering hypothesis and wrote themanuscript. E.A. Friedlander and I made figures and tables. M.J. Heap assisted in per-meameter measurements. J.K. Russell and L.A. Kennedy supervised the project. Allauthors contributed to the revision of the manuscript.The USGS Cascade Volcano Observatory, including John Pallister, David Sherrod, Cyn-thia Gardner, and Roger Denlinger supported with logistical planning for the field cam-paign carried out by E.A. Friedlander. Peter Frenzen arranged permitting for access toMount St. Helens National Volcanic Monument.v• A version of chapter 3 has been published: Ryan, A.G., Russell, J.K. and Heap, M.J.(2018b) Rapid solid-state sintering in volcanic systems. American Mineralogist, 103,2028-2031.I developed the experimental campaign, analyzed experimental materials, made figuresand tables, and wrote the manuscript. J.K. Russell and I developed the model. M.J.Heap measured the permeability of samples. All authors contributed to the revision ofthe manuscript. Dr. Laura Gardner at the University of Sheffield completed the HIPexperiments as a part of a paid contract.• A version of chapter 4 has been accepted in Earth and Planetary Science Letters pend-ing minor revisions: Ryan, A.G., Russell, J.K., Heap, M.J., Zimmerman, M.E. andWadsworth, F.B. Timescales of porosity and permeability loss by solid-state sintering.I developed the experimental campaign, analyzed experimental materials, made figuresand tables, and wrote the manuscript. J.K. Russell and I developed the model. M.J.Heap measured the permeability of samples. F.B. Wadsworth fit the permeability model.M.E. Zimmerman completed the Paterson experiments at the University of Minnesota.All authors contributed to the revision of the manuscript. Dr. Laura Gardner at theUniversity of Sheffield completed the HIP experiments as a part of a paid contract.• A version of chapter 5 has been published: Ryan, A.G., Heap, M.J., Russell, J.K.,Kennedy, L.A. and Clynne, M.A. (2020) Cyclic shear zone cataclasis and sintering dur-ing lava dome extrusion: Insights from Chaos Crags, Lassen Volcanic Center (USA).Journal of Volcanology and Geothermal Research, 401, 106935.I organized the field campaign, studied the microstructure of samples, completed thedata analysis and modelling, made figures and tables, and wrote the manuscript. M.J.Heap measured the density, permeability, compressive strength and Young’s modulus ofsamples. J.K. Russell, L.A. Kennedy and M.J. Heap gave input on the model parameters.M.A. Clynne introduced the Chaos Crags field site and its greater context within theLassen Volcanic Center. All authors participated in the fieldwork and contributed to therevision of the manuscript.Fieldwork and sample collection were permitted by the United States National Park Ser-vice (study number: LAVO-00050; permit number: LAVO-2019-SCI-0010).viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Solid-state sintering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Dissertation objectives and organization . . . . . . . . . . . . . . . . . . . . . 32 Hot pressing in conduit faults during lava dome extrusion: Insights from MountSt. Helens 2004-2008 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 A case study: Properties of MSH gouge . . . . . . . . . . . . . . . . . . . . . 72.2.1 Textural organization, granulometry and mineralogy . . . . . . . . . . 72.2.2 Porosity and permeability . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 Magma ascent in the conduit . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4 Hot pressing: A model for lithification of volcanic gouge . . . . . . . . . . . . 172.5 Implications for eruption dynamics and monitoring . . . . . . . . . . . . . . . 222.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.7 Access to Mount St. Helens National Volcanic Monument . . . . . . . . . . . . 24vii3 Rapid solid-state sintering in volcanic systems . . . . . . . . . . . . . . . . . . . 253.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2 Natural occurrence: An example from Mount St. Helens . . . . . . . . . . . . 263.3 Hot Isostatic Pressing (HIP) experiments . . . . . . . . . . . . . . . . . . . . . 273.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.5 Densification model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.6 Densification and permeability loss . . . . . . . . . . . . . . . . . . . . . . . . 313.7 Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 Timescales of porosity and permeability loss by solid-state sintering . . . . . . . 344.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.2 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.3.1 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.3.2 Hot-pressing experiments (HIP) . . . . . . . . . . . . . . . . . . . . . 374.3.3 Hot-pressing experiments (Paterson) . . . . . . . . . . . . . . . . . . . 374.3.4 Physical properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.3.5 Microstructure imaging and analysis . . . . . . . . . . . . . . . . . . . 414.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.4.1 Competence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.4.2 Relative density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.4.3 Porosity and permeability . . . . . . . . . . . . . . . . . . . . . . . . . 434.4.4 Microstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.5 Model development and analysis . . . . . . . . . . . . . . . . . . . . . . . . . 464.5.1 Densification model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504.5.2 Testing the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.5.3 Sintering mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544.6.1 Timescales for permeability reduction . . . . . . . . . . . . . . . . . . 554.6.2 Comparison to other densification mechanisms . . . . . . . . . . . . . 574.6.3 Strength recovery and its consequences for cyclical outgassing . . . . . 584.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605 Cyclic shear zone cataclasis and sintering during lava dome extrusion: Insightsfrom Chaos Crags, Lassen Volcanic Center (USA) . . . . . . . . . . . . . . . . . 615.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615.2 Geologic Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63viii5.2.1 Chaos Crags . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635.2.2 Dome C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645.2.3 Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695.4.1 Geochemistry and mineralogy . . . . . . . . . . . . . . . . . . . . . . 695.4.2 Microstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705.4.3 Physical and mechanical properties . . . . . . . . . . . . . . . . . . . . 715.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 795.5.1 Densification and lithification by solid-state sintering . . . . . . . . . . 795.5.2 Ascent rate and eruption duration . . . . . . . . . . . . . . . . . . . . . 815.5.3 Outgassing behavior during solid-state sintering . . . . . . . . . . . . . 855.5.4 Cyclical deformation and sintering in the shear zone . . . . . . . . . . 855.6 Implications beyond Chaos Crags . . . . . . . . . . . . . . . . . . . . . . . . . 865.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895.8 Access to Lassen Volcanic National Park . . . . . . . . . . . . . . . . . . . . . 896 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 906.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 906.2 Significance in volcanology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 936.3 Recommendations for future work . . . . . . . . . . . . . . . . . . . . . . . . 93Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95A Supporting Materials for Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . 111B Supporting Materials for Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . 114B.1 Extended methodology and model development . . . . . . . . . . . . . . . . . 116B.1.1 Physical property measurements . . . . . . . . . . . . . . . . . . . . . 116B.1.2 Model development . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118B.1.3 Model limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120C Supporting Materials for Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . 122C.1 Starting material characterization . . . . . . . . . . . . . . . . . . . . . . . . . 122C.2 Details of the Paterson sample assembly . . . . . . . . . . . . . . . . . . . . . 124C.3 SEM and FE-SEM imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125C.4 Effect of experimental methodologies on sintering . . . . . . . . . . . . . . . . 126C.5 Permeability modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128ixD Supporting Materials for Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . 131D.1 Sintering pressure modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . 131D.2 Transient pressure modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . 133xList of TablesTable 2.1 Surface observations of the 2004-2008 eruption at MSH . . . . . . . . . . . 8Table 2.2 Porosity and permeability of MSH gouge samples . . . . . . . . . . . . . . 12Table 2.3 Modeled parameters for the 2004-2008 MSH lava spine eruption . . . . . . 15Table 3.1 Experimental conditions and physical properties of HIP products . . . . . . 28Table 4.1 Experimental conditions and physical properties of hot pressing products . . 38Table 5.1 Description of Dome C units . . . . . . . . . . . . . . . . . . . . . . . . . . 66Table 5.2 Composition of Dome C units . . . . . . . . . . . . . . . . . . . . . . . . . 70Table 5.3 Mineral abundance of Dome C units . . . . . . . . . . . . . . . . . . . . . 71Table 5.4 Physical and mechanical properties of sample cores from Dome C units . . . 74Table 5.5 Summary of triaxial deformation experiments on Dome C dacite . . . . . . 76Table A.1 Results of Rietveld refinement of XRD spectra of MSH gouge . . . . . . . . 112Table B.1 Physical properties of MSH samples . . . . . . . . . . . . . . . . . . . . . 116Table B.2 Mineralogy of HIP starting material and experimental products . . . . . . . 117Table C.1 Mineralogy of experimental starting material and products. . . . . . . . . . 122xiList of FiguresFigure 1.1 Solid-state sintering mechanisms . . . . . . . . . . . . . . . . . . . . . . . 3Figure 2.1 Diversity of fault zone geometries and properties at MSH . . . . . . . . . . 9Figure 2.2 An extensively lithified gouge-rock at MSH . . . . . . . . . . . . . . . . . 10Figure 2.3 “Top-down” model for spine extrusion at MSH . . . . . . . . . . . . . . . 14Figure 2.4 Model for hot pressing in volcanic conduits . . . . . . . . . . . . . . . . . 20Figure 3.1 SEM images of sintering in MSH samples and HIP products . . . . . . . . 27Figure 3.2 Physical properties of HIP products . . . . . . . . . . . . . . . . . . . . . 29Figure 3.3 Sintering maps and timescales for porosity and permeability loss . . . . . . 31Figure 4.1 Relative density of hot-pressed samples . . . . . . . . . . . . . . . . . . . 42Figure 4.2 Porosity and permeability . . . . . . . . . . . . . . . . . . . . . . . . . . . 44Figure 4.3 Experimental products hot pressed at 800◦C, 70 MPa and 12 h. . . . . . . . 45Figure 4.4 Experimental products hot pressed at 800◦C and 70 MPa . . . . . . . . . . 47Figure 4.5 Element distribution maps . . . . . . . . . . . . . . . . . . . . . . . . . . 48Figure 4.6 Densification model and sintering maps . . . . . . . . . . . . . . . . . . . 51Figure 4.7 Test of the densification model . . . . . . . . . . . . . . . . . . . . . . . . 53Figure 4.8 Porosity and permeability maps . . . . . . . . . . . . . . . . . . . . . . . 56Figure 4.9 Strength recovery vs. fluid accumulation . . . . . . . . . . . . . . . . . . . 59Figure 5.1 Chaos Crags, Lassen Volcanic Center, California (USA) . . . . . . . . . . 63Figure 5.2 Chaos Crags study site . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65Figure 5.3 PPL photomicrographs and BSE images of units from Dome C . . . . . . . 72Figure 5.4 PPL and BSE images of textural features in cataclasites . . . . . . . . . . . 73Figure 5.5 Connected porosity and permeability . . . . . . . . . . . . . . . . . . . . . 77Figure 5.6 Distribution of porosity, permeability and strength across Dome C units . . 78Figure 5.7 Sintering time and ascent rate modelling . . . . . . . . . . . . . . . . . . . 82Figure 5.8 Shear zone strength and permeability . . . . . . . . . . . . . . . . . . . . . 87xiiFigure A.1 Composite log for spine 5 at MSH . . . . . . . . . . . . . . . . . . . . . . 112Figure A.2 Grain size distributions for unconsolidated MSH gouge . . . . . . . . . . . 113Figure B.1 SEM transect of variably lithified MSH sample . . . . . . . . . . . . . . . 115Figure B.2 Grain size distribution of HIP experimental material . . . . . . . . . . . . . 117Figure B.3 Additional sintering maps . . . . . . . . . . . . . . . . . . . . . . . . . . . 119Figure B.4 Additional SEM images of HIP products . . . . . . . . . . . . . . . . . . . 121Figure C.1 Grain size distribution of experimental starting material . . . . . . . . . . . 123Figure C.2 Paterson sample assembly . . . . . . . . . . . . . . . . . . . . . . . . . . 124Figure C.3 Additional element distribution maps . . . . . . . . . . . . . . . . . . . . . 125Figure C.4 Effect of methodology on sintering efficiency . . . . . . . . . . . . . . . . 126Figure C.5 Photos of Paterson and HIP canisters prior to and after hot pressing. . . . . 128Figure D.1 Triaxial deformation experiments on Dome C dacite . . . . . . . . . . . . . 131Figure D.2 Compressive pressures the gouge experiences over 1 km depth . . . . . . . 132Figure D.3 Porosity loss during ascent from 1 km at variable rates. . . . . . . . . . . . 134xiiiAcknowledgmentsI would like to thank UBC for awarding me the Four-Year Doctoral Fellowship whichhas supported me financially throughout my doctorate. I would also like to acknowledge theGeological Society of America and the Mineralogical Association of Canada for funding grantsrelated to research and conference participation.Thank you to members of my supervisory committees, including Lori Kennedy, ErikEberhardt and Marc Bustin. Also to the members of my examining committee, including ChadSinclair, Michael Bostock, James Watkins and Ed Grant.I would like to thank EOAS staff, including Elisabetta Pani, Jenny Lai, Edith Czech,Lan Kato, Jacob Kabel and Mati Raudsepp, for their help with imaging and analytical work. Inparticular I would like to thank Jo¨rn Unger who has helped me avoid equipment disasters timeand time again. I cannot tell you how much I have appreciated you sharing your time, expertiseand equipment with me over the years.To my collaborators and co-authors, including Mike Heap, Alessandro Vona, FabianWadsworth, Mark Zimmerman, Claudia Romano and Michael Clynne: it has been my greatpleasure to work with you in recent years. Thank you for giving me the opportunity to collabo-rate with and learn from you. It has been instructive, encouraging and has shaped how I work,communicate and conduct research. I look forward to working together going forward!To VPL members, past and present, including Jenny Haywood, Dan Woodell, MichelleCampbell, Alex Kushnir, James Welles, Marie Turnbull, Ryan Kroner, David Sasse, Mu Li,Martin Harris, Katherine Landoni, Sophie Leiter and Annie Borch: thank you for your com-pany over the last 8 years. Grad school can be lonely and isolating, but I’ve been lucky to avoidmuch of that thanks, in large part, to all of you.Special thanks to several VPL members: Steve Quane, without whom I would neverhave made my way in to geology; Betsy Friedlander, whose enthusiasm is infectious; DanGainer, the best “adventures in science” partner I could ask for; Mila Huebsch, a relentless rayof sunshine even when it doesn’t seem possible to be positive about anything; Alex Wilson– your friendship and comradery have been invaluable to me over the past 5 years; StephanKolzenburg – it’s been so fun to continue to work with you over the last few years. I lookxivforward to the next time we get to go in the field or crank out a bunch of experiments together;Ashley and Luke Hilchie, my pseudo-siblings, thank you for including me in your family.To the many friends in Vancouver, the US and abroad who have helped keep me teth-ered to the world, even when I was hell-bent on all-work-and-no-play: Tom Jones, NaderMostaghimi, Raja Yarra, Chris Herron, Dave Newton, Angie Lottes, Swetha Venugopal, OlenkaForde, Kelsey Pecherer, Gaia Posner, Pia Peterson, Elizabeth Packer, Kate Meyer, Sam Talbot,Ata Ojani, Marle Tyrrell, Stefania Sicola and Aurora Silleni.In particular I’d like to thank Lauren Harrison, whose transition from “hallway buddy”to roommate to lifelong friend has thoroughly enriched my life. I would also like to thankDevon Deckant who has been my partner in life for the last decade. Leaving you and Vancouverwill undoubtedly be hard but I’m excited for our future adventures.To my family, Joe, Nancy, Peter, Vina and Nick Ryan – thank you for encouragingme, listening while I rant about rocks and generally supporting me through this strange andstressful time. I love you. I would also like to thank my grandparents, Norm and Petie Miller.Lastly, Kelly Russell – whatever I write here will unfortunately never be able to conveythe depth of my gratitude to you for your mentorship and support over the last decade. Youhave profoundly shaped who I am, both as a scientist and a person. It is hard to imagine movingforward in science without you as a primary collaborator on every project, but I look forwardto doing my best to make you proud. Thank you for everything.xvChapter 1Introduction1.1 MotivationThe intensity and duration of explosive volcanic eruptions are largely dictated by thebehavior of volatile constituents in silicate magmas (Cassidy et al., 2018; Eichelberger et al.,1986; Sparks, 1978). Exsolution of the dissolved magmatic volatiles (e.g., H2O, CO2) duringascent creates a supercritical fluid phase. This phase reduces magma density, causing its buoy-ant rise through the crust. The volatile phase is also capable of rapid expansion at near-surfacepressures. If expansion of the exsolved fluids near-surface is restricted, gas overpressures de-velop. Where overpressures exceed the strength of the surrounding material, that material willfragment or fracture, initiating an explosive eruption (Dingwell, 1996; Sparks, 1978; Woodsand Koyaguchi, 1994; Zhang, 1999).Explosive activity can be avoided if gas overpressures are moderated. This occurs ifexsolved volatiles are vented from the volcanic system (i.e., outgassed) through pathways ofconnected void spaces (Castro et al., 2012; Gonnerman and Manga, 2003; Namiki and Manga,2008). Void spaces include pores, fractures and the spaces between particles in clastic material.Outgassing pathways can be within the magma (Castro et al., 2012; Eichelberger et al., 1986;Heap et al., 2019b; Yoshimura et al., 2019), in the magma’s sheared, fractured, brecciatedand/or comminuted margins (Gaunt et al., 2014; Gonnerman and Manga, 2003; Kushnir et al.,2017; Lavalle´e et al., 2013; Okumura et al., 2013; Tuffen et al., 2003) or in the surroundingcountry rock (Farquharson et al., 2017b; Jaupart and Allegre, 1991; Kolzenburg et al., 2019;Stasiuk et al., 1996). The efficacy of outgassing pathways depends on the pore space properties,including total volume (i.e., porosity), connectivity, and geometries (Colombier et al., 2017).Together these properties dictate the effective permeability of pathways critical for outgassing(Bernabe´ et al., 2003; Blower, 2001; Burgisser et al., 2017; Klug and Cashman, 1996).1Field-based and experimental studies of volcanic melts, magmas, glasses, pyroclasts,lavas and volcaniclastic materials have identified a range of processes that result in the re-organization and closure of void spaces (i.e., densification). Densification processes includemechanical wear and compaction of rock fragments and mineral grains (Heap et al., 2015b),precipitation of pore-filling minerals from liquids or gases (Horwell et al., 2013) and coales-cence of particles (Kendrick et al., 2016; Kolzenburg and Russell, 2014; Quane et al., 2009;Sparks et al., 1999; Vasseur et al., 2013; Wadsworth et al., 2016b). By driving the reductionin void space volume, densification processes eliminate outgassing pathways and increase thelikelihood of gas overpressure development and associated explosive activity.Given the explicit connection between porosity, permeability and explosivity, interpret-ing and predicting volcanic activity requires identification and knowledge of the processes thatdestroy porosity and permeability in volcanic materials. This includes a detailed understandingof the conditions at which the mechanisms are active and their operational timescales.1.2 Solid-state sinteringSintering is a general term for a family of processes that create composite materialsthrough coalescence of discrete particles. It is important for industrial processes, includingthe production of ceramics, glasses, metals and polymers, and has been extensively studiedin the field of materials science (e.g., Arzt et al., 1983; Ashby, 1974; Chen and Wang, 2000;Coble, 1961; German et al., 2009; Mackenzie and Shuttleworth, 1949; Rahaman, 2003; Ra-haman et al., 1987). The primary driving force for sintering is the reduction of surface freeenergy, which causes redistribution of matter from regions of high surface energy (and chemi-cal potential) to low energy sites (Rahaman, 2003).Sintering processes are “global” processes, operating not just in industrial settings butalso in natural environments at the Earth’s surface and within its interior. In many cases sin-tering processes require the presence of melt (e.g., welding in volcanic deposits; Grunder andRussell, 2005; Sparks et al., 1999) or fluid (e.g., diagenesis in sedimentary basins; Rutter,1983; Tada and Siever, 1989) to cause particles to coalesce. Solid-state sintering operates inthe absence of a melt or liquid phase and, at elevated temperatures and pressures, causes co-hesion and densification of particulate materials. The specific mechanisms active in solid-statesintering can be vapor transport, surface diffusion, grain boundary diffusion, lattice diffusion,and, where differential stresses are sufficiently high, dislocation motion (climb and/or glide)(Figure 1.1) (Rahaman, 2003).Volcanic settings can readily supply the requisite high temperatures and pressures toallow for densification by diffusion-driven solid-state sintering. However, the role of solid-2Grain BoundaryPoreGBDLDDC/DGGBD: Grain boundary diffusionLD: Lattice diffusion DC/DG: Dislocation creep or dislocation glideNeckFigure 1.1: Densifying solid-state sintering mechanisms, modified from Rahaman(2003) (figure 8.1). Necks are sinks of matter transport.state sintering of particles in volcanic settings is unknown – the timescales have previously beenconsidered too long to affect volcanic activity (e.g., Guest and Rogers, 1967) and, therefore,are unstudied.1.3 Dissertation objectives and organizationIn this dissertation I aim to (1) test whether solid-state sintering occurs in volcanicsettings, (2) constrain the operational timescale of solid-state sintering at volcanic conditionsand (3) determine whether solid-state sintering occurs fast enough to modulate eruptive activity.To address these research objectives, I use a combination of field-based studies of vol-canic shear zones, laboratory analysis of natural volcanic materials, and products of high-temperature-pressure experimentation (i.e., hot-pressing experiments) to answer the followingquestions:• Does solid-state sintering explain the diverse physical and mechanical properties of theshear zones that envelope extruded lava domes (e.g., Mount St. Helens, 2004-2008)?• What are the timescales of densification by solid-state sintering at volcanic pressure-temperature conditions, and do they overlap with the timescales of volcanic activity?• What are the implications of solid-state sintering for fluid flow and fracture healing involcanic and high-temperature tectonic systems?3• Can the properties of sintered shear zone materials be used to recover specific eruptiondynamics?I answer each question in an individual research chapter (Chapters 2-5).In these studies I demonstrate, for the first time, that solid-state sintering is effective atvolcanic pressure-temperature conditions (Chapter 2) and operates on short timescales (hoursto years) (Chapter 3). These sintering timescales are sufficiently short to influence other vol-canic processes, including the longevity of outgassing pathways (Chapter 4) and the ascent ofhigh viscosity magmas (Chapter 5). As such, solid-state sintering moderates processes govern-ing eruptions.I focus on solid-state sintering in volcanic systems of intermediate (dacitic) composi-tion in this dissertation. There are two reasons for this: firstly, the first evidence of solid-statesintering occurring in volcanic settings was recognized in the shear zones of dacitic lava domes(Chapter 2). The use of that dacitic fault gouge in subsequent hot-pressing experiments wasadvantageous, as it allowed for direct comparison of the textures and properties of experimen-tal products and natural cataclasites (Chapter 3). Secondly, dacitic systems are unpredictableand are prone to sudden transition from effusive to explosive activity. Highlighting the conse-quences of solid-state sintering in these systems is informative for volcanologists who assessthe hazards and propose strategies for risk mitigation at active, dacitic volcanoes.That said, I emphasize that solid-state sintering is a “global” phenomenon that oper-ates pervasively within the Earth’s crust, wherever granular materials are subjected to elevatedpressures and (sub-solidus) temperatures for protracted time. As such these results are relevantbeyond intermediate volcanic systems.4Chapter 2Hot pressing in conduit faults during lavadome extrusion: Insights from Mount St.Helens 2004-20082.1 IntroductionThe wide range of eruption styles and resulting landforms associated with the effusiveeruption of rhyodacitic magma are an expression of magma rheology and eruptive flux. This isparticularly true for the diverse array of morphologies presented by lava domes (Cashman et al.,2008; Fink and Griffiths, 1998; Heap et al., 2016; Sparks et al., 2000; Watts et al., 2002). Anend-member of rhyodacitic lava domes that has received much attention in recent years are thespectacular lava spines observed at Mount Unzen, Japan (1990-1995; Nakada and Motomura,1999; Nakada et al., 1999), Soufrie`re Hills volcano, Montserrat (1995-2003 and 2005-2013;Watts et al., 2002), and Mount St. Helens (MSH), Washington, USA (2004-2008; Cashmanet al., 2008; Iverson et al., 2006).These spines of lava share a number of features. First, the rocks that form the spines arehighly crystallized, typically featuring high phenocryst contents and a microlitic groundmass(Cashman et al., 2008; Cordonnier et al., 2009; Nakada and Motomura, 1999; Pallister et al.,2008; Sparks et al., 2000). Groundmass glass (quenched rhyolitic melt) is subordinate (<15vol%) and can be as low as <2 vol% (Smith et al., 2011; Sparks et al., 2000; Watts et al.,2002). Second, the spine-forming lava is typically dense – fractional porosities of extrudedspine lavas are often measured to be less than 0.10 (Cashman et al., 2008; Cordonnier et al.,2009; Gaunt et al., 2014; Heap et al., 2016; Kennedy et al., 2009). Third, lava spines eruptat low extrusion rates (0.25-2 m3/s; Cashman et al., 2008; Holland et al., 2011; Nakada et al.,51999; Watts et al., 2002) leading to low eruption temperatures and high degrees of crystallinity(i.e., low melt fraction) and, thus, high bulk viscosities (109 to 1014 Pa s; Cordonnier et al.,2009; Holland et al., 2011; Nakada and Motomura, 1999; Sparks et al., 2000). Indeed, instancesof spine formation are restricted to high viscosity magmas (andesite to dacite). Lastly, and mostpertinent to this study, extruded lava spines, including those erupted at MSH, Soufrie`re Hillsvolcano, Mount Unzen, Mount Usu (Japan) and Mount Pele´e (Martinique), commonly featuresmooth or striated surfaces (Cashman et al., 2008; Fink and Griffiths, 1998; Iverson et al., 2006;Minakami et al., 1951; Pallister et al., 2013; Sparks et al., 2000) comprising a cm to m thickcarapace of finely comminuted magma.The carapace material is fault gouge formed by brittle deformation at the conduit-wallrock interface, where shear stresses are greatest (Cashman et al., 2008; Hornby et al., 2015;Kendrick et al., 2012; Kennedy et al., 2009; Sparks et al., 2000). Small, rapid slip events atthis interface create a cylindrical fault zone along the outer margins of the highly viscous, ris-ing magma, and convert the crystallized lava into a fine-grained fault gouge (e.g., Cashmanet al., 2008; Gaunt et al., 2014; Hornby et al., 2015; Iverson et al., 2006; Kendrick et al.,2014; Kennedy and Russell, 2012; Kennedy et al., 2009; Lamb et al., 2015; Nakada and Moto-mura, 1999; Neuberg et al., 2006; Pallister et al., 2008; Watts et al., 2002). Evidence for theseslip events is provided by the shallow (depths of 1 to 0.5 km) “drumbeat” seismicity frequentlyrecorded during spine-forming eruptions (Hornby et al., 2015; Iverson et al., 2006; Lamb et al.,2015; Moran et al., 2008a; Pallister et al., 2013; Umakoshi et al., 2008). Of interest, the ex-truded fault gouge material is extremely variable in physical and textural properties, rangingfrom unconsolidated powder to dense lithified fault rock (Cashman et al., 2008; Hornby et al.,2015; Kendrick et al., 2012; Minakami et al., 1951; Pallister et al., 2013).Our question is: how does the conduit fault gouge lithify so effectively within the shorttimescales the shallow depths of origin imply? The process operates rapidly on essentially crys-talline material (i.e., little to no glass/melt) even at moderate volcanic temperatures (<750◦C;Vallance et al., 2008). The MSH 2004-2008 spine-forming eruptions offer a singular opportu-nity to address this question because of the extensive array of associated geological observa-tions and geophysical data. We use new laboratory measurements of porosity and permeabilityon samples of gouge rocks from three different spines at MSH to quantify the extent of lithi-fication. We then use the observations from the MSH eruptions to reconstruct the ascent andthermal history of the individual magma packets that fed each of the seven lava spines. Thereconstructions constrain the time-temperature-pressure window for the transformation pro-cesses that convert the fault gouge into competent, low-porosity and low-permeability faultrocks (i.e., lithification). Our analysis suggests that hot pressing, similar to that used com-mercially to produce ceramics and semi-conductors, drives lithification of the volcanic fault6gouge associated with lava spine-producing volcanoes. This result is notable because it in-dicates there is an undiscovered lithification mechanism operating within the upper conduitduring spine-producing eruption that, significantly, does not require the presence of melt or theprecipitation of new mineral phases.2.2 A case study: Properties of MSH gougeFrom 2004 to 2008 MSH produced seven discrete lava spines, each comprising a core oflow-porosity dacite enveloped by a carapace of variably indurated fault gouge (Cashman et al.,2008; Gaunt et al., 2014; Iverson et al., 2006; Kendrick et al., 2012; Kennedy et al., 2009).Prior studies concluded that the magma crystallized and solidified at ∼ 1 km depth (Cashmanet al., 2008; Iverson et al., 2006; Pallister et al., 2008) and then was pushed to the surface alongcylindrical, conduit wall-parallel, fault zones. Brittle deformation along these faults resulted inthe production of fine-grained, comminuted gouge from the solidified, crystal-rich, ascendingdacite. Rhythmic seismicity (i.e., “drumbeat” seismicity) was observed throughout the MSHeruption although the seismic energy released decreased with time (e.g., Iverson et al., 2006;Moran et al., 2008a) perhaps reflecting a decrease in ascent rate as the eruption waned. Previousworkers interpreted the microseismic events as stick-slip events localized in the gouge alongthe conduit-wall (Cashman et al., 2008; Iverson et al., 2006; Pallister et al., 2013). In contrast,we suggest the seismicity derives from relatively high stress drop events related dominantlyto the production of gouge from the crystallized dacite magma (i.e., Kennedy and Russell,2012; Kennedy et al., 2009). There were also low levels of magmatic outgassing measuredthroughout the eruption (Gerlach et al., 2008), with gas flux concentrated with the fault zone(Rowe et al., 2008).2.2.1 Textural organization, granulometry and mineralogyThe nature and properties of the enveloping fault gouge are well described in the liter-ature, with a particular focus on the carapaces at spines 4 and 7 (Cashman et al., 2008; Gauntet al., 2014; Kendrick et al., 2012; Kennedy et al., 2009; Pallister et al., 2008). Table 2.1 re-ports our field measurements of the thickness of the fault gouge carapaces. The gouge materialencasing spines 4 and 5 is 1 to 3 m thick whereas the gouge is considerably thinner (0.03-0.6m) at spine 7 (Table 2.1). The conduit-parallel fault zones show a lithostratigraphic organiza-tion that is generalized in Figure 2.1a using observations from spine 4. From the conduit wallto the interior of the spine, the fault zone comprises: (1) ultracataclastic slickensides on theexterior surface, (2) unconsolidated fault gouge hosting thin slickenside layers, (3) induratedgouge, (4) cohesive cataclasite, (5) sheared dacite, and (6) massive dacite (Figure 2.1a). Spine7Table 2.1: Surface observations of the 2004-2008 eruption at Mount St. Helens, including: date range for each event, onset day (t),duration (∆t; days), volumetric (Q; m3/s) and linear (U ; m/d) extrusion rates and spine volume (V ; × 106 m3) (Schilling et al.,2008; Vallance et al., 2008). We include calculated spine volumes (Vi; × 106 m3) and lengths (Li ; m), and the width of thefault zones occupied by gouge-derived material (w; m), measured in August 2010.Event Date a t ∆t Q U V d V ei Lei wPre-seismicity Sep 23 - 30 2004 0 8 - - - - - -Vent clearing Oct 1 - 10 2004 8 10 7 - 12 >10 10 8.2 ± 2.2 261 -Spine 1 Oct 11 -15 2004 18 5 2 - 3 15 - 20 2 1.1 ± 0.2 34 -Spine 2 Oct 15 - 24 2004 23 9 3 25 4 2.3 74 -Spine 3 Oct 25 - Dec 18 2004 32 55 4 - 6 8 - 11 21 23.8 ± 4.7 756 -Spine 4 Dec 19 2004 - Apr 9 2005 87 112 1.5 - 2.5 5 - 8 18 19.4 ± 4.8 616 0.2 - 2.6Spine 5 Apr 10 - Jul 31 2005 199 113 1 - 1.5 3 - 6 15 12.2 ± 2.4 388 1 - 1.5Spine 6 Aug 1 - Oct 9 2005 312 70 1.5 - 2 3 - 4 8 10.6 ± 1.5 337 -Spine 7 Oct 10 2005 - Jul 31 2007 b 382 660 0.5 - 1 0.5 - 2 c 25 d 42.8 ± 14.3 1361 0.03 - 0.6Endogenous growth Aug 1 2007 - Jan 27 2008 c 1042 180 - - 25 d 42.8 ± 14.3 1361 -Total 93 ± 4 d 112 ± 28 3829a transition periods included in duration of the following spine.b approxiate date for the end of spine 7 extrusion inferred from 2004-2008 time lapse videos for dome growth and crater glacier advance (https://volcanoes.usgs.gov/volcanoes/st helens/multimedia videos.html).c end date for eruption, and minimum extrusion rate for spine 7 from the Global Volcanism Program bulletins.d total volume from Mastin et al. (2009); volume of spine 7 by subtraction.e Vi = (Qi×∆ti);Li = (Qi×∆ti)/(pi× (100)2) where 100 m is the radius of the conduit (Iverson et al., 2006).80 0.1 0.2 0.3Porosity10-1810-1610-1410-12Permeability (m2 )dacitedaciteSpine interior0 1-1 2 (m)(m)0 1Wall RockSpine interiorWall Rockgouge zonegouge zone(c)(a)(b)Fractured dacite Shape fabric Dacite Folded shear bands LegendLineated ultrafine-grained black ultracataclasite  Fractured cataclasite  Cataclasite (+clasts)Fault GougeSlickensides12341 321parallelperpendicularunconsolidated43Gaunt et al. (2014) parallelGaunt et al. (2014) perpendicularFigure 2.1: Diversity of fault zone geometries and properties at MSH. (a) Summarylog for the fault zone at spine 4, a partially lithified carapace. Units include uncon-solidated gouge, indurated gouge crosscut by slickensides, and cataclasite. Num-bered regions show the approximate locations of samples shown in panel (c). (b)Summary log for the fault zone at spine 7, an extensively lithified carapace. Thefault zone is thin and the units are gradational from unconsolidated material tohighly competent ultracataclasite. The black box outlines the approximate loca-tion of sample shown in Figure 2.2. (c) Measured porosities and permeabilitiesfor unconsolidated gouge (gray circle), and variably lithified gouge from this study(circles) and Gaunt et al. (2014) (triangles). Sample cores were cut parallel (opensymbols) or perpendicular (closed symbols) to planar fabric taken as parallel to ex-trusion direction. Cores from the ultracataclasite have the lowest measured porosi-ties and permeabilities, while indurated gouge cores have the highest values.9sheared dacite1 cmslickensides ultracataclasitecataclasiteindurated gouge cataclasiteincreasing competenceFigure 2.2: Grain size, shape and texture of an extensively lithified gouge-rock (spine7). The composite photomicrograph is oriented as it formed in the conduit (seecartoon) and shows the gradation in competence and texture from spine exte-rior to the interior. From left to right the material includes: capping ultrafine-grained ultracataclasite layers (slickensides); large, angular mineral grains set in alight brown matrix (indurated gouge); mineral grains of gradually decreasing size,showing increased grain rounding (cataclasite); dark gray/black region having fewlarge and well-rounded mineral grains (ultracataclasite); mineral grains of gradu-ally increasing size set within a dark brown matrix (cataclasite); numerous angularphenocrysts within a microcrystalline groundmass showing a weak shape fabric(sheared dacite).7 is significantly different in that it hosts a foliated ultracataclasite immediately beneath theindurated gouge (Figure 2.1b, 2.2). This ultracataclasite is absent from other spines where lessdense cataclasite takes its place (Figure 2.1a, A.1) (Cashman et al., 2008; Gaunt et al., 2014;Pallister et al., 2013).The MSH gouge comprises mineral and lithic particles of varying size. Hand sampleand thin section observations on multiple spines, and quantitative analysis of the unconsol-idated gouge (Figure A.2), show grain sizes spanning 1 μm to 10 cm, which accords withprevious grain size determinations (e.g., Cashman et al., 2008; Iverson et al., 2006; Kendricket al., 2012; Kennedy and Russell, 2012; Kennedy et al., 2009; Pallister et al., 2013). All parti-cles, regardless of size, are angular to subrounded. Figure 2.2 illustrates the gradual change ingrain shape and size across the gouge carapace on spine 7, including the ultracataclasite.The fault gouge derives from the dacitic magma and is compositionally uniform, re-flecting the chemical homogeneity of the erupting magma (∼ 65 wt% SiO2; Cashman et al.,2008; Kendrick et al., 2012; Pallister et al., 2013, 2008; Thornber et al., 2008). In Table A.1 wereport the mineralogy of our gouge samples as determined by X-ray diffraction (XRD), whichincludes plagioclase, amphibole, orthopyroxene, oxides, quartz, tridymite and cristobalite (cf.Cashman et al., 2008; Kendrick et al., 2012; Pallister et al., 2013, 2008). The abundance of10these phases, including silica polymorphs, does not vary between spines or with increasingsample competence. Our analysis of the fault zone materials from spines 4, 5 and 7 indicates acommon macroscale textural organization, grain size distribution and composition. However,there are substantial differences in fault zone thicknesses and in the competence of the faultgouge.2.2.2 Porosity and permeabilityWe measured the porosity and permeability of samples of MSH gouge (Table 2.2) anduse these new measurements to quantify the changes in physical properties attending gougelithification. Previous measurements of porosity and permeability for MSH dome-forminglavas are available (see Heap et al. (2016) and references within) but measurements on the faultzone materials are few (Gaunt et al., 2014; Kendrick et al., 2012). Our measurements are madeon the unconsolidated material and on cylindrical samples (25.4 mm in diameter and 26-51mm in length) cored from blocks of the texturally distinct units within the fault zones at spines4, 5 and 7. Samples were cored in two orientations that are parallel and perpendicular to planarfabrics. We assume the planar fabrics are oriented parallel to extrusion direction and to theconduit walls. Connected porosity was measured using a helium pycnometer, and permeabilitywas measured using a benchtop helium permeameter (confining pressure of 2.5 MPa) on oven-dry cores using the steady-state flow method (see Heap et al. (2016) for a full description ofthe steady-state method) (Table 2.2).Values of permeability plotted as a function of total porosity (Figure 2.1c) show poros-ity and permeability to vary across the sample suite by one and four orders of magnitude,respectively. These two physical properties are strongly correlated with the apparent compe-tence of the fault gouge material (Figure 2.1c). The gouge rocks furthest from the conduitboundary have low porosities and permeabilities (0.03 and ∼ 10-16 m2; Figure 2.1; Table 2.2),whereas porosity and permeability are greatest at the wall-rock interface (0.32 and ∼ 10-12m2; Figure 2.1; Table 2.2). Gaunt et al. (2014) also measured an elevated porosity at the wall-rock interface. Our data show no measurable anisotropy in permeability in the low-porositysamples cored parallel and perpendicular to the direction of extrusion. In contrast, we ob-serve anisotropy in the permeability of higher porosity gouge samples (i.e., those closer to thewall-rock interface) up to 1 order of magnitude (Figure 2.1; Table 2.2). The data of Gauntet al. (2014) show an even larger anisotropy of permeability (four orders of magnitude) in theirhigh-porosity samples of gouge. Differences between data from these two studies attest to theheterogeneous nature of the fault zone materials.11Table 2.2: Measured total fractional porosity (φ ) and steady-state permeability (log10 k;m2) for MSH gouge samples from different spines, cored in different orientations.Replicate measurements are also reported.Spine Sample φ a log10 k log10 kParallel4 4 3a(2) 1 0.32 -11.95 5 2b(2) 1 0.26 -13.2 -13.57 7 3c 3 0.21 -13.5 -13.67 7 3c 1 0.18 -13.6 -13.97 7 4b 1 0.08 -15.07 7 4b 3 0.06 -15.27 7 4b 5 0.06 -15.3 -15.37 7 5j 1 0.03 -15.77 7 5j 3 0.03 -15.7Perpendicular4 4 3a(2) 4 0.30 -12.6 -12.64 4 3a(2) 2 0.28 -13.25 5 2b(3) 2 0.26 -13.8 -13.87 7 3c 4 0.12 -14.77 7 4b 2 0.07 -15.27 7 5j 2 0.03 -15.97 7 5j 4 0.03 -15.9 -15.8Unconsolidated5 5 0 SM 0.30 -13.0 -13.0a isolated porosity, calculated from the density of powdered gouge and the measured skeletal density ofthe cores, is 0.01-0.02 for all samples.2.3 Magma ascent in the conduitThe 2004-2008 eruption of MSH lasted 42 months, during which time seven spineswere extruded sequentially from the same vent. Drumbeat seismicity occurred for the durationof the eruption and is interpreted to result from repetitive stick-slip or fracture-slip faultinglocalized at the conduit margin (e.g., Iverson et al., 2006; Kendrick et al., 2012; Kennedyand Russell, 2012; Moran et al., 2008a; Pallister et al., 2013), resulting in the formation offault gouge. While the decrease in the rate and magnitude of these events over time (e.g.,Moran et al., 2008a) may signal the waning of the eruption (Scott et al., 2008), the persistentmicroseismicity suggests the continued production of crystal-rich (glass-poor), unconsolidatedfault gouge at depth. At the surface, the gouge layer is variably densified: spines 4 and 5 havecarapaces of loose powder, indurated gouge, and relatively porous cataclasite (Figure 2.1 andA.1). In contrast, the carapace enveloping spine 7 is composed of unconsolidated gouge that12grades to a highly competent, dense, low-permeability ultracataclasite (Figure 2.1, 2.2). Thevariable competence of the fault zone rocks enveloping these spines indicates that (1) the gougeis progressively lithified during transit to the surface, and (2) the conditions associated with theformation of the ultracataclasite at spine 7 are in some way different from the lithificationconditions for the less competent gouge-derived material at spines 4 and 5.Observations collected for each spine eruption include: surface-resolved linear extru-sion rates (U ; m/s), volumetric extrusion rates (Q; m3/s), eruption durations (Δt; days) andapproximate erupted volumes (V ; m3) (Table 2.1; Schilling et al., 2008; Vallance et al., 2008).The linear and volumetric extrusion rates decay logarithmically with time such that rates forspine 7 are an order of magnitude lower than for spine 1 (Table 2.1).We use these observational data to reconstruct the pre-2004 eruption magma column(Figure 2.3a) and to model the ascent of the individual (ith) parcels of magma that fed eachspine (Figure 2.3b; Table 2.3). We adopt a cylindrical geometry for the magma-filled conduit(as suggested by Pallister et al. (2013, 2008)), where the diameter (D) is approximated to 200 m(e.g., Iverson et al., 2006). Using this idealized geometry, the median observed volumetric ex-trusion rate (Qi) and eruption duration (∆ti), we calculate the length (Li; m) of each cylindricalparcel of lava (Table 2.1). The total length of the subsurface magma column at the start of theeruption is the sum of these modelled values, which we estimate as 3.8 km (Table 2.1). Thisapproach allows us to model the position of the discrete parcels of magma within a verticalcolumn at the start of the eruption (t = 0) and throughout the eruption. Figure 2.3 illustrates theprogressive ascent (i.e., position in the conduit) of these magma parcels as a function of timeincluding the time at which each portion of magma reaches depths of 1, 0.5, and 0 km (Figure2.3b; Table 2.3).The slopes of depth-time paths define ascent rates for the individual spine-formingmagma packets as a function of depth. These slopes, plotted as black lines in Figure 2.3b,show that the magma ascent rate was not constant but decreases with time throughout the2004-2008 eruption of MSH (values on Figure 2.3b). It is also clear that the ascent rates ofindividual packets of magma become more complex as the eruption progresses. Note that themodelled ascent rates differ from the values reported for spine extrusion rates because the ob-served linear extrusion rates (i.e., U) only correspond to magma ascent rate at the very top ofthe conduit. For example, later parcels of magma are moving faster in the subsurface than theextrusion rates observed at the surface would suggest. We report the maximum and minimumcalculated ascent rates (v) at depths <1 km in Table 2.3.Shear strain rates associated with syn-eruptive deformation of the conduit margin ma-terials during faulting are calculated from these reconstructed ascent rates at depths <1 km(v, Table 2.3). Shear strain rates (γ˙) within the fault zone core are calculated as v / w where1345677567Depth (km)t = 0  t = 87 t = 199 t = 38204(a)321(b) (c)0 200 400 600 800 1000Days into Eruption200400600800Temperature (oC)degassingmagmacrystallizeddacite76543765476570 200 400 600 800 1000Days into Eruption4 3 2 1 0 Depth (km) 2.14.83.45.513.726.16.88.2Figure 2.3: “Top-down” model for spine extrusion at MSH. (a) Schematic cross sec-tions of MSH showing the position of dacite spines at t = 0 (onset of seismicity), 87,199 and 382 days (the start of spine 4, 5 and 7 extrusion, respectively). The lengthof each spine (Li) is given in Table 2.1. The field of crosses (+) above 1 km and thecrosshatched region (1 to 0.5 km) denote the depth where the dacite is solidified,and the zone where gouge formation occurs, respectively (Cashman et al., 2008).(b) Modelled ascent paths for each spine. Colors and patterned fields as in panel (a).Ascent paths for the top and bottom of the parcel of solidified magma that makesup each spine (color bar) have been reconstructed in depth-time space. The ascentrate of a spine is not constant; the slopes (values on right side) are calculated bydividing Li by ∆ti. Black dots show when the top (or bottom) of each spine reaches1 and 0.5 km depth. As ascent rates decrease during the eruption (shallowing slopeof ascent path curves), the later spines (and gouge) have longer residence times. (c)Results of thermal model predicting the temperature of gouge as a function of time.Colors as in panel (a). Dashed lines are boundary condition temperatures: wall rock= 150◦C, ascending magma = 850◦C (see text). The modeled temperatures at thecontact with the wall rock, and 0.5 and 1 m in to the conduit are shown as closed,gray, and open circles respectively (Table 2.3).14Table 2.3: Modeled parameters for the 2004-2008 MSH lava spine eruption, including: the eruption day (tx) when the top of eachspine reached the surface (0 km), 0.5 km and 1 km; the residence time over those depth intervals (∆tx−x; d); ascent rates at<1 km depth (v; m/d); and calculated shear strain rates (γ˙; s-1). Also included are the Peclet number (Pe; see text) and modeltemperatures (◦C; at 1 km depth) at the conduit-wall rock interface (0 m), as well as 0.5 m and 1 m in to the conduit.Event Day Transit Day Ascent Rate Shear Strain Rate Peclet Number Temperature Residence Timet0 t0.5 t1 vmin vmax γ˙min γ˙max Pemin Pemax 0 m 0.5 m 1 m ∆t0.5−0 ∆t1−0.5Vent clearing 8 - - 26.1 26.1 - - 104.8 104.8 150 - - - -Spine 1 18 - - 6.8 26.1 - - 104.2 104.8 538 610 675 - -Spine 2 23 - - 6.8 26.1 - - 104.2 104.8 675 803 837 - -Spine 3 32 - - 6.8 26.1 - - 104.2 104.8 665 729 778 - -Spine 4 87 51 13 13.7 26.1 6.1 × 10-5 1.5 × 10-3 104.5 104.8 616 652 687 36 38Spine 5 199 108 59 5.5 13.7 4.2 × 10-5 1.6 × 10-4 104.1 104.5 620 646 670 91 49Spine 6 312 179 88 5.5 5.5 - - 104.1 104.1 650 672 693 133 91Spine 7 382 266 149 3.4 5.5 6.7 × 10-4 2.1 × 10-3 103.9 104.1 689 711 732 116 117Base of spine 7 1042 792 554 2.1 2.1 - - 103.7 103.7 612 624 634 250 238a γ˙min = vmin/wmax; γ˙max = vmax/wmin (Table 2.1).15w is the thickness of the unit over which strain is distributed (i.e., the thickness of fault zonecore; Table 2.1). Values for γ˙ vary from 4.3 × 10-5 to 2.1 × 10-3 s-1 (Table 2.3). The faultzones at spines 4 and 5 are significantly wider than those in spine 7 (1-3 m vs. 0.03-0.6 m)and, therefore, values of γ˙ are similar, despite the differences in ascent velocities (Table 2.3).Variations in shear strain rate are therefore unlikely to explain the differences in physical andtextural properties and densification of the fault gouge mantling the different spines.The reconstructed ascent rates are also used to constrain the temperatures in the risingpackets of magma for each spine (Table 2.3). The model is adapted from Jaluria and Torrance(1986) and Russell (1988) and accounts for conductive heat transfer to the conduit walls vs.advective transport within the magma as it ascends the conduit from a depth of ∼ 1 km. Themodelling establishes the temperature distributions at three points – at the conduit-wall rockinterface, and 0.5 and 1 m into the conduit from the interface. The thermal model uses aninitial temperature of 850◦C for the dacite magma, which is just below the peak temperatureestimated for crystallization at ∼ 1 km (857 to 936◦C; Blundy et al., 2008; Pallister et al.,2008). The Peclet number (Pe) is calculated as v×D/α , where α is the thermal diffusivity(taken as 10-6 m2/s). Even for the slowest ascent rates of the MSH dacite (e.g., 2.1 m/d) thecomputed Pe values are much greater than unity (103.7; Table 2.3), indicating that advectivetransport of heat dominates over conductive heat loss to the wall rocks during ascent (Russell,1988).At the start of the eruption, the ascent rates in the conduit are high (Table 2.3), heattransfer is dominantly advective (little conductive heat loss), and magma temperatures are kepthigh (Figure 2.3c). As the eruption proceeds and ascent rates decrease, there is a greater capac-ity for conductive heat loss (e.g., spine 7; Table 2.3), although this is mitigated somewhat bythe fact that the wall rocks have already been heated by the passage of previous magma (i.e.,spines 1-6) (Figure 2.3c; Table 2.3). The temperatures of wall rocks at the conduit interfaceincrease rapidly in the first three weeks of the eruption and remain between 620 and 690◦C forthe remainder of the eruption (Figure 2.3c; Table 2.3). Model temperatures for gouge 0.5 mand 1 m from the conduit-wall rock interface follow the same heating trend where temperaturespeak during the ascent of spine 2 (803 and 837◦C, respectively) and then stabilize at 630 and730◦C for the rest of the eruption (Figure 2.3c; Table 2.3). Our model values for the fault zonetemperature are similar to those measured at the surface by thermal imaging of cracks in thecarapace (Vallance et al., 2008). The results provide a range of temperatures at which gougelithification must operate. However, these calculations show that variations in temperature dur-ing ascent are insufficient to account for the variable lithification of fault gouge mantling thedifferent spines.162.4 Hot pressing: A model for lithification of volcanic gougeThe slow ascent of highly crystalline rhyodacite magma in volcanic conduits supportsboth viscous and brittle deformation (e.g., Cordonnier et al., 2009; Lavalle´e et al., 2007; Oku-mura et al., 2016; Smith et al., 2011). Brittle deformation is commonly restricted to the conduitwalls and manifest as a conduit-parallel fault zone composed of fault gouge derived from com-minuted, holocrystalline magma (e.g., Goto, 1999; Holland et al., 2011; Kendrick et al., 2014;Neuberg et al., 2006). At MSH, the gouge is produced at relatively shallow depths (∼ 0.5to 1 km; e.g., Cashman et al., 2008) corresponding to low lithostatic pressures (∼ 12.5 to 25MPa). Magma temperatures in the conduit are relatively low (630-730◦C; Table 2.3; Vallanceet al., 2008) and residence times within the volcanic conduit are generally short (months to<2 years). The resulting domes and spines are extruded with carapaces of fault gouge thatare extremely variable in terms of their physical properties (e.g., porosity, permeability), vary-ing from unconsolidated, low-cohesion powder to dense, low-permeability, fault rocks. Thesefacts prompt two questions: firstly, and empirically, what controls the degree of lithification ofthe volcanic fault gouge? Secondly, and more fundamentally, what is the process that driveslithification within the narrow time-temperature-pressure window?Our analysis of the MSH eruptions has shown that the most lithified gouge is associatedwith spine 7 (i.e., the low-porosity, low-permeability ultracataclasite). Previous work on spine7 by Kendrick et al. (2012) distinguished four structurally distinct layers within the spine 7fault zone: (1) an outer surface of indurated gouge (L1) that crosscuts (2) a dark, banded layer(L2; i.e., the ultracataclasite in Figure 2.1b, 2.2) which, itself, grades into (3) a moderatelysheared layer (L3), and (4) the undeformed dacite core (L4). These authors suggested thatthe L2 layer contained evidence of frictional melting within the gouge caused by seismogenicslip events that produced a pseudotachylite (e.g., Kendrick et al., 2012, 2014; Lavalle´e et al.,2012). Although localized frictional melting may be present, this mechanism cannot explainthe pervasive, variable densification and lithification of the fault gouge that envelops each spine(Figure 2.1c). Variably indurated fault gouge is found on all spines at MSH, although spine 7is noteworthy for the high degree of competence of the gouge-derived ultracataclasite. We alsoreiterate that the comminuted solidified magma is essentially devoid of glass, thus precludinglithification by viscous sintering (as is the case for glassy materials; see Quane et al. (2009);Vasseur et al. (2013); Wadsworth et al. (2017a)). There is also no textural evidence nor modalmineralogical variations (Table A.1) suggesting the gouge was lithified by cementation pro-cesses involving fluids. Though outgassing magmatic volatiles passed primarily through thegouge-filled fault zone (Rowe et al., 2008), the low initial volatile content of this MSH magma(e.g., Gerlach et al., 2008; Pallister et al., 2008; Scott et al., 2008) likely precludes cementationas a significant lithification mechanism.17The variations in the reconstructed ascent rates for each spine-forming magma translateinto substantial differences in subsurface residence times (Table 2.3). The ascent paths (depth-time; Figure 2.3b) define the total residence times for each packet of magma and its associatedfault gouge at depths <1 km (i.e., ∆t1−0.5, ∆t0.5−0; Table 2.3). The total subsurface residencetime for each magma packet increases as the eruption progresses from 74 to 488 days (Table2.3). The last material erupted (spine 7 extrusion) has the longest residence time. Therefore,the unconsolidated gouge associated with spine 7 would have remained at elevated pressureand temperature for ∼ 150-400 days longer than the gouge mantling spine 4, and ∼ 100-350days longer than the gouge mantling spine 5. We suggest that, to a first order, the degree oflithification of fault gouge reflects the total time (residence time) spent at elevated tempera-ture and at lithostatic pressure (i.e., depth). Based on the empirical evidence, it appears thatslower ascent rates provide the longer residence times at the elevated temperature and pressureconditions required for lithification of the fault gouge.Hot pressing (HP) and hot isostatic pressing (HIP) are two manufacturing processesused to densify granular material by subjecting the particles to high temperatures under differ-ential (HP) or hydrostatic (HIP) pressure (Rahaman, 2003; Ramqvist, 1966). These methodsare used extensively in metallurgy and the production of ceramics. They are also common prac-tice for fabricating synthetic samples for rock deformation experiments (e.g., Kushnir et al.,2015; Rybacki et al., 2003) or studying densification by viscous sintering (i.e., welding) involcanic systems (e.g., Heap et al., 2014a; Quane et al., 2009). They are effective in densi-fying materials where the elevated temperature-pressure conditions activate specific sinteringprocesses. In the case of crystalline materials, sintering occurs in the solid-state by diffusion.We contend that the dominant process for lithification of fault gouge materials derived fromcomminution of solidified magma is ‘volcanic hot pressing’. The hot pressing of the crystallinegranular material promotes solid-state diffusional processes that bind particles together.Experimental studies of hot pressing and sintering have explored the effects of tem-perature, pressure, grain size and time on sintering efficiency in crystalline materials (e.g.,Rahaman, 2003; Ramqvist, 1966; White, 1965). Rates of densification greatly increase withincreasing temperature owing to faster rates of atomic diffusion. Higher pressures can in-crease the stress on grain boundaries thereby accelerating grain boundary or lattice diffusionand densification rates. Increased time at these conditions leads to greater porosity reductionand increased competence and lithification. Reduced grain sizes support higher densificationrates because diffusion is facilitated by the increase in surface area to volume ratios, and thereduced distances to and between grain boundaries.To better constrain the grain radius of particles responsible for the gouge densificationprocess at MSH, we use the Wadsworth et al. (2016b) permeability model, which is applicable18to densifying granular materials. This universal scaling model illustrates the influence of par-ticle radius on densification dynamics regardless of the densifying mechanism. Specifically,it models the relationship between permeability and adjusted or ‘scaled’ porosity (i.e., totalporosity minus 0.03; see Wadsworth et al. (2016b) for justification) as a function of grain size.We have plotted our permeability and porosity (adjusted) data (Figure 2.1c; Table 2.2) on adiagram contoured for grain size using the Wadsworth et al. (2016b) model (Figure 2.4a). Ourdata, comprising a suite of materials from unconsolidated powders to dense rock, cluster alongthe 10 μm contour (Figure 2.4a).The distribution of our data suggests that the sintering process is facilitated by, or de-pends on, the smallest particles within the bulk fault gouge material. This inference is sup-ported by experimental and theoretical studies of sintering, which show increased densificationrates where particles are small (e.g., Rahaman, 2003; Vasseur et al., 2013; Wadsworth et al.,2017a). Furthermore, microstructural observations show that the well-lithified gouge (i.e., cat-aclasite and ultracataclasite), although poorly sorted, has a high abundance of small particles(Figure 2.2; Cashman et al., 2008; Kendrick et al., 2012; Kennedy et al., 2009; Pallister et al.,2013). The implication is that although the gouge comprises a wide range of grain sizes (1 μmto 10 cm; Cashman et al., 2008; Kendrick et al., 2012; Pallister et al., 2013), the larger particlesare not active in the lithification process. These passive particles are instead bound together bythe progressive sintering and densification of the finer grained matrix. Larger grains (radii up to100 μm) may only become involved in sintering once the population of smallest grain sizes hasbeen sufficiently reduced. This is shown in Figure 2.4a where data for the densest cataclasitesdeviate from the 10 μm contour. At this point, the change in the grain size of the particles mayincrease the densification time such that sample density would not change appreciably on thetimescale of the eruption.Several authors have developed models for the rate of densification as a function of theparameters discussed above (see references within Ramqvist (1966)). We use the followinggeneralized model from Rahaman (2003) to illustrate schematically the relative influences ofpressure (P) and temperature (T ) on the minimum time necessary to densify (t∆ρ ) a materialof a specified grain radius (G) by a fixed amount, dictated by the prescribed relative density(ρ/ρ i) (Figure 2.4b):t∆ρ = ln(ρρi)GmkTHDδP, (2.1)where k is the Boltzmann constant, H is a constant, D is the diffusion coefficient of the rate-controlling species, δ is a shape parameter, and m has a value that depends on the sinteringmechanism (e.g., boundary or lattice diffusion) (Rahaman, 2003). In Figure 2.4b we show19Figure 2.4: (following page) Model for hot pressing in volcanic conduits. (a) Ourporosity-permeability data (from Figure 2.1c) and the universal scaling model fromWadsworth et al. (2016b). Contours show the predicted porosity-permeability rela-tionship for particles of a specified grain radius densifying by any mechanism. Datafall along the 10 μm contour, but deviate toward the 100 μm contour at low porosi-ties. From this, we infer that densification of gouge occurs primarily by sintering ofsmall particles. (b) Modeled minimum densification time (t∆ρ ; contours) at a givenpressure (P) and temperature (T ) (Equation 2.1). The prescribed relative density(ρ/ρi) is equivalent to transforming an unconsolidated powder (initial porosity =0.33) to a dense solid (final porosity = 0.0) (ρ/ρi = 1.5). Grain radius (G) is 10μm in order to constrain the magnitude of t∆ρ . Where t∆ρ < 1 year, we define a“hot pressing window” (shaded region) where gouge will be extensively lithifiedon a short timescale. Where t∆ρ > 1 year densification is still occurring, but at adiminished rate so that gouge properties do not change substantially on a timescalesimilar to that of a spine-producing eruption (white region). An increase in G to 25μm shifts contours to the right (dashed curve). (c) Influence of ascent rate on thepotential for extensive lithification of gouge. Solid curve and shaded region definethe “hot pressing window”, where the residence time at depth is greater than t∆ρ (T= 700◦C, ρ/ρi = 1.5, G = 10 μm). An increase in G to 25 μm (dashed curve) shiftsthe “hot pressing window” to longer times. When the ascent rate of solidified lava(and gouge carapace) is high (10 m/d, steep line), it moves rapidly from a deeper re-gions in the conduit where t∆ρ is small to shallow regions where t∆ρ is large (shownby solid curve). Because residence time is less than t∆ρ the ascent path of the lavabypasses the “hot pressing window” and the gouge will be weakly consolidatedwhen it reaches the surface. Conversely, when ascent rate is slow (2 m/s, shallowline), gouge resides for an extended time at high P, where t∆ρ is small. At theseconditions, residence time is greater than t∆ρ so densification proceeds quickly andthe gouge will be a high competence material when it reaches the surface.200 0.1 0.2 0.3Porosity - c10-1810-1610-1410-12Permeability (m2 )100 m10 m5 m25 m1 m(a)(b)(c)0 100 200 300 400 500 600Time (days)00.250.50.751Depth (km) 10 m/d  2 m/dHOT PRESSINGWINDOW500 600 700 800 900Temperature (oC)01020304050Pressure (MPa)00.511.52Depth (km)10 m10 m25 m25 m10 years1 month1 week5 m/d  HOT PRESSINGWINDOW1 year 1 year21the relationships between temperature, pressure, grain size and minimum densification time,where the modelled change in density is equivalent to converting an unconsolidated power toa dense solid. At elevated pressures (> 30 MPa, ∼ 1.25 km), temperature is the dominantcontrol on densification time, as the steep-sloping contours in Figure 2.4b show. However, atpressures below 10 MPa (∼ 0.5 km), the contours in Figure 2.4b begin to flatten and becomemore closely spaced: densification rates remain temperature-dependent but the minimum timerequired for densification increases substantially compared to rates at higher pressures. Anincrease in the radius of the densifying particles shifts the contours to the right (more time isnecessary to densify the material) but does not affect the overall shape of the contours (dashedgray curve, Figure 2.4b). Finally, we define a “hot pressing window” (shaded region, Fig, 4b)where the minimum densification time is less than 1 year.Sintering efficiency depends on the particle size distribution, as well as pressure, tem-perature and time, which supports our assertion that the degree of lithification reflects residencetimes in the conduit, and indirectly informs on ascent rate. This relationship is illustrated inFigure 2.4c where potential ascent paths, defined by average ascent rate, are compared to thetime-pressure window for hot pressing at elevated temperatures. Where the gouge materialascends slowly (2 m/d, shallow line in Figure 2.4c), it remains for an extended time in a high-pressure region of the conduit, where densification rates are high (i.e., Equation 2.1). On thispath, material becomes fully lithified because the residence time exceeds the requisite timefor densification of this material at conduit temperatures: the result is extrusion of a highlycompetent, lithified rock (e.g., ultracataclasite; Figure 2.2). Conversely, higher ascent ratescreate paths that completely miss (10 m/d, Figure 2.4c) or only briefly transect (5 m/d, Figure2.4c) the “hot pressing window” and are subject to lower rates of densification. The shorterresidence times under pressure at depth (i.e., higher ascent rates) and the lower rates of den-sification preclude complete lithification: the gouge will be extruded unconsolidated or onlyweakly lithified.2.5 Implications for eruption dynamics and monitoringThe morphology and stability of lava domes have been shown to correlate with subsur-face ascent rates (e.g., Fink and Griffiths, 1998; Heap et al., 2016; Watts et al., 2002). Theserates, which differ from extrusion rates observed at the surface, can constrain the rheologicbehavior of the magma in the conduit, and can signal the waxing or waning of an eruption.The competence of gouge reflects subsurface residence times, suggesting that the properties offault gouge mantling lava spines could serve as a geospeedometer, informing on conduit ascentrates. For example, where the carapace comprises unconsolidated or partially indurated gouge,22one can forensically infer a relatively rapid subsurface ascent rate. Conversely a well-lithifiedgouge carapace implies substantially slower ascent rates.Mount Unzen offers another example. The remnant spines from the 1991-1995 eruptionare mantled in gouge layers described as “sintered”, “welded”, and/or “agglutinated” (e.g.,Hornby et al., 2015). A photo of the relict of the 1994-1995 spine and its marginal shearzone (Figure 2a; Hornby et al., 2015) shows well-lithified gouge, implying slow subsurfaceascent. This observation accords well with the low observed extrusion rates (0.25-0.5 m3/s;Nakada et al., 1999), although, as we have shown, observed extrusion rates are not the same assubsurface ascent rates. The spines produced during the 1995-1999 eruption of Soufrie`re Hillsvolcano have a different character: the gouge that envelops these spines is poorly-lithified. Forexample, Watts et al. (2002) describe a smooth-topped lava dome being extruded on October 1,1996 at a flux of 1.8 m3/s (faster than median extrusion rate of spine 4 at MSH; Table 2.1). ByOctober 10 portions of the carapace failed, exposing a thick layer of weakly indurated gougeand breccia (Figure 15a; Watts et al., 2002), reflecting the relatively high observed extrusionrate.Many active dome- or spine-producing volcanoes are remotely monitored using aerialand terrestrial photography/photogrammetry (e.g., Diefenbach et al., 2012; Ryan et al., 2010;Schilling et al., 2008; Watts et al., 2002), thermal imaging/photogrammetry (e.g., Bernsteinet al., 2013; Thiele et al., 2017), and webcams (e.g., Bull et al., 2013; Poland et al., 2008).Remote sensing may provide a means to qualitatively assess the competence of the envelopinggouge layer from the material’s angle of repose or from the frequency of sloughing or slump-ing events. Given the relationship between subsurface ascent rate and properties of the faultgouge, degree of gouge lithification may then be used to infer the acceleration or decelerationof magma in the conduit. Changes in gouge properties, coupled with other observational data,could indicate whether an eruption is waxing or waning.Marginal fault zones filled with fault gouge and cataclasites are expected to be high-porosity, high-permeability regions supporting efficient passive degassing. The presence ofpermeable fault zones should therefore inhibit build-up of gas overpressures and preclude theexplosive release of trapped gases. However, at dome- and spine-producing systems like MSH,gas-charged explosive outgassing events still occur and are localized in the fault zones at theconduit wall (e.g., Cashman et al., 2008; Gaunt et al., 2014; Holland et al., 2011; Lavalle´eet al., 2013; Moran et al., 2008b; Pallister et al., 2013; Rowe et al., 2008). Changes in faultproperties causing a reduction in permeability (e.g., cementation or welding) have been invokedas triggers for explosive events (e.g., Holland et al., 2011; Quane et al., 2009). Hot pressingrepresents another means of causing a permeability reduction leading to repressurization and23explosive outgassing behavior. The recurrence interval between explosive events can informon the requisite time for gouge densification in the conduit.2.6 SummaryLava spines produced during the effusive eruption of crystal-rich rhyodacitic magmasoften reach the surface enveloped in layers of texturally diverse volcanic fault gouge. Thegouge-derived materials extruded during the 2004-2008 eruption at MSH range from uncon-solidated powders to low-porosity, low-permeability fault rocks. We investigated the processresponsible for the lithification of gouge using observational data collected during the eruptionto reconstruct the ascent paths and thermal histories of the extruded lava spines. Using thetime-temperature-pressure information given by these reconstructions, and the association ofthe most competent gouge materials with the spines erupted at the slowest ascent rates, we sug-gest a new mechanism for the densification and lithification of crystalline volcanic materials atspine-producing volcanoes, including Soufrie`re Hills, Mount Unzen, Mount Pele´e and MSH:the competence of the gouge changes as a result of solid-state sintering, which has a rate dic-tated by the time-temperature-pressure conditions the gouge experiences in the conduit. Whensubjected to high pressures and temperatures, small particles coalesce as a result of sintering,and progressively bind larger particles within a densifying matrix. If the material remains atdepth for an extended period of time, the gouge will be extensively lithified, and will reachthe surface as highly competent material. Increasing gouge competence is accompanied bya reduction in permeability, suggesting lithification of the fault zone decreases outgassing ef-ficiency. Additionally, given the correlation between the physical properties of gouge and itsascent rate, analysis of fault zone rocks mantling lava spines can be used to infer magma ascentrates.2.7 Access to Mount St. Helens National VolcanicMonumentThe fieldwork and sample collection were permitted by the United States National ParkService.24Chapter 3Rapid solid-state sintering in volcanicsystems3.1 IntroductionAll volcanic deposits contain void spaces, including pores, fractures and the spaces be-tween particles in volcaniclastic deposits. These spaces, when abundant and interconnected,facilitate flow of volcanic fluids and outgassing. However, voids in hot, subsurface volcanicdeposits are generally ephemeral due to a variety of processes that reduce void space (densifica-tion). The best understood and most common densification process is welding (compaction andviscous sintering of amorphous material) of volcaniclastic deposits at temperatures above theirglass transition temperature (Tg). Welding of volcanic deposits is well documented in nature(e.g., Smith, 1960) and the timescales are well constrained (Quane et al., 2009; Vasseur et al.,2013; Wadsworth et al., 2017b). In materials that are crystalline and lacking glass, densificationdoes not occur by welding. Rather, densification of crystalline (non-glassy) materials can occurby solid-state sintering wherein adjacent crystalline particles become conjoined by diffusion atthe grain boundaries (Rahaman, 2003). As a diffusion-driven process, elevated temperatures(T ) and pressures (P), and substantial times (t) at these conditions facilitate both densification(loss of void space) and lithification (increase in material competence) by solid-state sintering(Rahaman, 2003). The question is: can solid-state sintering operate on timescales relevantto volcanic processes? To address this question, we present a set of hot isostatic pressing(HIP) experiments designed to test the feasibility of solid-state sintering occurring on the shorttimescales (2.5 days) and the P-T conditions characteristic of volcanic settings.253.2 Natural occurrence: An example from Mount St.HelensMagmas that ascend slowly (effusion rates of 0.5-2 m3/s (Cashman et al., 2008)) de-gas, crystallize and become nearly solidified within the conduit (Cashman et al., 2008). Theresulting magmas have high effective viscosities that promote fracturing and cataclasis due tohigh shear stresses localized along the lava-wall rock interface (Lavalle´e et al., 2013). As aresult, the ascending magma and extruded lava are commonly encased by meter-scale cylin-drical fault zones comprising comminuted crystal-rich gouge (Cashman et al., 2008). In somecases, extruded lava domes arrive at the surface still mantled by these fault zones (e.g., MountPele´e (Martinique) 1902-3; Mount Unzen (Japan) 1990-5; Cashman et al., 2008). The lavaspines produced during the 2004-8 eruption of Mount St. Helens also feature exhumed faultzones (Cashman et al., 2008). Notably, the fault zones are not comprised exclusively of uncon-solidated gouge, but show extreme variation in physical and textural properties, ranging fromunconsolidated powder to dense fault rock (i.e., cataclasite) (Gaunt et al., 2014; Kendrick et al.,2012; Pallister et al., 2013; Ryan et al., 2018a).In prior work, we (Ryan et al., 2018a) measured the porosity and permeability of vari-ably densified cataclasites from several spines at Mount St. Helens (Table B.1) and, based onthese measurements and observations of the eruption, concluded that (1) the initially uncon-solidated gouge densified during ascent in the conduit from ∼ 1 km depth, and (2) the extentof densification depended on the subsurface residence time (2.5 to 16 months). One explana-tion for the most densified material in the fault zone is that it is a product of seismogenic slipevents, which caused localized frictional melting and the formation of thin low-porosity glassypseudotachylite veins (Kendrick et al., 2012). Ryan et al. (2018a) put forward an alternate con-ceptual model, proposing that gradational changes in the competence, density and permeabilityof the exhumed cataclasites can be simply due to solid-state sintering occurring in the conduit.Scanning electron microscopy (SEM) of the Mount St. Helens cataclasites shows densi-fication and lithification to involve coalescence, without melting, of crystalline particles. Smallparticles <10 μm in diameter (d), often concentrated along the edge of larger particles, arejoined by necks of crystalline material (Figure 3.1, B.1). The patches of coalesced materialform a crude framework, and reduce the space between larger particles, leaving only smallirregular pores in the consolidated matrix (Figure 3.1). The competence of the formerly un-consolidated gouge increases as the proportion of coalesced materials increases.26Porosity ~ 0.30ExperimentalNatural(a)Porosity ~ 0.15(b)(d) (e)202050505050(c)(f)Figure 3.1: SEM images of sintering. Mount St. Helens samples (a-c) and HIP products(d-f) show coalescence of small (<10 μm) plagioclase (light grey) and silica (darkgrey) particles on the edge of larger particles, and within open void space. Lowporosity materials (b,c,e,f) have more sintered material and reduced inter-particlespace. Scale bars are in micrometers.3.3 Hot Isostatic Pressing (HIP) experimentsTo assess the feasibility of solid-state sintering occurring in volcanic settings, includingwithin conduits, we ran a series of hot isostatic pressing (HIP) experiments, using unconsol-idated samples of sieved crystalline gouge from Mount St. Helens as the starting material.We sieved the gouge (< 125 μm diameter) and measured the particle size distribution usinga Malvern Mastersizer 2000 laser particle size analyzer at the University of British Columbia(Canada). The greatest volume contribution is from clasts > 30 μm in diameter. However, ona number basis, these clasts are rare; most clasts are <10 μm in diameter. We provide particlesize distribution curves (volume and number percent) in Appendix B.2.The mineral assemblage of the gouge includes plagioclase, potassic feldspar, silicapolymorphs, amphibole, orthopyroxene and FeTi oxides (Pallister et al., 2013; Table B.2).Notably there is no glass – the groundmass is “an extremely fine-grained mosaic of micro-lites” (Pallister et al., 2013). The mineral contents of the experimental products, provided inAppendix B.2, are within analytical uncertainty of the starting material. Experimental pres-sure and temperature conditions were 40 and 70 MPa, and 700-900◦C, respectively (Table3.1). The low isostatic pressures and temperatures do not allow for plastic flow (Rybacki andDresen, 2004) or melting, and favor densification over grain coarsening (Rahaman, 2003). Ex-27Table 3.1: Experimental conditions (pressure (P), temperature (T ) and time (t)), andphysical properties of HIP products (bulk density (ρb), relative density (ρr), totalporosity (φ ) and permeability (k)).Sample P (MPa) T (◦C) t (h) ρb (kg/m3) a ρr b φ c k (m2) dHIP1 a 70 900 60 2332 0.859 0.141 1.02 × 10-15b 2341 0.862 0.138 9.88 × 10-16HIP2 a 70 800 60 2202 0.811 0.189 3.95 × 10-15b 2207 0.813 0.187 3.48 × 10-15HIP3 a 40 800 60 2073 0.763 0.237 9.12 × 10-15b 2062 0.759 0.241 9.67 × 10-15HIP4 a 40 700 60 1923 0.708 0.292 1.87 × 10-14b 1901 0.700 0.300 1.66 × 10-14a ρb = m / (pir2l) using the mass (m), radius (r) and length (l) of the sample core. Initial bulk density(ρi) is 1602 kg/m3.b ρr = ρb / ρp, where ρp is powder density (2716 kg/m3).c φ = 1 - ρr. Isolated porosities are <0.01. Initial porosity is 0.41d Steady-state measurement. Forchheimer correction applied. See Appendix B.1 for details of methods.perimental conditions were chosen to map densification efficiency across a part of P-T spacerelevant to shallow conduits and lava domes.Four aliquots of dacite powder (45-48 g each) were sintered using an AIP-630H hotisostatic press at the Department of Materials Science and Engineering at the University ofSheffield (UK). Powders were compressed in air at 25◦C in steel cylinders (∼ 3.5 × 3.8 cm)using a hydraulic press (1.8 kPa applied stress). Canisters were heated under a vacuum (∼ 5 Pa)and remained at 180◦C for 24 hours, then sealed. During experiments, single sealed canisterwere simultaneously heated (10◦C/min) and pressurized with argon gas (0.50-0.88 MPa/min)to the prescribed conditions (Table 3.1). Canisters remained at P-T condition for 2.5 daysbefore cooling (10◦C/min) and venting (0.50-0.88 MPa/min).See Appendix B.1 for details of density and permeability measurements (Table 3.1).3.4 ResultsSEM images of the experimental products show HIPing produced the same microstruc-tures in all densified materials, and that higher pressures and/or temperatures increased theefficacy of coalescence (Figure 3.1, B.4). Small particles (d <10 μm) dominate our experi-mental material (Figure B.2), and, as in the Mount St. Helens samples, this size fraction formsthe framework in the sintered material. Again coalescence is accomplished by the formation of28700 800 900Temperature (°C)0.60.81Relative DensityInitial MaterialDensification Limit70 MPa40 MPa60 hours(0.30)(0.24)(0.19)(0.14)Permeability (m2 )0.1 0.2 0.3 0.4Total Porosity10-1610-1410-1210-180HIP productsMSH samples(Ryan et al., 2018)(a)(b)100 m10 m5 mFigure 3.2: Physical properties of HIP products. (a) Relative density (ρr; Table 3.1) ofHIP products (open: 40 MPa; filled: 70 MPa). Error bars are 1σ . (b) Measured andmodeled permeability against total porosity for HIP products (circles) and MountSt. Helens samples (diamonds; Ryan et al., 2018a). Curves are Wadsworth et al.(2017b) model (contours show specified radius).thin necks of crystalline material between adjacent small particles, commonly localized alongthe edges of larger particles (Figure 3.1f).Relative density (ρr) is the ratio of sample bulk density (ρb) to the true density of thepowder (ρp), and is the conventional metric for tracking sintering (e.g., Rahaman, 2003). Rel-ative density increases with greater sintering, approaching the limiting value of 1. Measuredvalues of ρr for our HIP products increase as pressure and temperature increase, indicative ofmore extensive particle-particle sintering (Figure 3.2; Table 3.1). An additional implicationis that total porosity (φ = 1 – ρr; Rahaman, 2003) decreases with increased sintering and aspressure and temperature increase.The permeability (k) of the HIP products also decreases with increased sintering and de-creasing φ (Table 3.1). Values of φ -k for the experimental products parallel the measurements29on natural samples from Ryan et al. (2018a) (Figure 3.2; Table 3.1), and the φ -k relationshipsare described well by the permeability model of Wadsworth et al. (2017b) (Figure 3.2).The (1) microstructural similarities between the natural and experimental samples (Fig-ure 3.1), and (2) parallel φ -k trends suggest that the HIP experiments reproduce the densifica-tion and lithification process that occurred within the Mount St. Helens conduit (i.e., solid-statesintering). Sintering in the experimental and natural settings was facilitated by extended time atthe elevated P-T conditions supplied by the HIP apparatus and volcanic conduit, respectively.3.5 Densification modelWe use our data to constrain a preliminary predictive model for solid-state sinteringof crystalline granular material at elevated temperatures and pressures. The base form of themodel is an empirical semilogarithmic relationship between ρr and time (e.g., Coble, 1961;Vieira and Brook, 1984):ρr = ρo+α ln(tto)(3.1)where ρo is the relative density at to. The fit parameter, α , varies with the P and T (Rahaman,2003). This “semilogarithmic law” between ρr and t has been shown to be applicable to ex-perimental data, irrespective of the sintering material or mechanism, or whether grains growduring sintering (Rahaman, 2003; Vieira and Brook, 1984).We modify Equation 3.1 to include explicitly the P-T dependence of α (cf. AppendixB.1) subject to the boundary condition ρr = ρi / ρp at t = 1 s, where ρi is the bulk density ofthe starting material prior to the experiment (Table 3.1). Thus, for t ≥ 1 s, densification isdescribed by:ρr =(ρiρp)+aexp(bT)Pcc ln(t) (3.2)where P is pressure (MPa), T is temperature (K), and t is time (s). Although our experimentshave a single experimental time (60 h), we take advantage of the robust empirical relationshipbetween t and ρr in Equation 3.1, and the large differences in ρr achieved at different P-Tconditions to fit Equation 3.2 to the data for the adjustable parameters (a = 0.039 ± 0.019; b =–3064 ± 290; c = 0.482 ± 0.064).Appendix B.1 contains further explanation of our derivation of Equation 3.2. To avoidusing the model at conditions where it is not suitable, we (1) follow the work of Vieira andBrook (1984) and limit its application to the intermediate stage of sintering, before pores be-come isolated (ρr ∼ 0.97, φ ∼ 0.03; Wadsworth et al., 2017b), and (2) do not apply the model30500 700 900Temperature (°C)0.60.70.80.91Relative Density10 30 50 70log10  k (m2)-14-15-16-17Pressure (MPa)(a) (b)1 d10 d100 d1 y2.5 d1 d10 d100 d1 y(c)-18 -16 -14log10 k (m2)123Depth (km)1 d10 d100 d1 y2 y0.40.20.10.05Porosity-13Figure 3.3: Sintering maps and timescales for porosity and permeability loss. (a,b)Sintering maps showing the effects of temperature (P = 40 MPa) and pressure (T= 800◦C) on sintering time (contours). Dotted line marks where pores are isolated(ρr = 0.97; Wadsworth et al., 2017b). Experiments (circles) plot at 2.5 days. (c).Times to reduce porosity and permeability at a given depth (ρp = 2716 kg/m3; T =850◦C; particle size = 5 μm). Thick line shows the initial condition.far from our experimental P-T conditions. Nonetheless, this preliminary model (Equation 3.2)provides a means to explore the first order implications of solid-state sintering for volcanicsystems as a function of temperature, pressure, and time.3.6 Densification and permeability lossWe use Equation 3.2 to create preliminary sintering maps (e.g., Ashby, 1974) illus-trating the relative influences of pressure, temperature and time on ρr (Figure 3.3). The modelfaithfully captures the data, even in the new fields of view; the experiments plot on the contoursfor 2.5-days (our experiment time) to within experimental uncertainty (Figure 3.3). To predictthe concomitant loss of permeability as a result of sintering, we combine our time-dependentdensification model with Wadsworth et al.’s (2017b) model for permeability (k) evolution indensifying granular materials. Our sintering maps are contoured in time for, both, densifica-tion and permeability reduction, and track the sintering process from an unconsolidated state(ρi / ρp ∼ 0.60, φ ∼ 0.40) to a densified (ρr = 0.97, φ = 0.03) state (Figure 3.3). Increasingtemperature and pressure result in densification and permeability loss over shorter timescales.Notably the time to densify the material is short: after weeks at moderate conditions (850◦C,20 MPa), modelled values of ρr have increased to 0.85 and k has decreased by more than anorder of magnitude, respectively (Figure 3.3a).31We use this approach to model the P-T -t-dependent healing of crystalline granular ma-terial in an idealized volcanic conduit or edifice (Figure 3.3c). At ∼ 2 km depth (55 MPa),sintering reduces φ to ∼ 0.10 and k by 1.5 orders of magnitude in months. With increasingdepth (e.g., 3 km ∼ 75 MPa) the material heals more efficiently, and becomes effectively im-permeable (k < 10-16 m2), thereby creating a “closed system” (i.e., Collinson and Neuberg,2012) in less than a year.3.7 ImplicationsWelding causes the rapid densification of melt-rich (i.e., glassy) materials, and reducesthe porosity and permeability of volcaniclastic deposits in hours to days (e.g., Heap et al.,2015a; Quane et al., 2009; Vasseur et al., 2013; Wadsworth et al., 2017b). This process isaccelerated by the presence of H2O-rich fluids (Sparks et al., 1999). Welding, therefore, playsa primary role in the healing of tuffisite veins, pyroclastic deposits and obsidian flows (e.g.,Farquharson et al., 2017b; Kolzenburg and Russell, 2014). For example, welding of intra-conduit deposits is recognized as a means for reducing permeability and outgassing efficiency,thereby, promoting re-pressurization of the volcano and increasing the potential for explosiveactivity (Farquharson et al., 2017b; Kolzenburg and Russell, 2014; Quane et al., 2009).Solid-state sintering represents an alternative healing process that can cause repressur-ization of a volcanic conduit and cyclical explosive behavior. Our experiments demonstratethat the lifetime of permeable pathways in crystalline granular materials can be on the orderof weeks to months (Figure 3.3). These modelled timescales coincide with the observed in-tervals between explosive outgassing events at some dome-building volcanoes: for example,during the 1995-9 eruption of Soufrie`re Hills, small ash-venting explosions occurred every 5-6weeks (Norton et al., 2002). These events were attributed to the periodic resealing and re-pressurization of the conduit (Norton et al., 2002). Similarly, large outgassing events at MountSt. Helens in 2005 were interpreted as explosive releases of accumulating gas pressure (Roweet al., 2008). The material ejected was primarily fault gouge (Cashman et al., 2008; Roweet al., 2008). Some of the gouge, which is identical to our experimental material, appears tohave healed prior to fragmentation and ejection (see Figure 12 of Rowe et al. (2008)). This iscompelling evidence of solid-state sintering modulating eruptive behavior.Although timescales for permeability loss during welding are significantly shorter, ouranalysis demonstrates that even at shallow depths, low temperatures, and under anhydrousconditions, crystalline materials sinter rapidly within days, and will continue to densify formonths (Figure 3.2). These results highlight the extremely ephemeral nature of permeabilitynot only in the conduit, but also in fractured or crushed crystalline material held to moderate32temperatures and pressures, such as fractures within volcanic edifices (e.g., Heap et al., 2015b)and faults associated with calderas (e.g., Hurwitz and Lowenstern, 2014). We submit that themaximum longevity of permeable pathways in many of these settings is on the order of months.33Chapter 4Timescales of porosity and permeabilityloss by solid-state sintering4.1 IntroductionThe permeability of rocks – their capacity to transmit fluids – controls the movementof gases and liquids and distribution of pore pressure in Earth’s crust. Sustained high per-meabilities permit efficient fluid flow in the subsurface, and modulate pore pressures withinporous, fractured and comminuted rocks. Permeability is a transient physical property as, atelevated pressures and temperatures, void spaces in geologic materials are ephemeral. Depend-ing on the geologic setting, densification by porosity loss can occur by (1) mechanical wear andcompaction of rock and mineral clasts, (2) precipitation of pore-filling minerals from liquidsor gases (i.e., cementation, pressure solution), (3) coalescence of melt droplets (i.e., viscoussintering, welding), and (4) solid-state deformation of crystalline materials by diffusive masstransfer of atoms (i.e., diffusion creep), or involving migration of dislocations (i.e., dislocationcreep).In tectonic settings, densification suppresses crustal fluid flow, causing pore pressuresto rise and the effective normal stress acting on rocks to decrease. This can promote slip onexisting fault surfaces, or fracturing of intact rocks (e.g., Faulkner et al. (2010)) and referencestherein). Within volcanic edifices, densification and associated permeability loss can causegas overpressures to rise, priming the volcano for explosive eruption (e.g., Gonnermann andManga, 2007).Solid-state sintering is a diffusion-driven process that causes crystalline particles tocoalesce, resulting in the densification and lithification (increase in material competence) ofgranular materials (e.g., Rahaman, 2003). Solid-state sintering occurs in the absence of flu-34ids and melt, and has been shown to operate in ceramics and metals over a wide range ofpressure-temperature conditions (e.g., Ashby, 1974; Rahaman, 2003); sintering is acceleratedby increased effective pressure and temperature, and reduced particle grain size.Solid-state sintering and associated densification and lithification of granular bodies canbe expected to operate pervasively within the Earth’s crust wherever these crystalline materialsreside at elevated pressures and temperatures. However, there are few specific studies thatconstrain the critical conditions and timescales for solid-state sintering of geologic materials.A quantitative understanding of solid-state sintering processes is requisite to establishing thetimescales and extents of permeability loss in crustal and volcanic environments.Ryan et al. (2018b) demonstrated the feasibility of solid-state sintering occurring atvolcanic conditions. Here, we present new hot-pressing experiments on dry natural granularmaterial (glass-free dacitic fault gouge). The experiments were run under a range of condi-tions to establish how solid-state sintering progresses as a function of confining pressure (P),temperature (T ) and time (t); a subset of experiments involved small amounts of water (∼0.5 wt%). Solid-state sintering is evidenced by measured changes in sample density, materialcompetence, connected porosity and permeability. The experimental data show the efficiencyof solid-state sintering increases as t, P, or T increase. We use these data to develop a robustt-P-T -dependent densification model that predicts the evolution of the physical properties ofunconsolidated crystalline materials in Earth’s crust. Based on our experiments and modelling,we find that solid-state sintering causes significant porosity and permeability loss, and materialstrengthening, over a period of days to months in volcanic and some tectonic settings.4.2 MaterialsWe used volcanic fault gouge from the 2004-2008 eruption of Mount St. Helens as thestarting material for these experiments. In this eruption, dacitic lava degassed and crystallizedin the subsurface, solidifying at ∼ 1 km depth (e.g., Cashman et al., 2008). During ascent tothe surface, high shear stresses at the interface of the solidified lava and the wall rock causedthe lava to fracture and undergo cataclasis, generating fault gouge and forming a cylindrical,conduit-wall parallel shear zone (e.g., Kennedy et al., 2009). The shear zones, which facilitatedthe ascent of the solidified lava, were later extruded encasing the lava. Studies of the shear zonein situ show that it comprises variably densified cataclasites and unconsolidated fault gouge(e.g., Cashman et al., 2008; Kendrick et al., 2012; Pallister et al., 2013; Ryan et al., 2018a).Products from this eruption, including shear zone materials, were collected by theUnited States Geological Survey (USGS). The composition, grain size, microstructure, fric-tional properties and componentry of the gouge and cataclasites have previously been reported35(e.g., Cashman et al., 2008; Kendrick et al., 2012; Pallister et al., 2013; Thornber et al., 2008).The cataclasites result from densification and lithification of the fault gouge that occurred inthe subsurface, and provided the first evidence for solid-state sintering occurring in volcanicenvironments (Ryan et al., 2018a).The gouge used in this study is a portion of USGS sample SH320-1, collected on July13, 2005 from the carapace of spine 5 (Thornber et al., 2008). The gouge was described uponsampling as “unconsolidated [. . . ] fine-grained pink rock powder”, with an estimated extru-sion date of July 1, 2005 (Thornber et al., 2008). Mineralogically, Mount St. Helens gouge, asreported by Cashman et al. (2008), Kendrick et al. (2012) and Pallister et al. (2013) and con-firmed here by Rietveld refinement of X-ray diffraction (XRD) spectra (Table C.1), comprisesplagioclase, alkali feldspar, SiO2 polymorphs, FeMg silicates and FeTi oxides. Notably there isno glass present – the groundmass of the dacite is “an extremely fine-grained mosaic of micro-lites” (Pallister et al., 2013), including a cotectic assemblage of SiO2 polymorphs and Na- andK-rich feldspars, interpreted as evidence of late-stage precipitation of vapor phases (Pallisteret al., 2013). There is no significant or systematic change in the mineral contents as a result ofhot pressing (Table C.1; Ryan et al., 2018b). The temperature at which the natural Mount St.Helens dacite solidified in the subsurface is estimated to be between 840-960◦C based on Fe-Tioxide geothermometry (Kendrick et al., 2012; Pallister et al., 2008). The solidus of anhydrousdacite is higher: Holtz et al. (2001) show a dry solidus of ∼ 975◦C for synthetic dacitic melts.Though the gouge used in this study has a volcanic origin, it lacks glass and containsmineral phases that are abundant throughout the upper crust, including in intrusive igneous,sedimentary and metamorphic rocks (i.e., > 75 wt.% plagioclase and alkali feldspars, SiO2polymorphs; Table C.1)4.3 Methods4.3.1 Sample preparationWe sieved the gouge (< 125 μm diameter) and measured the particle size distribu-tion using a Malvern Mastersizer 2000 laser particle size analyzer at the University of BritishColumbia (Canada) (Ryan et al., 2018b). The greatest volume contribution is from clasts >30 μm in diameter. However, on a number basis, these clasts are rare; most clasts are <10 μmin diameter. We provide particle size distribution curves (volume and number percent) in thesupplementary material (Figure C.1).364.3.2 Hot-pressing experiments (HIP)Our hot-pressing experiments were conducted at the Department of Materials Scienceand Engineering at the University of Sheffield (UK), using an AIP-630H hot isostatic press(HIP). We ran four experiments in total. Two samples were hot pressed at 900◦C under a 70MPa confining pressure for 12 and 30 hours, respectively, and two samples were hot pressedat 800◦C under the same confining pressure and for the same experimental times (Table 4.1).These temperatures are both below the estimated solidus temperature of ∼ 975◦(Holtz et al.,2001).Aliquots of gouge (45-48 g each) were compressed under ambient conditions (25◦C, inair, atmospheric pressure) into steel canisters (∼ 3.5 cm diameter × 3.8 cm length; steel thick-ness: 1.9 mm) using a hydraulic press (1.8 kPa applied stress). The average initial density wasestimated from the calculated interior volume of the canisters, and measured gouge masses(Table 4.1). Canisters were heated under a vacuum (∼ 5 Pa), stored at 180◦C for 24 hours,and sealed. During experiments, single canisters were simultaneously heated (10◦C/min) andpressurized with argon gas (0.78-0.88 MPa/min) to the prescribed conditions (Table 4.1). Can-isters remained at the applied pressure and temperature for 12 or 30 hours before simultaneouscooling (10◦C/min) and venting (0.78-0.88 MPa/min) to ambient conditions.In a previous test of the feasibility of solid-state sintering operating at volcanic condi-tions, we used the same method and starting material to hot press four samples over greatertemperature and confining pressure ranges, but for a single dwell time (60 h) (Ryan et al.,2018b) (Table 4.1). In that study, we saw no evidence for melting during hot pressing (Ryanet al., 2018b). We compile the new results and those from Ryan et al. (2018b), and use the in-ternally consistent dataset to develop a t-P-T -dependent model of densification by solid-statesintering (Section 4.5.1).4.3.3 Hot-pressing experiments (Paterson)We performed additional hot-pressing experiments at the Rock and Mineral PhysicsLaboratory at the University of Minnesota (USA), using a Paterson gas-medium triaxial defor-mation apparatus (for apparatus details see Paterson and Olgaard (2000)). These experimentswere undertaken to test the model developed from the HIP data, to run shorter (4-12 h) experi-ments, and to test the effect of methodological differences on solid-state sintering processes.Aliquots of gouge (4-5 g each) were loaded into cylindrical copper canisters (∼ 1.4 cmdiameter × 2.2 cm length; copper thickness: 0.50 mm) and compressed by hand using a die toachieve approximately the same packing. The average initial density was estimated from themeasured mass and volume of gouge within the canisters (Table 4.1). Canisters were closed37Table 4.1: Experimental conditions (pressure, temperature, time (t), H2O content), and physical properties of experimental prod-ucts, including bulk density (ρb), relative density (ρr), total (φt) and connected porosity (φc), and measured permeability (k).Also a measure of the material competence, listed as the Mohs hardness of the pick that scratches the hot pressed sample. Allsamples were welded/sealed shut unless noted in the far column (“vented”).Sample t (h) H2O (wt%) ρb (kg/m3) a uncert. ρr b uncert. φt c φc d k (m2) Hardness900 ◦C, 70 MPaHIP1a 60 2332 5 0.859 0.002 0.141 0.136 1.02 × 10-15 6HIP1a e 2350 30 0.864 0.011 0.136 - - -HIP1b 60 2341 6 0.862 0.002 0.138 0.133 9.88 × 10-16 6HIP5a 30 2306 13 0.848 0.005 0.152 0.153 1.57 × 10-15 6HIP5b 30 2291 11 0.843 0.004 0.157 0.138 1.62 × 10-15 5HIP5c 30 2274 6 0.836 0.002 0.164 0.167 1.66 × 10-15 5HIP6a 12 2236 33 0.822 0.012 0.178 0.195 2.20 × 10-15 4HIP6b 12 2202 101 0.810 0.037 0.190 0.203 2.20 × 10-15 5HIP6c 12 2256 74 0.830 0.027 0.170 0.177 2.17 × 10-15 5800 ◦C, 70 MPaHIP2a 60 2202 2 0.811 0.001 0.189 0.186 3.95 × 10-15 4HIP2a e 2220 20 0.815 0.007 0.185 - - -HIP2b 60 2207 3 0.813 0.001 0.187 0.184 3.48 × 10-15 4HIP7a 30 2163 11 0.796 0.004 0.204 0.204 4.01 × 10-15 5HIP7b 30 2145 19 0.789 0.007 0.211 - - -HIP7c 30 2154 16 0.792 0.006 0.208 0.207 4.83 × 10-15 4HIP7d 30 2158 17 0.794 0.006 0.206 0.206 4.33 × 10-15 4HIP8a 12 2086 22 0.767 0.008 0.233 0.233 5.37 × 10-15 4HIP8b 12 2126 35 0.782 0.013 0.218 0.218 5.86 × 10-15 4HIP8c 12 2030 29 0.747 0.011 0.253 0.253 7.32 × 10-15 3HIP8d 12 2088 50 0.768 0.019 0.232 - - -UMN2030SD f 12 2144 19 0.789 0.007 0.211 0.196 - 4UMN2034WW e 12 0.5 2100 40 0.774 0.014 0.226 - - 338Sample t (h) H2O (wt%) ρb (kg/m3) a uncert. ρr b uncert. φt c φc d k (m2) HardnessUMN2034V e 12 2130 30 0.782 0.010 0.218 - - 2 ventedUMN2036WW e 8 0.5 2160 10 0.795 0.005 0.205 - - 3UMNtest 8 2188 4 0.805 0.002 0.195 0.173 3.39 × 10-15 2 ventedUMN2037WW e 4 0.5 2120 20 0.779 0.008 0.221 - - 2UMN2031V 4 2084 13 0.766 0.005 0.234 0.225 4.99 × 10-15 2 vented800 ◦C, 40 MPaHIP3a 60 2073 2 0.763 0.001 0.237 0.234 9.12 × 10-15 3HIP3b 60 2062 2 0.759 0.001 0.241 0.240 9.67 × 10-15 3UMN2038WW e 12 0.5 2100 30 0.772 0.012 0.228 - - 3800 ◦C, 20 MPaUMN2039WW e 12 0.5 1970 20 0.725 0.007 0.275 - - 2700 ◦C, 40 MPaHIP4a 60 1923 6 0.708 0.002 0.292 0.291 1.87 × 10-14 -HIP4b 60 1901 6 0.700 0.002 0.300 0.299 1.66 × 10-14 2UMN2040WW e 12 0.5 1940 90 0.714 0.033 0.286 - - 2Note: HIP1-4 previously reported in Ryan et al. (2018b).a ρb = m / (Vb) where m is the mass and Vb is the bulk volume measured by digital calipers or by buoyancy technique. Estimated initial bulk densities of gouge are1602 ± 78 kg/m3 for HIP experiments and 1526 ± 31 kg/m3 for Paterson experiments.b ρr = ρb / ρp, where ρp is powder (true) density (2718 ± 2 kg/m3) Estimated initial relative densities (ρi) of powders are 0.589 ± 0.029 and 0.561 ± 0.011 for HIPand Paterson experiments, respectively.c φ = 1 – ρr. Isolated porosities are < 0.02. Initial porosities of powders are 0.41 ± 0.02 and 0.44 ± 0.01 for HIP and Paterson experiments, respectively. 1σstandard deviation on φt is 0.01.d 1σ standard deviation on φc is 0.01.e Vb measured by buoyancy technique.f Irregular surface geometry precluded measurement of k.39in three ways: (1) copper lids of the canister were clamped on, or welded to seal the canister,(2) a permeable alumina spacer was used instead of a copper lid to allow pore fluids (air) tovent from the canister during hot pressing, and (3) a drop of deionized water (∼ 0.025 g; ∼ 0.5wt%) was added to the gouge and then a copper lid was welded to seal the canister. These threeassemblies allowed us to replicate the HIP conditions, and to determine the effects of trappedgases and small amounts of H2O on solid-state sintering efficiency.Individual canisters were placed between ceramic spacers within steel tubing (thick-ness: 0.25 mm), then placed vertically within the Paterson apparatus (Figure C.2). For sealedcanisters, a solid alumina spacer was placed above the canister lid (Figure C.2). For vented can-isters, this spacer was omitted so the porous spacer communicates with the atmosphere (FigureC.2). An R-type thermocouple threaded through the upper ceramic spacers monitored the tem-perature (Figure C.2). Canisters were pressurized with argon gas to the prescribed pressure andthen heated at ∼ 50◦C/min to the prescribed temperature (Table 4.1). The confining pressurewas manually vented during heating to maintain the set pressure. Pressurization and heatingtook ∼ 30 min. During hot pressing, no axial or shear stresses were applied, and canistersremained at elevated pressures and temperatures for 4-12 hours (Table 4.1) before the furnacewas turned off, initiating cooling and attendant confining pressure reduction. After ∼ 15 min,when the sample was at ∼ 100◦C, the remaining confining pressure was manually vented toambient room conditions within <10 min. Following cooling, we checked for H2O loss duringwater-added experiments by looking for water droplets in the thermocouple port – none wereobserved.4.3.4 Physical propertiesMost experimental products were cored to produce right cylinders (1.0 cm diameter× 0.5-1.8 cm length). Some Paterson canisters did not contract isotropically (Figure C.5),precluding regular core geometries (i.e., right cylinders) for some samples. Following coringand trimming, samples were dried for 24 h at 100◦C, and then their masses were measured (m,g).We used a set of Mineralab hardness picks to determine their resistances to beingscratched by conical points of different hardness (Table 4.1).Bulk volume (Vb, cm3; solid material + connected pores + isolated pores) was measuredby either: (intact cylinders; n = 24) measuring core length and diameter with digital calipers,or (irregular geometry; n = 8) using a buoyancy technique – the mass of cores saturated withwater was measured in air and while immersed in water (Ulusay and Hudson, 2007). Vb is themass difference divided by the density of water. We measured two intact cylinders using bothtechniques and found Vb values agree within 0.01 cm3.40Bulk densities (ρb, kg/m3) were calculated using Vb and m. The relative density (ρr,fractional) was calculated by dividing ρb by the powder (true) density (ρp = 2716 ± 2 kg/m3;Ryan et al., 2018b). We also calculated the total porosity (φt , fractional), as φt = 1 – ρr (Table4.1). For these calculations, measurement uncertainties for Vb (measured by both caliper mea-surements and buoyancy tests) and m were propagated to determine the uncertainties in ρb, ρrand φt (Table 4.1).The skeletal volumes of intact cylinders were measured using a Micromeritics AccuPycII 1340 helium pycnometer. The connected porosity (φc) of the cores was calculated from thesemeasurements (Table 4.1).The permeabilities (k, m2) of intact cylinders were measured using a benchtop gas (ni-trogen) permeameter at the Institut de Physique du Globe de Strasbourg (France) (see Heapand Kennedy (2016) for a schematic diagram). Samples were dried in a vacuum oven at 40◦Cfor at least 48 hours before measurements and, when at ambient temperature, placed withinthe permeameter and kept under a 1 MPa confining pressure for 1 h to ensure microstruc-tural equilibration. Measurements of permeability were performed using the steady-state flowmethod. Volumetric flow rates were measured (using a flowmeter) for several pore pressuredifferentials (measured using a pore pressure transducer). We calculated permeability fromthese data while checking whether the data required auxiliary corrections (i.e., Klinkenbergand Forchheimer corrections). In all cases, the Forchheimer correction was required and thetrue permeability was taken as the inverse of the y-intercept of the best-fit linear regressionin the plot of 1/kgas raw against volumetric flow rate, where kgas raw is the uncorrected (raw)gas permeability determined for each of the pore pressure differentials implemented during theexperiment.4.3.5 Microstructure imaging and analysisExtra cores and materials trimmed during core preparation were impregnated withepoxy and prepared as polished thin sections. Backscatter electron (BSE) images were col-lected using a Philips XL30 scanning electron microscope (SEM) and a FEI Helios NanoLab650 field emission scanning electron microscope (FE-SEM). During SEM imaging, energy-dispersive X-ray spectra (EDS) were collected using a Bruker Quantax 200 energy-dispersionX-ray microanalysis system. Based on collected spectra, we identify and label minerals inFigure 4.4. We used the same microanalysis system to qualitatively map the distribution ofelements in experimental products. See Appendix C.3 for details and additional maps.41t (h)0.50.60.70.80.9ρ r0 20 40 600.50.70.9900°C, 70 MPa900ºC, 70 MPa800ºC, 70 MPa800ºC, 40 MPa800ºC, 20 MPa700ºC, 40 MPadry0.5 wt% H2O(a)(c)ρ r0.50.70.9800°C, 70 MPa (b)ρ rt (h)0 30 60Figure 4.1: Relative density (ρr = ρb / ρp) versus experimental time for hot-pressedsamples. (a) All experimental data; symbols indicate apparatus (circle: HIP; trian-gle: Paterson), colors indicate experimental conditions (T , P, H2O content). Prop-agated uncertainties are less than symbol size unless shown otherwise. Over shorthot-pressing times (t), relative density (ρr) increases sharply, then plateaus past 12h. At constant experiment time, ρr increases with increasing temperature and con-fining pressure. (b) Data from experiments at 800◦C, 70 MPa. At 12 h, HIP andPaterson data agree to within uncertainty. (c) Data from HIP experiments performedat 900◦C, 70 MPa for variable times, and showing a sharp increase in relative den-sity at short times before plateauing.4.4 Results4.4.1 CompetenceOur experiments produced variably lithified composites that show an increase in mate-rial competence with increasing t-P-T (Table 4.1). For example, a sample hot pressed at 700◦Cand 40 MPa for 12 hours is fragile and flakes with light handling, and is scratched by a plasticpick (hardness of 2 on the Mohs’ scale). In contrast, materials hot pressed at 800◦C and 70MPa withstand handling better and, depending on the hot-pressing time, are scratched by pickswith hardnesses of 2-5. Materials hot pressed at 900◦C and 70 MPa are the most competent,are not fragile or damaged by handling, and are scratched by picks with hardnesses of 4-6.424.4.2 Relative densityMeasured ρr of HIP products are 0.70 to 0.86, 0.11-0.27 greater than ρi (Table 4.1).Relative densities of HIP products rise as t-P-T increase, achieving a maximum at 900◦C, 70MPa and 60 hours and minimum at 700◦C, 40 MPa and 60 hours (Figure 4.1). At a single P-Tcondition (e.g., HIP1, HIP5, HIP6), ρr increases rapidly over short times (0.23 over 12 h) andthen more slowly following∼ 12 hours (0.05 over 48 h) (Figure 4.1c; Table 4.1). Materials hotpressed for the same experiment time show final ρr values are reduced by 0.05-0.06 as a resultof either a 100◦C decrease in T or a 30 MPa decrease in P (Table 4.1).Products of hot pressing in the Paterson apparatus provide data below 12 hours at 800◦Cand 70 MPa, the same conditions used for some HIP samples (Figure 4.1b). After hot pressingfor just 4 hours, ρr is 0.77, 0.20 greater than ρi. Additional sintering time causes a smallincrease in ρr (<0.04). Paterson products hot pressed using a different method (i.e., ventedvs. sealed canisters, dry vs. H2O-undersaturated) show the same trends in ρr-t space (Figure4.1) and have ρr values within uncertainty (Figure C.4a). Therefore, sintering efficiency in ourexperiments is not influenced by the open or closed nature of the canister, nor by the additionof small amounts of H2O. See Appendix C.4 for additional details.At the same experimental t-P-T conditions, ρr for HIP products are 0.01-0.04 less thanfor Paterson products (Figure 4.1b). This small difference likely reflects the responses of thecanisters to pressurization rather than differences in sintering mechanism or efficiency – thePaterson canisters are thin-walled (0.50 mm) copper canisters within thin-walled (∼ 0.25 mm)steel tubing (Figure C.2). Following hot pressing, canisters show longitudinal wrinkles andbuckling, and a bowed shape (Figure C.5). In contrast, thick-walled (∼ 2 mm) steel HIP can-isters are only slightly bowed following hot pressing (Figure C.5). The different shapes of themetal canisters after hot pressing suggest they experience different amounts of deformation,likely during P application. As such, gouge in the Paterson experiences (non-sintering) den-sification during pressurization, resulting in an (unknown) effective initial bulk density that isgreater than ρi (Table 4.1), and likely greater than that for the HIP samples (Figure 4.1b).4.4.3 Porosity and permeabilityAcross the Paterson and HIP datasets, total porosity (φt = 1 – ρr) varies from 0.14 to0.30 and decreases as t-P-T increase (Table 4.1). Measured φc varies from 0.13 to 0.30 andalso decreases as t-P-T increase. φc and φt differ by <0.02. This difference can be ascribed tothe likely presence of some isolated pores, but is also of the same magnitude as the propagateduncertainties in φc and φt (Table 4.1).430 0.1 0.2 0.3 0.4Connected Porosity10-1610-1510-1410-13Permeability (m2 )initial porosityFigure 4.2: Porosity and permeability. Measured values of connected porosity and per-meability for hot-pressed samples (Table 4.1). Symbols indicate apparatus (circle:HIP; triangle: Paterson). Measurement uncertainties are less than symbol size. Per-meability decreases with connected porosity, varying by 1.5 orders of magnitude.Model permeability Wadsworth et al. (2016b) describes the data well. Further de-tails about the permeability model are given in Appendix C.5.Measured k varies from 9.88× 10-16 to 1.87× 10-14 m2 (Table 4.1). Across the dataset,k decreases with decreasing φc (Figure 4.2), and decreases as t-P-T increase. Samples hotpressed in the Paterson apparatus have measured permeabilities that agree within 0.25 logunits of HIP products with comparable φc (Figure 4.2). In log10(k)-φc space, the data areclosely spaced and appear near linear.In Figure 4.2 we also plot the Wadsworth et al. (2016b) permeability model. This gen-eral model predicts the porosity-dependent permeability of densifying granular materials thatare monodisperse and comprise spherical or near equant particles. In these granular materi-als the model can predict the porosity-permeability relationship irrespective of the densifyingmechanism or material (Wadsworth et al., 2016b). It is based on the Kozeny-Carman relation-ship between the specific surface area of a densifying particle pack (s) and permeability (k ∝φ3/s2). Using a mean particle size as an input, along with an assumption about how particlesinteract during densification and the percolation threshold porosity (φ ′), the model predicts sand k for values of φc. Further details about the assumptions and constitutive equations for thepermeability model are given in Appendix C.5 and in Wadsworth et al. (2016b).4440 μmUMN_2030SD HIP840 μm (b)(a)Figure 4.3: BSE images of experimental products hot pressed at 800◦C, 70 MPa and12 h. Samples hot pressed in (a) Paterson and (b) HIP. Distributions of large andsmall clasts are the same. Both have abundant inter-granular void space. Otherfeatures are consistent, including: (1) sub-rounded clasts (yellow outlines) showevidence of original solid-state sintering within Mount St. Helens conduit (Ryanet al., 2018a); (2) regions where coalescence has occurred between small clastsas a result of hot pressing (orange arrows), expressed as thin necks of crystallinematerial joining discrete clasts. In (a), clast outlined in white shows the primarygroundmass of the Mount St. Helens dacite – radiating, acicular crystals cross-cutthe clast. Crystals are cotectic assemblage of SiO2 polymorphs and Na- and K-richfeldspars.The particle size distribution of the gouge is given in Appendix C.1. Here we assumeφc ∼ φt in using the model. This is valid for φt > 0.08, above φ ′ (Wadsworth et al. 2017b).The permeability model has a steep positive slope at low φc that shallows as porosity increasesand reproduces our measured values of φc and k (Figure 4.2).4.4.4 MicrostructureExperimental products hot pressed at the same t-P-T conditions (800◦C, 70 MPa, 12 h)are texturally identical, despite the different experimental method used (e.g., HIP vs. Paterson)(Figure 4.3). BSE images of both experimental products show the distribution of few large (∼50-150 μm in diameter) clasts, numerous small clasts (<25 μm in diameter) and abundant inter-granular void space. Large clasts are single-mineral grains, rounded clasts showing texturesinherited by past coalescence (i.e., solid-state sintering) events or, rarely, rounded clasts ofdacite. Smaller clasts are frequently blocky, single-mineral grains. There is no evidence ofparticles melting.Samples shown in Figure 4.3 result from short hot-pressing times (12 h). Nevertheless,some small clasts have coalesced – thin necks of crystalline material connect adjacent clasts.45Larger patches of coalesced clasts are localized along the edge of large clasts (orange arrows;Figure 4.3b) while smaller patches are apparent in the space between large clasts (orange ar-rows; Figure 4.3a).Microstructures preserved in samples reflect hot-pressing conditions, including P-T(Ryan et al., 2018b). In Figure 4.4 we show the change with t: low magnification BSE images(Figure 4.4a,c) show large clasts are homogenously distributed and have no preferred orienta-tion. Medium and high magnification images show increased proportions of coalesced clasts ashot-pressing time increases from 4 to 60 hours (Figure 4.4b vs. Figure 4.4d). As the abundanceof coalesced clasts increases, the total volume of void space decreases. Where many clasts havecoalesced, small voids are isolated from one another by necks of material extending betweenclasts (Figure 4.4e-f).The textures of Figures 4.3 and 4.4 demonstrate densification (loss of void space) andlithification (an increase in material competence as crystalline necks of material form betweenclasts) as a result of solid-state sintering. Synthesizing these observations with those of Ryanet al. (2018b), with increasing t-P-T the proportion of sintered clasts increases and the volumeof void space decreases.EDS data show single-mineral clasts, both large and small, are often plagioclase, am-phibole or orthopyroxene (Figure 4.4). SiO2 polymorphs can be anhedral cores of small clastsor within sintered patches. There are no large clasts of alkali feldspar, despite it making up15-20 wt% of the gouge (Table C.1). This is consistent with the observations by Pallister et al.(2013), who note Na- and K-rich feldspars are restricted to the fine-grained dacite groundmassas a result of late-stage crystallization of the groundmass and/or precipitation of vapor phases.Maps of the distribution of elements in samples hot pressed for short (4 h) and long (60h) times show similar patterns: Ca is sequestered in larger plagioclase clasts (Figure 4.5e,f),while Al and Na are contained in both large and small particles (Figure 4.2g-j). The distribu-tions of Al and Na are nearly identical and indicate the distribution of feldspars. In contrast,K, an element we expect to be restricted to alkali feldspar, has a patchy distribution and isconcentrated within regions of sintered crystalline clasts (Figure 4.5k,l). A comparison of thedistributions of Al and K shows K to appear decoupled from Al and, by proxy, Na (Figure4.5m,n).4.5 Model development and analysisBelow, we use the HIP dataset to constrain a semi-empirical model for predicting den-sification by solid-state sintering as functions of t-P-T . We use data from Paterson products totest and interrogate the model and to elucidate details of the sintering process.46200 μm200 μm(b)(d)20 μmplpl opxsi20 μmplplsi4 hr60 hrLow magnification Medium magnification10 μmHigh magnification2 μmφt = 0.19φt = 0.2360 hr HIP2HIP2UMN_2031V(a)(c)(e)(d)(f)(b)Figure 4.4: BSE images of experimental products hot pressed at 800◦C and 70 MPafor variable time. (a) Sample hot pressed for 4 h in Paterson. Total porosity(φt) given in lower left corner. Highlighted box is location of higher magnifica-tion image. (b) Coalescence (necking) has occurred between small clasts of silicapolymorph (si; dark grey) and feldspar (pl; light grey). Abundant void spaces havehigh connectivity and are irregular in shape. (c) Sample hot pressed for 60 h inHIP showing an increased amount of sintered material and a greater reduction intotal void space. Highlighted box is location of higher magnification image. (d)Sintered patches extending between large plagioclase clasts. Void spaces in thesintered patch are irregularly shaped and isolated from one another. Most clastsare connected by necks of crystalline material. (e,f) High magnification images ofnecks of crystalline material within patches of sintered material. FE-SEM (5kVaccelerating voltage) image showing clasts less than 5 μm in size are joined by thin(<1 μm) necks of material as well as possible proto-necks (cloudy regions fillingthe small void space between clasts).47Figure 4.5: (following page) Element distribution maps. Left column of BSE images(a) are for 4 h at 800 ◦C and 70 MPa (sample: UMN 2031V; apparatus: Paterson;Figure 4.4b); Right column (b) is for a sample hot pressed for 60 h at 800 ◦C and 70MPa (sample: HIP2; apparatus: HIP; Figure 4.4f). (c,d). The regions undergoingsintering are shown as dark, un-masked areas. Element maps show distributions ofcalcium (e,f; blue), aluminum (g,h; red), sodium (i,j; yellow) and potassium (k,l;green), as well as, a map for combined aluminum and potassium (m,n). Ca, Na andAl are concentrated within plagioclase clasts. K appears more frequently in sinteredmaterial, in the space between particles clasts where, in the BSE image, crystallinenecks of material are discernible.4820 μm4 hr 60 hrBSECaAlNaKK + Al20 μmSintered(a)(c)(e)(g)(d)(f)(h)(b)(i)(k)(m)(j)(l)(n)494.5.1 Densification modelOur predictive model is developed from the empirical semilogarithmic relationship be-tween ρr and t (Coble, 1961; Vieira and Brook, 1984):ρr = ρo+K ln(tto), (4.1)where ρo is the relative density at to. The main attribute of this functional form is its capacityto describe experimental sintering data well and independently of the sintering material ormechanism, or whether grain growth occurs (Rahaman, 2003; Vieira and Brook, 1984).Densification rates (dρr / dt) are strongly dependent on the temperature and pressureapplied during hot pressing (e.g., Ashby, 1974; Rahaman, 2003; Rybacki and Dresen, 2004;Vieira and Brook, 1984). These dependences transcend differences in densification mecha-nisms, including: lattice diffusion, grain boundary diffusion, and plastic deformation by dislo-cation motion. General equations for the relationships between densification rates and P and Tare:dρrdt∝ Pnc (4.2)dρrdt∝ exp(bT)(4.3)respectively (e.g., Rahaman, 2003; Rybacki and Dresen, 2004). Pressure dependence containsa stress exponent (n) that changes based on the densification mechanism. Its dimensions alsochange with its value. Temperature dependence includes the diffusion coefficient (D) of therate-controlling species, which is expected to be Arrhenian in T and includes Ea, the activationenergy, and R, the universal gas constant.In Ryan et al. (2018b) we modified Equation 4.1 by including the relationships ex-pressed in Equations 4.3 and 4.4 in parallel to replace the empirical parameter K. We took ρoto represent the initial density (ρi, kg/m3) ratioed to the powder density (ρp, kg/m3). For t ≥ 1s, densification by solid-state sintering is described by:ρr = ρo+aexp(bT)Pcc ln(t), (4.4)where P is applied (confining) pressure (MPa), T is temperature (K), and t is time (s). Theempirical fit parameters (a, b, c) can be determined globally for any particular P-T condition.Here we assume a common but unidentified initial density for the HIP experiments (Ta-ble 4.1) and we estimate the coefficients (ρo, a, b, and c) of the non-linear function of Equation4.3 using an unweighted least squares approach. Through our fitting procedure, we find that500.50.60.70.80.9ρ r1000700 800 9000.70.80.91T (°C)ρ r60020 40 60 800.70.80.91Pc (MPa)ρ r0.7 0.8 0.90.70.80.9measured ρrmodelled ρr20 40 600t (h)ρo = 0.588a = 0.045b = -3049c = 0.442(a)(b)(c)900°C, 70 MPa800°C, 70 MPa800°C, 40 MPa700°C, 40 MPa102.50.5 603652.5102.50.5 603652.50.5900°C800°C2.5 d0.5 d70 MPa40 MPa2.5 d0.5 dFigure 4.6: Densification model and sintering maps. (a) Measured relative densities(ρr) of HIP products against time (as in Figure 4.1). Curves are Eq. 4.3, using theparameter values in the lower left, and experimental temperature (T ) and applied(confining) pressure (P) conditions (labels). Data plot along curves at both short (12h) and long (60 h) experiment times. (inset) Modelled and measured ρr plot alonga 1:1 line, indicating the model reproduces experimental data to within uncertainty.(b,c) Sintering maps show the effects of temperature (P = 70 MPa (black) or 40MPa (grey)) and confining pressure (T 900◦C (black) or 800◦C (grey)) and time(contours, in days) on ρr. Measured ρr for products of hot pressing for 0.5 and 2.5d are shown as filled rectangles and circles, respectively. Each dataset plots alongthe contour corresponding to the hot-pressing time. With increasing T , ρr increasesnear-linearly. Model ρr curves show a sharp increase with P at P<10 MPa. Curvesshallow with increasing P. As time increases both the temperature and pressuredependence increase (steeper slopes at long times).ρo=0.588 ± 0.004, a=0.045 ± 0.018, b=–3049 ± 231, and c=0.442 ± 0.006. The optimalvalue of ρo captures the estimated values of initial bulk density to within the measurementuncertainty (Table 4.1).The model reproduces the data well (Figure 4.6) – modelled and measured ρr valuessit, within uncertainty, along a 1:1 line (inset). In ρr-t space (Figure 4.6a) measured values ofρr plot along T -P dependent model curves. At short times (<1 h), model curves have steeppositive slopes. With increasing time (> 2 h) curves shallow. The curves have much shallowerpositive slopes > 10 hours. Following the trend of the data, model curves shift up by nearlyequivalent amounts with a 100◦C increase in T or 30 MPa increase in P.51Figures 4.6b,c are “sintering maps” (e.g., Ashby, 1974) that show the influences ofT , P, and t on ρr. HIP products hot pressed for 0.5 and 2.5 days plot along the correspondingmodelled t-contours. The slopes of ρr-T curves are nearly linear with increasing T and becomeonly slightly steeper with increasing t (Figure 4.6b). The slopes of ρr-P curves are relativelysteep at low P (< 30 MPa) and shallow with increasing P (Figure 4.6c). Slopes become onlyslightly steeper with increasing t (Figure 4.6c).4.5.2 Testing the modelWe used HIP data to calibrate Equation 4.3 and to fit for the coefficients a, b, c. Wenow use the relative densities of Paterson products to confirm whether the t-P-T -dependentmodel can predict the densification of gouge by solid-state sintering in a different environment(in this case, another apparatus) and over a greater range of t-P-T conditions. Figure 4.7 showsthe model results where a, b, c are as reported above, but ρo has been set to 0.61 (equivalentto ρi = 1660 kg/m3) as an estimate of the effective initial density. Again, the modelled andmeasured ρo values fall along or not far from the 1:1 line (inset). Model curves capture mostdata, including at short times (Figure 4.7a). The increase in ρo has shifted curves up along they-axis but otherwise their shapes are preserved.In additional sintering maps (Figure 4.7b,c), the Paterson data lie close to or alongthe appropriate t-contours (4 h, 0.5 d). This application of the predictive densification modelto the Paterson data demonstrates that it describes densification by solid-state sintering underconditions that differ from the data used to calibrate the model (Figure 4.7a). This suggeststhat our model is applicable wherever solid-state sintering is confirmed texturally.The model is written with the assumption of isobaric and isothermal conditions butcan be modified to approximate densification progress as a result of time-dependent changes intemperature (cooling or heating) or pressure (ascent or burial). An example of this modificationand approximation is shown in Appendix D.4.5.3 Sintering mechanismOur fit parameter b is related to the activation energy of the diffusing cation(s) causingsolid-state sintering (b = –Ea/R; Equation 4.3). Previous studies have used Ea values to revealdetails of sintering processes and to identify rate-controlling species (e.g., Rahaman, 2003).Here, the activation energy derived from b is 25 kJ/mol. This value is significantly less thanestimates of Ea for lattice diffusion of Na, Ca, K, Al and Si in feldspar, which can be 170-300kJ/mol depending on the experimental conditions and mineral composition (Cherniak (2010)and references therein).524 h4 h800°C, 70 MPa800°C, 40 MPa700°C, 40 MPa102.50.5 60365102.50.5 60365 800°C0.5 d4 h 40 MPa0.5 d4 h0.50.60.70.80.9ρ r 1000700 800 9000.70.80.91T (°C)ρ r60020 40 60 800.70.80.91Pc (MPa)ρ r0.7 0.8 0.90.70.8measured ρrmodelled ρr5 10 150t (h)ρo = 0.61a = 0.045b = -3049c = 0.442(a)(b)(c)Figure 4.7: Test of the densification model. (a) Measured relative densities (ρr) of Pa-terson products against time (as in Figure 4.1). As in Figure 4.6, curves are den-sification model, using given model parameters and experimental conditions. Dataat 800◦C, 70 MPa (triangles) plot along the corresponding curve even at very shorttimes (4 h). (inset) Modeled and measured ρr lie close to the 1:1 line – the modelreproduces most experimental data to within uncertainty. (b,c) Sintering maps showthe effects of temperature (P = 70 MPa) and pressure (T = 800◦C) on ρr and mod-eled sintering time (contours, in days unless labelled otherwise). Measured ρr forproducts of hot pressing for 4 h and 0.5 d are shown as filled rectangles and trian-gles, respectively. At short times Paterson experimental data plot on correspondingtime contours. As in (a), at longer times, data scatter on either side of correspond-ing model curves. The densification model captures the Paterson experimental data,despite the model having been fit using data from samples produced in a differentapparatus (HIP), using different canister geometry and materials and with a differ-ent methodology.53We use SEM-based textural analyses to examine the solid-state sintering process fur-ther. Element distribution maps of sintered materials show K, which is abundant in the pro-tolith (dacite) as a result of late-stage crystallization of alkali feldspars, has a unique spatialdistribution compared to other elements (Figure 4.5) – K is preferentially concentrated at clastinterfaces, and within the necks of crystalline material that join clasts. The concentration of Kwithin these necks formed during hot pressing suggests K plays a primary role in the sinteringprocess.Rates of intergranular/interphase cation diffusion in granular materials are not wellknown (Farver and Yund, 2005). Nonetheless, Farver and Yund (1995a,b) observed fast dif-fusion rates, and low Ea for K within feldspar and quartz aggregates hot pressed at dry andhydrothermal conditions. The fast diffusion rates and low Ea may be a consequence of theactivation of grain boundary diffusion rather than lattice diffusion. Studies that have measuredlattice diffusion in feldspar identify K as a cation that can diffuse at a faster rate and with alower Ea than Na, Ca, Al and Si (e.g., Cherniak, 2010). The same relationship is likely tobe true in the case of grain boundary diffusion. The distribution of K in element maps fromdensified, lithified hot-pressing products suggests that sintering of our experimental materialson short timescales (as little as 4 h) is the result of the fast diffusion of K along boundariesbetween adjacent clasts. On longer timescales we expect sintering to involve the diffusion ofadditional cations, either in parallel or series with K.In six experiments, we included 0.5 wt% H2O in the gouge (Table 4.1). Trace amountsof H2O have been shown to change deformation/sintering mechanisms, to reduce diffusivemass transfer Ea, and to increase the mobility of diffusing species (e.g., Kohlstedt, 2006).However, in our experiments there is evidently no change in microstructure (Figure 4.3, 4.4)or measured ρr (Figure 4.1, C.4c) as a result of the addition of H2O. Farver and Yund (1995a)observed a relatively small (∼ 5 fold) change in cation grain boundary diffusion rates at H2O-absent vs. H2O-undersaturated conditions in feldspar aggregates. Assuming that our gougebehaves as in other studies and H2O affects diffusive processes, the lack of evidence for H2Oinfluencing diffusion rates in our experiments reflects the small magnitude of change overthe short experimental timescales (4-12 h). Such a change in diffusion rate is apparently notcaptured using the microstructural analyses and physical property measurements employedhere.4.6 DiscussionIn tectonic and volcanic settings, unconsolidated granular materials are produced bybrittle deformation processes, including: shear-driven fracturing of intact rock or disruption of54existing fault zones (e.g., Faulkner et al., 2010; Sibson, 1986), gas-driven fragmentation (e.g.,Papale, 1999; Zhang, 1999), the formation of damage zones ahead of propagating veins anddikes (e.g., Rubin, 1995), and hydrostatic (e.g., Zhang et al., 1990) or shear-enhanced (e.g.,Wong et al., 1997) inelastic compaction and grain crushing in porous materials.The sustained presence of weak, porous granular materials provides a long-lived con-duit for fluids, minimizing the potential for fluid pressurization (e.g., Caine et al., 1996; Jaupartand Allegre, 1991). Deformation is often localized within granular materials, and moderatedby their frictional properties (e.g., Scholz, 1998). Long-lived bodies of granular material arelikely to be reworked, accommodating substantial strain (e.g., Faulkner et al., 2010).However, granular materials densify and become increasingly lithified, and their phys-ical properties and mechanical behavior change on timescales dictated by the operating densi-fication mechanism (e.g., Faulkner et al., 2010; Karner et al., 1997; Kolzenburg et al., 2012;Mitchell et al., 2016; Morrow et al., 2001; Russell and Quane, 2005; Rybacki and Dresen,2004; Scott and Driesner, 2018; Tenthorey and Cox, 2006; Vasseur et al., 2013). Over time,weak, permeable zones are eradicated and transformed into stronger, low-permeability regions.Below we model porosity and permeability loss as a result of solid-state sintering anddiscuss how solid-state sintering-driven densification and lithification affects other geologicprocesses.4.6.1 Timescales for permeability reductionWe combine our densification model (Equation 4.4) and the Wadsworth et al. (2016b)permeability model (Appendix C.5) to predict the transient permeability of a sintering mate-rial at a range of P-T conditions. The chosen conditions are applicable to high-temperaturegeologic settings, including volcanic conduit shear zones and breccias (e.g., Cashman et al.,2008; Watts et al., 2002), hydraulic fractures (i.e., tuffisites) in crystal-rich lavas and in edifices(e.g., Kolzenburg et al., 2012), breccias surrounding magmatic intrusions and cryptodomes(e.g., Burchardt et al., 2019; Saubin et al., 2019), and caldera-associated faults (e.g., Kim et al.,2019). Although this modelling does not extend to conditions at shallower depths and lowertemperatures, we anticipate solid-state sintering may occur at these conditions over longertimes.Figure 4.8 shows the reductions in total porosity and permeability from initial condi-tions (0.40 and 4.3 × 10-14 m2, respectively) after 10 days and 1 year of solid-state sintering,assuming isothermal and isobaric conditions. Because densification proceeds rapidly at shorttimes (Figure 4.6, 4.7), porosity has been reduced by more than half, to < 0.20, after just10 days at high P-T conditions (> 700◦C, > 20 MPa; Figure 4.8a). Modelled permeabilitiesare likewise reduced in these areas by 1-5 orders of magnitude (Figure 4.8b). After 1 year, a55Porosity500 700 900Temperature (°C)204060Pressure (MPa)-14-15-16< -18-16-15-140.100.200.30(c)< 0.050.100.200.30Permeability500 700 900Temperature (°C)204060Pressure (MPa)(d)1 year500 700 900Temperature (°C)204060Pressure (MPa)(a)10 days500 700 900Temperature (°C)204060Pressure (MPa)(b)depth increasesTMTECIFFigure 4.8: Porosity and permeability maps. (a) Modeled total porosity as a functionof confining pressure (15-75 MPa) and temperature (450-950◦C) after 10 d of sin-tering. Initial porosity is 0.40. Contours are 0.05 void fraction intervals. After 10 d,hot, deep regions have undergone significant densification, with modeled porosities<0.10. Near the surface at cooler conditions, densification is slower and porosity is0.30-0.35. Letters indicate (lithostatic) pressure-temperature domains that may rep-resent shear zones in a volcanic conduit (C), hydraulic fractures (tuffisites) withinmagma (TM) or in a volcanic edifice (TE), magmatic intrusions (I), and caldera-associated faults (F) (see text for relevant references) (b) Residual permeability at10 d calculated after Wadsworth et al. (2016b) from model porosity values (a).At 0.40 initial total porosity, initial permeability is 4.3 × 10-14 m2. Contours arehalf log units. The model relationship between permeability and porosity (Figure4.2) means in cool, shallow conditions, even limited densification by porosity lossresults in an order of magnitude decrease in permeability. At hotter, deeper con-ditions, permeability is greatly reduced, reaching a minimum of <10-18 m2. (c,d)Modeled porosity and permeability, respectively, after 1 year of solid-state sinter-ing. At cool, low pressure conditions, porosities and permeabilities are still rela-tively high, while at hotter, high pressure conditions, materials are well densifiedand permeabilities are low.56similar magnitude of porosity and permeability loss has occurred over a greater range of P-Tconditions (Figure 4.8c,d). Modelling longer sintering times would show significant porosityand permeability loss at even lower P-T conditions.The timescales for porosity and permeability loss can be reduced if the properties ofgranular material change: for example, greater initial packing increases the number of contactsbetween clasts and, by introducing more sites for diffusion and neck-formation, acceleratessolid-state sintering (Rahaman, 2003). Similarly, reduced particle size increases the efficiencyof sintering (Rahaman, 2003) and reduces k for a given φc (Wadsworth et al., 2016b). There-fore, densification and permeability loss by sintering will be greater in fine-grained deposits atgiven t-P-T conditions.Finally, geologic settings are dynamic and feature transient conditions (i.e., T , P, stressacting on particles, etc.). The rate and extent of sintering can be expected to change alongwith evolving P-T conditions. For example significant cooling or rapid exhumation will sup-press sintering efficiency, given the temperature and pressure dependences shown in Figures4.6b,c. An increase in lithostatic pressure, the addition of a differential stress, or heating willcause solid-state sintering to accelerate (Figure 4.6b,c). If temperatures rise above the solidus,melting may change the densification mechanism from solid-state to viscous sintering.4.6.2 Comparison to other densification mechanismsOur study demonstrates solid-state sintering drives rapid porosity and permeability lossat elevated P-T conditions common to volcanic environments and applicable to some crustalsettings. The time required for marked porosity and permeability loss at these conditions is onthe order of days to months (Figure 4.8). These densification timescales are short enough tocompete with or outpace other “active” geologic phenomena (e.g., fluid circulation in the crust,volcanic conduit processes, magma intrusion, deformation in fault and shear zones).Densification of granular material can be accelerated if fluids are present and alternatedensification mechanisms are activated. For example, hydrothermal experiments show poros-ity loss by pressure solution over several hours, faster than at dry conditions (i.e., by solid-statesintering) (e.g., Kanagawa et al., 2000; Lockner and Evans, 1995). Precipitation of mineralphases from intergranular liquids or vapors can also seal granular materials. However, the cor-responding densification timescales are difficult to constrain – they can exceed tens to hundredsof years (e.g., Morrow et al., 2001; Scott and Driesner, 2018), or be as short as hours to months(e.g., Horwell et al., 2013). Finally, if silicate melt is present, viscous sintering can eradicatevoid space within seconds to hours (e.g., Gardner et al., 2017, 2018; Russell and Quane, 2005;Vasseur et al., 2013).57The critical difference between solid-state sintering and these other densification pro-cesses is that solid-state sintering does not require restrictive environmental conditions to op-erate. It can operate without the sustained presence of fluids, whilst fluids are requisite forpressure solution and chemical precipitation. Viscous sintering can only occur where silicatemelt remains above or at its characteristic glass transition temperature (∼ 475-775◦C). In con-trast, solid-state sintering operates wherever comminuted rock is held at elevated pressure andtemperature (i.e., including < Tg) for times of hours to years – conditions that are easily satis-fied throughout Earth’s crust.4.6.3 Strength recovery and its consequences for cyclical outgassingMaterial competence increases as a result of solid-state sintering – our unconsolidatedmaterials are transformed into porous composites of variable hardness after only hours of sin-tering (Table 4.1). Studies of other processes show significant strength recovery (healing) ac-companies densification. For example, viscous sintering of melt particles (Vasseur et al., 2013)or planar fractures (Lamur et al., 2019; Mitchell et al., 2016) causes (compressive and tensile)strength to increase by 1-2 orders of magnitude, eventually restoring the material strength topre-fracture levels. Studies of densification by pressure solution have likewise shown granularmaterials can be healed and will continue to strengthen with time (e.g., Kanagawa et al., 2000;Karner et al., 1997; Tenthorey and Cox, 2006).Sample size precluded our measurement of the compressive strength of our experimen-tal products. Instead we use (1) the observed change in material competence, (2) the under-standing that the strength of granular materials is dictated by friction while the strength ofcohesive materials is related to fracture strength, and (3) many decades of experimental studiesshowing strength and porosity to be inversely related (e.g., Baud et al., 2014), to suggest thatstrength recovery is endemic to the solid-state sintering process.Hydraulic fractures are important conduits for fluid circulation in the upper crust andfor volcanic outgassing (e.g., Caine et al., 1996; Faulkner et al., 2010; Heap et al., 2019b;Kolzenburg et al., 2012) (Figure 4.9a). They form when accumulating fluid pressures lowerthe effective stresses acting on rock, inciting brittle deformation when they exceed the rock’stensile strength. New fractures, briefly propped open by pressurized fluids, fill with clastsliberated by wear and/or fluid pressure changes (e.g., Sibson, 1986). When fluids drain, theparticulate-filled fractures contract. “Downstream” from the fracture, its opening causes a highfluid flux event. Focusing on volcanic settings, where the ease of gas egress exerts controlon the effusive-explosive transition (e.g., Gonnermann and Manga, 2007), fluids are primarilygaseous and high flux events may appear at the surface as plumes of steam and ash.58Fluid pressure exceeds gouge strengthFracture reopens and fills with gougeSintering begins; fluid pressure rises Fracture opens and fills with gougeGouge recovers significant strengthFluid pressure cannot overcome gouge strengthSintering begins; fluid pressure rises Fracture opens and fills with gougePressurization  >  Strength RecoveryStrength Recovery  >  Pressurization(b)(c)(a) Volcanic settinghotter and deeperFigure 4.9: Strength recovery vs. fluid accumulation. (a) Schematic of a high temper-ature volcanic system where hydraulic fracturing has occurred as a result of fluidpressurization (see text for details). Fractures are filled with gouge liberated duringbrittle event. (b) Following the opening of the gouge filled fracture (first panel),clasts begin to sinter (second panel; indicated by color and morphology change)while gas pressures accumulate (intensity of blue color indicates higher pressure).In this instance gas overpressures build and exceed the strength of the sinteringgouge (third panel), causing brittle failure of the composite (yellow stars), reopen-ing of the fracture and draining of the gas (fourth panel). (c) Alternatively, if sinter-ing outpaces fluid accumulation (second panel), gouge recovers significant strength(third panel). Gas pressures may then be insufficient to overcome the evolvinggouge strength (fourth panel) and no outgassing will occur.Void space in granular materials is ephemeral. As densification begins, permeabilitydrops and fluid transmission is suppressed, causing gas pressures to rise again. A fracture canbe reopened and the clasts fluidized, if fluid pressures, at short times, overcome the frictionalstrength of the granular material (e.g., Scholz, 1998). However, as lithification accompaniesdensification, at longer times the re-opening of a fracture will depend on the evolving strengthof the nascent composite.Simultaneous densification and lithification create a competition between rising fluidpressures and material strengthening. If gas pressures rise more quickly than the weak zoneheals, a fracture will reopen when the strength of partially sintered gouge is exceeded (Figure4.9b). In a volcanic setting, frequent, cyclic reactivation of fractures may appear as near-continuous outgassing at the surface, and associated quiescent eruptive activity. However, ifsintering outpaces gas pressurization, the healing gouge may resist fracture reopening (Figure4.9c). If overpressures eventually become great enough to exceed the composite strength, the59resulting gas flux event will be large. In a volcanic environment, the pressure differentialcaused by an energetic outgassing event may be sufficient to fragment porous (intact) magma,leading to explosive activity. The transition between these regimes is dictated by the behaviorof the fluids, as well as the factors that control the magnitude and rate of sintering (i.e., t-P-T ,grain size, initial porosity).Though we have focused on the effects of solid-state sintering on volcanic processes,the competition between healing and fluid pressurization is not unique to volcanic settings –fundamentally the same processes influence the dynamics and recurrence interval of slip eventsin tectonic fault and shear zones (e.g., Kanagawa et al., 2000; Karner et al., 1997; Morrow et al.,2001; Tenthorey and Cox, 2006). In the absence of other densification processes, the rates ofmaterial strengthening and permeability reduction in these settings will be dictated by solid-state sintering.4.7 ConclusionsThe physical and mechanical properties of granular geologic materials are inherentlytransient. We have used hot-pressing experiments to study solid-state sintering, an understud-ied densification mechanism that operates throughout Earth’s crust. Our experimental resultsconstrain a model for the relative density increase (i.e., porosity loss) accompanying solid-statesintering, which we test against densification results obtained using an alternative experimentalprocedure. We find that at hot-pressing conditions representing high-temperature, near-surfacecrustal environments, solid-state sintering transforms crystalline granular material into solidcomposites over a period of hours to days. With densification, sintering materials lose per-meability and gain strength. By reducing porosity and permeability and increasing materialstrength, solid-state sintering reduces the capacity of comminuted geologic materials to trans-mit fluids and may alter their deformational behavior. In volcanic settings, as an example,solid-state sintering may determine the efficiency of outgassing, which in turn affects eruptiondynamics and the potential for explosivity.60Chapter 5Cyclic shear zone cataclasis and sinteringduring lava dome extrusion: Insights fromChaos Crags, Lassen Volcanic Center(USA)5.1 IntroductionThe rate at which magma transits the crust has a strong influence on the magma’s phys-ical, chemical and transport properties, and can control the nature of eruption and the eruptionproducts (Rutherford and Devine, 2008). Slow ascent rates can induce decompression-drivendegassing and crystallization causing increases in magma viscosity and resulting in the for-mation of lava domes (Cashman et al., 2008; Edmonds and Herd, 2007; Husain et al., 2014;Nakada et al., 1995b; Rutherford and Devine, 2008; Sparks, 1997; Sparks et al., 2000; Voightet al., 1999). During particularly slow ascent of intermediate magmas (e.g., extrusion rates <7 m3/s; Watts et al., 2002), extensive degassing and crystallization create strong, stiff magmasthat favor brittle deformation rather than viscous flow (Hale and Wadge, 2008; Heap et al.,2016; Pallister et al., 2008; Sparks et al., 2000; Zorn et al., 2018).Forced ascent of such magma causes extremely localized deformation at the interfacewith the surrounding wall rock where shear stresses are greatest (Hale and Wadge, 2008;Kennedy and Russell, 2012; Okumura et al., 2016; Smith et al., 2011). Strain localization isevidenced by the formation of an annular shear zone around the solidifying magma plug (Cash-man et al., 2008; Hale and Wadge, 2008; Holland et al., 2011; Hornby et al., 2015; Kendricket al., 2012; Lavalle´e et al., 2013; Pallister et al., 2013; Sparks et al., 2000; Wallace et al.,612019b; Watts et al., 2002). Further deformation sequestered in the shear zone facilitates transitof the plug over hundreds to thousands of meters to the surface (Cashman et al., 2008; Okumuraand Kozono, 2017).These processes produce high aspect ratio lava domes and spines (Cashman et al., 2008;Heap et al., 2016; Sparks et al., 2000) such as observed at Soufrie`re Hills (Montserrat, 1995-2010; Loughlin et al., 2010; Ryan et al., 2010; Voight et al., 1999; Watts et al., 2002), Mount St.Helens (USA, 2004-2008; Dzurisin et al., 2015; Iverson et al., 2006; Scott et al., 2008); MountUnzen (Japan, 1991-1995; Nakada et al., 1995a, 1999) and Santiaguito (Guatemala, 1922-present; Holland et al., 2011; Rhodes et al., 2018; Rose, 1972). Many of these lava domesare enveloped in cataclastic carapaces of variably densified volcanic fault gouge representativeof the conduit shear zone (Cashman et al., 2008; Iverson et al., 2006; Kennedy and Russell,2012; Nakada et al., 1995a; Pallister et al., 2013; Rhodes et al., 2018; Watts et al., 2002). Thefault gouge results from fracturing of the coherent magma/lava, followed by cataclasis of theparticles (i.e., comminution, translation and rotation; Engelder, 1974) and simultaneous me-chanical compaction. The physical properties and microstructures of the cataclastic materialsrecord information about magma ascent and eruption processes including: i) the deformationalprocesses governing magma ascent (e.g., Cashman et al., 2008; Kendrick et al., 2012; Kennedyet al., 2009; Pallister et al., 2013), ii) the extent and implications of in-conduit alteration (e.g.,Wallace et al., 2019b), and iii) the efficiency of volcanic outgassing (e.g., Gaunt et al., 2014).Here we describe the shear zone encasing a crystal-rich, glass-poor rhyodacitic lavadome (Dome C), part of Chaos Crags within the Lassen Volcanic Center (California, USA).The enveloping conduit-parallel shear zone is well-exposed by the partial collapse of the orig-inal lava dome, and the outcroppings reveal it to comprise unconsolidated gouge and variablycompetent cataclasites. Below we document the structural organization and textural propertiesof the Dome C cataclasites, as well as their microstructural, physical and mechanical proper-ties. We use these observations and data on the Dome C shear zone materials to show that: (1)fracturing and cataclasis of the dacite at depth produced unconsolidated volcanic fault gouge,and (2) much of the gouge underwent solid-state sintering within the conduit to become thevariably densified and lithified cataclasites observed at the surface. Solid-state sintering is adiffusion-driven process that causes crystalline particles to coalesce and results in densification(loss of porosity) and lithification (increase in competence/strength) (e.g., Rahaman, 2003).Here we show that solid-state sintering of the gouge must have occurred on the timescale ofthe dome-producing eruption. We conclude with microstructural evidence for re-fracturing ofthe sintered cataclasites at depth, indicating cycles of cataclasite reworking and re-sinteringaccompanied the extrusion process. These processes imply shear zone properties (i.e., perme-620.5 kmNChaos JumblesDome BDome FDome EDome DDome CDome AFigure 5.1: Chaos Crags, Lassen Volcanic Center, California (USA). Chaos Cragsconsists of six rhyodacitic domes (from oldest to youngest: Domes A to F). DomeC partially collapsed ∼350 years ago to form the Chaos Jumbles deposit. Cameraelevation 6.6 km (Google Earth, c©2020 Google).ability, porosity, strength) are highly transient and can modulate eruptive behavior during theeruption of crystal-rich, glass-poor lava domes.5.2 Geologic Setting5.2.1 Chaos CragsChaos Crags is within Lassen Volcanic National Park (California, USA) and is a part ofthe Lassen Volcanic Center, the southernmost volcanic center in the Cascades (Clynne, 1990;Heiken and Eichelberger, 1980). Chaos Crags is the youngest eruption in the Eagle Peak se-quence, occurring 1103 ± 13 years B.P. (∼ 850 C.E.; Clynne et al., 2008a) and contributingto the formation of the silicic Lassen dome field (Clynne and Muffler, 2010, 2017; Mufflerand Clynne, 2015). Chaos Crags consists of six rhyodacitic domes (from oldest to youngest:Domes A to F) and associated pyroclastic deposits (Christiansen et al., 2002; Clynne and Muf-fler, 2010, 2017; Muffler and Clynne, 2015) (Figure 5.1). Although the precise duration of thetotal eruption is unknown, paleomagnetic directions measured in pyroclastic units and in thedome lavas indicate it may have been less than a few decades (Clynne et al., 2008a).63Eruptive products from Chaos Crags are subdivided by their lithology. Dome C is theoldest of the Group 2 products, which generally have devitrified, microlite-rich groundmassesand whole rock SiO2 contents from 67 to 68.5 wt.% (Clynne and Muffler, 2010; Clynne et al.,2008b; Quinn, 2014). The phenocryst assemblage includes plagioclase, biotite, hornblendeand quartz, in order of decreasing abundance (Clynne and Muffler, 2010). Similar to otherGroup 2 products, Dome C lavas contain abundant (up to 20%) mafic magmatic inclusions –basaltic andesite to andesite inclusions principally composed of amphibole, pyroxene and pla-gioclase microphenocrysts with subordinate amounts of olivine, clinopyroxene and plagioclasephenocrysts (Scruggs and Putirka, 2018; Tepley et al., 1999; Underwood et al., 2012).5.2.2 Dome CApproximately 350 years ago (mid 1600s C.E.; Clynne and Muffler, 2017; Heath,1959), a majority of the over-steepened Dome C collapsed in three cold rock avalanches toform the 0.12-0.17 km3 Chaos Jumbles deposit that extends NW of Dome C (Clynne and Muf-fler, 2017; Eppler et al., 1987) (Figure 5.1). The partial collapse bisected the dome (Figure5.2a). The remnant of Dome C is semi-spherical in shape, with a near-vertical NW-facing ex-posure of the dome interior. The interior is pervasively oxidized and heavily jointed (Wattset al., 2013; Figure 5.2a). We sampled material that is representative of the dome’s unalteredinterior from the Chaos Jumbles deposit. A description of the dacite (hereafter unit “D”) isgiven in Table 5.1.Along the SW and NE margins of Dome C, the heavily jointed interior of the domeis overlain by a smooth upper surface. Where exposed on the SW margin (Figure 5.2b-d),this layer comprises three volcaniclastic units, which we sampled in situ (Figure 5.2c-d): (1)a pink, clast-supported breccia consisting of angular, interlocking clasts of dacite, and (2) apink, high-porosity cataclasite (hereafter “CHi”) containing patches and discontinuous bandsof (3) dark red, low-porosity cataclasite (hereafter “CLo”) (detail in Figure 5.2e). The unit CLoshows a fracture pattern (Riedel shears) consistent with those observed in another volcanicshear zones (e.g., Mount St. Helens; Cashman et al., 2008; Friedlander, 2012; Pallister et al.,2013) (Figure 5.2c-d). Unconsolidated grey fault gouge (hereafter unit “G”) is also exposedat the outermost edge of the SW margin (light grey region in Figure 5.2a). Where observedin situ, unit G is sandwiched between fractured grey dacite and an older, oxidized, dark greyhypersthene, augite and plagioclase-phyric andesite (“WR” in Figure 5.2a), which erupted inthe middle Pleistocene (Christiansen et al., 2002; Clynne and Muffler, 2010).These volcaniclastic units (Table 5.1) are parts of the shear zone that facilitated theascent of Dome C lava to the surface. Figure 5.2f is a schematic showing the general structuralorganization of the shear zone.64shear zonelava dome(a) (b)(c) (d)xzy(e)DB CHiCLoCLoCHiCHiDCHiDG WR(f) lithofacies:rock type:unit:daciteDdacite brecciaDBlow-porosity cataclasiteCLohigh-porosity cataclasiteCHigougeGsample location:shear zone wall rockdomeandesiteWRL0L1L2L3L4L5(down)(out)0.5 m 0.25 m 2.5 cm50 m 5 mFigure 5.2: Field photographs of Chaos Crags study site on Dome C at differentscales: (a) Exposed face of Dome C, looking SE, showing the interior of lava domeand the shear zone, including a fault gouge (G), between the massive dacite lava (D)and the older andesitic wall rocks (WR) on SW margin. Photo credit: S. Kolzen-burg. Black arrow shows orientation and location of next photo. (b) Photograph,looking N, of outcrop of preserved shear zone outlined in black box and enlargedin (c,d); black arrow shows orientation and location of next photo. (c,d) This out-crop exposes the larger structural organization of the shear zone from close to thedome interior (left) to the edge of the preserved shear zone (dashed line). Blackstars show same feature in both photos. Shear zone consists of a pink dacite breccia(DB), high-porosity, pink cataclasite (CHi) containing bands of low-porosity, darkred to brown cataclasite (CLo). Black box in (d) shows the location of the nextphoto. (e) Band of CLo containing fractured and sheared plagioclase grains. Con-tact with CHi can be sharp (right side of (e)) or gradational (left side of (e)). (f)Lower panel shows representation of transition from lava dome to shear zone toconduit wall and sample locations.65Table 5.1: Suite of samples of Dome C dacite and shear zone units, including: sample label, location, and textural and mineralogicaldescription.Lava DomeUnit Location Descriptive Name Mineralogy Additional FeaturesD 40◦32′ 30.28′′N121◦32′ 35.33′′WPervasively oxidized, non-vesicular,massive, dacite with fine-grainedgroundmass.Phenocrysts (35-40%): quartz (2-5 mm), hornblende (2-5 mm),biotite (1-3 mm) and plagioclase (2-5 mm) (in order of increasingabundance).Mafic magmatic inclusions (10%;dark grey, non-vesicular, massive,aphanitic basalt) are millimeter todecimeter-sized. Subrounded toameboidal in shape.Shear ZoneUnit Samples Location Descriptive Name Componentry Additional FeaturesG 40◦31′ 38.99′′N121◦31′ 31.85′′WUnconsolidated fresh, light grey,crystal-bearing, lithic-rich ash tolapilli-sized fault gougeLithics (90%): dacite (fresh, light grey, non-vesicular, massive,quartz- (2-5 mm), hornblende- (2-5 mm), biotite- (1-3 mm),plagioclase- (2-5 mm) phyric dacite with fine-grained groundmassor occasionally glassy groundmass). Angular to subroundedclasts. Crystals (10%): 1-3 mm fragments of minerals liberatedfrom the dacite. Angular to subrounded grains.Contact with mostly-intact freshdacite is gradiational. Contact withwall rocks (andesite) is sharp.CHi L0, L1,L2, L3,L440◦31′ 39.82′′N121◦31′ 26.37′′WPervasively oxidized, pink, porous,non-graded, matrix supported, wellsorted, lithic- and crystal-bearing,cataclasite.Crystals (10-15%): plagioclase (1-3 mm) and subordinateamounts of quartz (2-5 mm), hornblende (1-3 mm) and biotite (1-3mm). Subangular to rounded. Lithics (5%): 0.2-3 cm thick,discontinuous linear/planar features and 1-5 cm clasts/blebs aredeformed and undeformed mafic magmatic inclusions.Unit shows fracture pattern (Riedelshears) consistent with thoseobserved in another volcanic shearzone (Cashman et al., 2008;Friedlander, 2012; Pallister et al.,2013).CLo L5 1,L5 7,L5 8,L5 940◦31′ 39.82′′N121◦31′ 26.37′′WSurficially oxidized, dark red tobrown (oxidized)/light grey (fresh),dense, non-graded, matrix supported,well sorted, lithic- andcrystal-bearing cataclasite.Crystals (15-20%): same crystal assemblage as porous cataclasite.Angular to subrounded. White lenses containing fragmentedplagioclase crystals are apparent in hand-samples, often along themargins of the bands. Lithics (5%): Inclusions are more intenselydeformed.Often form discontinuous,near-planar to anastomosing bands(up to 3 cm). Contact with CHi canbe sharp or gradational, materialscan be interfingered, or CLo patcheswill be within CHi.665.2.3 SamplingWe collected samples from the units D, CHi, CLo and G. Samples of the cataclasite unitshave specific sample IDs (L0 to L5; Table 5.1) and are shown in their respective collection loca-tions within the shear zone in Figure 5.2f. For these samples, we assume the outermost planarsurface of the outcrop was oriented vertically in the conduit during ascent (Figure 5.2b,d), anduse this as a reference plane to orient samples for thin section preparation and coring. Weestimate the thickness of the outcrop, from this outer surface to the start of the dacite breccia,to be 1.4 m.5.3 MethodsThe whole rock major element chemical compositions of samples of units D, CHi, CLoand G were determined by XRF analysis at ALS Geochemistry laboratory in Vancouver (BC,Canada), based on 2 g aliquots of each crushed sample (Table 5.2). Replicate analysis ofaliquots of sample L2 from unit CHi was used to establish analytical uncertainty. The mineralcomponentry of the same samples (Table 5.3) was determined by Rietveld refinement of X-raydiffraction spectra (Raudsepp et al., 1999).Thin section billets oriented parallel (x-z plane in Figure 5.2) and perpendicular (y-zplane in Figure 5.2) to the kinematic plane were cut from samples of units CHi and CLo. Abillet was cut from an unoriented sample of unit D. These thin sections were analyzed using anoptical microscope and a scanning electron microscope in back-scattered mode (BSE SEM) atthe University of British Columbia (UBC; Canada).We determined the powder (true) density (ρp; kg/m3) of samples from units D, G, CHiand CLo using the following procedure: we crushed 10-15 g of material using a mortar andpestle to produce a fine powder. Each powder was then subdivided in to five aliquots. Themass of the first aliquot was measured using a high precision balance then transferred into aMicromeritics AccuPyc II 1340 helium pycnometer (at UBC) to determine the sample volume.The mass of a second aliquot was measured, added to the first aliquot in the helium pycnometerand then the powder’s volume was remeasured. This additive process was repeated until all fivealiquots were measured together in the pycnometer. Plotting the measured masses against themeasured powder volumes, ρp is the slope of the best-fit line that goes through the data and theorigin (Table 5.4).Thirty-seven right cylinders (12 or 20 mm in diameter, 15-40 mm in length) were coredfrom samples of units D, CHi and CLo. Of the four cores taken from each cataclasite sample(Table 5.4), half are oriented so their lengths are parallel to the extrusion direction (z-axisin Figure 5.2), and half perpendicular to the extrusion direction (x-axis in Figure 5.2). The67thirteen cores prepared from blocks of dacite dome (unit D; Figure 5.2) collected from theChaos Jumbles deposit were unoriented. Core ends were ground to parallel and then driedin a vacuum-oven at 40◦C for at least 48 hours. Core diameters and lengths were measuredusing digital calipers, and core masses were measured using a high precision balance. Theskeletal volume of each sample was measured using a Micromeritics AccuPyc II 1340 heliumpycnometer at the Institut de Physique du Globe de Strasbourg (IPGS; France). Using thesemeasurements and ρp, sample bulk density (ρb; kg/m3), total porosity (φt ; fractional) andconnected porosity (φc; fractional) were calculated (Table 5.4,5.5).The permeability (k; m2) of each core was measured using a benchtop gas (nitrogen)permeameter at the IPGS (see Heap and Kennedy (2016) for a schematic diagram) (Table5.4,5.5). Samples were placed within the permeameter and were pressurized around their cir-cumference to a confining pressure of 1 MPa and kept at these conditions for 1 h to ensuremicrostructural equilibration. Following equilibration, measurements of permeability wereperformed using the steady-state flow method: volumetric flow rates (Q; L/min) were mea-sured using a flowmeter for several pore pressure differentials (∆P; mbar) measured using apore pressure transducer. We calculated permeability from these data while checking whetherthe data required auxiliary corrections (i.e., Klinkenberg and Forchheimer corrections). To doso, the raw permeability (kraw; m2) was first calculated for each pore pressure differential:kraw =Q∆PPmµLPdA, (5.1)where µ is the viscosity of the pore fluid (Pa s), L is the sample length (m), Pd is the downstreampore fluid pressure (mbar), ∆P is the difference between the upstream pore fluid pressure (Pu)and Pd , Pm is the mean pore fluid pressure (Pm = (Pu – Pd)/2) and A is the sample cross-sectionalarea (m2). If these data, when plotted as 1/kraw as a function of Q, can be well described by apositive linear slope, the Forchheimer correction is required (Table D.1). Forchheimer correc-tions were necessary for most cores (Table 5.4,5.5) and the true permeability was taken as theinverse of the y-intercept of the best-fit linear regression in the plot of 1/kraw as a function ofQ. To check whether the Klinkenberg correction was also needed, the Forchheimer correctedpermeability values for each pressure differential were plotted as a function of 1/Pm. The sam-ples that required a Forchheimer correction did not also require a Klinkenberg correction. Forthe samples that did not require a Forchheimer correction, we checked whether a Klinkenbergcorrection was necessary. A Klinkenberg correction is required when the data on a plot of krawas a function of 1/Pm can be well described by a positive linear slope. This was not the case forour data and so when a Forchheimer correction was not needed, the permeability (kD; m2) wascalculated using the following relation:68kD =dQd(∆PPm)µLPdA, (5.2)Seven cataclasite cores, at least one from each of the identified layers, and eight coresof the dacite were deformed uniaxially in compression until failure. See Heap et al. (2014b)for press schematic and details of method. All of the experiments were performed on oven-drysamples at a constant strain rate of 10-5 s-1. A lubricating wax was applied to the end-facesof the samples to avoid problems with friction between the sample and the pistons. Duringdeformation, we recorded axial displacement and force using, respectively, a linear variabledifferential transducer (LVDT) and a load cell. Axial displacement was corrected for the de-formation of the loading column. Axial displacement and force were converted to axial strainand stress using the sample dimensions. The uniaxial compressive strength (UCS; MPa) ofthe cores was taken as the peak axial stress the sample sustained before succumbing to macro-scopic failure. We also determined the static Young’s modulus (E; GPa) for each of the samplesfrom the pseudo-linear elastic portions of the stress-strain curves (see Heap et al. (2020)).Four cores of dacite dome were deformed triaxially in compression. See Farquharsonet al. (2017a) for press schematic and details of method. These samples were vacuum-saturatedin deionized water, inserted into a viton jacket and placed inside the pressure vessel. Confin-ing (Pc; MPa) and pore fluid (Pp; MPa) pressures were then increased using servo-controlledpumps. Once the samples reached their target pressure (between 15 and 30 MPa and 10 MPafor the confining and pore fluid pressures, respectively), they were left for a couple of hours toensure microstructural equilibration. Pc and Pp were held constant during the experiment bythe servo-controlled pumps. The samples were then deformed at a constant strain rate of 10-5s-1. During deformation, axial displacement and force were measured by an LVDT and a loadcell, respectively, which were converted to axial strain and stress using the sample dimensions.The axial displacement was corrected for the deformation of the loading column. We assumehere a simple effective pressure law, where the effective pressure (Pe f f ; MPa) is the confiningpressure minus the pore fluid pressure. The final dacite dome core, also vacuum-saturated indeionized water, was deformed uniaxially (using the same protocol described above) inside awater-filled cup.5.4 Results5.4.1 Geochemistry and mineralogyThe units D, G, CHi and CLo have common chemical compositions (Table 5.2) andmodal mineralogy (Table 5.3). Mineralogically, the rocks comprise plagioclase (andesine, 40-69Table 5.2: Whole rock chemical compositions (wt.%) for samples described in Table 5.1as measured by X-ray fluorescence by ALS Geochemistry (Vancouver, BC, Canada).Unit D G CHi CHi CHi CLoSample L0 L2 L2 (repeat) L5 7SiO2 67.17 66.75 66.57 66.87 67.51 67.38TiO2 0.44 0.44 0.45 0.41 0.42 0.40Al2O3 15.20 15.73 15.84 15.66 15.78 15.58FeOT 3.55 3.59 3.54 3.42 3.46 3.23MnO 0.08 0.08 0.08 0.07 0.08 0.08MgO 1.82 1.88 1.90 1.71 1.73 1.60CaO 3.81 4.22 4.29 4.07 4.11 3.81Na2O 3.89 3.94 3.94 3.94 3.95 4.04K2O 2.50 2.39 2.34 2.38 2.31 2.49P2O5 0.11 0.11 0.11 0.11 0.11 0.11SO3 <0.01 <0.01 <0.01 <0.01 <0.01 <0.01Total 98.61 99.06 99.28 98.80 99.62 98.73LOI 0.04 -0.07 0.22 0.16 0.16 0.0145 wt.%), high-temperature (anorthoclase to sanidine) and low-temperature (microcline) alkalifeldspars (20-25 wt.%), SiO2 polymorphs (quartz, 12-15 wt.%; cristobalite, 4-9 wt.%) andminor (5-8 wt.%) other constituents (Table 5.3). The XRD spectra also suggest the presence ofa small quantity (4-8 wt.%) of amorphous material which can be amorphous mineral phases,volcanic glass or highly comminuted mineral grains (Yund et al., 1990) (Table 5.3). Thereis no systematic variation in the proportion of minerals (including cristobalite) or amorphousmaterial between units (Table 5.3). Based on the identical geochemistry and mineralogy ofthe units, all shear zone materials appear to originate from the Dome C dacite. There is noevidence for precipitation of additional phases or melting of the gouge or dacite.5.4.2 MicrostructureLow magnification photomicrographs show the representative colors and textures ofthe groundmass of the unit D (Figure 5.3a) and the matrices of units CHi (Figure 5.3d) andCLo (Figure 5.3g). At high magnification, BSE SEM images of the dacite (Figure 5.3b,c)and cataclasites (Figure 5.3d,e,h,i) are different. The groundmass of the dacite is crossed byacicular microlites (Figure 5.3c) and features roughly circular, fractured patches of cristobalite(see Figure 5.3b). Irregularly shaped pores are present throughout the groundmass but showno specific relationship to mineral phases. In unit CHi, the matrix comprises many blocky orsubrounded clasts often connected to one another by thin necks of crystalline material (arrows70Table 5.3: Mineral abundances (wt.%) determined by Rietveld refinement of X-raydiffraction spectra collected in the Electron Microbeam and X-Ray Diffraction Fa-cility at UBC.Unit D G CHi CHi CLoSample L0 L2 L5 7Quartz 13.1 12.2 14.5 15.0 14.9Cristobalite 6.6 8.3 7.4 8.5 4.1Plagioclase (An30-50) 42.5 45.1 40.9 42.3 50.0Alkali feldspar 23.9 22.3 24.9 22.2 18.4FeMg Silicates 5.4 7.9 4.0 3.6 3.5Fe Oxide 1.6 0.3 2.2 2.3 1.3Amorphous 6.9 3.8 6.1 5.4 7.8Total 99.99 99.98 99.98 99.32 99.94in Figure 5.3f); both acicular mineral grains and patches of cristobalite are absent (Figure5.3e). The necks, which extend between particles of various shape, size and composition, areoriented at high angles to the surfaces of the substrate grains, rather than at low contact anglescommonly associated with wetting of particles. Interconnected irregular or subrounded voidspaces sit between necks, at the junction points of the coalescing clasts. Particle coalescenceis often concentrated at the edge of larger grains (Figure 5.3e). In unit CLo, nearly all particleshave coalesced (Figure 5.3h,i). The number and size of void spaces has decreased relative toCHi, and many of the remaining pore spaces are isolated from one another. Lastly, no glass wasidentified in samples of cataclasite.There are other notable textural features found only within the cataclasite units (Fig-ure 5.4). For example, there are shattered plagioclase grains that have been sheared to formhigh-porosity monomineralic lenses in CLo (Figure 5.4a,b) and CHi (Figure 5.4c). The plagio-clase particles in the lenses are angular and have jig-saw-fit textures. In addition, mafic inclu-sions in CHi and CLo are oxidized and have been sheared to form overall elongated curvilinearshapes (Figure 5.4c,d). In contrast, mafic inclusions in unit D are frequently fresh, typicallynear-equant in their dimensions, and show no textures consistent with having been viscouslystretched. Finally, there are rounded clasts of CLo within CHi (Figure 5.4e,f). We discuss theseclasts further in Section 5.5.4.5.4.3 Physical and mechanical propertiesTable 5.4 summarizes the results of physical property measurements of cores taken fromsamples of units D, CHi and CLo. Across the dataset, φt and φc are within uncertainty (± 0.01)711 mm1 mm1 mm70 μm70 μm70 μm40 μmD(a) (c)CHi(d) (e) (f)CLo40 μm(g) (h) (i)40 μmcrcr(b)plplplsisiplplsiFigure 5.3: Plain polarized light (PPL) photomicrographs and backscatter electron(BSE) images of units from Dome C. (a,b,c) Undeformed dacite (D) showinggroundmass texture and porosity distribution. Patches of cristobalite (cr) and phe-nocrysts of plagioclase (pl) are labelled in (b). Acicular crystals are apparent in(c). (d,e,f) High-porosity cataclasite (CHi). The groundmass of D and matrix ofCHi look similar in PPL (d) but are distinguishable in SEM images (e,f). CHi showsblocky and subrounded clasts joined by necks of material (examples shown withyellow arrows in (f)) and a high proportion of interconnected, irregularly shapedintergranular porosity. Clasts of plagioclase (pl) or a silica polymorph (si) are la-belled in (e). (g,h,i) Low-porosity cataclasite (CLo). Matrix is dark brown to darkgrey in PPL. SEM shows little residual porosity and an increased proportion of coa-lesced clasts, some of which still show necks of crystalline material (yellow arrowsin (i)).72250 μm150 μm1 mm1 mm250 μm(c) (d)(e) (f)1 mm(a) (b)Figure 5.4: PPL and BSE images of textural features in cataclasites. (a) CHi and CLocontaining lenses of shattered, sheared plagioclase grains. White box shows loca-tion of (b). (b) Plagioclase lenses are high porosity relative to surrounding CLo, andcontain angular fragments that have not been significantly displaced. (c) CHi con-taining a diffuse patch of CLo (color difference in lower left quadrant) and a shearedmafic inclusion (through middle of photomicrograph; indicated by an abundanceof juxtaposed small, subangular plagioclase and oxidized amphiboles microphe-nocrysts). A shattered and sheared single plagioclase grain is above the image – its“tail” extends into image (dashed line). White box shows location of (d). (d) SEMimage shows very low porosity of sheared mafic inclusion relative to surroundingcataclasite. (e) Rounded clast of CLo within CHi. Segments of dashed line defineportions of clast edge. (f) Contact between rounded, low-porosity CLo clast andhigh-porosity CHi matrix.73Table 5.4: Physical and mechanical properties of sample cores from units CHi, CLo and D. Includes sample ID, powder density (ρp)representative of the sample, as well as core orientation, measured bulk density (ρb), connected (φc) and total (φt), permeability(k), dry uniaxial compressive strength (UCS) and Young’s modulus (E).Unit Sample ρp (kg/m3) orientation a ρp (kg/m3) φc (fractional) φt (fractional) k (m2) b UCS (MPa) E (GPa)CHi L0 2683 Z 2238 0.169 0.166 1.02 × 10-14 37.6 8.0Z 2226 0.178 0.170 3.50 × 10-14 bX 2338 0.134 0.129 7.51 × 10-15X 2301 0.146 0.142 9.37 × 10-15L1 2688 Z 2201 0.187 0.181 1.31 × 10-14 38.4 9.2Z 2091 0.226 0.222 2.77 × 10-14X 2185 0.197 0.187 2.25 × 10-14X 2219 0.185 0.175 9.30 × 10-15L2 2680 Z 2083 0.232 0.223 4.04 × 10-14 20.4 5.0Z 2110 0.224 0.213 3.47 × 10-14 21.5 5.0X 2127 0.214 0.206 2.29 × 10-14X 2128 0.217 0.206 2.71 × 10-14 bL3 2665 Z 2155 0.203 0.192 2.98 × 10-14 b 36.1 7.9Z 2172 0.199 0.185 2.07 × 10-14 bX 2170 0.206 0.186 1.42 × 10-14X 2099 0.220 0.212 2.59 × 10-14L4 2694 Z 2226 0.178 0.174 1.61 × 10-14 42.0 9.0Z 2192 0.194 0.186 2.17 × 10-14X 2219 0.185 0.176 1.79 × 10-14X 2246 0.175 0.166 1.79 × 10-14CLo L5 7 2706 Z 2497 0.081 0.077 1.22 × 10-15 86.0 16.0Z 2494 0.076 0.078 1.91 × 10-15 bX 2507 0.073 0.074 1.18 × 10-15X 2447 0.092 0.096 7.46 × 10-15 cD 2662 - 0.148 - 9.36 × 10-15 48.5 9.074Unit Sample ρp (kg/m3) orientation a ρp (kg/m3) φc (fractional) φt (fractional) k (m2) b UCS (MPa) E (GPa)- 0.146 - 8.58 × 10-15 51.8 9.9- 0.153 - 1.29 × 10-14 46.7 9.4- 0.150 - 9.33 × 10-15 46.3 9.0- 0.151 - 1.05 × 10-14 49.2 10.0- 0.152 - 9.83 × 10-15 46.8 9.3- 0.158 - 1.02 × 10-14 53.2 10.2- 0.157 - 1.27 × 10-14 47.6 9.52347 0.157 0.118 7.21 × 10-152346 0.126 0.119 5.63 × 10-152295 0.145 0.138 6.50 × 10-152343 0.126 0.120 5.06 × 10-152356 0.121 0.115 3.86 × 10-15a orientation of core: none = unoriented; z = parallel to extrusion direction; x = perpendicular to extrusion direction. See Figure 5.1.b Forchheimer correction applied to all samples except for those designated by this superscript.c anomalously high measured permeability results from a crack in the sample. This measurement is excluded from further analyses and discussion.75Table 5.5: Summary of four triaxial deformation experiments and one H2O-saturated uni-axial compressive test performed on cores of intact dacite (unit D) (see text for de-tails). Includes initial total porosity (φt), confining pressure (Pc), pore pressure (Pp),effective pressure (Pe f f ) and peak differential stress (Pdi f f ).φt (fractional) Pc (MPa) Pp (MPa) Pe f f (MPa) a Pdi f f (MPa)0.119 15 10 5 109.50.138 20 10 10 124.70.120 25 10 15 169.90.115 30 10 20 228.60.118 0 0 0 50.2a Pe f f = Pc - Ppof one another, indicating there is little to no isolated porosity. φt and φc vary from 0.07 to 0.23(Table 5.4). Permeability is positively correlated with porosity, and varies from 1.18 × 10-15to 4.04 × 10-14 m2. By unit, cores of CLo have the lowest porosities and permeabilities, whilecores of CHi have the highest (Table 5.4). CHi shows the most variability in physical propertyvalues (Table 5.4). Cataclasite units show weak porosity and permeability anisotropy as bothvalues are often higher in cores oriented parallel to the extrusion direction. Cores of D haveintermediate porosities and permeabilities (Table 5.4).The measured uniaxial compressive strengths and Young’s moduli of the units are alsocorrelated to their porosities: CLo is strong and stiff (UCS: 86.0 MPa; E: 16.0 GPa), while coresof CHi are considerably weaker and have lower Young’s moduli, with UCS varying from 20.4to 42.0 MPa and E varying from 5.0 to 9.2 GPa (Table 5.4). Cores of D have an intermediatestrength and Young’s modulus (UCS: 46.3 to 53.2 MPa; E: 9.0 to 10.2 GPa; Table 5.4).The failure mode of the dacite cores deformed triaxially was brittle over the testedpressure range (i.e., up to an effective pressure of 20 MPa) (Figure D.1). These experimentsshow that the compressive strength (Pdi f f ; MPa) of unit D increased from 50.2 to 228.6 MPaas the effective pressure was increased from 0 to 20 MPa (Table 5.5).Measured values of permeability and connected porosity for samples of cataclasite areplotted in Figure 5.5 and compared to a model curve for the permeability and porosity ofgranular material undergoing isotropic densification Wadsworth et al. (2016b). The close fitbetween the model and the measured values of φc and k for the cataclasites suggests that theshear zone materials have been mainly subject to isotropic densification and that shear stressesdid not play a major role (Figure 5.5). The measured physical properties of the coherent daciteare added for comparison.760 0.1 0.2 0.3 0.4φc10-1510-1410-13k (m2 )CLoCHiDGFigure 5.5: Connected porosity and permeability. Measured permeability (k) againstconnected porosity (φc) for cores from samples of the cataclasite units (circles)and the dacite (diamonds). CLo and CHi occupy distinct regions in φc-k space.Also plotted, the mono-disperse permeability model of Wadsworth et al. (2016b)(particle radius = 10 µm). Data for cataclastic materials (circles) scatter along themodel curve.Direct measurement of porosity and permeability for the unconsolidated gouge wasnot possible. We infer its porosity to be 0.40, equal to that of a packed powder (Rahaman,2003). The Wadsworth et al. (2016b) model would predict a permeability of 2.4 × 10-13 m2based on that porosity value (Figure 5.5). The gouge is expected to have little to no cohesivestrength (e.g., Moore et al., 2008; Samuelson et al., 2008; Lavalle´e et al., 2014). Includingthese approximations, physical properties across the shear zone vary substantially, includingfor connected porosity (∆∼ 0.33), permeability (∆∼ 102), strength (∆> 80 MPa) and Young’smodulus (∆ > 16 GPa).Figure 5.6 shows the spatial distribution of physical and mechanical properties. Themajority of the shear zone is made up of weak, high porosity and high permeability CHi. How-ever, the shear zone close to the dacite dome contains thin, discontinuous bands (Figure 5.2d,e)and diffuse patches (Figure 5.4c) of strong, stiff, low-porosity and low-permeability CLo. As aresult, the porosity and permeability of the shear zone decrease and the strength and Young’smodulus increase as the margin between the dome and the cataclastic rocks is approached (Fig-ure 5.6). Notably, the porosity and permeability and the strength and Young’s modulus of CLoare, respectively, lower and higher than the dacite dome.77dense catdense cat10-1510-1410-13k (m2 )00.10.20.3φt0.41.4 m(a)(b)0255075100UCS (MPa)(c)(d)L1L2L3L5 L0L4zxxzyCLoD CHi G051015E (GPa)(e)UnitFigure 5.6: Distribution of porosity, permeability and strength across Dome C units.(a) Schematic summary of textural zonation of shear zone and relative sample lo-cations. (b,c) Total porosity (φt) and permeability (k) of units measured on coresoriented parallel (along z-axis; open circles) and perpendicular (along x-axis; filledcircles) to the extrusion direction. φc and k are lowest in CLo and increase towardsthe edge of shear zone (CHi to G). Cores oriented along the x-axis are weakly lessporous and permeable than cores oriented along the z-axis. (d) Measured uniaxialcompressive strength (UCS). CLo is the strongest unit. Strength decreases acrossthe shear zone. (e) Young’s modulus (E). CLo is the stiffest unit in the shear zone.Gouge properties are inferred (see text).785.5 DiscussionThe variably densified and lithified cataclasite units that make up the Dome C shearzone evidence a deep-seated gouge production event followed by the densification and lithi-fication of the gouge within the conduit on the timescale of the eruption. The lithificationprocess was so effective that it created cataclasites that are stronger and less permeable thanthe dome interior (Figure 5.6). Identifying the relevant lithification mechanism, and the asso-ciated magnitudes and timescales of densification and lithification, inform on Dome C ascentconditions.5.5.1 Densification and lithification by solid-state sinteringDensification and lithification of granular volcanic materials can occur by a number ofmechanisms, including viscous sintering or annealing and compaction (welding) (e.g., Heapet al., 2014a; Kolzenburg et al., 2019; Quane et al., 2009; Vasseur et al., 2013; Wright andCashman, 2014), and pore occlusion by mineral precipitation (e.g., Heap et al., 2019a; Hor-well et al., 2013; Wright et al., 2011). However, the lack of groundmass glass in thin section,the paucity of amorphous material, the absence of low-temperature precipitated phases, andthe consistency in modal mineralogy across the shear zone and dacite lava do not support den-sification and lithification by viscous processes, cementation, or melting. In addition, there isno mineralogical or textural evidence to support the presence of a permeating liquid and den-sification by the dissolution and re-precipitation of minerals (i.e., Ostwald ripening, pressuresolution).Simultaneous mechanical compaction and shear-driven particle rearrangement can con-tribute to the densification of an unconsolidated granular material (e.g., Faulkner et al., 2018;Marone et al., 1990). However, the extent of mechanical densification is limited to the poros-ity of densely packed powders (i.e., ∼ 0.40; Rahaman, 2003). In addition, the timescales ofthese mechanical densification processes may be very short, especially when compared to thetimescales required for other densification mechanisms. In the volcanic setting considered here,maximum mechanical densification, forming a gouge having φt ∼ 0.40, likely occurs almostinstantaneously following the magma/lava fracturing event.In the Dome C cataclasites, lithification and densification to φt  0.40 involves crys-talline particles of varying sizes becoming conjoined by thin necks of new crystalline material.This particle coalescence evidences solid-state sintering, a diffusion-driven process akin todiffusion creep that converts unconsolidated crystalline granular materials into porous com-posites (Arzt et al., 1983; Ashby, 1974; Rahaman, 2003; Ryan et al., 2018b; Zhu et al., 1999).Solid-state sintering operates at temperatures as low as half of the crystalline material’s melting79temperature and does not require the presence of fluid or melt (e.g., Ashby, 1974; Rahaman,2003). The rates of sintering are accelerated by increases in effective pressure and temperatureand by reductions in particle size. The extent of solid-state sintering depends on temperatureand pressure, as well as the time spent at those conditions (e.g., Rahaman, 2003; Ryan et al.,2018b). Long dwell times result in more extensive sintering, producing denser, more compe-tent (stronger), less porous and less permeable materials (Ryan et al., 2018b).Ryan et al. (accepted) conducted hot-pressing experiments to determine solid-state sin-tering efficiency as a function of the experimental confining pressure (P, MPa), temperature (T ,K) and time (t, s). These high-temperature (700-900◦C), high-pressure (20-70 MPa) experi-ments on unconsolidated dacitic fault gouge from the 2004-2008 eruption of Mount St. Helensproduced dense, competent rocks by solid-state sintering over a period of hours to days. Theyused the data to create a t-P-T -dependent model for densification by solid-state sintering:ρr = ρo+aexp(bT)Pc ln(t), (5.3)where ρr is the relative density (ρr = 1 – φt = ρb/ρp, where ρb is bulk density and ρp is powderdensity), ρo is the initial relative density, and the coefficients a (0.045 ± 0.018), b (–3049 ±231), and c (0.442± 0.006) are the adjustable model parameters fit using an unweighted leastsquares approach (Ryan et al., accepted). Equation 5.3 can also be rearranged to solve for thesintering time necessary to achieve a specified porosity:t = exp(ρr−ρoaexp( bT)Pc). (5.4)In volcanic conduits we expect mechanical densification to occur immediately, imply-ing that the rate-limiting densification process is solid-state sintering. To model the extent ofsintering and minimum sintering times for the cataclasites enveloping the Chaos Crags DomeC, we assume the following:• The initial gouge formed by syn-ascent faulting at a depth of ∼ 1 km. This is informedby the observation and interpretation of repetitive seismic events at depths < 1.5 kmat other dome-building volcanoes (Goto, 1999; Iverson et al., 2006; Lamb et al., 2015;Melnik and Sparks, 2002; Moran et al., 2008a; Nakada et al., 1999; Neuberg et al., 2006;Thelen et al., 2008).• The minimum pressure acting on the conduit wall rock-gouge layer (Pmin; MPa) was thedepth-dependent lithostatic load (Pmin = ρ g h, where ρ is a representative bulk density(2300 kg/m3; Table 5.4), g is gravitational acceleration (9.81 m/s2) and h is the depth (upto 1000 m)) (Figure 5.7a).80• The maximum compressive pressure (Pmax; MPa) acting on the gouge was dictated bythe compressive fracture strength of the dacite as a function of depth (h). We use theuniaxial and triaxial strength data (Table 5.5) to constrain the relationship between Pmaxand h – by solving for h that corresponds to a lithostatic pressure equal to Pe f f , we plotPdi f f as a function of depth and fit the triaxial and uniaxial data (Table 5.4,5.5). Theresulting linear best-fit line is shown in Figure 5.7a. See Appendix D.2 for additionaldetails.• Phase equilibria experiments suggest pre-eruptive storage conditions for Chaos Cragslavas were 770 ± 10◦C at 145 ± 25 MPa (∼ 4.5-6.5 km) (Quinn, 2014). Allowing forslight cooling during ascent to the surface, we assume the gouge temperature was ∼725◦C. This value is in agreement with thermal measurements of surficial exposures ofother domes, their fumaroles and associated pyroclastic flows (650-800◦C; Goto, 1999;Schneider et al., 2008; Scott et al., 2008; Sparks et al., 2000; Vallance et al., 2008; Voightet al., 1999).Figure 5.7b shows the decrease in porosity as a result of solid-state sintering, as a func-tion of depth, pressure acting on the gouge (Pmin vs. Pmax) and time. Three shaded fields showthe porosities of units G (the starting condition; φt = 0.40), CLo and CHi. Porosity loss withtime is greatest at the depth of gouge generation (1 km) – after 10 days modelled porosities are∼ 0.07 to 0.28, depending on P. At 500 m depth, sintering is less efficient, so after 10 daysmodelled porosities are ∼ 0.13 to 0.30. At any depth, with increasing time, porosity continuesto decrease but at a slower rate.We model the minimum sintering time required to form cataclasites having porosityvalues observed in CHi (φt ∼ 0.20) and CLo (φt ∼ 0.08). Where P = Pmax, the minimum sinteringtimes needed to produce CHi and CLo at 1 km depth are 1 hour and 6 days, respectively (Figure5.7c). With decreasing depth, minimum sintering times increase as follows: i) at 750 m depth,sintering times are 2.5 hours and 24 days, ii) at 500 m depth sintering times are 8 hours and170 days.5.5.2 Ascent rate and eruption durationThere are no direct determinations of ascent (m/s) or extrusion (m3/s) rates for themagma plug that produced Dome C, nor estimates of the eruption duration. Watts et al. (2013)suggested, based on morphology and the character of the shear zones, that Dome C was com-parable to the “shear lobes” at Soufrie`re Hills suggesting extrusion rates of < 7 m3/s (Wattset al., 2002). Quinn (2014) used continuous decompression experiments to determine the de-compression rates needed to produce Chaos Crags Group 1-type and Group 2-type magmas.81Figure 5.7: (following page) Sintering time and ascent rate modelling. (a) Modelledrange of compressive pressures the gouge experiences over 1 km depth. Pmin is thelithostat (dotted) and Pmax is a best-fit line for the compressive strength of the daciteas a function of depth (solid). Experimental data are plotted: open circles are Pe f ffor the corresponding measured strength (filled circles), connected by dashed tie-lines (Table 5.5). See Appendix D.2 for details. (b) Change in total porosity withtime (days; contours) plotted against depth for Pmin (dotted curves) or Pmax (solidcurves). Shaded fields are the porosities of units G, CHi and CLo. Model curves arenot extended past 0.05 as at low porosities sintering dynamics change (Wadsworthet al., 2017a). (c) Minimum time needed to sinter gouge to form cataclasites withtotal porosities measured in units CHi (φt = 0.20) and CLo (φt = 0.08), against depth(dashed curves). Modelled linear ascent rates (m/d; solid curves) ≤10 m/d passthrough the “sintering window” for CLo (dark grey region).82200Compressive Pressure (MPa)00.250.500.751Depth (km)50 100 1500PminPmax2500.40 0.30 0.20 0.10Total Porosity00.250.500.751Depth (km)1 100 10000Minimum Sintering Time (d)00.250.500.751Depth (km)C Lo (φ t = 0.08)C Hi (φt = 0.20)2.5 m/d5 m/d10 m/d20 m/dSintering window 1 d10 d100 d1000 d1 d1000 dCLoCHiGFeasible values of P (Eqs. 3,4)(a)(b)(c)Initial ConditionPmin = ρ g hPmax = 0.194 h + 49.5283Based on phenocryst textures (e.g., presence or absence of dehydration reaction rims on biotiteand amphibole) and systematic changes in glass composition (e.g., increasing SiO2 and K2Oand decreasing Al2O3 and CaO with decreasing decompression rate, corresponding to trends inthe change in the composition of Chaos Crags glasses with time), Quinn (2014) showed Group1-type lavas can be produced where decompression rates are > 2.6 MPa/hr (> 100 m/hr ascentvelocities), while Group 2-type lavas (i.e., Dome C dacite) require decompression rates < 2.6MPa/hr (< 100 m/hr ascent velocities).Ryan et al. (2018a) suggested the physical properties of shear zone materials that hadundergone solid-state sintering could be used as a geospeedometer and could inform on cata-clasite (and, by proxy, lava) ascent rate. Here we test this conceptual model for the first time:the shaded fields in Figure 5.7c define the critical depth-time conditions (“sintering windows”)for CHi or CLo. At Chaos Crags the occurrence of CLo dictates the minimum required sinter-ing time. That window therefore constrains the range of possible gouge ascent rates. Evenwhen accounting for Pmax decreasing during gouge ascent (see Appendix D.3 for details), onlyat ascent rates ≤ 10 m/d does the ascending magma intersect the sintering window needed toproduce CLo (Figure 5.7c; Figure D.3). Assuming ascent of the magma plug is coupled to thatof these sintered cataclasites, 10 m/d represents a maximum ascent rate for the Dome C lavas.The width of the Dome C remnant (Figure 5.1, 5.2) limits the maximum diameter of the ventto ∼ 250 m; a linear ascent rate of 10 m/d would yield a maximum volumetric extrusion rateof 5.7 m3/s.Our modelled ascent and extrusion rates agree well with observations from other inter-mediate dome-building volcanic systems. During the 2004-2008 eruption of Mount St. Helens(conduit diameter: 150-200 m), spine extrusion was initially fast (15-25 m/d) but slowed withtime, featuring linear effusion rates ≤ 10 m/d during the eruption of spines 3-7 (Schneideret al., 2012; Vallance et al., 2008). Corresponding measured extrusion rates were ≤ 6 m3/s(Schneider et al., 2012; Vallance et al., 2008). During the 1991-1995 eruption of Mount Un-zen, subsurface magma ascent rates were estimated to be 13-40 m/d (Nakada et al., 1995b).Extrusion rates measured at the surface were∼ 3-6× 105 m3/d (3.5-7.0 m3/s) in the first pulseof exogenous growth and ∼ 1-3 × 105 m3/d (1.2-3.5 m3/s) in the second pulse (Nakada et al.,1999).With estimates of the depth of gouge generation (1 km), the pre-eruptive surface (breakin the slope of Chaos Crags deposits at ∼ 2100 masl) and the original maximum height ofthe dome (peak of the Dome C remnant at ∼ 2495 masl), we use our modelled maximumlinear ascent rate to constrain the duration of the Dome C eruption: Dome C magmas spent aminimum of 100 days in transit from 1 km depth, and erupted at the surface for a minimum of39.5 days, producing a dome 395 m high.845.5.3 Outgassing behavior during solid-state sinteringPermeability loss accompanies densification and lithification by solid-state sintering(Ryan et al., 2018b, accepted; Zhu et al., 1999). At Dome C, solid-state sintering has causedCHi and CLo to be 1 and > 2 orders of magnitude less permeable than the unconsolidated gouge(Figure 5.5). Permeability losses of these magnitudes can occur over a period of hours to daysdepending on the densification depth (Figure 5.7b). Rapid loss of connected void spaces involcanic systems will inevitably inhibit the egress of volcanic gases, leading to their accumu-lation in the subsurface. In the case of the Dome C shear zone, building fluid pressures likelypromoted vertical gas transmission through the cataclasite units or, to some degree, throughthe relatively low-permeability lavas (∼ 8 × 10-15 m2; Table 5.4). Given the weak perme-ability anisotropy observed in units sampled at the surface, some horizontal transmission mayalso have occurred, allowing gases to reach less-densified cataclasites or even unconsolidatedgouge. Irrespective of the orientation of gas transmission, the extent of outgassing was ul-timately moderated by the competition between sintering-driven permeability loss and risinggas overpressures. In Section 5.6 we discuss further the competition between these effects fordome-building systems generally.5.5.4 Cyclical deformation and sintering in the shear zoneMicrostructural features in CHi and CLo (e.g., sheared plagioclase lenses and maficinclusions in Figure 5.4) support a complex deformation history for these densified units. Thereis microstructural evidence for at least two cycles of cataclasis and sintering within the shearzone during ascent, expressed by rounded clasts of CLo within the CHi unit (Figure 5.4e,f).This suggests the following series of events occurred: (1) gouge formed by fracturing andcataclasis; (2) initial sintering produced CLo; (3) CLo fractured at depth and fragments werecomminuted to produce a cataclasite-derived gouge; (4) shear concentrated in the gouge layercaused rounding of what were presumably angular clasts of pre-existing sintered gouge; (5) thecataclasite-derived gouge re-sintered to produce CHi.The time required for re-sintering depends on the depth at which cataclasis occurs.For example, the fracturing and cataclasis event that formed the clasts in Figure 5.4e,f likelyoccurred deeper in the conduit, allowing for sintering times of a few hours to days (Figure5.7b,c). These short sintering times allow for the re-densification and re-lithification of thegouge to form CHi. In contrast, we suggest that the gouge unit observed at the surface (Figure5.2) likely formed in a similar secondary gouge-generation event, albeit closer to the surfacewhere sintering times are significantly longer, approaching hundreds of days (Figure 5.7b,c).85With these long sintering times, there was no opportunity for unit G to re-densify and re-lithify,so it extruded at the surface as unconsolidated granular material.Overall, the features in Figure 5.4 demonstrate that deformation attending ascent andextrusion of Dome C lavas was partitioned, at least partially, into competent cataclasites. De-spite solid-state sintering transforming them into strong, low-porosity materials (Figure 5.6),the competent cataclasites continued to play an active role in facilitating ascent of the dacitemagma plug. This is in conflict with expectation that deformation would be sequestered withinthe weakest shear zone unit (i.e., gouge). In light of these observations we consider below theconsequences of shear zone densification and lithification for ascent and eruptive processes forDome C and lava domes generally.5.6 Implications beyond Chaos CragsThe exposed shear zone at Dome C of Chaos Crags preserves evidence of solid-statesintering occurring within the hot volcanic conduit, leading to the densification and lithificationof the gouge over hours to hundreds of days (Figure 5.7b,c). Microstructures in the catacla-sites also show that despite associated porosity loss and material strengthening, deformationcontinued to occur within the sintering portions of the shear zone.In general, the properties of intra-conduit shear zones govern magma plug ascent pro-cesses. For example, in shear zones composed of unconsolidated gouge, the frictional behaviorof the gouge dictates the force resisting the magma’s advance to the surface (Cashman et al.,2008; Costa et al., 2012; de’ Michieli Vitturi et al., 2013; Iverson et al., 2006; Kennedy andRussell, 2012; Lavalle´e et al., 2014; Moore et al., 2008; Okumura et al., 2015; Samuelson et al.,2008). In shear zones containing silicate melt, the distribution and rheological response of themelt may facilitate ascent (e.g., Di Toro et al., 2006; Wallace et al., 2019a), or cause the plug tostall in the subsurface (e.g., Hornby et al., 2015; Kendrick et al., 2014; Okumura et al., 2015).Similarly, the evolving connectivity of void spaces in gouge-filled or melt-bearing shear zonescan suppress or enhance volatile outgassing (Colombier et al., 2017; Edmonds and Herd, 2007;Gaunt et al., 2014; Heap et al., 2015a; Holland et al., 2011; Kolzenburg et al., 2019; Lavalle´eet al., 2013; Okumura and Sasaki, 2014; Rust et al., 2004; Tuffen and Dingwell, 2005).Based on our analysis and modelling, we suggest the rapid densification and lithifica-tion of crystal-rich volcanic shear zones by solid-state sintering will change the efficiency ofmagma ascent and volatile outgassing. This is shown schematically in Figure 5.8: upon shearzone formation, it comprises unconsolidated high-porosity, high-permeability gouge with lowcohesion (Figure 5.8a,b). Volcanic gases are easily transmitted through the gouge to the sur-face, and magma plug ascends as a result of frictional sliding (Figure 5.8b). With time, the86(f)(e)0.1110100Relative Permeability12Relative Strength(b)(a)(b) (c) (d)surficial gas flowmagmacataclasissintering(c) (d)(e)σSZ < σMkSZ > kMFSZ << σMkSZ >> kMσSZ > σM kSZ < kM Time(f)sinteringcataclasisFSZ << σMkSZ >> kMFigure 5.8: Effects of evolving shear zone strength and permeability on lava domeeruptions. (a) Shear zone (SZ) permeability (black curve) and strength (grey curve)relative to the solidifying magma plug (M; where y = 1). Fracturing (black star) ofthe margins of the plug initiates cataclasis and the formation of the gouge-filledshear zone. Vertical boxes correspond to snapshots (b-f). A second cycle of cata-clasis and sintering occurs following a second fracturing event (black star in verticalbox e). (b) Initial shear zone, comprised of unconsolidated gouge (dotted region)with a frictional shear resistance (Fsz) less than plug strength (σM). Magma plug caneasily advance (black half arrows; length∼ ease of shear deformation). Also, shearzone permeability (kSZ) is greater than magma permeability (kM) (grey arrows; size∼ permeability) and transmits gaseous volatiles (grey curves). (c) With time, shearzone comprises a permeable cataclasite (light grey region) with a shear strength(σSZ) less than σM. (d) With increasing time the cataclasite becomes stronger andless permeable than the magma (e.g. CLo; dark grey region). The plug stalls andpore pressures below the magma increase (shaded region). (e) Shear zone fractures,causing the explosive release of trapped volatiles. Fracturing initiates another cycleof gouge-generation (i.e., shearing, grain size reduction and compaction). (f) Thegouge-filled shear zone can undergo another cycle of sintering.87gouge sinters in response to stresses acting on particles and high temperatures within the con-duit. Sintering converts the gouge to a cataclasite. Over short times, the cataclasite is still morepermeable and less strong than the magma plug itself (Figure 5.8c). However, as the shear zonecontinues to sinter, cataclasites are less permeable and considerably stronger (Figure 5.8d).There are two major consequences of these changes in the physical and mechanicalproperties of the shear zone: the movement of the plug is resisted by an increasingly strong,lithifying margin but is also driven by rising gas pressures as solid-state sintering suppressesoutgassing. The competition between these effects will dictate whether the plug stalls in thesubsurface (Figure 5.8d) or the sintered cataclasite undergoes hydrofracturing in response toelevated pore pressures (Figure 5.8e). In the latter case, fracturing could release sufficientstored energy to generate a small, impulsive earthquake (e.g., Iverson et al., 2006; Lamb et al.,2015), and could cause the sudden, explosive release of trapped pressurized gases at the surface.In the subsurface, subsequent cataclasis would result in the incorporation (cannibalization) ofsintered gouge fragments, producing fault gouge (Figure 5.8f) and initiating another cycle ofsintering (Figure 5.8a).At other volcanoes, unexpected changes in the rate, intensity or style of eruptive behav-ior, including transitions from effusive to explosive activity, are common during dome-buildingeruptions (e.g., Holland et al., 2011; Norton et al., 2002; Rowe et al., 2008). In crystal-rich sys-tems, these shifts may reflect the evolving physical and mechanical properties of the shear zoneas it undergoes solid-state sintering. As an example, there were several large outgassing eventsin 2005 at Mount St. Helens, in the middle of the 2004-2008 spine-producing eruption (Roweet al., 2008). These energetic outgassing events have been interpreted as explosive releasesof accumulated gas pressure; the material ejected was primarily fault gouge (Cashman et al.,2008; Rowe et al., 2008). BSE images of the ash (Figure 12c,f in Rowe et al. (2008)) showsseveral of the subrounded ash particles to have similar textures as in the Chaos Crags catacla-sites. We propose the formation and ejection of these particles may have resulted from the samesequence shown in Figure 5.8: (1) solid-state sintering of gouge creates low-permeability den-sified cataclasite that limit the egress of magmatic fluids, (2) in response to gas overpressures,the cataclasite in the shear zone undergoes near-simultaneous fracturing and cataclasis, and (3)rounded clasts of densified cataclasites are ejected during the explosive release of pressurizedgases. Comparison of modelled sintering times and the recurrence interval of explosive activityin crystal-rich volcanic systems may reveal the catalyst for transitions in eruptive behavior.885.7 ConclusionThe shear zone of Dome C at Chaos Crags comprises cataclastic units that preserve tex-tural evidence of (1) gouge generation at depth, (2) syn-eruption densification and lithificationof the shear zone by solid-state sintering, (3) deformation of competent, sintered cataclasites,despite their considerable strength, and (4) cyclical cataclasis and re-sintering of the shear zonewithin the conduit during the eruption (a period of hundreds of days). In previous models forthe ascent of crystal-rich, glass-poor magma plugs and the eruption of lava domes, the potentialfor the lithification of the shear zones was not considered. We suggest rapid strengthening andpermeability loss within the sintering shear zone will influence ascent and eruption dynam-ics, perhaps initiating or perpetuating the cycles of effusive-to-explosive behavior observed atmany dome-producing volcanoes.5.8 Access to Lassen Volcanic National ParkThe fieldwork and sample collection were permitted by the United States National ParkService (study number: LAVO-00050; permit number: LAVO-2019-SCI-0010).89Chapter 6Conclusion6.1 SummaryIn this dissertation I investigated the occurrence of solid-state sintering in volcanic set-tings. I used the analysis of natural volcanic materials and products synthesized during hot-pressing experiments to (1) test whether solid-state sintering occurs in volcanic settings, (2)constrain the operational timescale of solid-state sintering at volcanic conditions and (3) de-termine whether solid-state sintering occurs fast enough to moderate eruptive activity. Theseobjectives were addressed by answering the following specific research questions:• Does solid-state sintering explain the diverse physical and mechanical properties of theshear zones that envelope extruded lava domes (e.g., Mount St. Helens, 2004-2008)?[Chapter 2]• What are the timescales of densification by solid-state sintering at volcanic pressure-temperature conditions, and do they overlap with the timescales of volcanic activity?[Chapter 3]• What are the implications of solid-state sintering for fluid flow and fracture healing involcanic and high-temperature tectonic systems? [Chapter 4]• Can the properties of sintered shear zone materials be used to recover specific eruptiondynamics? [Chapter 5]As a cohesive body of work, my dissertation contains the following key findings andcontributions:1. Solid-state sintering is effective at volcanic pressure-temperature conditions.90The physical properties and microstructures of exhumed volcanic shear zones record in-formation about processes occurring within the conduit during the ascent and eruption of highviscosity magmas. The shear zones encasing lava domes and spines erupted at Mount St. He-lens (2004-2008) and Chaos Crags (∼ 1100 years B.P.) consist of unconsolidated crystal-rich,glass-poor fault gouge and variably densified cataclasites. The physical properties, composi-tion and microstructure of the cataclasites evidence densification by solid-state sintering. Thisdemonstrates solid-state sintering causes the lithification of crystalline gouge within volcanicconduits of dome-producing systems.Complementary hot-pressing experiments using unconsolidated Mount St. Helens gougeas the starting material test sintering efficacy at a wider range of pressure-temperature condi-tions (e.g., shallow (< 2.5 km depth), hot (700-900◦C) environments), and in the absence of asignificant shear component. The experiments produce strong, dense, low-permeability rocks,demonstrating that volcanic pressure-temperature conditions cause densification and lithifica-tion by solid-state sintering. Therefore, solid-state sintering can be expected to occur perva-sively in volcanic environments.2. Solid-state operates on short timescales.Reconstruction of the 2004-2008 eruption of Mount St. Helens shows solid-state sin-tering of gouge in the shear zone occurred during transit from ∼ 1 km depth, over a periodof 2.5 months to 1.25 years. This constraint on subsurface residence times give a first-orderestimate of the timescale of solid-state sintering in volcanic settings. Hot-pressing experimentsshow solid-state sintering to be more rapid than this initial estimate: unconsolidated powdersare transformed into solid composite within hours. Increasing hot-pressing time causes a con-tinuous increase in material competence and reductions in porosity and permeability. After2.5 days of hot pressing, experimental products have porosities and permeabilities comparableto those measured in natural volcanic shear zone samples. Both analyses of natural samplesand experimental results illustrate the short (hours to years) operating timescales of solid-statesintering at volcanic pressure-temperature conditions.3. I developed and tested the first predictive model for densification of volcanic materialsby solid-state sintering.I used experimental conditions and the measured relative density of products of hotisostatic pressing (HIP) experiments to develop a time-dependent densification model:ρr = ρo+aexp(bT)Pcc ln(t),91where ρr is relative density (fractional), ρo is the initial relative density (fractional), P is applied(confining) pressure (MPa), T is temperature (K), and t is time (s). The empirical fit parametersa, b, and c were determined globally, and applicable to the total range of P-T condition.I used experimental products from a second suite of hot-pressing experiments, con-ducted using a different apparatus (Paterson rig), to test the model – modelled and measuredρr for the experimental products are within uncertainty. This demonstrates the model is ro-bust and adequately describes densification by solid-state sintering under conditions that differfrom the data used to calibrate the model. This model can therefore be used to predict increasesin relative density over a pressure-temperature range that represents volcanic and some uppercrustal environments.4. Solid-state sintering influences processes governing volcanic eruptions.In volcanic settings, solid-state sintering can cause marked porosity and permeabilityloss and material strengthening. As such, sintering has the potential to close existing vol-canic outgassing pathways and to suppress their re-opening. Because the ease of gas egressis thought to dictate eruption intensity and the potential for explosivity, the short timescalesof sintering may control the magnitude and recurrence interval of outgassing events and, as aresult, influence eruption dynamics.In addition, during the ascent and eruption of high viscosity magmas that produce lavadomes and spines, strain is localized within annular shear zones. Rapid lithification of theshear zone by solid-state sintering has the potential to halt the eruption of the nascent dome,plugging the conduit until sufficient fluid pressures can re-fracture the shear zone, facilitatingcontinued ascent. The shear zone of Dome C of Chaos Crags preserves evidence of cycles ofsintering and cataclasis during a single dome-producing eruption. The eruptions that producelava domes are notorious for unexpected changes in eruption rate, intensity or style of eruptivebehavior, including transitions from effusive to explosive activity. These shifts may reflectthe evolving physical and mechanical properties of the shear zone as it undergoes solid-statesintering.5. I developed a new volcanic geospeedometer and demonstrated its capacity to elucidateeruption dynamics.There is a correlation between the density of shear zone materials from Mount St. He-lens and their modelled in-conduit residence times and observed lava linear ascent rates – densecataclasites spent more time in the conduit thanks to slow ascent. On this basis I proposed theproperties of sintered cataclasites may be used as a volcanic geospeedometer. I demonstratedthe use of this geospeedometer by using the physical properties of Dome C shear zone materials92and my time-dependent densification model to estimate the minimum ascent time (100 days)and maximum linear ascent rate (10 m/d) for the eruption of Dome C lavas. These are the firstestimates of eruption timescale and rate for this unobserved eruption. With this geospeedome-ter, I have introduced a new paradigm for relating the properties of sintered natural materialsto the timescales of ascent and to eruption dynamics.6.2 Significance in volcanologyThis dissertation, and the published manuscripts herein, are the first studies of solid-state sintering in volcanic settings. As the first of their kind, they elucidate a newly discoveredprocess operating in volcanic conduits and controlling eruptive behaviour. Viscous sinteringhas long been recognized as a process that is capable of re-lithifying and densifying volcani-clastic material in pyroclastic flow deposits or volcanic conduits. Viscous sintering, however,requires a substantial volume fraction of glassy material held at temperatures above its glasstransition temperature. Crystalline volcanic materials are not susceptible to viscous sinteringand have been thought of a means of maintaining porosity and permeability in volcanic sys-tems, supporting passive degassing, and suppressing explosive behaviour.My work demonstrates that solid-state sintering causes rapid densification and lithifica-tion of comminuted crystalline materials in volcanic environments. It challenges the perceptionthat crystal-rich aggregates in volcanic settings are persistently permeable and weak areas, in-capable of recovery and of influencing the magnitude or timescales of volcanic processes. Italso shows solid-state sintering to control processes that contribute to cyclical explosivity involcanic systems. As such my work has the potential to form the backbone of a new area ofvolcanic and Earth science research. It should also encourage the volcanological communityto re-examine other “global” mechanisms and consider whether they also influence volcanicprocesses.6.3 Recommendations for future work• Quantitative measurement of strength recovery: I was unable to create experimentalproducts of sufficient size and aspect ratio to test their strength. I propose designingexperiments to produce sintered samples large enough and with suitable geometries todirectly measure their fracture strength. I suggest using the coupled change in materialporosity and strength to either test the suitability of existing porosity-dependent strengthmodels (e.g., Baud et al., 2014; Chang et al., 2006; Sammis and Ashby, 1986; Zhu et al.,2010) or to develop a new one.93• TEM-supported examination of solid-state sintering mechanism: I did not have the op-portunity to analyze experimental products and natural samples to exactly determine therelevant solid-state sintering mechanism (Figure 1.1). I suggest using transmission elec-tron microscopy (TEM) to examine coalesced crystalline particles, and to characterizethe crystalline necks of material using diffraction methods to determine their crystal-lography (amorphous vs. ordered) and composition (multi-phase vs. single-phase). Aspart of these analyses, I recommend examining dislocation density within the startingmaterial and sintered experimental products. Finally, use these results to definitivelyidentify the sintering mechanism (diffusive mass transfer vs. dislocation movement) andthe cations involved in diffusion.• Microstructural studies of volcanic shear zones: The microstructure of volcanic shearzones are complex and warrant thorough structural analyses. I propose examining themicrostructures of sintered materials from Mount St. Helens and Chaos Crags (and othervolcanoes if available), and determining their microstructural similarities and differencesto identify generic processes. In addition, use the distribution of complex microstruc-tural features (well-sintered materials juxtaposed to poorly-sintered materials; recycledsintered clasts; lenses of shattered plagioclase; sheared inclusions) to constrain the distri-bution of stress and strain within the shear zones. Finally, reconstruct the temporo-spatialevolution of the shear zones, and examine further the deformational processes that allowa solidified lava dome to transit > 1 km over a period of days to years.• Transition from viscous to solid-state sintering: There is a transition from viscous tosolid-state sintering that could not be investigated here, as experimental starting materi-als do not include glass. I suggest completing hot-pressing experiments using variableproportions of crystalline and glassy materials, and comparing the timescales and mag-nitude of porosity and permeability reduction and strength recovery as a function ofglass content. 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Earth and PlanetaryScience Letters, 482, 171-180.111(m)daciteWall Rock0 1 2Spine interior-1primary gouge zonesecondarygouge zoneFractured dacite Shape fabric Dacite Folded shear bands LegendFractured cataclasite  Cataclasite (+clasts)Fault GougeSlickensidesSub-angular cataclastic brecciaFigure A.1: Spine 5 composite log summarizing the structures and progression offault rocks across the damage zone within the local kinematic plane. Legend ismodified from Figure 2.1. Spine 5, in contrast to spines 4 and 7, has two fault coresbetween two brittle damage zones. The secondary fault core contains a sub-angularcataclastic breccia not present in the fault zones at spines 4 or 7.Table A.1: Results of Rietveld refinement of X-Ray Diffraction (XRD) spectra (Raud-sepp et al., 1999). Mineral abundances in weight percent for samples of varyingcompetence from the listed spines.Spine 5 5 7Description unconsolidated gouge indurated gouge ultracataclasiteAndesine 57.5 50.7 50.4Anorthoclase 8.8 12.7 14.1Augite 1.8 1.9 2.5Enstatite ferroan 4.9 3.8 6.2Pargasite 2.6 1.5 1.2Cristobalite 8.5 14.4 9.8Quartz 4.4 2.5 3.6Tridymite 0.8 - 2.6Hematite 1.1 2.1 0.2Amorphous 9.6 10.5 9.4Total 100.0 100.0 100.0112400020001000500250diameter ( m)0102030wt %1 10 100 1000diameter ( m)00.511.522.5vol % (a)(b)Figure A.2: Grain size distributions for unconsolidated gouge collected from spine5 at MSH (SH320-1; Thornber et al., 2008) as determined by (a) dry sieving,for particles with diameters >250 μm, and (a) laser particle size analysis using aMalvern Mastersizer 2000 for particles with diameters <250 μm (based on siev-ing). Particles with diameters greater than 4 mm were removed by the USGS priorto shipping the sample to UBC (pers. comm.).113Appendix BSupporting Materials for Chapter 3These are supplementary materials published with the manuscript: Ryan, A.G., Rus-sell, J.K. and Heap, M.J. (2018b) Rapid solid-state sintering in volcanic systems. AmericanMineralogist, 103, 2028-2031.114b c d e fgaφ ~ 0.14 φ ~ 0.04b c dφ ~ 0.02 φ ~ 0.02 φ ~ 0.01e f gφ ~ 0.25Figure B.1: SEM transect of variably lithified MSH sample. (a) Photomicrograph of a thin section that grades from poorlyconsolidated to lithified gouge. The thin section and SEM images are oriented parallel to the extrusion direction. Labeledcircles are locations of SEM image pairs (b-g). Top image of each pair shows the lithified crystalline material at lowermagnification image. White boxes show the location of higher magnification images (bottom image of pairs). Total porosityvalues (φ ) (measured by image analysis) are given. From (b) to (g) the proportion of sintered material increases, and theporosity decreases. In the most sintered materials (e-g), small irregular voids in the consolidated matrix and small fracturesare the only void spaces. Scale bars are 100 μm.115Table B.1: Physical properties of MSH samples.Sample Bulk density (ρb, kg/m3)a Total porosity b Permeability (m2)c7 5j 4 2605 0.032 1.26 × 10-167 5j 1 2603 0.033 2.00 × 10-167 4b 3 2521 0.064 6.31 × 10-167 3c 4 2397 0.121 2.00 × 10-157 3c 1 2227 0.183 2.51 × 10-145 2b(2) 1 1983 0.264 6.31 × 10-144 3a(2) 2 1896 0.282 6.31 × 10-144 3a(2) 1 1791 0.321 1.26 × 10-12Notes: Full dataset in Ryan et al. (2018a). Values are representative of MSH materials.a ρb = m / (pir2l) using the mass (m), radius (r) and length (l) of the sample core.b Isolated porosities are <0.02.c Steady-state measurement (see Appendix B.1).B.1 Extended methodology and model developmentB.1.1 Physical property measurementsThe top and bottom surfaces of the cylindrical HIP canisters were removed and 3-4cores (1-2 cm length, 1 cm diameter) were drilled from the experimental products. One corefrom each HIP sample was used for thin sectioning and subsequent SEM imaging (e.g., Figure3.1).The ends of two cores from each HIP sample were ground to parallel surfaces, andthe mass, length and diameter of the cores were measured using a high-precision balance anddigital calipers. These data were used to calculate the bulk volume and bulk density (ρb) ofeach core (Table 3.1). The propagated uncertainty in bulk density measurements is 20-70kg/m3. The skeletal volumes of cores were measured using a Micromeritics AccuPyc II 1340helium pycnometer at the University of British Columbia (Canada). The uncertainty in thesemeasurements is 0.02-0.04 cm3. The volume of a known mass of the starting material was alsomeasured by helium pycnometry to retrieve the powder density (ρp = 2716 kg/m3; uncertaintyis < 10 kg/m3). The connected, total and isolated porosities of the cores was calculated usingthe measured bulk, skeletal and powder (true) densities (Table 3.1). The propagated uncertaintyfor porosities is < 0.01.Permeabilities were measured using a benchtop gas (nitrogen) permeameter at the In-stitut de Physique du Globe de Strasbourg (IPGS) at the Universite´ de Strasbourg (France). Allpermeabilities were measured on dry samples (dried in a vacuum oven at 40◦C for at least 48116Table B.2: Mineralogy of HIP starting material and experimental products.Mineral Starting Material (wt%) HIP1 (wt%) HIP1 (wt%) a HIP4 (wt%)Feldspar 60.0 59.2 60.6 61.0SiO2 polymorphs 21.2 19.0 21.9 22.4FeMg silicates 16.1 17.7 13.8 15.4FeTi oxides 2.8 4.1 3.7 1.3Total 100.1 100.0 100.0 100.0Note: Mineral constituents determined by Rietveld refinement of X-Ray Diffraction (XRD) spectra(Raudsepp et al., 1999).a Repeat analysis.10 0Diameter ( m)0510152025Num%10 0Diameter ( m)10 -810 -610 -410 -210 010 2r = 5 m r = 5 m10 2 10 210 0 10 1 10 2 10 3Diameter ( m)123456Vol%r = 5 m10 -1(a)(b) (c)Figure B.2: Particle size distribution curves for HIP experimental material. MSHdacitic fault gouge sieved to <125 μm. Particle size distributions for 5 aliquotswere measured using a laser particle size analyzer. Dashed lines show where par-ticle radius is 5 μm. (a) Volume percent (vol%) of particles of a given diameter inthe starting material. Data from different aliquots agree well (curves overlap). Thegreatest volume contribution is from particles >30 μm in diameter. (b) The samedata shown as number percent (assuming spherical particles; num%) on both linear(left) and log (right) axes. Most particles in the sieved gouge have diameters <10μm.117h) at room temperature and a confining pressure of 1 MPa. Prior to their measurement, thesamples were kept under a confining pressure of 1 MPa for 1 h to ensure microstructural equi-libration. Following microstructural equilibration, measurements of permeability were per-formed using the steady-state flow method. Steady-state volumetric flow rate measurementswere taken (using a flowmeter) under several pore pressure gradients. These data allow us tocalculate permeability whilst checking whether the data require auxiliary corrections, such asthe Klinkenberg and Forchheimer corrections. In all cases, the Forchheimer correction wasrequired and the true permeability is taken as the inverse of the y-intercept of the best-fit lin-ear regression in the plot of 1/kgasraw as a function of the volumetric flow rate, where kgasrawis the uncorrected (raw) gas permeability determined for each of the pore pressure gradientsimplemented during the experiment.B.1.2 Model developmentWe use the experimental conditions and the final density of the experimental productsto develop a model for densification by solid-state sintering. An empirical equation, termedthe “semilogarithmic law” (e.g., Coble, 1961; Rahaman, 2003; Vieira and Brook, 1984) iscommonly used to fit experimental hot (isostatic) pressing data and has the form:ρr = ρo+α ln(tt0)(B.1)where ρo is the relative density at an initial time to, ρr is relative density at time t, and α is a fitparameter dependent on the experimental temperature and pressure (e.g., Rahaman, 2003). Weinclude T and P in α by using established thermodynamic and kinetic relationships, includingthose in general forms of the power law creep equations (e.g., Rybacki and Dresen, 2004):dρ(T )dt≈ aexp(bT)(B.2)dρ(P)dt≈ Pc (B.3)dρdt=αt= aexp(bT)Pc1t(B.4)Integration yields:ρr = aexp(bT)Pc ln(t)+ ln(ρiρp)+d (B.5)11820406080Pressure (MPa)20406080Pressure (MPa)600 800 100020406080Pressure (MPa)Temperature (°C)ρr = 0.65 φ = 0.35ρr = 0.80 φ = 0.10ρr = 0.97 φ = 0.03increasing timeContours:6 h1 d2.5 d10 d100 d Contours:1 d2.5 d10 d100 d 1 y5 yContours:10 d100 d 1 y5 y10 yincreasing timeincreasing time(a)(b)(c)Figure B.3: Temperature-pressure sintering maps. Contours show the time to reach arelative density of (a) 0.65, (b) 0.80 and (c) 0.97. At low T -P conditions sinteringtime is not controlled by P (steep slope of contours), but a 100◦C increase in T issufficient to reduce sintering time. Above ∼ 750◦C, the effect of T on sinteringtime diminishes (contours flatten). Increasing P reduces sintering time at theseconditions.119and at t = 1 the value of ρr = ρi / ρp (the initial relative density where ρi is the initial densityand ρp is the powder density (Table 3.1)). Then for t ≥ 1 the Equation B.5 becomes:ρr =(ρiρp)+aexp(bT)Pc ln(t) (B.6)The model, which is dependent on temperature (T ; K), pressure (P; MPa), and time (t; s), has3 unknown parameters (a, b, c). Solving for the unknown parameters we find a = 0.039 ±0.019, b = –3064± 290 and c = 0.482 ± 0.064. The model fits our experimental data to withinuncertainty (Figure 3.3).B.1.3 Model limitationsExperimental data has been shown to deviate from Equation 3.1 where ρr > 0.95 (e.g.,Vieira and Brook, 1984). The deviation is attributed to the isolation of small pore spaces(Coble, 1961). We therefore Equation 3.2 is not applicable at ρr > 0.97, where ρr = 0.97 (φ= 0.03) is the percolation threshold where pores become isolated (Wadsworth et al., 2017a,2016b). Additionally, the limited range of our experimental P-T conditions means that whenapplied far from these conditions, Equation 3.2 may be poorly unconstrained.120bcφ ~ 0.13 φ ~ 0.15a b cfeφ ~ 0.19 φ ~ 0.18d e fhiφ ~ 0.14 φ ~ 0.25g h iklφ ~ 0.29 φ ~ 0.27j k lFigure B.4: Additional SEM images of HIP products. (a,d,g,j) Photomicrographs of thin sections of HIP products (labeled).Figure layout as in Figure B.1. The material subjected to the greatest experimental conditions (HIP1; Table 3.1) showsthe greatest proportion of sintered material and the least pore space. The opposite is true for the sample sintered at theleast extreme experimental conditions (HIP4; Table 3.1). Because the applied pressure was isotropic there is no preferredorientation of crystals or pore spaces. Scale bars are 50 μm.121Appendix CSupporting Materials for Chapter 4These are supplementary materials accompany the accepted manuscript: Ryan, A.G.,Russell, J.K., Heap, M.J., Zimmerman, M.E. and Wadsworth, F.B. Timescales of porosity andpermeability loss by solid-state sintering. Earth and Planetary Science Letters.C.1 Starting material characterizationTable C.1: Mineral abundances in weight percent.Mineral Starting Material (wt%) HIP1 (wt%) HIP1 (wt%) a HIP4 (wt%)Plagioclase 45.2 41.7 41.3 43.9Alkali feldspar 14.8 17.5 19.3 17.1SiO2 polymorphs 21.2 19.0 21.9 22.4FeMg silicates 16.1 17.7 13.8 15.4FeTi oxides 2.8 4.1 3.7 1.3Total 100.1 100.0 100.0 100.0Note: Previously published in Ryan et al. (2018b).a replicate measurement.12210-2 100 102 104Diameter (μm)0123456Vol%0510152025Num%10-2 100 102 104Diameter (μm)(a) (b)Figure C.1: Grain size distribution of experimental starting material. This figure wasmodified from Ryan et al. (2018b). Dacitic fault gouge from Mount St. Helenswas sieved to <125 μm. The grain size distribution of five aliquots of this materialwas measured using a Malvern Mastersizer 2000 laser particle size analyzer. Themeasured (a) volume percent (vol%) and (b) number percent (num%, assumingspherical particles) of grains are given against diameter. Curves overlap, indicat-ing no change in grain size distribution between aliquots of gouge. Large particles(>30 μm in diameter) are volumetrically dominant, while small particles (<10 μmin diameter) are most abundant. For (a), we note here that on a vol.% basis, themean (1st moment), variance (2nd moment), and skewness (3rd moment) of the par-ticle radius distribution are 12.76 µm, 292.93 µm2, and 8446.16 µm3, respectively.123C.2 Details of the Paterson sample assemblyalumina insulation paperO-ringsTOPBOTTOMalumina pistonszirconia pistonssample canisterO-ringthermocoupleFigure C.2: Paterson sample assembly. Typical construction of the assembly for com-pression experiments using a sealed canister. The steel tubing that encloses theceramic (zirconia and alumina) spacers and the sample canister is not shown. Forvented canisters, the upper copper lid of the canister is replaced by a porous ceram-ics spacer, and the thin solid alumina spacer typically placed between the R-typethermocouple and the upper lid of the canister is removed.124C.3 SEM and FE-SEM imagingPhilips XL30• Imaging, mapping, point spectra accelerating voltage: 15.0 kV• Point spectra count time: 30 s• Mapping count time: 900 sFEI Helios NanoLab 650• Imaging accelerating voltage: 10.0 kV• Mapping accelerating voltage: 20.0 kV• Mapping count time: 600 s5 μm(a) (b) (c)(d) (e) (f )Figure C.3: Additional element distribution maps. Maps collected using FEI HeliosNanoLab 650. (a) Sample hot pressed for 60 hours, shown in Figure 4f. Mapshave not been overlain on the BSE image. (b) Sintered regions in each field ofview. Distributions of calcium (c), aluminum (d), sodium (e) and potassium (f) areshown. Ca is concentrated in the cores of larger plagioclase grains and in minorphases. It is less abundant in small particles within sintered patches. Na and Alhave the same distributions, and are concentrated in large plagioclase grains and insmall feldspar grains, including in sintered patches. K is concentrated in sinteredmaterial along the edges of and between large plagioclase grains.125C.4 Effect of experimental methodologies on sinteringFigure C.4: (following page) Effect of methodology on sintering efficiency. Compari-son of measured relative densities (ρr) for samples hot pressed at the same T -Pc-tconditions but with methodological differences including: (a) samples hot pressedin the Paterson in sealed and vented canisters, (b) dry and H2O-undersaturatedsamples hot pressed in the Paterson (three in vented canisters (open symbol), onein sealed canister (closed symbol)), and (c) samples hot pressed in the Patersonand in the HIP (closed symbol is average ρr value for HIP samples). In (a,b) dataplot within uncertainty along the 1:1 line – in these experiments sealed vs. ventedcanisters and the addition of H2O have no effect on sintering efficiency. A samplehot pressed in the Paterson has a higher measured ρr than a sample hot pressed inthe HIP at the same T -Pc-t conditions.126ventedsealed ρrventedsealedρ rρr0.5 wt% H2Odryρ r0.7 0.8 0.90.70.80.9ρrPatersonHIP ρ rindividualaverage1:11:11:1(a)(b)(c)0.7 0.8 0.90.70.80.90.7 0.8 0.90.70.80.91271 cm1 cm1 cm1 cm(a)(b)(c)(d)(e)wrinkling/buckling of canisterslightbowing of canisterFigure C.5: Photos of Paterson and HIP canisters prior to and after hot pressing. (a)Paterson inner copper lid and canister with thin (0.5 mm) straight walls, packedwith gouge, prior to being inserted within thin (0.25 mm) steel tubing (not pic-tured). (b,c) Paterson canisters following hot pressing showing wrinkling and buck-ling of the canister walls. Black outer layer is the oxidized steel tubing. (d) SteelHIP canister (1.9 mm thick) prior to hot pressing. (e) HIP canister following hotpressing, showing slight bowing of the canister walls. The different deformationpattern recorded by the canisters shows their different responses to pressurization,which in turn reflects the thickness and properties of the metals used to make thecanisters.C.5 Permeability modellingWe use the polydisperse solution of the permeability model presented in the data repos-itory of Wadsworth et al. (2016b) to predict the permeability of sintering materials as a functionof their connected porosities. This model assumes that the permeability k is proportional to theinverse square of the specific surface area (s) of the porous medium (i.e., k ∝ 1/s2). This isa re-stating of most widely used permeability models, including the Kozeny-Carman models,acknowledging that the pore size and tortuosity are parameters that manifest as s. We there-fore have two steps to take in order to apply this model: (1) we must predict s, which changes128during sintering, and (2) we must use s to predict k via a constitutive model. Here we describethose steps:Modelling permeability involves the following steps:1. Input initial grain size distribution (GSD; Figure C.1) and an estimate of the initial poros-ity (0.44; Table 4.1). The GSD is used to find the first, second and third moments of thepolydisperse pack of particles (given in the caption to Figure C.1). We term these mo-ments 〈 R 〉, 〈 R2 〉 and 〈 R3 〉, respectively.2. The steps that follow require us to designate a scenario that best describes how the poresand particles change and interact during densification. Given that the models for randomheterogeneous media geometries on which the Wadsworth et al. (2016b) model is basedare predicated on systems of spherical objects (pores with mean radius 〈 a 〉 or particleswith mean radius 〈 R 〉) that can overlap or not depending on the system of interest, thereare a number of combinations we could explore:(a) Assume particles are initially rigid in a pack and that they define a pore size distri-bution. Use pore size distribution to determine how surface area evolves as poresshrink and overlap with one another. This is hard particles overlapping pores.(b) Assume particles are initially rigid in a pack and that they define a pore size distri-bution. Use pore size distribution to determine how surface area evolves as poresshrink and do not overlap with one another. This is hard particles hard pores.(c) Assume particles initially overlap in a pack and that they define a pore size distri-bution. Use pore size distribution to determine how surface area evolves as poresshrink and overlap with one another. This is overlapping particles overlappingpores.(d) Assume particles initially overlap in a pack and that they define a pore size distri-bution. Use pore size distribution to determine how surface area evolves as poresshrink and do not overlap with one another. This is overlapping particles hardpores.3. Calculate the effective pore radius as a function of particle radii, described by the first,second and third moment of the GSD. We use general statistical models for randomheterogeneous media (Torquato, 2013) to convert 〈 R 〉, 〈 R2 〉 and 〈 R3 〉, to a predictionof the pore size distribution that exists between the particles when packed together attheir initial packing porosity. Defined for sintering systems such as the one examinedhere, these are defined elsewhere and we direct the reader to those studies for more129information (Wadsworth et al., 2016a,b). These models are strictly for spherical particles,but deviations from spherical assumptions have been shown to play only a negligible rolein terms of affecting the applicability of this model approach to hydraulic properties, suchas permeability (cf., Wadsworth et al., 2016b).4. Knowing 〈 a 〉 and the distribution thereof, for each of the scenarios given above (i.e.,hard particles overlapping pores, hard particles hard pores, overlapping particles overlap-ping pores, overlapping particles hard pores), we have different relationships to predicts.(a) The initial si is given by si = 3(1−φi)/〈R〉. Then s changes as sintering progressesaccording to s(t) = 3φc ln(φc)/〈a〉.(b) The initial si is given bysi = 3(1−φi)/〈R〉. Then s changes as sintering progressesaccording to s(t) = 3φc/〈a〉.(c) The initial si is given by si = 3(1−φi) ln(1−φi)/〈R〉. Then s changes as sinteringprogresses according to s(t) = 3φc ln(φc)/〈a〉.(d) The initial si is given by si = 3(1−φi) ln(1−φi)/〈R〉. Then s changes as sinteringprogresses according to s(t) = 3φc/〈a〉.5. Finally, we calculate permeability (k; m2) using the following equation:k =2φ∗s2(φc−φ ′)4.4 (C.1)where φ∗ = 1 – (φc – φ ′), φc is the fractional connected porosity of the densifying materialand φ ′ is the percolation threshold porosity (0.05; fractional). The exponent 4.4 arisesfrom theoretical predictions for sphere pack systems (Feng et al., 1987).The model curve presented in Figure 4.2 and used for t-P-T dependent modelling in Figure 4.8,assumes hard particles overlapping pores. The only fit parameter to this equation is φ ′, whichwe find using a minimisation of the root mean square error between the model prediction andthe data, and constrain this to be φ ′ = 0.05 ± 0.012, which is broadly consistent with previouspredictions for sintering systems of φ ′ ≈ 0.03 (Wadsworth et al., 2016a).130Appendix DSupporting Materials for Chapter 5These are supplementary materials published with the manuscript: Ryan, A.G., Heap,M.J., Russell, J.K., Kennedy, L.A. and Clynne, M.A. (2020) Cyclic shear zone cataclasis andsintering during lava dome extrusion: Insights from Chaos Crags, Lassen Volcanic Center(USA). Journal of Volcanology and Geothermal Research, 401, 106935.D.1 Sintering pressure modelling0 0.5 1 1.5 2Axial Strain (%)050100150200250Differential Stress (MPa)Peff = 0Peff = 5Peff = 10Peff =15Peff = 20Figure D.1: Measured differential stress against axial strain for triaxial deformationexperiments on Dome C dacite. Effective pressure (Pe f f = Pc – Pp) shown for allexperiments. Peak differential stresses reported in Table 5.5.131To determine residence times for porous and dense cataclasites, the pressures that couldbe acting on gouge at depth in the Dome C conduit must be constrained. Ignoring pore pres-sures (densification of the gouge alone indicates pore pressures in the subsurface were insuf-ficient to stop sintering), we define the minimum pressure (Pmin; MPa) as the lithostat (Plith,MPa):Plith = ρgh (D.1)where ρ is a representative bulk density (2300 kg/m3; Table 5.4), g is gravitational acceleration(9.81 m/s2) and h is the depth (up to 1000 m).100 150 200 250Compressive Pressure (MPa)02505007501000Depth (m)0 50Plithcompressive pressure range the gouge experiences during ascentPmax = 0.194 h + 49.52Figure D.2: Modelled range of compressive pressures the gouge experiences over 1km depth. Pmin is the lithostat (solid) and Pmax is a best-fit line for the compressivestrength of the dacite as a function of depth (dashed). Experimental data are plot-ted: open circles are the effective pressure for the corresponding measured strength(filled circles), connected by dotted tie-lines.The maximum compressive pressure (Pmax; MPa) that could be acting on the gouge atany given depth must be less than the pressure required to fracture the dacite. At the surfacethis is the measured UCS (Table 5.4). With increasing depth, Pmax is approximated using datafrom the triaxial experiments (Table 5.5) – using Equation D.1 we solved for the depth (h) thatcorresponds to a lithostatic pressure equal to Pe f f , then plotted Pdi f f as a function of depth. Alinear best-fit line fit to these data as well as the UCS data give the following equation:132Pmax = 0.194h+49.52 (D.2)where h is depth in meters. Figure D.2 shows model lines for both Pmin and Pmax.D.2 Transient pressure modellingOur Figure 5.7c shows (1) generic ascent rate curves (v; m/d) that predict depth (ht ; m)at any time (t; d) given a prescribed rate (ht = 1000 m – vt), and (2) fields showing sinteringtime require to achieve a prescribed porosity (CHi = 0.20; CLo = 0.08) given a constant pressuredefined by depth (Pmax = 0.194 h + 49.52). From this field of view we identify 10 m/d as themaximum ascent rate that passes through the “sintering window” that allows for the formationof CLo. This constrains the maximum ascent rate of the cataclasite materials and magma,assuming they are well-coupled.Figure 5.7c does not account for the change in pressure attending magma ascent. Toexplore how transient pressures may affect sintering efficiency and porosity loss we modifyEquation 5.3 in the following ways:Pt = 0.194ht +49.52 = 0.194(1000–vt)+49.52 (D.3)ρr = ρo+aexp(bT)Pct ln(t) (D.4)φt = 1−(ρo+aexp(bT)Pct ln(t))(D.5)With these changes to Equation 5.3 we plot time-dependent porosity loss at prescribed ascentrates. The chosen rates are 2.5, 5, 10 and 20 m/d (corresponding to those shown in Figure5.7c). These curves are shown in Figure D.3.As shown in Figure 5.7b, sintering is very efficient at short times. Therefore, despiteimposed ascent rates, model curves agree to t ∼ 1 d, equivalent to φt ∼ 0.15 (Figure D.3a).Past this time curves deviate from the fixed P trend depending on ascent rate: curves for ascentrates ≤ 10 m/d pass below the porosity threshold for CLo (φt = 0.08) (Figure D.3b). This isequivalent to passing in to the sintering window in Figure 5.7c. In contrast, ascent rates >10 m/d result in pressure changes during ascent that do not allow for sintering to produce thelow porosities measured in CLo samples (Figure D.3b). Based on this we reaffirm that themaximum ascent rate needed to produce the shear zone units exposed at Dome C is 10 m/d.133(a)(b)(b)0.01 1 50Time (d)0.10.20.30.4PorosityCHi (φt = 0.20)CLo (φt = 0.08)1 10Time (d)0.060.080.100.120.14Porosity50CLo (φt = 0.08)10 m/d20 m/d5 m/d2.5 m/dfixed PInitial ConditionFigure D.3: Modelled porosity loss during ascent from 1 km at variable rates. (a)From an initial condition (φt = 0.40) porosity decreases rapidly at short times (notelog scale), irrespective of whether P is fixed (e.g., Eq. 5.3; red line) or changesas a function of ascent rate (e.g., Eq. D.3-5; black curves). (b) Past 1 day, time-dependent porosity loss reflects changing Pt – curves shallow and plateau with in-creasing time. At fast ascent rates, pressure changes quickly and the curve plateausabove the porosity threshold for CLo (φt = 0.08). For ascent rates≤10 m/d, pressurechanges more slowly and sintering can still produce low-porosity materials.134

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